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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8355])).
% 5.70/5.68 tff(8357,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8356, 24])).
% 5.70/5.68 tff(8358,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8357])).
% 5.70/5.68 tff(8359,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[694, 8358, 23])).
% 5.70/5.68 tff(8360,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8359])).
% 5.70/5.68 tff(8361,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8360, 58])).
% 5.70/5.68 tff(8362,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8337])).
% 5.70/5.68 tff(8363,plain,
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% 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,
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% 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,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8366, 48])).
% 5.70/5.68 tff(8368,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8367])).
% 5.70/5.68 tff(8369,plain,
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% 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,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8373])).
% 5.70/5.68 tff(8375,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8374, 39])).
% 5.70/5.68 tff(8376,plain,
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% 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,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8377])).
% 5.70/5.68 tff(8379,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8378, 45])).
% 5.70/5.68 tff(8380,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8379])).
% 5.70/5.68 tff(8381,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8380, 28])).
% 5.70/5.68 tff(8382,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8381])).
% 5.70/5.68 tff(8383,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[717, 8382, 42])).
% 5.70/5.68 tff(8384,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8383])).
% 5.70/5.68 tff(8385,plain,
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% 5.70/5.68 tff(8386,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8385, 8361])).
% 5.70/5.68 tff(8387,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8386, 57])).
% 5.70/5.68 tff(8388,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8388, 57])).
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% 5.70/5.68 tff(8391,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8390, 57])).
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% 5.70/5.68 tff(8393,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8393])).
% 5.70/5.68 tff(8395,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8394, 22])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8395])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8396, 21])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8397])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8398, 20])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8399])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8400, 19])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8401])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8402, 18])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8403])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8404, 17])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8405])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8406, 16])).
% 5.70/5.68 tff(8408,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8407])).
% 5.70/5.68 tff(8409,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8408, 15])).
% 5.70/5.68 tff(8410,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8409])).
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% 5.70/5.68 inference(transitivity,[status(thm)],[8410, 25])).
% 5.70/5.68 tff(8412,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8411])).
% 5.70/5.68 tff(8413,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8412, 24])).
% 5.70/5.68 tff(8414,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8413])).
% 5.70/5.68 tff(8415,plain,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 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,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8441])).
% 5.70/5.68 tff(8443,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8442, 22])).
% 5.70/5.68 tff(8444,plain,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8443, 8419])).
% 5.70/5.68 tff(8445,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[772, 8444, 57])).
% 5.70/5.68 tff(8446,plain,
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% 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,
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8447])).
% 5.70/5.68 tff(8449,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8448, 21])).
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% 5.70/5.68 inference(monotonicity,[status(thm)],[8449])).
% 5.70/5.68 tff(8451,plain,
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% 5.70/5.68 inference(transitivity,[status(thm)],[8450, 20])).
% 5.70/5.68 tff(8452,plain,
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% 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])).
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% 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)) <