TSTP Solution File: NUM377+1.010 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM377+1.010 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:03:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 3.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM377+1.010 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 10:00:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(tptp_fun_Y1_18_type, type, (
% 0.19/0.42 tptp_fun_Y1_18: $i)).
% 0.19/0.42 tff(tptp_fun_X1_19_type, type, (
% 0.19/0.42 tptp_fun_X1_19: $i)).
% 0.19/0.42 tff(sum_type, type, (
% 0.19/0.42 sum: ( $i * $i ) > $i)).
% 0.19/0.42 tff(succ_type, type, (
% 0.19/0.42 succ: $i > $i)).
% 0.19/0.42 tff(tptp_fun_Y0_20_type, type, (
% 0.19/0.42 tptp_fun_Y0_20: $i)).
% 0.19/0.42 tff(pred_type, type, (
% 0.19/0.42 pred: $i > $i)).
% 0.19/0.42 tff(tptp_fun_X0_21_type, type, (
% 0.19/0.42 tptp_fun_X0_21: $i)).
% 0.19/0.42 tff(n10_type, type, (
% 0.19/0.42 n10: $i)).
% 0.19/0.42 tff(n9_type, type, (
% 0.19/0.42 n9: $i)).
% 0.19/0.42 tff(n8_type, type, (
% 0.19/0.42 n8: $i)).
% 0.19/0.42 tff(n7_type, type, (
% 0.19/0.42 n7: $i)).
% 0.19/0.42 tff(n6_type, type, (
% 0.19/0.42 n6: $i)).
% 0.19/0.42 tff(n5_type, type, (
% 0.19/0.42 n5: $i)).
% 0.19/0.42 tff(n4_type, type, (
% 0.19/0.42 n4: $i)).
% 0.19/0.42 tff(n3_type, type, (
% 0.19/0.42 n3: $i)).
% 0.19/0.42 tff(n2_type, type, (
% 0.19/0.42 n2: $i)).
% 0.19/0.42 tff(n1_type, type, (
% 0.19/0.42 n1: $i)).
% 0.19/0.42 tff(n0_type, type, (
% 0.19/0.42 n0: $i)).
% 0.19/0.42 tff(tptp_fun_Y2_16_type, type, (
% 0.19/0.42 tptp_fun_Y2_16: $i)).
% 0.19/0.42 tff(tptp_fun_X2_17_type, type, (
% 0.19/0.42 tptp_fun_X2_17: $i)).
% 0.19/0.42 tff(tptp_fun_Y3_14_type, type, (
% 0.19/0.42 tptp_fun_Y3_14: $i)).
% 0.19/0.42 tff(tptp_fun_X3_15_type, type, (
% 0.19/0.42 tptp_fun_X3_15: $i)).
% 0.19/0.42 tff(tptp_fun_Y4_12_type, type, (
% 0.19/0.42 tptp_fun_Y4_12: $i)).
% 0.19/0.42 tff(tptp_fun_X4_13_type, type, (
% 0.19/0.42 tptp_fun_X4_13: $i)).
% 0.19/0.42 tff(tptp_fun_Y5_10_type, type, (
% 0.19/0.42 tptp_fun_Y5_10: $i)).
% 0.19/0.42 tff(tptp_fun_X5_11_type, type, (
% 0.19/0.42 tptp_fun_X5_11: $i)).
% 0.19/0.42 tff(tptp_fun_Y6_8_type, type, (
% 0.19/0.42 tptp_fun_Y6_8: $i)).
% 0.19/0.42 tff(tptp_fun_X6_9_type, type, (
% 0.19/0.42 tptp_fun_X6_9: $i)).
% 0.19/0.42 tff(tptp_fun_Y7_6_type, type, (
% 0.19/0.42 tptp_fun_Y7_6: $i)).
% 0.19/0.42 tff(tptp_fun_X7_7_type, type, (
% 0.19/0.42 tptp_fun_X7_7: $i)).
% 0.19/0.42 tff(tptp_fun_Y8_4_type, type, (
% 0.19/0.42 tptp_fun_Y8_4: $i)).
% 0.19/0.42 tff(tptp_fun_X8_5_type, type, (
% 0.19/0.42 tptp_fun_X8_5: $i)).
% 0.19/0.42 tff(tptp_fun_Y9_2_type, type, (
% 0.19/0.42 tptp_fun_Y9_2: $i)).
% 0.19/0.42 tff(tptp_fun_X9_3_type, type, (
% 0.19/0.42 tptp_fun_X9_3: $i)).
% 0.19/0.42 tff(tptp_fun_Y10_0_type, type, (
% 0.19/0.42 tptp_fun_Y10_0: $i)).
% 0.19/0.42 tff(tptp_fun_X10_1_type, type, (
% 0.19/0.42 tptp_fun_X10_1: $i)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (((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!21 = n10) | (X0!21 = n9) | (X0!21 = n8) | (X0!21 = n7) | (X0!21 = n6) | (X0!21 = n5) | (X0!21 = n4) | (X0!21 = n3) | (X0!21 = n2) | (X0!21 = n1) | (X0!21 = n0)) & ((Y0!20 = n10) | (Y0!20 = n9) | (Y0!20 = n8) | (Y0!20 = n7) | (Y0!20 = n6) | (Y0!20 = n5) | (Y0!20 = n4) | (Y0!20 = n3) | (Y0!20 = n2) | (Y0!20 = n1) | (Y0!20 = n0)) & (X1!19 = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))) & (Y1!18 = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))) & (X2!17 = sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19)))) & (Y2!16 = sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18)))) & (X3!15 = sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17)))) & (Y3!14 = sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16)))) & (X4!13 = sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15)))) & (Y4!12 = sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14)))) & (X5!11 = sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13)))) & (Y5!10 = sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12)))) & (X6!9 = sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11)))) & (Y6!8 = sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10)))) & (X7!7 = sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9)))) & (Y7!6 = sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8)))) & (X8!5 = sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7)))) & (Y8!4 = sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6)))) & (X9!3 = sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5)))) & (Y9!2 = sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4)))) & (X10!1 = sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3)))) & (Y10!0 = sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2)))) & ((~(X10!1 = Y10!0)) | (~(X9!3 = Y9!2)) | (~(X8!5 = Y8!4)) | (~(X7!7 = Y7!6)) | (~(X6!9 = Y6!8)) | (~(X5!11 = Y5!10)) | (~(X4!13 = Y4!12)) | (~(X3!15 = Y3!14)) | (~(X2!17 = Y2!16)) | (~(X1!19 = Y1!18))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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!21 = n10) | (X0!21 = n9) | (X0!21 = n8) | (X0!21 = n7) | (X0!21 = n6) | (X0!21 = n5) | (X0!21 = n4) | (X0!21 = n3) | (X0!21 = n2) | (X0!21 = n1) | (X0!21 = n0)) & ((Y0!20 = n10) | (Y0!20 = n9) | (Y0!20 = n8) | (Y0!20 = n7) | (Y0!20 = n6) | (Y0!20 = n5) | (Y0!20 = n4) | (Y0!20 = n3) | (Y0!20 = n2) | (Y0!20 = n1) | (Y0!20 = n0)) & (X1!19 = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))) & (Y1!18 = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))) & (X2!17 = sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19)))) & (Y2!16 = sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18)))) & (X3!15 = sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17)))) & (Y3!14 = sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16)))) & (X4!13 = sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15)))) & (Y4!12 = sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14)))) & (X5!11 = sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13)))) & (Y5!10 = sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12)))) & (X6!9 = sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11)))) & (Y6!8 = sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10)))) & (X7!7 = sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9)))) & (Y7!6 = sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8)))) & (X8!5 = sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7)))) & (Y8!4 = sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6)))) & (X9!3 = sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5)))) & (Y9!2 = sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4)))) & (X10!1 = sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3)))) & (Y10!0 = sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2)))) & ((~(X10!1 = Y10!0)) | (~(X9!3 = Y9!2)) | (~(X8!5 = Y8!4)) | (~(X7!7 = Y7!6)) | (~(X6!9 = Y6!8)) | (~(X5!11 = Y5!10)) | (~(X4!13 = Y4!12)) | (~(X3!15 = Y3!14)) | (~(X2!17 = Y2!16)) | (~(X1!19 = Y1!18))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (?[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] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(3,plain,
% 0.19/0.47 (^[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] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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))) & (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))) & (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))) & (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)) & (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))) & (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)) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(X1 = Y1)) | (~(X2 = Y2))) <=> ((~(X2 = Y2)) | (~(X1 = Y1)))), ((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) <=> (((~(X2 = Y2)) | (~(X1 = Y1))) | (~(X3 = Y3))))), rewrite((((~(X2 = Y2)) | (~(X1 = Y1))) | (~(X3 = Y3))) <=> ((~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), ((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) <=> ((~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), (((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) <=> (((~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X4 = Y4))))), rewrite((((~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X4 = Y4))) <=> ((~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), (((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) <=> ((~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), ((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) <=> (((~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X5 = Y5))))), rewrite((((~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X5 = Y5))) <=> ((~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), ((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) <=> ((~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), (((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) <=> (((~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X6 = Y6))))), rewrite((((~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X6 = Y6))) <=> ((~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), (((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) <=> ((~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), ((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) <=> (((~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X7 = Y7))))), rewrite((((~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X7 = Y7))) <=> ((~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), ((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) <=> ((~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), (((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) | (~(X8 = Y8))) <=> (((~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X8 = Y8))))), rewrite((((~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X8 = Y8))) <=> ((~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), (((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) | (~(X8 = Y8))) <=> ((~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) | (~(X8 = Y8))) | (~(X9 = Y9))) <=> (((~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X9 = Y9))))), rewrite((((~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X9 = Y9))) <=> ((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) | (~(X8 = Y8))) | (~(X9 = Y9))) <=> ((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))))), (((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10))) <=> (((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X10 = Y10))))), rewrite((((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) | (~(X10 = Y10))) <=> ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))), (((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(X7 = Y7))) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10))) <=> ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = 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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = 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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1)))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)))))),
% 3.35/3.53 inference(bind,[status(th)],[])).
% 3.35/3.53 tff(4,plain,
% 3.35/3.53 (?[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] : (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)))),
% 3.35/3.54 inference(quant_intro,[status(thm)],[3])).
% 3.35/3.54 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] : (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9))))) & ((((((((((~(X1 = Y1)) | (~(X2 = Y2))) | (~(X3 = Y3))) | (~(X4 = Y4))) | (~(X5 = Y5))) | (~(X6 = Y6))) | (~(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')).
% 3.41/3.55 tff(6,plain,
% 3.41/3.55 (?[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] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)))),
% 3.41/3.55 inference(modus_ponens,[status(thm)],[5, 4])).
% 3.41/3.55 tff(7,plain,
% 3.41/3.55 (?[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] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(sum(pred(X0), succ(X0)), sum(pred(Y0), succ(Y0)))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(sum(pred(X1), succ(X1)), sum(pred(Y1), succ(Y1)))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(sum(pred(X2), succ(X2)), sum(pred(Y2), succ(Y2)))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(sum(pred(X3), succ(X3)), sum(pred(Y3), succ(Y3)))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(sum(pred(X4), succ(X4)), sum(pred(Y4), succ(Y4)))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(sum(pred(X5), succ(X5)), sum(pred(Y5), succ(Y5)))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(sum(pred(X6), succ(X6)), sum(pred(Y6), succ(Y6)))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(sum(pred(X7), succ(X7)), sum(pred(Y7), succ(Y7)))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(sum(pred(X8), succ(X8)), sum(pred(Y8), succ(Y8)))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(sum(pred(X9), succ(X9)), sum(pred(Y9), succ(Y9)))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)) | (~(X6 = Y6)) | (~(X5 = Y5)) | (~(X4 = Y4)) | (~(X3 = Y3)) | (~(X2 = Y2)) | (~(X1 = Y1))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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)))),
% 3.41/3.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.41/3.55 tff(8,plain,(
% 3.41/3.55 (succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0!21 = n10) | (X0!21 = n9) | (X0!21 = n8) | (X0!21 = n7) | (X0!21 = n6) | (X0!21 = n5) | (X0!21 = n4) | (X0!21 = n3) | (X0!21 = n2) | (X0!21 = n1) | (X0!21 = n0)) & ((Y0!20 = n10) | (Y0!20 = n9) | (Y0!20 = n8) | (Y0!20 = n7) | (Y0!20 = n6) | (Y0!20 = n5) | (Y0!20 = n4) | (Y0!20 = n3) | (Y0!20 = n2) | (Y0!20 = n1) | (Y0!20 = n0)) & (X1!19 = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))) & (Y1!18 = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))) & (X2!17 = sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19)))) & (Y2!16 = sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18)))) & (X3!15 = sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17)))) & (Y3!14 = sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16)))) & (X4!13 = sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15)))) & (Y4!12 = sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14)))) & (X5!11 = sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13)))) & (Y5!10 = sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12)))) & (X6!9 = sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11)))) & (Y6!8 = sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10)))) & (X7!7 = sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9)))) & (Y7!6 = sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8)))) & (X8!5 = sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7)))) & (Y8!4 = sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6)))) & (X9!3 = sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5)))) & (Y9!2 = sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4)))) & (X10!1 = sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3)))) & (Y10!0 = sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2)))) & ((~(X10!1 = Y10!0)) | (~(X9!3 = Y9!2)) | (~(X8!5 = Y8!4)) | (~(X7!7 = Y7!6)) | (~(X6!9 = Y6!8)) | (~(X5!11 = Y5!10)) | (~(X4!13 = Y4!12)) | (~(X3!15 = Y3!14)) | (~(X2!17 = Y2!16)) | (~(X1!19 = Y1!18))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))),
% 3.43/3.56 inference(skolemize,[status(sab)],[7])).
% 3.43/3.56 tff(9,plain,
% 3.43/3.56 ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0!21 = n10) | (X0!21 = n9) | (X0!21 = n8) | (X0!21 = n7) | (X0!21 = n6) | (X0!21 = n5) | (X0!21 = n4) | (X0!21 = n3) | (X0!21 = n2) | (X0!21 = n1) | (X0!21 = n0)) & ((Y0!20 = n10) | (Y0!20 = n9) | (Y0!20 = n8) | (Y0!20 = n7) | (Y0!20 = n6) | (Y0!20 = n5) | (Y0!20 = n4) | (Y0!20 = n3) | (Y0!20 = n2) | (Y0!20 = n1) | (Y0!20 = n0)) & (X1!19 = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))) & (Y1!18 = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))) & (X2!17 = sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19)))) & (Y2!16 = sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18)))) & (X3!15 = sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17)))) & (Y3!14 = sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16)))) & (X4!13 = sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15)))) & (Y4!12 = sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14)))) & (X5!11 = sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13)))) & (Y5!10 = sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12)))) & (X6!9 = sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11)))) & (Y6!8 = sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10)))) & (X7!7 = sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9)))) & (Y7!6 = sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8)))) & (X8!5 = sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7)))) & (Y8!4 = sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6)))) & (X9!3 = sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5)))) & (Y9!2 = sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4)))) & (X10!1 = sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3)))) & (Y10!0 = sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2)))) & ((~(X10!1 = Y10!0)) | (~(X9!3 = Y9!2)) | (~(X8!5 = Y8!4)) | (~(X7!7 = Y7!6)) | (~(X6!9 = Y6!8)) | (~(X5!11 = Y5!10)) | (~(X4!13 = Y4!12)) | (~(X3!15 = Y3!14)) | (~(X2!17 = Y2!16)) | (~(X1!19 = Y1!18))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(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))),
% 3.43/3.56 inference(modus_ponens,[status(thm)],[8, 1])).
% 3.43/3.56 tff(10,plain,
% 3.43/3.56 (Y1!18 = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.56 inference(and_elim,[status(thm)],[9])).
% 3.43/3.56 tff(11,plain,
% 3.43/3.56 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = Y1!18),
% 3.43/3.56 inference(symmetry,[status(thm)],[10])).
% 3.43/3.56 tff(12,plain,
% 3.43/3.56 (sum(n0, n2) = n2),
% 3.43/3.56 inference(and_elim,[status(thm)],[9])).
% 3.43/3.56 tff(13,plain,
% 3.43/3.56 (succ(n1) = n2),
% 3.43/3.56 inference(and_elim,[status(thm)],[9])).
% 3.43/3.56 tff(14,assumption,(~(X1!19 = Y1!18)), introduced(assumption)).
% 3.43/3.56 tff(15,plain,
% 3.43/3.56 (sum(n8, n10) = n7),
% 3.43/3.56 inference(and_elim,[status(thm)],[9])).
% 3.43/3.56 tff(16,plain,
% 3.43/3.56 (succ(n9) = n10),
% 3.43/3.56 inference(and_elim,[status(thm)],[9])).
% 3.43/3.56 tff(17,assumption,(Y0!20 = n9), introduced(assumption)).
% 3.43/3.57 tff(18,plain,
% 3.43/3.57 (succ(Y0!20) = succ(n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[17])).
% 3.43/3.57 tff(19,plain,
% 3.43/3.57 (succ(Y0!20) = n10),
% 3.43/3.57 inference(transitivity,[status(thm)],[18, 16])).
% 3.43/3.57 tff(20,plain,
% 3.43/3.57 (pred(n9) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(21,plain,
% 3.43/3.57 (pred(Y0!20) = pred(n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[17])).
% 3.43/3.57 tff(22,plain,
% 3.43/3.57 (pred(Y0!20) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[21, 20])).
% 3.43/3.57 tff(23,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = sum(n8, n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[22, 19])).
% 3.43/3.57 tff(24,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[23, 15])).
% 3.43/3.57 tff(25,plain,
% 3.43/3.57 (sum(n7, n9) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(26,plain,
% 3.43/3.57 (succ(n8) = n9),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(27,plain,
% 3.43/3.57 (sum(n5, n7) = n1),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(28,plain,
% 3.43/3.57 (succ(n6) = n7),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(29,assumption,(X0!21 = n6), introduced(assumption)).
% 3.43/3.57 tff(30,plain,
% 3.43/3.57 (succ(X0!21) = succ(n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[29])).
% 3.43/3.57 tff(31,plain,
% 3.43/3.57 (succ(X0!21) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[30, 28])).
% 3.43/3.57 tff(32,plain,
% 3.43/3.57 (pred(n6) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(33,plain,
% 3.43/3.57 (pred(X0!21) = pred(n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[29])).
% 3.43/3.57 tff(34,plain,
% 3.43/3.57 (pred(X0!21) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[33, 32])).
% 3.43/3.57 tff(35,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(n5, n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[34, 31])).
% 3.43/3.57 tff(36,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n1),
% 3.43/3.57 inference(transitivity,[status(thm)],[35, 27])).
% 3.43/3.57 tff(37,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[36, 24])).
% 3.43/3.57 tff(38,plain,
% 3.43/3.57 (sum(n1, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[37])).
% 3.43/3.57 tff(39,plain,
% 3.43/3.57 (sum(n1, n7) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(40,plain,
% 3.43/3.57 (n8 = sum(n1, n7)),
% 3.43/3.57 inference(symmetry,[status(thm)],[39])).
% 3.43/3.57 tff(41,plain,
% 3.43/3.57 (sum(n4, n4) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(42,plain,
% 3.43/3.57 (sum(n8, n7) = n4),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(43,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[22, 31])).
% 3.43/3.57 tff(44,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.57 inference(transitivity,[status(thm)],[43, 42])).
% 3.43/3.57 tff(45,plain,
% 3.43/3.57 (sum(n5, n10) = n4),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(46,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[34, 19])).
% 3.43/3.57 tff(47,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.57 inference(transitivity,[status(thm)],[46, 45])).
% 3.43/3.57 tff(48,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[47, 44])).
% 3.43/3.57 tff(49,plain,
% 3.43/3.57 (X1!19 = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(50,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 48, 41, 40, 38, 11])).
% 3.43/3.57 tff(51,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 50])).
% 3.43/3.57 tff(52,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n9))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(53,plain,
% 3.43/3.57 (~(X0!21 = n6)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[52, 17, 14])).
% 3.43/3.57 tff(54,assumption,(X0!21 = n7), introduced(assumption)).
% 3.43/3.57 tff(55,assumption,(Y0!20 = n1), introduced(assumption)).
% 3.43/3.57 tff(56,plain,
% 3.43/3.57 (succ(Y0!20) = succ(n1)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[55])).
% 3.43/3.57 tff(57,plain,
% 3.43/3.57 (succ(Y0!20) = n2),
% 3.43/3.57 inference(transitivity,[status(thm)],[56, 13])).
% 3.43/3.57 tff(58,plain,
% 3.43/3.57 (pred(n1) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(59,plain,
% 3.43/3.57 (pred(Y0!20) = pred(n1)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[55])).
% 3.43/3.57 tff(60,plain,
% 3.43/3.57 (pred(Y0!20) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[59, 58])).
% 3.43/3.57 tff(61,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = sum(n0, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[60, 57])).
% 3.43/3.57 tff(62,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = n2),
% 3.43/3.57 inference(transitivity,[status(thm)],[61, 12])).
% 3.43/3.57 tff(63,plain,
% 3.43/3.57 (sum(n6, n8) = n3),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(64,plain,
% 3.43/3.57 (succ(n7) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(65,plain,
% 3.43/3.57 (succ(X0!21) = succ(n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[54])).
% 3.43/3.57 tff(66,plain,
% 3.43/3.57 (succ(X0!21) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[65, 64])).
% 3.43/3.57 tff(67,plain,
% 3.43/3.57 (pred(n7) = n6),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(68,plain,
% 3.43/3.57 (pred(X0!21) = pred(n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[54])).
% 3.43/3.57 tff(69,plain,
% 3.43/3.57 (pred(X0!21) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[68, 67])).
% 3.43/3.57 tff(70,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(n6, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[69, 66])).
% 3.43/3.57 tff(71,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n3),
% 3.43/3.57 inference(transitivity,[status(thm)],[70, 63])).
% 3.43/3.57 tff(72,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[71, 62])).
% 3.43/3.57 tff(73,plain,
% 3.43/3.57 (sum(n3, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[72])).
% 3.43/3.57 tff(74,plain,
% 3.43/3.57 (sum(n3, n2) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(75,plain,
% 3.43/3.57 (n5 = sum(n3, n2)),
% 3.43/3.57 inference(symmetry,[status(thm)],[74])).
% 3.43/3.57 tff(76,plain,
% 3.43/3.57 (sum(n8, n8) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(77,plain,
% 3.43/3.57 (sum(n0, n8) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(78,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[60, 66])).
% 3.43/3.57 tff(79,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[78, 77])).
% 3.43/3.57 tff(80,plain,
% 3.43/3.57 (sum(n6, n2) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(81,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[69, 57])).
% 3.43/3.57 tff(82,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[81, 80])).
% 3.43/3.57 tff(83,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[82, 79])).
% 3.43/3.57 tff(84,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 83, 76, 75, 73, 11])).
% 3.43/3.57 tff(85,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 84])).
% 3.43/3.57 tff(86,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(87,plain,
% 3.43/3.57 (~(Y0!20 = n1)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[86, 54, 14])).
% 3.43/3.57 tff(88,plain,
% 3.43/3.57 (sum(n1, n3) = n4),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(89,plain,
% 3.43/3.57 (succ(n2) = n3),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(90,assumption,(Y0!20 = n2), introduced(assumption)).
% 3.43/3.57 tff(91,plain,
% 3.43/3.57 (succ(Y0!20) = succ(n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[90])).
% 3.43/3.57 tff(92,plain,
% 3.43/3.57 (succ(Y0!20) = n3),
% 3.43/3.57 inference(transitivity,[status(thm)],[91, 89])).
% 3.43/3.57 tff(93,plain,
% 3.43/3.57 (pred(n2) = n1),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(94,plain,
% 3.43/3.57 (pred(Y0!20) = pred(n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[90])).
% 3.43/3.57 tff(95,plain,
% 3.43/3.57 (pred(Y0!20) = n1),
% 3.43/3.57 inference(transitivity,[status(thm)],[94, 93])).
% 3.43/3.57 tff(96,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = sum(n1, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[95, 92])).
% 3.43/3.57 tff(97,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = n4),
% 3.43/3.57 inference(transitivity,[status(thm)],[96, 88])).
% 3.43/3.57 tff(98,assumption,(X0!21 = n9), introduced(assumption)).
% 3.43/3.57 tff(99,plain,
% 3.43/3.57 (succ(X0!21) = succ(n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[98])).
% 3.43/3.57 tff(100,plain,
% 3.43/3.57 (succ(X0!21) = n10),
% 3.43/3.57 inference(transitivity,[status(thm)],[99, 16])).
% 3.43/3.57 tff(101,plain,
% 3.43/3.57 (pred(X0!21) = pred(n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[98])).
% 3.43/3.57 tff(102,plain,
% 3.43/3.57 (pred(X0!21) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[101, 20])).
% 3.43/3.57 tff(103,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(n8, n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[102, 100])).
% 3.43/3.57 tff(104,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[103, 15])).
% 3.43/3.57 tff(105,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n4)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[104, 97])).
% 3.43/3.57 tff(106,plain,
% 3.43/3.57 (sum(n7, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[105])).
% 3.43/3.57 tff(107,plain,
% 3.43/3.57 (sum(n7, n4) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(108,plain,
% 3.43/3.57 (n0 = sum(n7, n4)),
% 3.43/3.57 inference(symmetry,[status(thm)],[107])).
% 3.43/3.57 tff(109,plain,
% 3.43/3.57 (sum(n0, n0) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(110,plain,
% 3.43/3.57 (sum(n1, n10) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(111,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[95, 100])).
% 3.43/3.57 tff(112,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[111, 110])).
% 3.43/3.57 tff(113,plain,
% 3.43/3.57 (sum(n8, n3) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(114,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[102, 92])).
% 3.43/3.57 tff(115,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[114, 113])).
% 3.43/3.57 tff(116,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[115, 112])).
% 3.43/3.57 tff(117,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 116, 109, 108, 106, 11])).
% 3.43/3.57 tff(118,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 117])).
% 3.43/3.57 tff(119,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(120,plain,
% 3.43/3.57 (~(X0!21 = n9)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[119, 90, 14])).
% 3.43/3.57 tff(121,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n4)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[36, 97])).
% 3.43/3.57 tff(122,plain,
% 3.43/3.57 (sum(n1, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[121])).
% 3.43/3.57 tff(123,plain,
% 3.43/3.57 (sum(n1, n4) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(124,plain,
% 3.43/3.57 (n5 = sum(n1, n4)),
% 3.43/3.57 inference(symmetry,[status(thm)],[123])).
% 3.43/3.57 tff(125,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[95, 31])).
% 3.43/3.57 tff(126,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[125, 39])).
% 3.43/3.57 tff(127,plain,
% 3.43/3.57 (sum(n5, n3) = n8),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(128,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[34, 92])).
% 3.43/3.57 tff(129,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[128, 127])).
% 3.43/3.57 tff(130,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[129, 126])).
% 3.43/3.57 tff(131,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 130, 76, 124, 122, 11])).
% 3.43/3.57 tff(132,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 131])).
% 3.43/3.57 tff(133,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(134,plain,
% 3.43/3.57 (~(X0!21 = n6)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[133, 90, 14])).
% 3.43/3.57 tff(135,assumption,(X0!21 = n10), introduced(assumption)).
% 3.43/3.57 tff(136,plain,
% 3.43/3.57 (sum(n10, n1) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(137,plain,
% 3.43/3.57 (succ(n0) = n1),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(138,assumption,(Y0!20 = n0), introduced(assumption)).
% 3.43/3.57 tff(139,plain,
% 3.43/3.57 (succ(Y0!20) = succ(n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[138])).
% 3.43/3.57 tff(140,plain,
% 3.43/3.57 (succ(Y0!20) = n1),
% 3.43/3.57 inference(transitivity,[status(thm)],[139, 137])).
% 3.43/3.57 tff(141,plain,
% 3.43/3.57 (pred(n0) = n10),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(142,plain,
% 3.43/3.57 (pred(Y0!20) = pred(n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[138])).
% 3.43/3.57 tff(143,plain,
% 3.43/3.57 (pred(Y0!20) = n10),
% 3.43/3.57 inference(transitivity,[status(thm)],[142, 141])).
% 3.43/3.57 tff(144,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = sum(n10, n1)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[143, 140])).
% 3.43/3.57 tff(145,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[144, 136])).
% 3.43/3.57 tff(146,plain,
% 3.43/3.57 (sum(n9, n0) = n9),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(147,plain,
% 3.43/3.57 (succ(n10) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(148,plain,
% 3.43/3.57 (succ(X0!21) = succ(n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[135])).
% 3.43/3.57 tff(149,plain,
% 3.43/3.57 (succ(X0!21) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[148, 147])).
% 3.43/3.57 tff(150,plain,
% 3.43/3.57 (pred(n10) = n9),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(151,plain,
% 3.43/3.57 (pred(X0!21) = pred(n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[135])).
% 3.43/3.57 tff(152,plain,
% 3.43/3.57 (pred(X0!21) = n9),
% 3.43/3.57 inference(transitivity,[status(thm)],[151, 150])).
% 3.43/3.57 tff(153,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(n9, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[152, 149])).
% 3.43/3.57 tff(154,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n9),
% 3.43/3.57 inference(transitivity,[status(thm)],[153, 146])).
% 3.43/3.57 tff(155,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[154, 145])).
% 3.43/3.57 tff(156,plain,
% 3.43/3.57 (sum(n9, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[155])).
% 3.43/3.57 tff(157,plain,
% 3.43/3.57 (n9 = sum(n9, n0)),
% 3.43/3.57 inference(symmetry,[status(thm)],[146])).
% 3.43/3.57 tff(158,plain,
% 3.43/3.57 (sum(n10, n10) = n9),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(159,plain,
% 3.43/3.57 (sum(n10, n0) = n10),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(160,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[143, 149])).
% 3.43/3.57 tff(161,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.57 inference(transitivity,[status(thm)],[160, 159])).
% 3.43/3.57 tff(162,plain,
% 3.43/3.57 (sum(n9, n1) = n10),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(163,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n1)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[152, 140])).
% 3.43/3.57 tff(164,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.57 inference(transitivity,[status(thm)],[163, 162])).
% 3.43/3.57 tff(165,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[164, 161])).
% 3.43/3.57 tff(166,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 165, 158, 157, 156, 11])).
% 3.43/3.57 tff(167,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 166])).
% 3.43/3.57 tff(168,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(169,plain,
% 3.43/3.57 (~(Y0!20 = n0)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[168, 135, 14])).
% 3.43/3.57 tff(170,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[154, 62])).
% 3.43/3.57 tff(171,plain,
% 3.43/3.57 (sum(n9, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[170])).
% 3.43/3.57 tff(172,plain,
% 3.43/3.57 (sum(n9, n2) = n0),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(173,plain,
% 3.43/3.57 (n0 = sum(n9, n2)),
% 3.43/3.57 inference(symmetry,[status(thm)],[172])).
% 3.43/3.57 tff(174,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[60, 149])).
% 3.43/3.57 tff(175,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[174, 109])).
% 3.43/3.57 tff(176,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[152, 57])).
% 3.43/3.57 tff(177,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.57 inference(transitivity,[status(thm)],[176, 172])).
% 3.43/3.57 tff(178,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[177, 175])).
% 3.43/3.57 tff(179,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 178, 109, 173, 171, 11])).
% 3.43/3.57 tff(180,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 179])).
% 3.43/3.57 tff(181,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(182,plain,
% 3.43/3.57 (~(Y0!20 = n1)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[181, 135, 14])).
% 3.43/3.57 tff(183,assumption,(Y0!20 = n8), introduced(assumption)).
% 3.43/3.57 tff(184,plain,
% 3.43/3.57 (succ(Y0!20) = succ(n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[183])).
% 3.43/3.57 tff(185,plain,
% 3.43/3.57 (succ(Y0!20) = n9),
% 3.43/3.57 inference(transitivity,[status(thm)],[184, 26])).
% 3.43/3.57 tff(186,plain,
% 3.43/3.57 (pred(n8) = n7),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(187,plain,
% 3.43/3.57 (pred(Y0!20) = pred(n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[183])).
% 3.43/3.57 tff(188,plain,
% 3.43/3.57 (pred(Y0!20) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[187, 186])).
% 3.43/3.57 tff(189,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = sum(n7, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[188, 185])).
% 3.43/3.57 tff(190,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[189, 25])).
% 3.43/3.57 tff(191,assumption,(X0!21 = n8), introduced(assumption)).
% 3.43/3.57 tff(192,plain,
% 3.43/3.57 (succ(X0!21) = succ(n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[191])).
% 3.43/3.57 tff(193,plain,
% 3.43/3.57 (succ(X0!21) = n9),
% 3.43/3.57 inference(transitivity,[status(thm)],[192, 26])).
% 3.43/3.57 tff(194,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[188, 193])).
% 3.43/3.57 tff(195,plain,
% 3.43/3.57 (pred(n8) = pred(Y0!20)),
% 3.43/3.57 inference(symmetry,[status(thm)],[187])).
% 3.43/3.57 tff(196,plain,
% 3.43/3.57 (pred(X0!21) = pred(n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[191])).
% 3.43/3.57 tff(197,plain,
% 3.43/3.57 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.57 inference(transitivity,[status(thm)],[196, 195])).
% 3.43/3.57 tff(198,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.57 inference(monotonicity,[status(thm)],[197])).
% 3.43/3.57 tff(199,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[198, 194, 25])).
% 3.43/3.57 tff(200,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[199, 190])).
% 3.43/3.57 tff(201,plain,
% 3.43/3.57 (sum(n5, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[200])).
% 3.43/3.57 tff(202,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[194, 25])).
% 3.43/3.57 tff(203,plain,
% 3.43/3.57 (pred(X0!21) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[196, 186])).
% 3.43/3.57 tff(204,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[203, 185])).
% 3.43/3.57 tff(205,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[204, 25])).
% 3.43/3.57 tff(206,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[205, 202])).
% 3.43/3.57 tff(207,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 206, 201, 11])).
% 3.43/3.57 tff(208,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 207])).
% 3.43/3.57 tff(209,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n8))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(210,plain,
% 3.43/3.57 (~(X0!21 = n8)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[209, 183, 14])).
% 3.43/3.57 tff(211,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[104, 190])).
% 3.43/3.57 tff(212,plain,
% 3.43/3.57 (sum(n7, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[211])).
% 3.43/3.57 tff(213,plain,
% 3.43/3.57 (sum(n7, n5) = n1),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(214,plain,
% 3.43/3.57 (n1 = sum(n7, n5)),
% 3.43/3.57 inference(symmetry,[status(thm)],[213])).
% 3.43/3.57 tff(215,plain,
% 3.43/3.57 (sum(n6, n6) = n1),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(216,plain,
% 3.43/3.57 (sum(n7, n10) = n6),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(217,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n10)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[188, 100])).
% 3.43/3.57 tff(218,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[217, 216])).
% 3.43/3.57 tff(219,plain,
% 3.43/3.57 (sum(n8, n9) = n6),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(220,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[102, 185])).
% 3.43/3.57 tff(221,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[220, 219])).
% 3.43/3.57 tff(222,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[221, 218])).
% 3.43/3.57 tff(223,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 222, 215, 214, 212, 11])).
% 3.43/3.57 tff(224,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 223])).
% 3.43/3.57 tff(225,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n8))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(226,plain,
% 3.43/3.57 (~(X0!21 = n9)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[225, 183, 14])).
% 3.43/3.57 tff(227,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[154, 190])).
% 3.43/3.57 tff(228,plain,
% 3.43/3.57 (sum(n9, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[227])).
% 3.43/3.57 tff(229,plain,
% 3.43/3.57 (sum(n9, n5) = n3),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(230,plain,
% 3.43/3.57 (n3 = sum(n9, n5)),
% 3.43/3.57 inference(symmetry,[status(thm)],[229])).
% 3.43/3.57 tff(231,plain,
% 3.43/3.57 (sum(n7, n7) = n3),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(232,plain,
% 3.43/3.57 (sum(n7, n0) = n7),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(233,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[188, 149])).
% 3.43/3.57 tff(234,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[233, 232])).
% 3.43/3.57 tff(235,plain,
% 3.43/3.57 (sum(n9, n9) = n7),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(236,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[152, 185])).
% 3.43/3.57 tff(237,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[236, 235])).
% 3.43/3.57 tff(238,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[237, 234])).
% 3.43/3.57 tff(239,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 238, 231, 230, 228, 11])).
% 3.43/3.57 tff(240,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 239])).
% 3.43/3.57 tff(241,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n8))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(242,plain,
% 3.43/3.57 (~(X0!21 = n10)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[241, 183, 14])).
% 3.43/3.57 tff(243,assumption,(X0!21 = n5), introduced(assumption)).
% 3.43/3.57 tff(244,plain,
% 3.43/3.57 (sum(n4, n6) = n10),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(245,plain,
% 3.43/3.57 (succ(n5) = n6),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(246,plain,
% 3.43/3.57 (succ(X0!21) = succ(n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[243])).
% 3.43/3.57 tff(247,plain,
% 3.43/3.57 (succ(X0!21) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[246, 245])).
% 3.43/3.57 tff(248,plain,
% 3.43/3.57 (pred(n5) = n4),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(249,plain,
% 3.43/3.57 (pred(X0!21) = pred(n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[243])).
% 3.43/3.57 tff(250,plain,
% 3.43/3.57 (pred(X0!21) = n4),
% 3.43/3.57 inference(transitivity,[status(thm)],[249, 248])).
% 3.43/3.57 tff(251,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(n4, n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[250, 247])).
% 3.43/3.57 tff(252,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n10),
% 3.43/3.57 inference(transitivity,[status(thm)],[251, 244])).
% 3.43/3.57 tff(253,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n0)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[252, 145])).
% 3.43/3.57 tff(254,plain,
% 3.43/3.57 (sum(n10, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[253])).
% 3.43/3.57 tff(255,plain,
% 3.43/3.57 (n10 = sum(n10, n0)),
% 3.43/3.57 inference(symmetry,[status(thm)],[159])).
% 3.43/3.57 tff(256,plain,
% 3.43/3.57 (sum(n5, n5) = n10),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(257,plain,
% 3.43/3.57 (sum(n10, n6) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(258,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[143, 247])).
% 3.43/3.57 tff(259,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[258, 257])).
% 3.43/3.57 tff(260,plain,
% 3.43/3.57 (sum(n4, n1) = n5),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(261,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n1)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[250, 140])).
% 3.43/3.57 tff(262,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[261, 260])).
% 3.43/3.57 tff(263,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[262, 259])).
% 3.43/3.57 tff(264,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 263, 256, 255, 254, 11])).
% 3.43/3.57 tff(265,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 264])).
% 3.43/3.57 tff(266,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(267,plain,
% 3.43/3.57 (~(Y0!20 = n0)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[266, 243, 14])).
% 3.43/3.57 tff(268,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[252, 62])).
% 3.43/3.57 tff(269,plain,
% 3.43/3.57 (sum(n10, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[268])).
% 3.43/3.57 tff(270,plain,
% 3.43/3.57 (sum(n10, n2) = n1),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(271,plain,
% 3.43/3.57 (n1 = sum(n10, n2)),
% 3.43/3.57 inference(symmetry,[status(thm)],[270])).
% 3.43/3.57 tff(272,plain,
% 3.43/3.57 (sum(n0, n6) = n6),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(273,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[60, 247])).
% 3.43/3.57 tff(274,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[273, 272])).
% 3.43/3.57 tff(275,plain,
% 3.43/3.57 (sum(n4, n2) = n6),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(276,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n2)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[250, 57])).
% 3.43/3.57 tff(277,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[276, 275])).
% 3.43/3.57 tff(278,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[277, 274])).
% 3.43/3.57 tff(279,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 278, 215, 271, 269, 11])).
% 3.43/3.57 tff(280,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 279])).
% 3.43/3.57 tff(281,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(282,plain,
% 3.43/3.57 (~(Y0!20 = n1)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[281, 243, 14])).
% 3.43/3.57 tff(283,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n4)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[252, 97])).
% 3.43/3.57 tff(284,plain,
% 3.43/3.57 (sum(n10, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[283])).
% 3.43/3.57 tff(285,plain,
% 3.43/3.57 (sum(n10, n4) = n3),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(286,plain,
% 3.43/3.57 (n3 = sum(n10, n4)),
% 3.43/3.57 inference(symmetry,[status(thm)],[285])).
% 3.43/3.57 tff(287,plain,
% 3.43/3.57 (sum(n1, n6) = n7),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(288,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n6)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[95, 247])).
% 3.43/3.57 tff(289,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[288, 287])).
% 3.43/3.57 tff(290,plain,
% 3.43/3.57 (sum(n4, n3) = n7),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(291,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[250, 92])).
% 3.43/3.57 tff(292,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.43/3.57 inference(transitivity,[status(thm)],[291, 290])).
% 3.43/3.57 tff(293,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[292, 289])).
% 3.43/3.57 tff(294,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 293, 231, 286, 284, 11])).
% 3.43/3.57 tff(295,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 294])).
% 3.43/3.57 tff(296,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(297,plain,
% 3.43/3.57 (~(Y0!20 = n2)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[296, 243, 14])).
% 3.43/3.57 tff(298,assumption,(Y0!20 = n7), introduced(assumption)).
% 3.43/3.57 tff(299,plain,
% 3.43/3.57 (succ(Y0!20) = succ(n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[298])).
% 3.43/3.57 tff(300,plain,
% 3.43/3.57 (succ(Y0!20) = n8),
% 3.43/3.57 inference(transitivity,[status(thm)],[299, 64])).
% 3.43/3.57 tff(301,plain,
% 3.43/3.57 (pred(Y0!20) = pred(n7)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[298])).
% 3.43/3.57 tff(302,plain,
% 3.43/3.57 (pred(Y0!20) = n6),
% 3.43/3.57 inference(transitivity,[status(thm)],[301, 67])).
% 3.43/3.57 tff(303,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = sum(n6, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[302, 300])).
% 3.43/3.57 tff(304,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(Y0!20)) = n3),
% 3.43/3.57 inference(transitivity,[status(thm)],[303, 63])).
% 3.43/3.57 tff(305,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[302, 66])).
% 3.43/3.57 tff(306,plain,
% 3.43/3.57 (pred(n7) = pred(Y0!20)),
% 3.43/3.57 inference(symmetry,[status(thm)],[301])).
% 3.43/3.57 tff(307,plain,
% 3.43/3.57 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.57 inference(transitivity,[status(thm)],[68, 306])).
% 3.43/3.57 tff(308,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.57 inference(monotonicity,[status(thm)],[307])).
% 3.43/3.57 tff(309,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n3),
% 3.43/3.57 inference(transitivity,[status(thm)],[308, 305, 63])).
% 3.43/3.57 tff(310,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[309, 304])).
% 3.43/3.57 tff(311,plain,
% 3.43/3.57 (sum(n3, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[310])).
% 3.43/3.57 tff(312,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.57 inference(transitivity,[status(thm)],[305, 63])).
% 3.43/3.57 tff(313,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[69, 300])).
% 3.43/3.57 tff(314,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.57 inference(transitivity,[status(thm)],[313, 63])).
% 3.43/3.57 tff(315,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[314, 312])).
% 3.43/3.57 tff(316,plain,
% 3.43/3.57 (X1!19 = Y1!18),
% 3.43/3.57 inference(transitivity,[status(thm)],[49, 315, 311, 11])).
% 3.43/3.57 tff(317,plain,
% 3.43/3.57 ($false),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[14, 316])).
% 3.43/3.57 tff(318,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.57 tff(319,plain,
% 3.43/3.57 (~(X0!21 = n7)),
% 3.43/3.57 inference(unit_resolution,[status(thm)],[318, 298, 14])).
% 3.43/3.57 tff(320,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = sum(n7, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[203, 193])).
% 3.43/3.57 tff(321,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(X0!21)) = n5),
% 3.43/3.57 inference(transitivity,[status(thm)],[320, 25])).
% 3.43/3.57 tff(322,plain,
% 3.43/3.57 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n3)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[321, 304])).
% 3.43/3.57 tff(323,plain,
% 3.43/3.57 (sum(n5, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.57 inference(symmetry,[status(thm)],[322])).
% 3.43/3.57 tff(324,plain,
% 3.43/3.57 (n8 = sum(n5, n3)),
% 3.43/3.57 inference(symmetry,[status(thm)],[127])).
% 3.43/3.57 tff(325,plain,
% 3.43/3.57 (sum(n6, n9) = n4),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(326,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n9)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[302, 193])).
% 3.43/3.57 tff(327,plain,
% 3.43/3.57 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.57 inference(transitivity,[status(thm)],[326, 325])).
% 3.43/3.57 tff(328,plain,
% 3.43/3.57 (sum(n7, n8) = n4),
% 3.43/3.57 inference(and_elim,[status(thm)],[9])).
% 3.43/3.57 tff(329,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n8)),
% 3.43/3.57 inference(monotonicity,[status(thm)],[203, 300])).
% 3.43/3.57 tff(330,plain,
% 3.43/3.57 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[329, 328])).
% 3.43/3.58 tff(331,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[330, 327])).
% 3.43/3.58 tff(332,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 331, 41, 324, 323, 11])).
% 3.43/3.58 tff(333,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 332])).
% 3.43/3.58 tff(334,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(335,plain,
% 3.43/3.58 (~(X0!21 = n8)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[334, 298, 14])).
% 3.43/3.58 tff(336,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[104, 304])).
% 3.43/3.58 tff(337,plain,
% 3.43/3.58 (sum(n7, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[336])).
% 3.43/3.58 tff(338,plain,
% 3.43/3.58 (sum(n7, n3) = n10),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(339,plain,
% 3.43/3.58 (n10 = sum(n7, n3)),
% 3.43/3.58 inference(symmetry,[status(thm)],[338])).
% 3.43/3.58 tff(340,plain,
% 3.43/3.58 (sum(n6, n10) = n5),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(341,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[302, 100])).
% 3.43/3.58 tff(342,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[341, 340])).
% 3.43/3.58 tff(343,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n8)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[102, 300])).
% 3.43/3.58 tff(344,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[343, 76])).
% 3.43/3.58 tff(345,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[344, 342])).
% 3.43/3.58 tff(346,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 345, 256, 339, 337, 11])).
% 3.43/3.58 tff(347,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 346])).
% 3.43/3.58 tff(348,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(349,plain,
% 3.43/3.58 (~(X0!21 = n9)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[348, 298, 14])).
% 3.43/3.58 tff(350,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[154, 304])).
% 3.43/3.58 tff(351,plain,
% 3.43/3.58 (sum(n9, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[350])).
% 3.43/3.58 tff(352,plain,
% 3.43/3.58 (sum(n9, n3) = n1),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(353,plain,
% 3.43/3.58 (n1 = sum(n9, n3)),
% 3.43/3.58 inference(symmetry,[status(thm)],[352])).
% 3.43/3.58 tff(354,plain,
% 3.43/3.58 (sum(n6, n0) = n6),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(355,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n0)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[302, 149])).
% 3.43/3.58 tff(356,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.58 inference(transitivity,[status(thm)],[355, 354])).
% 3.43/3.58 tff(357,plain,
% 3.43/3.58 (sum(n9, n8) = n6),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(358,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n8)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[152, 300])).
% 3.43/3.58 tff(359,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.58 inference(transitivity,[status(thm)],[358, 357])).
% 3.43/3.58 tff(360,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[359, 356])).
% 3.43/3.58 tff(361,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 360, 215, 353, 351, 11])).
% 3.43/3.58 tff(362,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 361])).
% 3.43/3.58 tff(363,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(364,plain,
% 3.43/3.58 (~(X0!21 = n10)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[363, 298, 14])).
% 3.43/3.58 tff(365,assumption,(X0!21 = n4), introduced(assumption)).
% 3.43/3.58 tff(366,plain,
% 3.43/3.58 (sum(n3, n5) = n8),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(367,plain,
% 3.43/3.58 (succ(n4) = n5),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(368,plain,
% 3.43/3.58 (succ(X0!21) = succ(n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[365])).
% 3.43/3.58 tff(369,plain,
% 3.43/3.58 (succ(X0!21) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[368, 367])).
% 3.43/3.58 tff(370,plain,
% 3.43/3.58 (pred(n4) = n3),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(371,plain,
% 3.43/3.58 (pred(X0!21) = pred(n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[365])).
% 3.43/3.58 tff(372,plain,
% 3.43/3.58 (pred(X0!21) = n3),
% 3.43/3.58 inference(transitivity,[status(thm)],[371, 370])).
% 3.43/3.58 tff(373,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = sum(n3, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[372, 369])).
% 3.43/3.58 tff(374,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = n8),
% 3.43/3.58 inference(transitivity,[status(thm)],[373, 366])).
% 3.43/3.58 tff(375,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[374, 24])).
% 3.43/3.58 tff(376,plain,
% 3.43/3.58 (sum(n8, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[375])).
% 3.43/3.58 tff(377,plain,
% 3.43/3.58 (n4 = sum(n8, n7)),
% 3.43/3.58 inference(symmetry,[status(thm)],[42])).
% 3.43/3.58 tff(378,plain,
% 3.43/3.58 (sum(n2, n2) = n4),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(379,plain,
% 3.43/3.58 (sum(n8, n5) = n2),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(380,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[22, 369])).
% 3.43/3.58 tff(381,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.58 inference(transitivity,[status(thm)],[380, 379])).
% 3.43/3.58 tff(382,plain,
% 3.43/3.58 (sum(n3, n10) = n2),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(383,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[372, 19])).
% 3.43/3.58 tff(384,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.58 inference(transitivity,[status(thm)],[383, 382])).
% 3.43/3.58 tff(385,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[384, 381])).
% 3.43/3.58 tff(386,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 385, 378, 377, 376, 11])).
% 3.43/3.58 tff(387,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 386])).
% 3.43/3.58 tff(388,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(389,plain,
% 3.43/3.58 (~(Y0!20 = n9)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[388, 365, 14])).
% 3.43/3.58 tff(390,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n0)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[374, 145])).
% 3.43/3.58 tff(391,plain,
% 3.43/3.58 (sum(n8, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[390])).
% 3.43/3.58 tff(392,plain,
% 3.43/3.58 (sum(n8, n0) = n8),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(393,plain,
% 3.43/3.58 (n8 = sum(n8, n0)),
% 3.43/3.58 inference(symmetry,[status(thm)],[392])).
% 3.43/3.58 tff(394,plain,
% 3.43/3.58 (sum(n10, n5) = n4),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(395,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[143, 369])).
% 3.43/3.58 tff(396,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[395, 394])).
% 3.43/3.58 tff(397,plain,
% 3.43/3.58 (sum(n3, n1) = n4),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(398,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[372, 140])).
% 3.43/3.58 tff(399,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[398, 397])).
% 3.43/3.58 tff(400,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[399, 396])).
% 3.43/3.58 tff(401,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 400, 41, 393, 391, 11])).
% 3.43/3.58 tff(402,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 401])).
% 3.43/3.58 tff(403,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(404,plain,
% 3.43/3.58 (~(Y0!20 = n0)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[403, 365, 14])).
% 3.43/3.58 tff(405,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n2)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[374, 62])).
% 3.43/3.58 tff(406,plain,
% 3.43/3.58 (sum(n8, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[405])).
% 3.43/3.58 tff(407,plain,
% 3.43/3.58 (sum(n8, n2) = n10),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(408,plain,
% 3.43/3.58 (n10 = sum(n8, n2)),
% 3.43/3.58 inference(symmetry,[status(thm)],[407])).
% 3.43/3.58 tff(409,plain,
% 3.43/3.58 (sum(n0, n5) = n5),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(410,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[60, 369])).
% 3.43/3.58 tff(411,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[410, 409])).
% 3.43/3.58 tff(412,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n2)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[372, 57])).
% 3.43/3.58 tff(413,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[412, 74])).
% 3.43/3.58 tff(414,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[413, 411])).
% 3.43/3.58 tff(415,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 414, 256, 408, 406, 11])).
% 3.43/3.58 tff(416,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 415])).
% 3.43/3.58 tff(417,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(418,plain,
% 3.43/3.58 (~(Y0!20 = n1)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[417, 365, 14])).
% 3.43/3.58 tff(419,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[374, 97])).
% 3.43/3.58 tff(420,plain,
% 3.43/3.58 (sum(n8, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[419])).
% 3.43/3.58 tff(421,plain,
% 3.43/3.58 (sum(n8, n4) = n1),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(422,plain,
% 3.43/3.58 (n1 = sum(n8, n4)),
% 3.43/3.58 inference(symmetry,[status(thm)],[421])).
% 3.43/3.58 tff(423,plain,
% 3.43/3.58 (sum(n1, n5) = n6),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(424,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[95, 369])).
% 3.43/3.58 tff(425,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.58 inference(transitivity,[status(thm)],[424, 423])).
% 3.43/3.58 tff(426,plain,
% 3.43/3.58 (sum(n3, n3) = n6),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(427,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[372, 92])).
% 3.43/3.58 tff(428,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.58 inference(transitivity,[status(thm)],[427, 426])).
% 3.43/3.58 tff(429,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[428, 425])).
% 3.43/3.58 tff(430,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 429, 215, 422, 420, 11])).
% 3.43/3.58 tff(431,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 430])).
% 3.43/3.58 tff(432,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(433,plain,
% 3.43/3.58 (~(Y0!20 = n2)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[432, 365, 14])).
% 3.43/3.58 tff(434,assumption,(Y0!20 = n6), introduced(assumption)).
% 3.43/3.58 tff(435,plain,
% 3.43/3.58 (succ(Y0!20) = succ(n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[434])).
% 3.43/3.58 tff(436,plain,
% 3.43/3.58 (succ(Y0!20) = n7),
% 3.43/3.58 inference(transitivity,[status(thm)],[435, 28])).
% 3.43/3.58 tff(437,plain,
% 3.43/3.58 (pred(Y0!20) = pred(n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[434])).
% 3.43/3.58 tff(438,plain,
% 3.43/3.58 (pred(Y0!20) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[437, 32])).
% 3.43/3.58 tff(439,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(Y0!20)) = sum(n5, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[438, 436])).
% 3.43/3.58 tff(440,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(Y0!20)) = n1),
% 3.43/3.58 inference(transitivity,[status(thm)],[439, 27])).
% 3.43/3.58 tff(441,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[438, 31])).
% 3.43/3.58 tff(442,plain,
% 3.43/3.58 (pred(n6) = pred(Y0!20)),
% 3.43/3.58 inference(symmetry,[status(thm)],[437])).
% 3.43/3.58 tff(443,plain,
% 3.43/3.58 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.58 inference(transitivity,[status(thm)],[33, 442])).
% 3.43/3.58 tff(444,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.58 inference(monotonicity,[status(thm)],[443])).
% 3.43/3.58 tff(445,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = n1),
% 3.43/3.58 inference(transitivity,[status(thm)],[444, 441, 27])).
% 3.43/3.58 tff(446,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[445, 440])).
% 3.43/3.58 tff(447,plain,
% 3.43/3.58 (sum(n1, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[446])).
% 3.43/3.58 tff(448,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.58 inference(transitivity,[status(thm)],[441, 27])).
% 3.43/3.58 tff(449,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[34, 436])).
% 3.43/3.58 tff(450,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.58 inference(transitivity,[status(thm)],[449, 27])).
% 3.43/3.58 tff(451,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[450, 448])).
% 3.43/3.58 tff(452,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 451, 447, 11])).
% 3.43/3.58 tff(453,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 452])).
% 3.43/3.58 tff(454,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(455,plain,
% 3.43/3.58 (~(X0!21 = n6)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[454, 434, 14])).
% 3.43/3.58 tff(456,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[71, 440])).
% 3.43/3.58 tff(457,plain,
% 3.43/3.58 (sum(n3, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[456])).
% 3.43/3.58 tff(458,plain,
% 3.43/3.58 (n4 = sum(n3, n1)),
% 3.43/3.58 inference(symmetry,[status(thm)],[397])).
% 3.43/3.58 tff(459,plain,
% 3.43/3.58 (sum(n5, n8) = n2),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(460,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n8)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[438, 66])).
% 3.43/3.58 tff(461,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.58 inference(transitivity,[status(thm)],[460, 459])).
% 3.43/3.58 tff(462,plain,
% 3.43/3.58 (sum(n6, n7) = n2),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(463,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[69, 436])).
% 3.43/3.58 tff(464,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.58 inference(transitivity,[status(thm)],[463, 462])).
% 3.43/3.58 tff(465,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[464, 461])).
% 3.43/3.58 tff(466,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 465, 378, 458, 457, 11])).
% 3.43/3.58 tff(467,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 466])).
% 3.43/3.58 tff(468,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(469,plain,
% 3.43/3.58 (~(X0!21 = n7)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[468, 434, 14])).
% 3.43/3.58 tff(470,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[321, 440])).
% 3.43/3.58 tff(471,plain,
% 3.43/3.58 (sum(n5, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[470])).
% 3.43/3.58 tff(472,plain,
% 3.43/3.58 (sum(n5, n1) = n6),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(473,plain,
% 3.43/3.58 (n6 = sum(n5, n1)),
% 3.43/3.58 inference(symmetry,[status(thm)],[472])).
% 3.43/3.58 tff(474,plain,
% 3.43/3.58 (sum(n5, n9) = n3),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(475,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n9)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[438, 193])).
% 3.43/3.58 tff(476,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.58 inference(transitivity,[status(thm)],[475, 474])).
% 3.43/3.58 tff(477,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[203, 436])).
% 3.43/3.58 tff(478,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.58 inference(transitivity,[status(thm)],[477, 231])).
% 3.43/3.58 tff(479,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[478, 476])).
% 3.43/3.58 tff(480,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 479, 426, 473, 471, 11])).
% 3.43/3.58 tff(481,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 480])).
% 3.43/3.58 tff(482,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(483,plain,
% 3.43/3.58 (~(X0!21 = n8)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[482, 434, 14])).
% 3.43/3.58 tff(484,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[104, 440])).
% 3.43/3.58 tff(485,plain,
% 3.43/3.58 (sum(n7, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[484])).
% 3.43/3.58 tff(486,plain,
% 3.43/3.58 (sum(n7, n1) = n8),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(487,plain,
% 3.43/3.58 (n8 = sum(n7, n1)),
% 3.43/3.58 inference(symmetry,[status(thm)],[486])).
% 3.43/3.58 tff(488,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[438, 100])).
% 3.43/3.58 tff(489,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[488, 45])).
% 3.43/3.58 tff(490,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[102, 436])).
% 3.43/3.58 tff(491,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[490, 42])).
% 3.43/3.58 tff(492,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[491, 489])).
% 3.43/3.58 tff(493,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 492, 41, 487, 485, 11])).
% 3.43/3.58 tff(494,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 493])).
% 3.43/3.58 tff(495,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(496,plain,
% 3.43/3.58 (~(X0!21 = n9)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[495, 434, 14])).
% 3.43/3.58 tff(497,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[154, 440])).
% 3.43/3.58 tff(498,plain,
% 3.43/3.58 (sum(n9, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[497])).
% 3.43/3.58 tff(499,plain,
% 3.43/3.58 (n10 = sum(n9, n1)),
% 3.43/3.58 inference(symmetry,[status(thm)],[162])).
% 3.43/3.58 tff(500,plain,
% 3.43/3.58 (sum(n5, n0) = n5),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(501,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n0)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[438, 149])).
% 3.43/3.58 tff(502,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[501, 500])).
% 3.43/3.58 tff(503,plain,
% 3.43/3.58 (sum(n9, n7) = n5),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(504,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[152, 436])).
% 3.43/3.58 tff(505,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[504, 503])).
% 3.43/3.58 tff(506,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[505, 502])).
% 3.43/3.58 tff(507,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 506, 256, 499, 498, 11])).
% 3.43/3.58 tff(508,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 507])).
% 3.43/3.58 tff(509,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(510,plain,
% 3.43/3.58 (~(X0!21 = n10)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[509, 434, 14])).
% 3.43/3.58 tff(511,assumption,(X0!21 = n3), introduced(assumption)).
% 3.43/3.58 tff(512,plain,
% 3.43/3.58 (sum(n2, n4) = n6),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(513,plain,
% 3.43/3.58 (succ(n3) = n4),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(514,plain,
% 3.43/3.58 (succ(X0!21) = succ(n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[511])).
% 3.43/3.58 tff(515,plain,
% 3.43/3.58 (succ(X0!21) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[514, 513])).
% 3.43/3.58 tff(516,plain,
% 3.43/3.58 (pred(n3) = n2),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(517,plain,
% 3.43/3.58 (pred(X0!21) = pred(n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[511])).
% 3.43/3.58 tff(518,plain,
% 3.43/3.58 (pred(X0!21) = n2),
% 3.43/3.58 inference(transitivity,[status(thm)],[517, 516])).
% 3.43/3.58 tff(519,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = sum(n2, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[518, 515])).
% 3.43/3.58 tff(520,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = n6),
% 3.43/3.58 inference(transitivity,[status(thm)],[519, 512])).
% 3.43/3.58 tff(521,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[520, 190])).
% 3.43/3.58 tff(522,plain,
% 3.43/3.58 (sum(n6, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[521])).
% 3.43/3.58 tff(523,plain,
% 3.43/3.58 (sum(n6, n5) = n0),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(524,plain,
% 3.43/3.58 (n0 = sum(n6, n5)),
% 3.43/3.58 inference(symmetry,[status(thm)],[523])).
% 3.43/3.58 tff(525,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[188, 515])).
% 3.43/3.58 tff(526,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.58 inference(transitivity,[status(thm)],[525, 107])).
% 3.43/3.58 tff(527,plain,
% 3.43/3.58 (sum(n2, n9) = n0),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(528,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n9)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[518, 185])).
% 3.43/3.58 tff(529,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.58 inference(transitivity,[status(thm)],[528, 527])).
% 3.43/3.58 tff(530,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[529, 526])).
% 3.43/3.58 tff(531,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 530, 109, 524, 522, 11])).
% 3.43/3.58 tff(532,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 531])).
% 3.43/3.58 tff(533,plain,((~(Y0!20 = n8)) | (X1!19 = Y1!18) | (~(X0!21 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(534,plain,
% 3.43/3.58 (~(Y0!20 = n8)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[533, 511, 14])).
% 3.43/3.58 tff(535,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[520, 24])).
% 3.43/3.58 tff(536,plain,
% 3.43/3.58 (sum(n6, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[535])).
% 3.43/3.58 tff(537,plain,
% 3.43/3.58 (n2 = sum(n6, n7)),
% 3.43/3.58 inference(symmetry,[status(thm)],[462])).
% 3.43/3.58 tff(538,plain,
% 3.43/3.58 (sum(n1, n1) = n2),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(539,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[22, 515])).
% 3.43/3.58 tff(540,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.58 inference(transitivity,[status(thm)],[539, 421])).
% 3.43/3.58 tff(541,plain,
% 3.43/3.58 (sum(n2, n10) = n1),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(542,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[518, 19])).
% 3.43/3.58 tff(543,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.58 inference(transitivity,[status(thm)],[542, 541])).
% 3.43/3.58 tff(544,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[543, 540])).
% 3.43/3.58 tff(545,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 544, 538, 537, 536, 11])).
% 3.43/3.58 tff(546,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 545])).
% 3.43/3.58 tff(547,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(548,plain,
% 3.43/3.58 (~(Y0!20 = n9)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[547, 511, 14])).
% 3.43/3.58 tff(549,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n0)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[520, 145])).
% 3.43/3.58 tff(550,plain,
% 3.43/3.58 (sum(n6, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[549])).
% 3.43/3.58 tff(551,plain,
% 3.43/3.58 (n6 = sum(n6, n0)),
% 3.43/3.58 inference(symmetry,[status(thm)],[354])).
% 3.43/3.58 tff(552,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[143, 515])).
% 3.43/3.58 tff(553,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.58 inference(transitivity,[status(thm)],[552, 285])).
% 3.43/3.58 tff(554,plain,
% 3.43/3.58 (sum(n2, n1) = n3),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(555,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n1)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[518, 140])).
% 3.43/3.58 tff(556,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.58 inference(transitivity,[status(thm)],[555, 554])).
% 3.43/3.58 tff(557,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[556, 553])).
% 3.43/3.58 tff(558,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 557, 426, 551, 550, 11])).
% 3.43/3.58 tff(559,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 558])).
% 3.43/3.58 tff(560,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(561,plain,
% 3.43/3.58 (~(Y0!20 = n0)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[560, 511, 14])).
% 3.43/3.58 tff(562,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n2)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[520, 62])).
% 3.43/3.58 tff(563,plain,
% 3.43/3.58 (sum(n6, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[562])).
% 3.43/3.58 tff(564,plain,
% 3.43/3.58 (n8 = sum(n6, n2)),
% 3.43/3.58 inference(symmetry,[status(thm)],[80])).
% 3.43/3.58 tff(565,plain,
% 3.43/3.58 (sum(n0, n4) = n4),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(566,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[60, 515])).
% 3.43/3.58 tff(567,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[566, 565])).
% 3.43/3.58 tff(568,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n2)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[518, 57])).
% 3.43/3.58 tff(569,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[568, 378])).
% 3.43/3.58 tff(570,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[569, 567])).
% 3.43/3.58 tff(571,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 570, 41, 564, 563, 11])).
% 3.43/3.58 tff(572,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 571])).
% 3.43/3.58 tff(573,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(574,plain,
% 3.43/3.58 (~(Y0!20 = n1)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[573, 511, 14])).
% 3.43/3.58 tff(575,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[520, 97])).
% 3.43/3.58 tff(576,plain,
% 3.43/3.58 (sum(n6, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[575])).
% 3.43/3.58 tff(577,plain,
% 3.43/3.58 (sum(n6, n4) = n10),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(578,plain,
% 3.43/3.58 (n10 = sum(n6, n4)),
% 3.43/3.58 inference(symmetry,[status(thm)],[577])).
% 3.43/3.58 tff(579,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n4)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[95, 515])).
% 3.43/3.58 tff(580,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[579, 123])).
% 3.43/3.58 tff(581,plain,
% 3.43/3.58 (sum(n2, n3) = n5),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(582,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n3)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[518, 92])).
% 3.43/3.58 tff(583,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.58 inference(transitivity,[status(thm)],[582, 581])).
% 3.43/3.58 tff(584,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[583, 580])).
% 3.43/3.58 tff(585,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 584, 256, 578, 576, 11])).
% 3.43/3.58 tff(586,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 585])).
% 3.43/3.58 tff(587,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(588,plain,
% 3.43/3.58 (~(Y0!20 = n2)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[587, 511, 14])).
% 3.43/3.58 tff(589,assumption,(Y0!20 = n5), introduced(assumption)).
% 3.43/3.58 tff(590,plain,
% 3.43/3.58 (succ(Y0!20) = succ(n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[589])).
% 3.43/3.58 tff(591,plain,
% 3.43/3.58 (succ(Y0!20) = n6),
% 3.43/3.58 inference(transitivity,[status(thm)],[590, 245])).
% 3.43/3.58 tff(592,plain,
% 3.43/3.58 (pred(Y0!20) = pred(n5)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[589])).
% 3.43/3.58 tff(593,plain,
% 3.43/3.58 (pred(Y0!20) = n4),
% 3.43/3.58 inference(transitivity,[status(thm)],[592, 248])).
% 3.43/3.58 tff(594,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(Y0!20)) = sum(n4, n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[593, 591])).
% 3.43/3.58 tff(595,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(Y0!20)) = n10),
% 3.43/3.58 inference(transitivity,[status(thm)],[594, 244])).
% 3.43/3.58 tff(596,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[593, 247])).
% 3.43/3.58 tff(597,plain,
% 3.43/3.58 (pred(n5) = pred(Y0!20)),
% 3.43/3.58 inference(symmetry,[status(thm)],[592])).
% 3.43/3.58 tff(598,plain,
% 3.43/3.58 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.58 inference(transitivity,[status(thm)],[249, 597])).
% 3.43/3.58 tff(599,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.58 inference(monotonicity,[status(thm)],[598])).
% 3.43/3.58 tff(600,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(X0!21)) = n10),
% 3.43/3.58 inference(transitivity,[status(thm)],[599, 596, 244])).
% 3.43/3.58 tff(601,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[600, 595])).
% 3.43/3.58 tff(602,plain,
% 3.43/3.58 (sum(n10, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[601])).
% 3.43/3.58 tff(603,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.58 inference(transitivity,[status(thm)],[596, 244])).
% 3.43/3.58 tff(604,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[250, 591])).
% 3.43/3.58 tff(605,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.58 inference(transitivity,[status(thm)],[604, 244])).
% 3.43/3.58 tff(606,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[605, 603])).
% 3.43/3.58 tff(607,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 606, 602, 11])).
% 3.43/3.58 tff(608,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 607])).
% 3.43/3.58 tff(609,plain,((~(X0!21 = n5)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(610,plain,
% 3.43/3.58 (~(X0!21 = n5)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[609, 589, 14])).
% 3.43/3.58 tff(611,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n10)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[36, 595])).
% 3.43/3.58 tff(612,plain,
% 3.43/3.58 (sum(n1, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.58 inference(symmetry,[status(thm)],[611])).
% 3.43/3.58 tff(613,plain,
% 3.43/3.58 (n0 = sum(n1, n10)),
% 3.43/3.58 inference(symmetry,[status(thm)],[110])).
% 3.43/3.58 tff(614,plain,
% 3.43/3.58 (sum(n4, n7) = n0),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(615,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n7)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[593, 31])).
% 3.43/3.58 tff(616,plain,
% 3.43/3.58 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.58 inference(transitivity,[status(thm)],[615, 614])).
% 3.43/3.58 tff(617,plain,
% 3.43/3.58 (sum(n5, n6) = n0),
% 3.43/3.58 inference(and_elim,[status(thm)],[9])).
% 3.43/3.58 tff(618,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n6)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[34, 591])).
% 3.43/3.58 tff(619,plain,
% 3.43/3.58 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.58 inference(transitivity,[status(thm)],[618, 617])).
% 3.43/3.58 tff(620,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.58 inference(monotonicity,[status(thm)],[619, 616])).
% 3.43/3.58 tff(621,plain,
% 3.43/3.58 (X1!19 = Y1!18),
% 3.43/3.58 inference(transitivity,[status(thm)],[49, 620, 109, 613, 612, 11])).
% 3.43/3.58 tff(622,plain,
% 3.43/3.58 ($false),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[14, 621])).
% 3.43/3.58 tff(623,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.58 tff(624,plain,
% 3.43/3.58 (~(X0!21 = n6)),
% 3.43/3.58 inference(unit_resolution,[status(thm)],[623, 589, 14])).
% 3.43/3.58 tff(625,plain,
% 3.43/3.58 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[71, 595])).
% 3.43/3.59 tff(626,plain,
% 3.43/3.59 (sum(n3, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[625])).
% 3.43/3.59 tff(627,plain,
% 3.43/3.59 (n2 = sum(n3, n10)),
% 3.43/3.59 inference(symmetry,[status(thm)],[382])).
% 3.43/3.59 tff(628,plain,
% 3.43/3.59 (sum(n4, n8) = n1),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(629,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[593, 66])).
% 3.43/3.59 tff(630,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.59 inference(transitivity,[status(thm)],[629, 628])).
% 3.43/3.59 tff(631,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n6)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[69, 591])).
% 3.43/3.59 tff(632,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.59 inference(transitivity,[status(thm)],[631, 215])).
% 3.43/3.59 tff(633,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[632, 630])).
% 3.43/3.59 tff(634,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 633, 538, 627, 626, 11])).
% 3.43/3.59 tff(635,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 634])).
% 3.43/3.59 tff(636,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(637,plain,
% 3.43/3.59 (~(X0!21 = n7)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[636, 589, 14])).
% 3.43/3.59 tff(638,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[321, 595])).
% 3.43/3.59 tff(639,plain,
% 3.43/3.59 (sum(n5, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[638])).
% 3.43/3.59 tff(640,plain,
% 3.43/3.59 (n4 = sum(n5, n10)),
% 3.43/3.59 inference(symmetry,[status(thm)],[45])).
% 3.43/3.59 tff(641,plain,
% 3.43/3.59 (sum(n4, n9) = n2),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(642,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[593, 193])).
% 3.43/3.59 tff(643,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[642, 641])).
% 3.43/3.59 tff(644,plain,
% 3.43/3.59 (sum(n7, n6) = n2),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(645,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n6)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[203, 591])).
% 3.43/3.59 tff(646,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[645, 644])).
% 3.43/3.59 tff(647,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[646, 643])).
% 3.43/3.59 tff(648,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 647, 378, 640, 639, 11])).
% 3.43/3.59 tff(649,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 648])).
% 3.43/3.59 tff(650,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(651,plain,
% 3.43/3.59 (~(X0!21 = n8)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[650, 589, 14])).
% 3.43/3.59 tff(652,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[104, 595])).
% 3.43/3.59 tff(653,plain,
% 3.43/3.59 (sum(n7, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[652])).
% 3.43/3.59 tff(654,plain,
% 3.43/3.59 (n6 = sum(n7, n10)),
% 3.43/3.59 inference(symmetry,[status(thm)],[216])).
% 3.43/3.59 tff(655,plain,
% 3.43/3.59 (sum(n4, n10) = n3),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(656,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[593, 100])).
% 3.43/3.59 tff(657,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[656, 655])).
% 3.43/3.59 tff(658,plain,
% 3.43/3.59 (sum(n8, n6) = n3),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(659,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n6)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[102, 591])).
% 3.43/3.59 tff(660,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[659, 658])).
% 3.43/3.59 tff(661,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[660, 657])).
% 3.43/3.59 tff(662,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 661, 426, 654, 653, 11])).
% 3.43/3.59 tff(663,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 662])).
% 3.43/3.59 tff(664,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(665,plain,
% 3.43/3.59 (~(X0!21 = n9)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[664, 589, 14])).
% 3.43/3.59 tff(666,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[154, 595])).
% 3.43/3.59 tff(667,plain,
% 3.43/3.59 (sum(n9, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[666])).
% 3.43/3.59 tff(668,plain,
% 3.43/3.59 (sum(n9, n10) = n8),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(669,plain,
% 3.43/3.59 (n8 = sum(n9, n10)),
% 3.43/3.59 inference(symmetry,[status(thm)],[668])).
% 3.43/3.59 tff(670,plain,
% 3.43/3.59 (sum(n4, n0) = n4),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(671,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n0)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[593, 149])).
% 3.43/3.59 tff(672,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.59 inference(transitivity,[status(thm)],[671, 670])).
% 3.43/3.59 tff(673,plain,
% 3.43/3.59 (sum(n9, n6) = n4),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(674,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n6)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[152, 591])).
% 3.43/3.59 tff(675,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.59 inference(transitivity,[status(thm)],[674, 673])).
% 3.43/3.59 tff(676,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[675, 672])).
% 3.43/3.59 tff(677,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 676, 41, 669, 667, 11])).
% 3.43/3.59 tff(678,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 677])).
% 3.43/3.59 tff(679,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(680,plain,
% 3.43/3.59 (~(X0!21 = n10)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[679, 589, 14])).
% 3.43/3.59 tff(681,assumption,(X0!21 = n2), introduced(assumption)).
% 3.43/3.59 tff(682,plain,
% 3.43/3.59 (succ(X0!21) = succ(n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[681])).
% 3.43/3.59 tff(683,plain,
% 3.43/3.59 (succ(X0!21) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[682, 89])).
% 3.43/3.59 tff(684,plain,
% 3.43/3.59 (pred(X0!21) = pred(n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[681])).
% 3.43/3.59 tff(685,plain,
% 3.43/3.59 (pred(X0!21) = n1),
% 3.43/3.59 inference(transitivity,[status(thm)],[684, 93])).
% 3.43/3.59 tff(686,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = sum(n1, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 683])).
% 3.43/3.59 tff(687,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = n4),
% 3.43/3.59 inference(transitivity,[status(thm)],[686, 88])).
% 3.43/3.59 tff(688,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[687, 304])).
% 3.43/3.59 tff(689,plain,
% 3.43/3.59 (sum(n4, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[688])).
% 3.43/3.59 tff(690,plain,
% 3.43/3.59 (n7 = sum(n4, n3)),
% 3.43/3.59 inference(symmetry,[status(thm)],[290])).
% 3.43/3.59 tff(691,plain,
% 3.43/3.59 (sum(n6, n3) = n9),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(692,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[302, 683])).
% 3.43/3.59 tff(693,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.43/3.59 inference(transitivity,[status(thm)],[692, 691])).
% 3.43/3.59 tff(694,plain,
% 3.43/3.59 (sum(n1, n8) = n9),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(695,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 300])).
% 3.43/3.59 tff(696,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.43/3.59 inference(transitivity,[status(thm)],[695, 694])).
% 3.43/3.59 tff(697,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[696, 693])).
% 3.43/3.59 tff(698,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 697, 235, 690, 689, 11])).
% 3.43/3.59 tff(699,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 698])).
% 3.43/3.59 tff(700,plain,((~(Y0!20 = n7)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(701,plain,
% 3.43/3.59 (~(Y0!20 = n7)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[700, 681, 14])).
% 3.43/3.59 tff(702,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[687, 190])).
% 3.43/3.59 tff(703,plain,
% 3.43/3.59 (sum(n4, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[702])).
% 3.43/3.59 tff(704,plain,
% 3.43/3.59 (sum(n4, n5) = n9),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(705,plain,
% 3.43/3.59 (n9 = sum(n4, n5)),
% 3.43/3.59 inference(symmetry,[status(thm)],[704])).
% 3.43/3.59 tff(706,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[188, 683])).
% 3.43/3.59 tff(707,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.59 inference(transitivity,[status(thm)],[706, 338])).
% 3.43/3.59 tff(708,plain,
% 3.43/3.59 (sum(n1, n9) = n10),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(709,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 185])).
% 3.43/3.59 tff(710,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.59 inference(transitivity,[status(thm)],[709, 708])).
% 3.43/3.59 tff(711,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[710, 707])).
% 3.43/3.59 tff(712,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 711, 158, 705, 703, 11])).
% 3.43/3.59 tff(713,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 712])).
% 3.43/3.59 tff(714,plain,((~(Y0!20 = n8)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(715,plain,
% 3.43/3.59 (~(Y0!20 = n8)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[714, 681, 14])).
% 3.43/3.59 tff(716,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n7)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[687, 24])).
% 3.43/3.59 tff(717,plain,
% 3.43/3.59 (sum(n4, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[716])).
% 3.43/3.59 tff(718,plain,
% 3.43/3.59 (n0 = sum(n4, n7)),
% 3.43/3.59 inference(symmetry,[status(thm)],[614])).
% 3.43/3.59 tff(719,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[22, 683])).
% 3.43/3.59 tff(720,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.59 inference(transitivity,[status(thm)],[719, 113])).
% 3.43/3.59 tff(721,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 19])).
% 3.43/3.59 tff(722,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.59 inference(transitivity,[status(thm)],[721, 110])).
% 3.43/3.59 tff(723,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[722, 720])).
% 3.43/3.59 tff(724,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 723, 109, 718, 717, 11])).
% 3.43/3.59 tff(725,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 724])).
% 3.43/3.59 tff(726,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(727,plain,
% 3.43/3.59 (~(Y0!20 = n9)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[726, 681, 14])).
% 3.43/3.59 tff(728,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n0)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[687, 145])).
% 3.43/3.59 tff(729,plain,
% 3.43/3.59 (sum(n4, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[728])).
% 3.43/3.59 tff(730,plain,
% 3.43/3.59 (n4 = sum(n4, n0)),
% 3.43/3.59 inference(symmetry,[status(thm)],[670])).
% 3.43/3.59 tff(731,plain,
% 3.43/3.59 (sum(n10, n3) = n2),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(732,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[143, 683])).
% 3.43/3.59 tff(733,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[732, 731])).
% 3.43/3.59 tff(734,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n1)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 140])).
% 3.43/3.59 tff(735,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[734, 538])).
% 3.43/3.59 tff(736,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[735, 733])).
% 3.43/3.59 tff(737,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 736, 378, 730, 729, 11])).
% 3.43/3.59 tff(738,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 737])).
% 3.43/3.59 tff(739,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(740,plain,
% 3.43/3.59 (~(Y0!20 = n0)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[739, 681, 14])).
% 3.43/3.59 tff(741,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[687, 62])).
% 3.43/3.59 tff(742,plain,
% 3.43/3.59 (sum(n4, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[741])).
% 3.43/3.59 tff(743,plain,
% 3.43/3.59 (n6 = sum(n4, n2)),
% 3.43/3.59 inference(symmetry,[status(thm)],[275])).
% 3.43/3.59 tff(744,plain,
% 3.43/3.59 (sum(n0, n3) = n3),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(745,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[60, 683])).
% 3.43/3.59 tff(746,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[745, 744])).
% 3.43/3.59 tff(747,plain,
% 3.43/3.59 (sum(n1, n2) = n3),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(748,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 57])).
% 3.43/3.59 tff(749,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[748, 747])).
% 3.43/3.59 tff(750,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[749, 746])).
% 3.43/3.59 tff(751,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 750, 426, 743, 742, 11])).
% 3.43/3.59 tff(752,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 751])).
% 3.43/3.59 tff(753,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(754,plain,
% 3.43/3.59 (~(Y0!20 = n1)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[753, 681, 14])).
% 3.43/3.59 tff(755,plain,
% 3.43/3.59 (succ(n2) = succ(X0!21)),
% 3.43/3.59 inference(symmetry,[status(thm)],[682])).
% 3.43/3.59 tff(756,plain,
% 3.43/3.59 (succ(Y0!20) = succ(X0!21)),
% 3.43/3.59 inference(transitivity,[status(thm)],[91, 755])).
% 3.43/3.59 tff(757,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(Y0!20)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.59 inference(monotonicity,[status(thm)],[756])).
% 3.43/3.59 tff(758,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[685, 92])).
% 3.43/3.59 tff(759,plain,
% 3.43/3.59 (sum(n1, n3) = sum(pred(X0!21), succ(Y0!20))),
% 3.43/3.59 inference(symmetry,[status(thm)],[758])).
% 3.43/3.59 tff(760,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = sum(pred(X0!21), succ(Y0!20))),
% 3.43/3.59 inference(transitivity,[status(thm)],[686, 759])).
% 3.43/3.59 tff(761,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))),
% 3.43/3.59 inference(monotonicity,[status(thm)],[760, 757])).
% 3.43/3.59 tff(762,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[761])).
% 3.43/3.59 tff(763,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 762, 11])).
% 3.43/3.59 tff(764,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 763])).
% 3.43/3.59 tff(765,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(766,plain,
% 3.43/3.59 (~(Y0!20 = n2)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[765, 681, 14])).
% 3.43/3.59 tff(767,assumption,(Y0!20 = n4), introduced(assumption)).
% 3.43/3.59 tff(768,plain,
% 3.43/3.59 (succ(Y0!20) = succ(n4)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[767])).
% 3.43/3.59 tff(769,plain,
% 3.43/3.59 (succ(Y0!20) = n5),
% 3.43/3.59 inference(transitivity,[status(thm)],[768, 367])).
% 3.43/3.59 tff(770,plain,
% 3.43/3.59 (pred(Y0!20) = pred(n4)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[767])).
% 3.43/3.59 tff(771,plain,
% 3.43/3.59 (pred(Y0!20) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[770, 370])).
% 3.43/3.59 tff(772,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(Y0!20)) = sum(n3, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 769])).
% 3.43/3.59 tff(773,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(Y0!20)) = n8),
% 3.43/3.59 inference(transitivity,[status(thm)],[772, 366])).
% 3.43/3.59 tff(774,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 369])).
% 3.43/3.59 tff(775,plain,
% 3.43/3.59 (pred(n4) = pred(Y0!20)),
% 3.43/3.59 inference(symmetry,[status(thm)],[770])).
% 3.43/3.59 tff(776,plain,
% 3.43/3.59 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.59 inference(transitivity,[status(thm)],[371, 775])).
% 3.43/3.59 tff(777,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.59 inference(monotonicity,[status(thm)],[776])).
% 3.43/3.59 tff(778,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = n8),
% 3.43/3.59 inference(transitivity,[status(thm)],[777, 774, 366])).
% 3.43/3.59 tff(779,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[778, 773])).
% 3.43/3.59 tff(780,plain,
% 3.43/3.59 (sum(n8, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[779])).
% 3.43/3.59 tff(781,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.59 inference(transitivity,[status(thm)],[774, 366])).
% 3.43/3.59 tff(782,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[372, 769])).
% 3.43/3.59 tff(783,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.59 inference(transitivity,[status(thm)],[782, 366])).
% 3.43/3.59 tff(784,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[783, 781])).
% 3.43/3.59 tff(785,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 784, 780, 11])).
% 3.43/3.59 tff(786,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 785])).
% 3.43/3.59 tff(787,plain,((~(X0!21 = n4)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(788,plain,
% 3.43/3.59 (~(X0!21 = n4)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[787, 767, 14])).
% 3.43/3.59 tff(789,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[252, 773])).
% 3.43/3.59 tff(790,plain,
% 3.43/3.59 (sum(n10, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[789])).
% 3.43/3.59 tff(791,plain,
% 3.43/3.59 (sum(n10, n8) = n7),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(792,plain,
% 3.43/3.59 (n7 = sum(n10, n8)),
% 3.43/3.59 inference(symmetry,[status(thm)],[791])).
% 3.43/3.59 tff(793,plain,
% 3.43/3.59 (sum(n3, n6) = n9),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(794,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n6)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 247])).
% 3.43/3.59 tff(795,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.43/3.59 inference(transitivity,[status(thm)],[794, 793])).
% 3.43/3.59 tff(796,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[250, 769])).
% 3.43/3.59 tff(797,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.43/3.59 inference(transitivity,[status(thm)],[796, 704])).
% 3.43/3.59 tff(798,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[797, 795])).
% 3.43/3.59 tff(799,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 798, 235, 792, 790, 11])).
% 3.43/3.59 tff(800,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 799])).
% 3.43/3.59 tff(801,plain,((~(X0!21 = n5)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(802,plain,
% 3.43/3.59 (~(X0!21 = n5)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[801, 767, 14])).
% 3.43/3.59 tff(803,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[36, 773])).
% 3.43/3.59 tff(804,plain,
% 3.43/3.59 (sum(n1, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[803])).
% 3.43/3.59 tff(805,plain,
% 3.43/3.59 (n9 = sum(n1, n8)),
% 3.43/3.59 inference(symmetry,[status(thm)],[694])).
% 3.43/3.59 tff(806,plain,
% 3.43/3.59 (sum(n3, n7) = n10),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(807,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n7)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 31])).
% 3.43/3.59 tff(808,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.59 inference(transitivity,[status(thm)],[807, 806])).
% 3.43/3.59 tff(809,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[34, 769])).
% 3.43/3.59 tff(810,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.59 inference(transitivity,[status(thm)],[809, 256])).
% 3.43/3.59 tff(811,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[810, 808])).
% 3.43/3.59 tff(812,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 811, 158, 805, 804, 11])).
% 3.43/3.59 tff(813,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 812])).
% 3.43/3.59 tff(814,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(815,plain,
% 3.43/3.59 (~(X0!21 = n6)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[814, 767, 14])).
% 3.43/3.59 tff(816,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[71, 773])).
% 3.43/3.59 tff(817,plain,
% 3.43/3.59 (sum(n3, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[816])).
% 3.43/3.59 tff(818,plain,
% 3.43/3.59 (sum(n3, n8) = n0),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(819,plain,
% 3.43/3.59 (n0 = sum(n3, n8)),
% 3.43/3.59 inference(symmetry,[status(thm)],[818])).
% 3.43/3.59 tff(820,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 66])).
% 3.43/3.59 tff(821,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.59 inference(transitivity,[status(thm)],[820, 818])).
% 3.43/3.59 tff(822,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[69, 769])).
% 3.43/3.59 tff(823,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.59 inference(transitivity,[status(thm)],[822, 523])).
% 3.43/3.59 tff(824,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[823, 821])).
% 3.43/3.59 tff(825,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 824, 109, 819, 817, 11])).
% 3.43/3.59 tff(826,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 825])).
% 3.43/3.59 tff(827,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(828,plain,
% 3.43/3.59 (~(X0!21 = n7)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[827, 767, 14])).
% 3.43/3.59 tff(829,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[321, 773])).
% 3.43/3.59 tff(830,plain,
% 3.43/3.59 (sum(n5, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[829])).
% 3.43/3.59 tff(831,plain,
% 3.43/3.59 (n2 = sum(n5, n8)),
% 3.43/3.59 inference(symmetry,[status(thm)],[459])).
% 3.43/3.59 tff(832,plain,
% 3.43/3.59 (sum(n3, n9) = n1),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(833,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 193])).
% 3.43/3.59 tff(834,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.59 inference(transitivity,[status(thm)],[833, 832])).
% 3.43/3.59 tff(835,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[203, 769])).
% 3.43/3.59 tff(836,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.59 inference(transitivity,[status(thm)],[835, 213])).
% 3.43/3.59 tff(837,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[836, 834])).
% 3.43/3.59 tff(838,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 837, 538, 831, 830, 11])).
% 3.43/3.59 tff(839,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 838])).
% 3.43/3.59 tff(840,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(841,plain,
% 3.43/3.59 (~(X0!21 = n8)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[840, 767, 14])).
% 3.43/3.59 tff(842,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[104, 773])).
% 3.43/3.59 tff(843,plain,
% 3.43/3.59 (sum(n7, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[842])).
% 3.43/3.59 tff(844,plain,
% 3.43/3.59 (n4 = sum(n7, n8)),
% 3.43/3.59 inference(symmetry,[status(thm)],[328])).
% 3.43/3.59 tff(845,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n10)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 100])).
% 3.43/3.59 tff(846,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[845, 382])).
% 3.43/3.59 tff(847,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[102, 769])).
% 3.43/3.59 tff(848,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[847, 379])).
% 3.43/3.59 tff(849,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[848, 846])).
% 3.43/3.59 tff(850,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 849, 378, 844, 843, 11])).
% 3.43/3.59 tff(851,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 850])).
% 3.43/3.59 tff(852,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(853,plain,
% 3.43/3.59 (~(X0!21 = n9)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[852, 767, 14])).
% 3.43/3.59 tff(854,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[154, 773])).
% 3.43/3.59 tff(855,plain,
% 3.43/3.59 (sum(n9, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[854])).
% 3.43/3.59 tff(856,plain,
% 3.43/3.59 (n6 = sum(n9, n8)),
% 3.43/3.59 inference(symmetry,[status(thm)],[357])).
% 3.43/3.59 tff(857,plain,
% 3.43/3.59 (sum(n3, n0) = n3),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(858,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n0)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[771, 149])).
% 3.43/3.59 tff(859,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[858, 857])).
% 3.43/3.59 tff(860,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[152, 769])).
% 3.43/3.59 tff(861,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.59 inference(transitivity,[status(thm)],[860, 229])).
% 3.43/3.59 tff(862,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[861, 859])).
% 3.43/3.59 tff(863,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 862, 426, 856, 855, 11])).
% 3.43/3.59 tff(864,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 863])).
% 3.43/3.59 tff(865,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(866,plain,
% 3.43/3.59 (~(X0!21 = n10)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[865, 767, 14])).
% 3.43/3.59 tff(867,assumption,(X0!21 = n1), introduced(assumption)).
% 3.43/3.59 tff(868,plain,
% 3.43/3.59 (succ(X0!21) = succ(n1)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[867])).
% 3.43/3.59 tff(869,plain,
% 3.43/3.59 (succ(X0!21) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[868, 13])).
% 3.43/3.59 tff(870,plain,
% 3.43/3.59 (pred(X0!21) = pred(n1)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[867])).
% 3.43/3.59 tff(871,plain,
% 3.43/3.59 (pred(X0!21) = n0),
% 3.43/3.59 inference(transitivity,[status(thm)],[870, 58])).
% 3.43/3.59 tff(872,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = sum(n0, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[871, 869])).
% 3.43/3.59 tff(873,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(X0!21)) = n2),
% 3.43/3.59 inference(transitivity,[status(thm)],[872, 12])).
% 3.43/3.59 tff(874,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n1)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[873, 440])).
% 3.43/3.59 tff(875,plain,
% 3.43/3.59 (sum(n2, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[874])).
% 3.43/3.59 tff(876,plain,
% 3.43/3.59 (n3 = sum(n2, n1)),
% 3.43/3.59 inference(symmetry,[status(thm)],[554])).
% 3.43/3.59 tff(877,plain,
% 3.43/3.59 (sum(n5, n2) = n7),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(878,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[438, 869])).
% 3.43/3.59 tff(879,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.43/3.59 inference(transitivity,[status(thm)],[878, 877])).
% 3.43/3.59 tff(880,plain,
% 3.43/3.59 (sum(n0, n7) = n7),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(881,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n7)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[871, 436])).
% 3.43/3.59 tff(882,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.43/3.59 inference(transitivity,[status(thm)],[881, 880])).
% 3.43/3.59 tff(883,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[882, 879])).
% 3.43/3.59 tff(884,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 883, 231, 876, 875, 11])).
% 3.43/3.59 tff(885,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 884])).
% 3.43/3.59 tff(886,plain,((~(Y0!20 = n6)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(887,plain,
% 3.43/3.59 (~(Y0!20 = n6)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[886, 867, 14])).
% 3.43/3.59 tff(888,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n3)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[873, 304])).
% 3.43/3.59 tff(889,plain,
% 3.43/3.59 (sum(n2, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[888])).
% 3.43/3.59 tff(890,plain,
% 3.43/3.59 (n5 = sum(n2, n3)),
% 3.43/3.59 inference(symmetry,[status(thm)],[581])).
% 3.43/3.59 tff(891,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[302, 869])).
% 3.43/3.59 tff(892,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.59 inference(transitivity,[status(thm)],[891, 80])).
% 3.43/3.59 tff(893,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[871, 300])).
% 3.43/3.59 tff(894,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.59 inference(transitivity,[status(thm)],[893, 77])).
% 3.43/3.59 tff(895,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[894, 892])).
% 3.43/3.59 tff(896,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 895, 76, 890, 889, 11])).
% 3.43/3.59 tff(897,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 896])).
% 3.43/3.59 tff(898,plain,((~(Y0!20 = n7)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(899,plain,
% 3.43/3.59 (~(Y0!20 = n7)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[898, 867, 14])).
% 3.43/3.59 tff(900,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n5)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[873, 190])).
% 3.43/3.59 tff(901,plain,
% 3.43/3.59 (sum(n2, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.59 inference(symmetry,[status(thm)],[900])).
% 3.43/3.59 tff(902,plain,
% 3.43/3.59 (sum(n2, n5) = n7),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(903,plain,
% 3.43/3.59 (n7 = sum(n2, n5)),
% 3.43/3.59 inference(symmetry,[status(thm)],[902])).
% 3.43/3.59 tff(904,plain,
% 3.43/3.59 (sum(n7, n2) = n9),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(905,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n2)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[188, 869])).
% 3.43/3.59 tff(906,plain,
% 3.43/3.59 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.43/3.59 inference(transitivity,[status(thm)],[905, 904])).
% 3.43/3.59 tff(907,plain,
% 3.43/3.59 (sum(n0, n9) = n9),
% 3.43/3.59 inference(and_elim,[status(thm)],[9])).
% 3.43/3.59 tff(908,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[871, 185])).
% 3.43/3.59 tff(909,plain,
% 3.43/3.59 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.43/3.59 inference(transitivity,[status(thm)],[908, 907])).
% 3.43/3.59 tff(910,plain,
% 3.43/3.59 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.43/3.59 inference(monotonicity,[status(thm)],[909, 906])).
% 3.43/3.59 tff(911,plain,
% 3.43/3.59 (X1!19 = Y1!18),
% 3.43/3.59 inference(transitivity,[status(thm)],[49, 910, 235, 903, 901, 11])).
% 3.43/3.59 tff(912,plain,
% 3.43/3.59 ($false),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[14, 911])).
% 3.43/3.59 tff(913,plain,((~(Y0!20 = n8)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.59 tff(914,plain,
% 3.43/3.59 (~(Y0!20 = n8)),
% 3.43/3.59 inference(unit_resolution,[status(thm)],[913, 867, 14])).
% 3.43/3.60 tff(915,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n7)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[873, 24])).
% 3.43/3.60 tff(916,plain,
% 3.43/3.60 (sum(n2, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[915])).
% 3.43/3.60 tff(917,plain,
% 3.43/3.60 (sum(n2, n7) = n9),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(918,plain,
% 3.43/3.60 (n9 = sum(n2, n7)),
% 3.43/3.60 inference(symmetry,[status(thm)],[917])).
% 3.43/3.60 tff(919,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[22, 869])).
% 3.43/3.60 tff(920,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.60 inference(transitivity,[status(thm)],[919, 407])).
% 3.43/3.60 tff(921,plain,
% 3.43/3.60 (sum(n0, n10) = n10),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(922,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[871, 19])).
% 3.43/3.60 tff(923,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.60 inference(transitivity,[status(thm)],[922, 921])).
% 3.43/3.60 tff(924,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[923, 920])).
% 3.43/3.60 tff(925,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 924, 158, 918, 916, 11])).
% 3.43/3.60 tff(926,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 925])).
% 3.43/3.60 tff(927,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(928,plain,
% 3.43/3.60 (~(Y0!20 = n9)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[927, 867, 14])).
% 3.43/3.60 tff(929,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n0)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[873, 145])).
% 3.43/3.60 tff(930,plain,
% 3.43/3.60 (sum(n2, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[929])).
% 3.43/3.60 tff(931,plain,
% 3.43/3.60 (sum(n2, n0) = n2),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(932,plain,
% 3.43/3.60 (n2 = sum(n2, n0)),
% 3.43/3.60 inference(symmetry,[status(thm)],[931])).
% 3.43/3.60 tff(933,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[143, 869])).
% 3.43/3.60 tff(934,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[933, 270])).
% 3.43/3.60 tff(935,plain,
% 3.43/3.60 (sum(n0, n1) = n1),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(936,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[871, 140])).
% 3.43/3.60 tff(937,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[936, 935])).
% 3.43/3.60 tff(938,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[937, 934])).
% 3.43/3.60 tff(939,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 938, 538, 932, 930, 11])).
% 3.43/3.60 tff(940,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 939])).
% 3.43/3.60 tff(941,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(942,plain,
% 3.43/3.60 (~(Y0!20 = n0)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[941, 867, 14])).
% 3.43/3.60 tff(943,plain,
% 3.43/3.60 (succ(n1) = succ(X0!21)),
% 3.43/3.60 inference(symmetry,[status(thm)],[868])).
% 3.43/3.60 tff(944,plain,
% 3.43/3.60 (succ(Y0!20) = succ(X0!21)),
% 3.43/3.60 inference(transitivity,[status(thm)],[56, 943])).
% 3.43/3.60 tff(945,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(Y0!20)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[944])).
% 3.43/3.60 tff(946,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[871, 57])).
% 3.43/3.60 tff(947,plain,
% 3.43/3.60 (sum(n0, n2) = sum(pred(X0!21), succ(Y0!20))),
% 3.43/3.60 inference(symmetry,[status(thm)],[946])).
% 3.43/3.60 tff(948,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(X0!21)) = sum(pred(X0!21), succ(Y0!20))),
% 3.43/3.60 inference(transitivity,[status(thm)],[872, 947])).
% 3.43/3.60 tff(949,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[948, 945])).
% 3.43/3.60 tff(950,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[949])).
% 3.43/3.60 tff(951,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 950, 11])).
% 3.43/3.60 tff(952,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 951])).
% 3.43/3.60 tff(953,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(954,plain,
% 3.43/3.60 (~(Y0!20 = n1)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[953, 867, 14])).
% 3.43/3.60 tff(955,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[873, 97])).
% 3.43/3.60 tff(956,plain,
% 3.43/3.60 (sum(n2, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[955])).
% 3.43/3.60 tff(957,plain,
% 3.43/3.60 (n6 = sum(n2, n4)),
% 3.43/3.60 inference(symmetry,[status(thm)],[512])).
% 3.43/3.60 tff(958,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[95, 869])).
% 3.43/3.60 tff(959,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.60 inference(transitivity,[status(thm)],[958, 747])).
% 3.43/3.60 tff(960,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n3)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[871, 92])).
% 3.43/3.60 tff(961,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.60 inference(transitivity,[status(thm)],[960, 744])).
% 3.43/3.60 tff(962,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[961, 959])).
% 3.43/3.60 tff(963,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 962, 426, 957, 956, 11])).
% 3.43/3.60 tff(964,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 963])).
% 3.43/3.60 tff(965,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(966,plain,
% 3.43/3.60 (~(Y0!20 = n2)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[965, 867, 14])).
% 3.43/3.60 tff(967,assumption,(Y0!20 = n3), introduced(assumption)).
% 3.43/3.60 tff(968,plain,
% 3.43/3.60 (succ(Y0!20) = succ(n3)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[967])).
% 3.43/3.60 tff(969,plain,
% 3.43/3.60 (succ(Y0!20) = n4),
% 3.43/3.60 inference(transitivity,[status(thm)],[968, 513])).
% 3.43/3.60 tff(970,plain,
% 3.43/3.60 (pred(Y0!20) = pred(n3)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[967])).
% 3.43/3.60 tff(971,plain,
% 3.43/3.60 (pred(Y0!20) = n2),
% 3.43/3.60 inference(transitivity,[status(thm)],[970, 516])).
% 3.43/3.60 tff(972,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(Y0!20)) = sum(n2, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 969])).
% 3.43/3.60 tff(973,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(Y0!20)) = n6),
% 3.43/3.60 inference(transitivity,[status(thm)],[972, 512])).
% 3.43/3.60 tff(974,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 515])).
% 3.43/3.60 tff(975,plain,
% 3.43/3.60 (pred(n3) = pred(Y0!20)),
% 3.43/3.60 inference(symmetry,[status(thm)],[970])).
% 3.43/3.60 tff(976,plain,
% 3.43/3.60 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.60 inference(transitivity,[status(thm)],[517, 975])).
% 3.43/3.60 tff(977,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[976])).
% 3.43/3.60 tff(978,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(X0!21)) = n6),
% 3.43/3.60 inference(transitivity,[status(thm)],[977, 974, 512])).
% 3.43/3.60 tff(979,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[978, 973])).
% 3.43/3.60 tff(980,plain,
% 3.43/3.60 (sum(n6, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[979])).
% 3.43/3.60 tff(981,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.60 inference(transitivity,[status(thm)],[974, 512])).
% 3.43/3.60 tff(982,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[518, 969])).
% 3.43/3.60 tff(983,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.60 inference(transitivity,[status(thm)],[982, 512])).
% 3.43/3.60 tff(984,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[983, 981])).
% 3.43/3.60 tff(985,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 984, 980, 11])).
% 3.43/3.60 tff(986,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 985])).
% 3.43/3.60 tff(987,plain,((~(X0!21 = n3)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(988,plain,
% 3.43/3.60 (~(X0!21 = n3)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[987, 967, 14])).
% 3.43/3.60 tff(989,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[374, 973])).
% 3.43/3.60 tff(990,plain,
% 3.43/3.60 (sum(n8, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[989])).
% 3.43/3.60 tff(991,plain,
% 3.43/3.60 (n3 = sum(n8, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[658])).
% 3.43/3.60 tff(992,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n5)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 369])).
% 3.43/3.60 tff(993,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.43/3.60 inference(transitivity,[status(thm)],[992, 902])).
% 3.43/3.60 tff(994,plain,
% 3.43/3.60 (sum(n3, n4) = n7),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(995,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[372, 969])).
% 3.43/3.60 tff(996,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.43/3.60 inference(transitivity,[status(thm)],[995, 994])).
% 3.43/3.60 tff(997,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[996, 993])).
% 3.43/3.60 tff(998,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 997, 231, 991, 990, 11])).
% 3.43/3.60 tff(999,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 998])).
% 3.43/3.60 tff(1000,plain,((~(X0!21 = n4)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1001,plain,
% 3.43/3.60 (~(X0!21 = n4)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1000, 967, 14])).
% 3.43/3.60 tff(1002,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[252, 973])).
% 3.43/3.60 tff(1003,plain,
% 3.43/3.60 (sum(n10, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1002])).
% 3.43/3.60 tff(1004,plain,
% 3.43/3.60 (n5 = sum(n10, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[257])).
% 3.43/3.60 tff(1005,plain,
% 3.43/3.60 (sum(n2, n6) = n8),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1006,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 247])).
% 3.43/3.60 tff(1007,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.60 inference(transitivity,[status(thm)],[1006, 1005])).
% 3.43/3.60 tff(1008,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[250, 969])).
% 3.43/3.60 tff(1009,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.60 inference(transitivity,[status(thm)],[1008, 41])).
% 3.43/3.60 tff(1010,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1009, 1007])).
% 3.43/3.60 tff(1011,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1010, 76, 1004, 1003, 11])).
% 3.43/3.60 tff(1012,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1011])).
% 3.43/3.60 tff(1013,plain,((~(X0!21 = n5)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1014,plain,
% 3.43/3.60 (~(X0!21 = n5)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1013, 967, 14])).
% 3.43/3.60 tff(1015,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[36, 973])).
% 3.43/3.60 tff(1016,plain,
% 3.43/3.60 (sum(n1, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1015])).
% 3.43/3.60 tff(1017,plain,
% 3.43/3.60 (n7 = sum(n1, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[287])).
% 3.43/3.60 tff(1018,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n7)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 31])).
% 3.43/3.60 tff(1019,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.43/3.60 inference(transitivity,[status(thm)],[1018, 917])).
% 3.43/3.60 tff(1020,plain,
% 3.43/3.60 (sum(n5, n4) = n9),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1021,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[34, 969])).
% 3.43/3.60 tff(1022,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.43/3.60 inference(transitivity,[status(thm)],[1021, 1020])).
% 3.43/3.60 tff(1023,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1022, 1019])).
% 3.43/3.60 tff(1024,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1023, 235, 1017, 1016, 11])).
% 3.43/3.60 tff(1025,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1024])).
% 3.43/3.60 tff(1026,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1027,plain,
% 3.43/3.60 (~(X0!21 = n6)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1026, 967, 14])).
% 3.43/3.60 tff(1028,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[71, 973])).
% 3.43/3.60 tff(1029,plain,
% 3.43/3.60 (sum(n3, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1028])).
% 3.43/3.60 tff(1030,plain,
% 3.43/3.60 (n9 = sum(n3, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[793])).
% 3.43/3.60 tff(1031,plain,
% 3.43/3.60 (sum(n2, n8) = n10),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1032,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n8)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 66])).
% 3.43/3.60 tff(1033,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.60 inference(transitivity,[status(thm)],[1032, 1031])).
% 3.43/3.60 tff(1034,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[69, 969])).
% 3.43/3.60 tff(1035,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.60 inference(transitivity,[status(thm)],[1034, 577])).
% 3.43/3.60 tff(1036,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1035, 1033])).
% 3.43/3.60 tff(1037,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1036, 158, 1030, 1029, 11])).
% 3.43/3.60 tff(1038,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1037])).
% 3.43/3.60 tff(1039,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1040,plain,
% 3.43/3.60 (~(X0!21 = n7)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1039, 967, 14])).
% 3.43/3.60 tff(1041,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[321, 973])).
% 3.43/3.60 tff(1042,plain,
% 3.43/3.60 (sum(n5, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1041])).
% 3.43/3.60 tff(1043,plain,
% 3.43/3.60 (n0 = sum(n5, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[617])).
% 3.43/3.60 tff(1044,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n9)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 193])).
% 3.43/3.60 tff(1045,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.60 inference(transitivity,[status(thm)],[1044, 527])).
% 3.43/3.60 tff(1046,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[203, 969])).
% 3.43/3.60 tff(1047,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.60 inference(transitivity,[status(thm)],[1046, 107])).
% 3.43/3.60 tff(1048,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1047, 1045])).
% 3.43/3.60 tff(1049,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1048, 109, 1043, 1042, 11])).
% 3.43/3.60 tff(1050,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1049])).
% 3.43/3.60 tff(1051,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1052,plain,
% 3.43/3.60 (~(X0!21 = n8)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1051, 967, 14])).
% 3.43/3.60 tff(1053,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[104, 973])).
% 3.43/3.60 tff(1054,plain,
% 3.43/3.60 (sum(n7, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1053])).
% 3.43/3.60 tff(1055,plain,
% 3.43/3.60 (n2 = sum(n7, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[644])).
% 3.43/3.60 tff(1056,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 100])).
% 3.43/3.60 tff(1057,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[1056, 541])).
% 3.43/3.60 tff(1058,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[102, 969])).
% 3.43/3.60 tff(1059,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[1058, 421])).
% 3.43/3.60 tff(1060,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1059, 1057])).
% 3.43/3.60 tff(1061,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1060, 538, 1055, 1054, 11])).
% 3.43/3.60 tff(1062,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1061])).
% 3.43/3.60 tff(1063,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1064,plain,
% 3.43/3.60 (~(X0!21 = n9)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1063, 967, 14])).
% 3.43/3.60 tff(1065,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[154, 973])).
% 3.43/3.60 tff(1066,plain,
% 3.43/3.60 (sum(n9, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1065])).
% 3.43/3.60 tff(1067,plain,
% 3.43/3.60 (n4 = sum(n9, n6)),
% 3.43/3.60 inference(symmetry,[status(thm)],[673])).
% 3.43/3.60 tff(1068,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n0)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[971, 149])).
% 3.43/3.60 tff(1069,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.60 inference(transitivity,[status(thm)],[1068, 931])).
% 3.43/3.60 tff(1070,plain,
% 3.43/3.60 (sum(n9, n4) = n2),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1071,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[152, 969])).
% 3.43/3.60 tff(1072,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.60 inference(transitivity,[status(thm)],[1071, 1070])).
% 3.43/3.60 tff(1073,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1072, 1069])).
% 3.43/3.60 tff(1074,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1073, 378, 1067, 1066, 11])).
% 3.43/3.60 tff(1075,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1074])).
% 3.43/3.60 tff(1076,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1077,plain,
% 3.43/3.60 (~(X0!21 = n10)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1076, 967, 14])).
% 3.43/3.60 tff(1078,assumption,(X0!21 = n0), introduced(assumption)).
% 3.43/3.60 tff(1079,plain,
% 3.43/3.60 (succ(X0!21) = succ(n0)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1078])).
% 3.43/3.60 tff(1080,plain,
% 3.43/3.60 (succ(X0!21) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[1079, 137])).
% 3.43/3.60 tff(1081,plain,
% 3.43/3.60 (pred(X0!21) = pred(n0)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1078])).
% 3.43/3.60 tff(1082,plain,
% 3.43/3.60 (pred(X0!21) = n10),
% 3.43/3.60 inference(transitivity,[status(thm)],[1081, 141])).
% 3.43/3.60 tff(1083,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(X0!21)) = sum(n10, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 1080])).
% 3.43/3.60 tff(1084,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(X0!21)) = n0),
% 3.43/3.60 inference(transitivity,[status(thm)],[1083, 136])).
% 3.43/3.60 tff(1085,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 595])).
% 3.43/3.60 tff(1086,plain,
% 3.43/3.60 (sum(n0, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1085])).
% 3.43/3.60 tff(1087,plain,
% 3.43/3.60 (n10 = sum(n0, n10)),
% 3.43/3.60 inference(symmetry,[status(thm)],[921])).
% 3.43/3.60 tff(1088,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[593, 1080])).
% 3.43/3.60 tff(1089,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.60 inference(transitivity,[status(thm)],[1088, 260])).
% 3.43/3.60 tff(1090,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 591])).
% 3.43/3.60 tff(1091,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.60 inference(transitivity,[status(thm)],[1090, 257])).
% 3.43/3.60 tff(1092,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1091, 1089])).
% 3.43/3.60 tff(1093,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1092, 256, 1087, 1086, 11])).
% 3.43/3.60 tff(1094,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1093])).
% 3.43/3.60 tff(1095,plain,((~(Y0!20 = n5)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1096,plain,
% 3.43/3.60 (~(Y0!20 = n5)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1095, 1078, 14])).
% 3.43/3.60 tff(1097,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 440])).
% 3.43/3.60 tff(1098,plain,
% 3.43/3.60 (sum(n0, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1097])).
% 3.43/3.60 tff(1099,plain,
% 3.43/3.60 (n1 = sum(n0, n1)),
% 3.43/3.60 inference(symmetry,[status(thm)],[935])).
% 3.43/3.60 tff(1100,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[438, 1080])).
% 3.43/3.60 tff(1101,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.60 inference(transitivity,[status(thm)],[1100, 472])).
% 3.43/3.60 tff(1102,plain,
% 3.43/3.60 (sum(n10, n7) = n6),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1103,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n7)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 436])).
% 3.43/3.60 tff(1104,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.60 inference(transitivity,[status(thm)],[1103, 1102])).
% 3.43/3.60 tff(1105,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1104, 1101])).
% 3.43/3.60 tff(1106,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1105, 215, 1099, 1098, 11])).
% 3.43/3.60 tff(1107,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1106])).
% 3.43/3.60 tff(1108,plain,((~(Y0!20 = n6)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1109,plain,
% 3.43/3.60 (~(Y0!20 = n6)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1108, 1078, 14])).
% 3.43/3.60 tff(1110,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n3)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 304])).
% 3.43/3.60 tff(1111,plain,
% 3.43/3.60 (sum(n0, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1110])).
% 3.43/3.60 tff(1112,plain,
% 3.43/3.60 (n3 = sum(n0, n3)),
% 3.43/3.60 inference(symmetry,[status(thm)],[744])).
% 3.43/3.60 tff(1113,plain,
% 3.43/3.60 (sum(n6, n1) = n7),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1114,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[302, 1080])).
% 3.43/3.60 tff(1115,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.43/3.60 inference(transitivity,[status(thm)],[1114, 1113])).
% 3.43/3.60 tff(1116,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n8)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 300])).
% 3.43/3.60 tff(1117,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.43/3.60 inference(transitivity,[status(thm)],[1116, 791])).
% 3.43/3.60 tff(1118,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1117, 1115])).
% 3.43/3.60 tff(1119,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1118, 231, 1112, 1111, 11])).
% 3.43/3.60 tff(1120,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1119])).
% 3.43/3.60 tff(1121,plain,((~(Y0!20 = n7)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1122,plain,
% 3.43/3.60 (~(Y0!20 = n7)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1121, 1078, 14])).
% 3.43/3.60 tff(1123,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n5)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 190])).
% 3.43/3.60 tff(1124,plain,
% 3.43/3.60 (sum(n0, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1123])).
% 3.43/3.60 tff(1125,plain,
% 3.43/3.60 (n5 = sum(n0, n5)),
% 3.43/3.60 inference(symmetry,[status(thm)],[409])).
% 3.43/3.60 tff(1126,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[188, 1080])).
% 3.43/3.60 tff(1127,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.60 inference(transitivity,[status(thm)],[1126, 486])).
% 3.43/3.60 tff(1128,plain,
% 3.43/3.60 (sum(n10, n9) = n8),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1129,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n9)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 185])).
% 3.43/3.60 tff(1130,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.60 inference(transitivity,[status(thm)],[1129, 1128])).
% 3.43/3.60 tff(1131,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1130, 1127])).
% 3.43/3.60 tff(1132,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1131, 76, 1125, 1124, 11])).
% 3.43/3.60 tff(1133,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1132])).
% 3.43/3.60 tff(1134,plain,((~(Y0!20 = n8)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1135,plain,
% 3.43/3.60 (~(Y0!20 = n8)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1134, 1078, 14])).
% 3.43/3.60 tff(1136,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n7)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 24])).
% 3.43/3.60 tff(1137,plain,
% 3.43/3.60 (sum(n0, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1136])).
% 3.43/3.60 tff(1138,plain,
% 3.43/3.60 (n7 = sum(n0, n7)),
% 3.43/3.60 inference(symmetry,[status(thm)],[880])).
% 3.43/3.60 tff(1139,plain,
% 3.43/3.60 (sum(n8, n1) = n9),
% 3.43/3.60 inference(and_elim,[status(thm)],[9])).
% 3.43/3.60 tff(1140,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[22, 1080])).
% 3.43/3.60 tff(1141,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.43/3.60 inference(transitivity,[status(thm)],[1140, 1139])).
% 3.43/3.60 tff(1142,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 19])).
% 3.43/3.60 tff(1143,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.43/3.60 inference(transitivity,[status(thm)],[1142, 158])).
% 3.43/3.60 tff(1144,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1143, 1141])).
% 3.43/3.60 tff(1145,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1144, 235, 1138, 1137, 11])).
% 3.43/3.60 tff(1146,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1145])).
% 3.43/3.60 tff(1147,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1148,plain,
% 3.43/3.60 (~(Y0!20 = n9)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1147, 1078, 14])).
% 3.43/3.60 tff(1149,plain,
% 3.43/3.60 (succ(n0) = succ(X0!21)),
% 3.43/3.60 inference(symmetry,[status(thm)],[1079])).
% 3.43/3.60 tff(1150,plain,
% 3.43/3.60 (succ(Y0!20) = succ(X0!21)),
% 3.43/3.60 inference(transitivity,[status(thm)],[139, 1149])).
% 3.43/3.60 tff(1151,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(Y0!20)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1150])).
% 3.43/3.60 tff(1152,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 140])).
% 3.43/3.60 tff(1153,plain,
% 3.43/3.60 (sum(n10, n1) = sum(pred(X0!21), succ(Y0!20))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1152])).
% 3.43/3.60 tff(1154,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(X0!21)) = sum(pred(X0!21), succ(Y0!20))),
% 3.43/3.60 inference(transitivity,[status(thm)],[1083, 1153])).
% 3.43/3.60 tff(1155,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21)))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1154, 1151])).
% 3.43/3.60 tff(1156,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1155])).
% 3.43/3.60 tff(1157,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1156, 11])).
% 3.43/3.60 tff(1158,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1157])).
% 3.43/3.60 tff(1159,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1160,plain,
% 3.43/3.60 (~(Y0!20 = n0)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1159, 1078, 14])).
% 3.43/3.60 tff(1161,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 62])).
% 3.43/3.60 tff(1162,plain,
% 3.43/3.60 (sum(n0, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1161])).
% 3.43/3.60 tff(1163,plain,
% 3.43/3.60 (n2 = sum(n0, n2)),
% 3.43/3.60 inference(symmetry,[status(thm)],[12])).
% 3.43/3.60 tff(1164,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[60, 1080])).
% 3.43/3.60 tff(1165,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[1164, 935])).
% 3.43/3.60 tff(1166,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 57])).
% 3.43/3.60 tff(1167,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.60 inference(transitivity,[status(thm)],[1166, 270])).
% 3.43/3.60 tff(1168,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1167, 1165])).
% 3.43/3.60 tff(1169,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1168, 538, 1163, 1162, 11])).
% 3.43/3.60 tff(1170,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1169])).
% 3.43/3.60 tff(1171,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1172,plain,
% 3.43/3.60 (~(Y0!20 = n1)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1171, 1078, 14])).
% 3.43/3.60 tff(1173,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n4)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1084, 97])).
% 3.43/3.60 tff(1174,plain,
% 3.43/3.60 (sum(n0, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.60 inference(symmetry,[status(thm)],[1173])).
% 3.43/3.60 tff(1175,plain,
% 3.43/3.60 (n4 = sum(n0, n4)),
% 3.43/3.60 inference(symmetry,[status(thm)],[565])).
% 3.43/3.60 tff(1176,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n1)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[95, 1080])).
% 3.43/3.60 tff(1177,plain,
% 3.43/3.60 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.60 inference(transitivity,[status(thm)],[1176, 538])).
% 3.43/3.60 tff(1178,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n3)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1082, 92])).
% 3.43/3.60 tff(1179,plain,
% 3.43/3.60 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.60 inference(transitivity,[status(thm)],[1178, 731])).
% 3.43/3.60 tff(1180,plain,
% 3.43/3.60 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1179, 1177])).
% 3.43/3.60 tff(1181,plain,
% 3.43/3.60 (X1!19 = Y1!18),
% 3.43/3.60 inference(transitivity,[status(thm)],[49, 1180, 378, 1175, 1174, 11])).
% 3.43/3.60 tff(1182,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[14, 1181])).
% 3.43/3.60 tff(1183,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(1184,plain,
% 3.43/3.60 (~(Y0!20 = n2)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1183, 1078, 14])).
% 3.43/3.60 tff(1185,assumption,(Y0!20 = n10), introduced(assumption)).
% 3.43/3.60 tff(1186,plain,
% 3.43/3.60 (succ(Y0!20) = succ(n10)),
% 3.43/3.60 inference(monotonicity,[status(thm)],[1185])).
% 3.43/3.61 tff(1187,plain,
% 3.43/3.61 (succ(Y0!20) = n0),
% 3.43/3.61 inference(transitivity,[status(thm)],[1186, 147])).
% 3.43/3.61 tff(1188,plain,
% 3.43/3.61 (pred(Y0!20) = pred(n10)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1185])).
% 3.43/3.61 tff(1189,plain,
% 3.43/3.61 (pred(Y0!20) = n9),
% 3.43/3.61 inference(transitivity,[status(thm)],[1188, 150])).
% 3.43/3.61 tff(1190,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(Y0!20)) = sum(n9, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 1187])).
% 3.43/3.61 tff(1191,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(Y0!20)) = n9),
% 3.43/3.61 inference(transitivity,[status(thm)],[1190, 146])).
% 3.43/3.61 tff(1192,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[687, 1191])).
% 3.43/3.61 tff(1193,plain,
% 3.43/3.61 (sum(n4, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1192])).
% 3.43/3.61 tff(1194,plain,
% 3.43/3.61 (n2 = sum(n4, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[641])).
% 3.43/3.61 tff(1195,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n3)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 683])).
% 3.43/3.61 tff(1196,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.43/3.61 inference(transitivity,[status(thm)],[1195, 352])).
% 3.43/3.61 tff(1197,plain,
% 3.43/3.61 (sum(n1, n0) = n1),
% 3.43/3.61 inference(and_elim,[status(thm)],[9])).
% 3.43/3.61 tff(1198,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[685, 1187])).
% 3.43/3.61 tff(1199,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.43/3.61 inference(transitivity,[status(thm)],[1198, 1197])).
% 3.43/3.61 tff(1200,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1199, 1196])).
% 3.43/3.61 tff(1201,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1200, 538, 1194, 1193, 11])).
% 3.43/3.61 tff(1202,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1201])).
% 3.43/3.61 tff(1203,plain,((~(X0!21 = n2)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1204,plain,
% 3.43/3.61 (~(X0!21 = n2)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1203, 1185, 14])).
% 3.43/3.61 tff(1205,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[520, 1191])).
% 3.43/3.61 tff(1206,plain,
% 3.43/3.61 (sum(n6, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1205])).
% 3.43/3.61 tff(1207,plain,
% 3.43/3.61 (n4 = sum(n6, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[325])).
% 3.43/3.61 tff(1208,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 515])).
% 3.43/3.61 tff(1209,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.43/3.61 inference(transitivity,[status(thm)],[1208, 1070])).
% 3.43/3.61 tff(1210,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[518, 1187])).
% 3.43/3.61 tff(1211,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.43/3.61 inference(transitivity,[status(thm)],[1210, 931])).
% 3.43/3.61 tff(1212,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1211, 1209])).
% 3.43/3.61 tff(1213,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1212, 378, 1207, 1206, 11])).
% 3.43/3.61 tff(1214,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1213])).
% 3.43/3.61 tff(1215,plain,((~(X0!21 = n3)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1216,plain,
% 3.43/3.61 (~(X0!21 = n3)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1215, 1185, 14])).
% 3.43/3.61 tff(1217,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[374, 1191])).
% 3.43/3.61 tff(1218,plain,
% 3.43/3.61 (sum(n8, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1217])).
% 3.43/3.61 tff(1219,plain,
% 3.43/3.61 (n6 = sum(n8, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[219])).
% 3.43/3.61 tff(1220,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n5)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 369])).
% 3.43/3.61 tff(1221,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.61 inference(transitivity,[status(thm)],[1220, 229])).
% 3.43/3.61 tff(1222,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[372, 1187])).
% 3.43/3.61 tff(1223,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.61 inference(transitivity,[status(thm)],[1222, 857])).
% 3.43/3.61 tff(1224,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1223, 1221])).
% 3.43/3.61 tff(1225,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1224, 426, 1219, 1218, 11])).
% 3.43/3.61 tff(1226,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1225])).
% 3.43/3.61 tff(1227,plain,((~(X0!21 = n4)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1228,plain,
% 3.43/3.61 (~(X0!21 = n4)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1227, 1185, 14])).
% 3.43/3.61 tff(1229,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[252, 1191])).
% 3.43/3.61 tff(1230,plain,
% 3.43/3.61 (sum(n10, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1229])).
% 3.43/3.61 tff(1231,plain,
% 3.43/3.61 (n8 = sum(n10, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[1128])).
% 3.43/3.61 tff(1232,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n6)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 247])).
% 3.43/3.61 tff(1233,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1232, 673])).
% 3.43/3.61 tff(1234,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[250, 1187])).
% 3.43/3.61 tff(1235,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1234, 670])).
% 3.43/3.61 tff(1236,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1235, 1233])).
% 3.43/3.61 tff(1237,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1236, 41, 1231, 1230, 11])).
% 3.43/3.61 tff(1238,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1237])).
% 3.43/3.61 tff(1239,plain,((~(X0!21 = n5)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1240,plain,
% 3.43/3.61 (~(X0!21 = n5)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1239, 1185, 14])).
% 3.43/3.61 tff(1241,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[36, 1191])).
% 3.43/3.61 tff(1242,plain,
% 3.43/3.61 (sum(n1, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1241])).
% 3.43/3.61 tff(1243,plain,
% 3.43/3.61 (n10 = sum(n1, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[708])).
% 3.43/3.61 tff(1244,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n7)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 31])).
% 3.43/3.61 tff(1245,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.61 inference(transitivity,[status(thm)],[1244, 503])).
% 3.43/3.61 tff(1246,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[34, 1187])).
% 3.43/3.61 tff(1247,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.61 inference(transitivity,[status(thm)],[1246, 500])).
% 3.43/3.61 tff(1248,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1247, 1245])).
% 3.43/3.61 tff(1249,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1248, 256, 1243, 1242, 11])).
% 3.43/3.61 tff(1250,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1249])).
% 3.43/3.61 tff(1251,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1252,plain,
% 3.43/3.61 (~(X0!21 = n6)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1251, 1185, 14])).
% 3.43/3.61 tff(1253,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[71, 1191])).
% 3.43/3.61 tff(1254,plain,
% 3.43/3.61 (sum(n3, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1253])).
% 3.43/3.61 tff(1255,plain,
% 3.43/3.61 (n1 = sum(n3, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[832])).
% 3.43/3.61 tff(1256,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n8)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 66])).
% 3.43/3.61 tff(1257,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.43/3.61 inference(transitivity,[status(thm)],[1256, 357])).
% 3.43/3.61 tff(1258,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[69, 1187])).
% 3.43/3.61 tff(1259,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.43/3.61 inference(transitivity,[status(thm)],[1258, 354])).
% 3.43/3.61 tff(1260,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1259, 1257])).
% 3.43/3.61 tff(1261,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1260, 215, 1255, 1254, 11])).
% 3.43/3.61 tff(1262,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1261])).
% 3.43/3.61 tff(1263,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1264,plain,
% 3.43/3.61 (~(X0!21 = n7)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1263, 1185, 14])).
% 3.43/3.61 tff(1265,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[321, 1191])).
% 3.43/3.61 tff(1266,plain,
% 3.43/3.61 (sum(n5, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1265])).
% 3.43/3.61 tff(1267,plain,
% 3.43/3.61 (n3 = sum(n5, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[474])).
% 3.43/3.61 tff(1268,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 193])).
% 3.43/3.61 tff(1269,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.43/3.61 inference(transitivity,[status(thm)],[1268, 235])).
% 3.43/3.61 tff(1270,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[203, 1187])).
% 3.43/3.61 tff(1271,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.43/3.61 inference(transitivity,[status(thm)],[1270, 232])).
% 3.43/3.61 tff(1272,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1271, 1269])).
% 3.43/3.61 tff(1273,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1272, 231, 1267, 1266, 11])).
% 3.43/3.61 tff(1274,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1273])).
% 3.43/3.61 tff(1275,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1276,plain,
% 3.43/3.61 (~(X0!21 = n8)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1275, 1185, 14])).
% 3.43/3.61 tff(1277,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[104, 1191])).
% 3.43/3.61 tff(1278,plain,
% 3.43/3.61 (sum(n7, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1277])).
% 3.43/3.61 tff(1279,plain,
% 3.43/3.61 (n5 = sum(n7, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[25])).
% 3.43/3.61 tff(1280,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n10)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 100])).
% 3.43/3.61 tff(1281,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.43/3.61 inference(transitivity,[status(thm)],[1280, 668])).
% 3.43/3.61 tff(1282,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[102, 1187])).
% 3.43/3.61 tff(1283,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.43/3.61 inference(transitivity,[status(thm)],[1282, 392])).
% 3.43/3.61 tff(1284,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1283, 1281])).
% 3.43/3.61 tff(1285,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1284, 76, 1279, 1278, 11])).
% 3.43/3.61 tff(1286,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1285])).
% 3.43/3.61 tff(1287,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1288,plain,
% 3.43/3.61 (~(X0!21 = n9)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1287, 1185, 14])).
% 3.43/3.61 tff(1289,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 149])).
% 3.43/3.61 tff(1290,plain,
% 3.43/3.61 (pred(n10) = pred(Y0!20)),
% 3.43/3.61 inference(symmetry,[status(thm)],[1188])).
% 3.43/3.61 tff(1291,plain,
% 3.43/3.61 (pred(X0!21) = pred(Y0!20)),
% 3.43/3.61 inference(transitivity,[status(thm)],[151, 1290])).
% 3.43/3.61 tff(1292,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1291])).
% 3.43/3.61 tff(1293,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(X0!21)) = n9),
% 3.43/3.61 inference(transitivity,[status(thm)],[1292, 1289, 146])).
% 3.43/3.61 tff(1294,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1293, 1191])).
% 3.43/3.61 tff(1295,plain,
% 3.43/3.61 (sum(n9, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1294])).
% 3.43/3.61 tff(1296,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.43/3.61 inference(transitivity,[status(thm)],[1289, 146])).
% 3.43/3.61 tff(1297,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[152, 1187])).
% 3.43/3.61 tff(1298,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.43/3.61 inference(transitivity,[status(thm)],[1297, 146])).
% 3.43/3.61 tff(1299,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1298, 1296])).
% 3.43/3.61 tff(1300,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1299, 1295, 11])).
% 3.43/3.61 tff(1301,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1300])).
% 3.43/3.61 tff(1302,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1303,plain,
% 3.43/3.61 (~(X0!21 = n10)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1302, 1185, 14])).
% 3.43/3.61 tff(1304,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[873, 1191])).
% 3.43/3.61 tff(1305,plain,
% 3.43/3.61 (sum(n2, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1304])).
% 3.43/3.61 tff(1306,plain,
% 3.43/3.61 (n0 = sum(n2, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[527])).
% 3.43/3.61 tff(1307,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n2)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 869])).
% 3.43/3.61 tff(1308,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.43/3.61 inference(transitivity,[status(thm)],[1307, 172])).
% 3.43/3.61 tff(1309,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[871, 1187])).
% 3.43/3.61 tff(1310,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.43/3.61 inference(transitivity,[status(thm)],[1309, 109])).
% 3.43/3.61 tff(1311,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1310, 1308])).
% 3.43/3.61 tff(1312,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1311, 109, 1306, 1305, 11])).
% 3.43/3.61 tff(1313,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1312])).
% 3.43/3.61 tff(1314,plain,((~(X0!21 = n1)) | (X1!19 = Y1!18) | (~(Y0!20 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1315,plain,
% 3.43/3.61 (~(X0!21 = n1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1314, 1185, 14])).
% 3.43/3.61 tff(1316,plain,
% 3.43/3.61 ((X0!21 = n10) | (X0!21 = n9) | (X0!21 = n8) | (X0!21 = n7) | (X0!21 = n6) | (X0!21 = n5) | (X0!21 = n4) | (X0!21 = n3) | (X0!21 = n2) | (X0!21 = n1) | (X0!21 = n0)),
% 3.43/3.61 inference(and_elim,[status(thm)],[9])).
% 3.43/3.61 tff(1317,plain,
% 3.43/3.61 (X0!21 = n0),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1316, 1315, 1303, 1288, 1276, 1264, 1252, 1240, 1228, 1216, 1204])).
% 3.43/3.61 tff(1318,plain,
% 3.43/3.61 (succ(X0!21) = succ(n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1317])).
% 3.43/3.61 tff(1319,plain,
% 3.43/3.61 (succ(X0!21) = n1),
% 3.43/3.61 inference(transitivity,[status(thm)],[1318, 137])).
% 3.43/3.61 tff(1320,plain,
% 3.43/3.61 (pred(X0!21) = pred(n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1317])).
% 3.43/3.61 tff(1321,plain,
% 3.43/3.61 (pred(X0!21) = n10),
% 3.43/3.61 inference(transitivity,[status(thm)],[1320, 141])).
% 3.43/3.61 tff(1322,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(X0!21)) = sum(n10, n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1321, 1319])).
% 3.43/3.61 tff(1323,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(X0!21)) = n0),
% 3.43/3.61 inference(transitivity,[status(thm)],[1322, 136])).
% 3.43/3.61 tff(1324,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n9)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1323, 1191])).
% 3.43/3.61 tff(1325,plain,
% 3.43/3.61 (sum(n0, n9) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1324])).
% 3.43/3.61 tff(1326,plain,
% 3.43/3.61 (n9 = sum(n0, n9)),
% 3.43/3.61 inference(symmetry,[status(thm)],[907])).
% 3.43/3.61 tff(1327,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n9, n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1189, 1319])).
% 3.43/3.61 tff(1328,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.43/3.61 inference(transitivity,[status(thm)],[1327, 162])).
% 3.43/3.61 tff(1329,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n0)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1321, 1187])).
% 3.43/3.61 tff(1330,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.43/3.61 inference(transitivity,[status(thm)],[1329, 159])).
% 3.43/3.61 tff(1331,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1330, 1328])).
% 3.43/3.61 tff(1332,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1331, 158, 1326, 1325, 11])).
% 3.43/3.61 tff(1333,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1332])).
% 3.43/3.61 tff(1334,plain,((~(Y0!20 = n10)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1335,plain,
% 3.43/3.61 (~(Y0!20 = n10)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1334, 14])).
% 3.43/3.61 tff(1336,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n8)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1084, 773])).
% 3.43/3.61 tff(1337,plain,
% 3.43/3.61 (sum(n0, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1336])).
% 3.43/3.61 tff(1338,plain,
% 3.43/3.61 (n8 = sum(n0, n8)),
% 3.43/3.61 inference(symmetry,[status(thm)],[77])).
% 3.43/3.61 tff(1339,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[771, 1080])).
% 3.43/3.61 tff(1340,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1339, 397])).
% 3.43/3.61 tff(1341,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n5)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1082, 769])).
% 3.43/3.61 tff(1342,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1341, 394])).
% 3.43/3.61 tff(1343,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1342, 1340])).
% 3.43/3.61 tff(1344,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1343, 41, 1338, 1337, 11])).
% 3.43/3.61 tff(1345,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1344])).
% 3.43/3.61 tff(1346,plain,((~(Y0!20 = n4)) | (X1!19 = Y1!18) | (~(X0!21 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1347,plain,
% 3.43/3.61 (~(Y0!20 = n4)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1346, 1078, 14])).
% 3.43/3.61 tff(1348,plain,
% 3.43/3.61 ((Y0!20 = n10) | (Y0!20 = n9) | (Y0!20 = n8) | (Y0!20 = n7) | (Y0!20 = n6) | (Y0!20 = n5) | (Y0!20 = n4) | (Y0!20 = n3) | (Y0!20 = n2) | (Y0!20 = n1) | (Y0!20 = n0)),
% 3.43/3.61 inference(and_elim,[status(thm)],[9])).
% 3.43/3.61 tff(1349,plain,
% 3.43/3.61 (Y0!20 = n3),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1348, 1347, 1335, 1184, 1172, 1160, 1148, 1135, 1122, 1109, 1096])).
% 3.43/3.61 tff(1350,plain,
% 3.43/3.61 (succ(Y0!20) = succ(n3)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1349])).
% 3.43/3.61 tff(1351,plain,
% 3.43/3.61 (succ(Y0!20) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1350, 513])).
% 3.43/3.61 tff(1352,plain,
% 3.43/3.61 (pred(Y0!20) = pred(n3)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1349])).
% 3.43/3.61 tff(1353,plain,
% 3.43/3.61 (pred(Y0!20) = n2),
% 3.43/3.61 inference(transitivity,[status(thm)],[1352, 516])).
% 3.43/3.61 tff(1354,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(Y0!20)) = sum(n2, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1353, 1351])).
% 3.43/3.61 tff(1355,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(Y0!20)) = n6),
% 3.43/3.61 inference(transitivity,[status(thm)],[1354, 512])).
% 3.43/3.61 tff(1356,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n0, n6)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1084, 1355])).
% 3.43/3.61 tff(1357,plain,
% 3.43/3.61 (sum(n0, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1356])).
% 3.43/3.61 tff(1358,plain,
% 3.43/3.61 (n6 = sum(n0, n6)),
% 3.43/3.61 inference(symmetry,[status(thm)],[272])).
% 3.43/3.61 tff(1359,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1353, 1080])).
% 3.43/3.61 tff(1360,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.43/3.61 inference(transitivity,[status(thm)],[1359, 554])).
% 3.43/3.61 tff(1361,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n10, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1082, 1351])).
% 3.43/3.61 tff(1362,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.43/3.61 inference(transitivity,[status(thm)],[1361, 285])).
% 3.43/3.61 tff(1363,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1362, 1360])).
% 3.43/3.61 tff(1364,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1363, 426, 1358, 1357, 11])).
% 3.43/3.61 tff(1365,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1364])).
% 3.43/3.61 tff(1366,plain,((~(X0!21 = n0)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1367,plain,
% 3.43/3.61 (~(X0!21 = n0)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1366, 14])).
% 3.43/3.61 tff(1368,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n6)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[687, 973])).
% 3.43/3.61 tff(1369,plain,
% 3.43/3.61 (sum(n4, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1368])).
% 3.43/3.61 tff(1370,plain,
% 3.43/3.61 (n10 = sum(n4, n6)),
% 3.43/3.61 inference(symmetry,[status(thm)],[244])).
% 3.43/3.61 tff(1371,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n3)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[971, 683])).
% 3.43/3.61 tff(1372,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.43/3.61 inference(transitivity,[status(thm)],[1371, 581])).
% 3.43/3.61 tff(1373,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[685, 969])).
% 3.43/3.61 tff(1374,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.43/3.61 inference(transitivity,[status(thm)],[1373, 123])).
% 3.43/3.61 tff(1375,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1374, 1372])).
% 3.43/3.61 tff(1376,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1375, 256, 1370, 1369, 11])).
% 3.43/3.61 tff(1377,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1376])).
% 3.43/3.61 tff(1378,plain,((~(X0!21 = n2)) | (X1!19 = Y1!18) | (~(Y0!20 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1379,plain,
% 3.43/3.61 (~(X0!21 = n2)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1378, 967, 14])).
% 3.43/3.61 tff(1380,plain,
% 3.43/3.61 (X0!21 = n1),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1316, 1379, 1367, 1077, 1064, 1052, 1040, 1027, 1014, 1001, 988])).
% 3.43/3.61 tff(1381,plain,
% 3.43/3.61 (succ(X0!21) = succ(n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1380])).
% 3.43/3.61 tff(1382,plain,
% 3.43/3.61 (succ(X0!21) = n2),
% 3.43/3.61 inference(transitivity,[status(thm)],[1381, 13])).
% 3.43/3.61 tff(1383,plain,
% 3.43/3.61 (pred(X0!21) = pred(n1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1380])).
% 3.43/3.61 tff(1384,plain,
% 3.43/3.61 (pred(X0!21) = n0),
% 3.43/3.61 inference(transitivity,[status(thm)],[1383, 58])).
% 3.43/3.61 tff(1385,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(X0!21)) = sum(n0, n2)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1384, 1382])).
% 3.43/3.61 tff(1386,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(X0!21)) = n2),
% 3.43/3.61 inference(transitivity,[status(thm)],[1385, 12])).
% 3.43/3.61 tff(1387,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n6)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1386, 973])).
% 3.43/3.61 tff(1388,plain,
% 3.43/3.61 (sum(n2, n6) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[1387])).
% 3.43/3.61 tff(1389,plain,
% 3.43/3.61 (n8 = sum(n2, n6)),
% 3.43/3.61 inference(symmetry,[status(thm)],[1005])).
% 3.43/3.61 tff(1390,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n2, n2)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[971, 1382])).
% 3.43/3.61 tff(1391,plain,
% 3.43/3.61 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1390, 378])).
% 3.43/3.61 tff(1392,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1384, 969])).
% 3.43/3.61 tff(1393,plain,
% 3.43/3.61 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.43/3.61 inference(transitivity,[status(thm)],[1392, 565])).
% 3.43/3.61 tff(1394,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[1393, 1391])).
% 3.43/3.61 tff(1395,plain,
% 3.43/3.61 (X1!19 = Y1!18),
% 3.43/3.61 inference(transitivity,[status(thm)],[49, 1394, 41, 1389, 1388, 11])).
% 3.43/3.61 tff(1396,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14, 1395])).
% 3.43/3.61 tff(1397,plain,((~(Y0!20 = n3)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(1398,plain,
% 3.43/3.61 (~(Y0!20 = n3)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1397, 14])).
% 3.43/3.61 tff(1399,plain,
% 3.43/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n10)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[873, 595])).
% 3.43/3.61 tff(1400,plain,
% 3.43/3.61 (sum(n2, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.61 inference(symmetry,[status(thm)],[1399])).
% 3.48/3.61 tff(1401,plain,
% 3.48/3.61 (n1 = sum(n2, n10)),
% 3.48/3.61 inference(symmetry,[status(thm)],[541])).
% 3.48/3.61 tff(1402,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n2)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[593, 869])).
% 3.48/3.61 tff(1403,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.48/3.61 inference(transitivity,[status(thm)],[1402, 275])).
% 3.48/3.61 tff(1404,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n6)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[871, 591])).
% 3.48/3.61 tff(1405,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.48/3.61 inference(transitivity,[status(thm)],[1404, 272])).
% 3.48/3.61 tff(1406,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1405, 1403])).
% 3.48/3.61 tff(1407,plain,
% 3.48/3.61 (X1!19 = Y1!18),
% 3.48/3.61 inference(transitivity,[status(thm)],[49, 1406, 215, 1401, 1400, 11])).
% 3.48/3.61 tff(1408,plain,
% 3.48/3.61 ($false),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[14, 1407])).
% 3.48/3.61 tff(1409,plain,((~(Y0!20 = n5)) | (X1!19 = Y1!18) | (~(X0!21 = n1))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.61 tff(1410,plain,
% 3.48/3.61 (~(Y0!20 = n5)),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[1409, 867, 14])).
% 3.48/3.61 tff(1411,plain,
% 3.48/3.61 (Y0!20 = n4),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[1348, 1410, 1335, 1398, 966, 954, 942, 928, 914, 899, 887])).
% 3.48/3.61 tff(1412,plain,
% 3.48/3.61 (succ(Y0!20) = succ(n4)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1411])).
% 3.48/3.61 tff(1413,plain,
% 3.48/3.61 (succ(Y0!20) = n5),
% 3.48/3.61 inference(transitivity,[status(thm)],[1412, 367])).
% 3.48/3.61 tff(1414,plain,
% 3.48/3.61 (pred(Y0!20) = pred(n4)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1411])).
% 3.48/3.61 tff(1415,plain,
% 3.48/3.61 (pred(Y0!20) = n3),
% 3.48/3.61 inference(transitivity,[status(thm)],[1414, 370])).
% 3.48/3.61 tff(1416,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(Y0!20)) = sum(n3, n5)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1415, 1413])).
% 3.48/3.61 tff(1417,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(Y0!20)) = n8),
% 3.48/3.61 inference(transitivity,[status(thm)],[1416, 366])).
% 3.48/3.61 tff(1418,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n2, n8)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[873, 1417])).
% 3.48/3.61 tff(1419,plain,
% 3.48/3.61 (sum(n2, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.61 inference(symmetry,[status(thm)],[1418])).
% 3.48/3.61 tff(1420,plain,
% 3.48/3.61 (n10 = sum(n2, n8)),
% 3.48/3.61 inference(symmetry,[status(thm)],[1031])).
% 3.48/3.61 tff(1421,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n2)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1415, 869])).
% 3.48/3.61 tff(1422,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.48/3.61 inference(transitivity,[status(thm)],[1421, 74])).
% 3.48/3.61 tff(1423,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n0, n5)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[871, 1413])).
% 3.48/3.61 tff(1424,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.48/3.61 inference(transitivity,[status(thm)],[1423, 409])).
% 3.48/3.61 tff(1425,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1424, 1422])).
% 3.48/3.61 tff(1426,plain,
% 3.48/3.61 (X1!19 = Y1!18),
% 3.48/3.61 inference(transitivity,[status(thm)],[49, 1425, 256, 1420, 1419, 11])).
% 3.48/3.61 tff(1427,plain,
% 3.48/3.61 ($false),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[14, 1426])).
% 3.48/3.61 tff(1428,plain,((~(X0!21 = n1)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.61 tff(1429,plain,
% 3.48/3.61 (~(X0!21 = n1)),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[1428, 14])).
% 3.48/3.61 tff(1430,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n8)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[520, 773])).
% 3.48/3.61 tff(1431,plain,
% 3.48/3.61 (sum(n6, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.61 inference(symmetry,[status(thm)],[1430])).
% 3.48/3.61 tff(1432,plain,
% 3.48/3.61 (n3 = sum(n6, n8)),
% 3.48/3.61 inference(symmetry,[status(thm)],[63])).
% 3.48/3.61 tff(1433,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n4)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[771, 515])).
% 3.48/3.61 tff(1434,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.48/3.61 inference(transitivity,[status(thm)],[1433, 994])).
% 3.48/3.61 tff(1435,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n5)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[518, 769])).
% 3.48/3.61 tff(1436,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.48/3.61 inference(transitivity,[status(thm)],[1435, 902])).
% 3.48/3.61 tff(1437,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1436, 1434])).
% 3.48/3.61 tff(1438,plain,
% 3.48/3.61 (X1!19 = Y1!18),
% 3.48/3.61 inference(transitivity,[status(thm)],[49, 1437, 231, 1432, 1431, 11])).
% 3.48/3.61 tff(1439,plain,
% 3.48/3.61 ($false),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[14, 1438])).
% 3.48/3.61 tff(1440,plain,((~(X0!21 = n3)) | (X1!19 = Y1!18) | (~(Y0!20 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.61 tff(1441,plain,
% 3.48/3.61 (~(X0!21 = n3)),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[1440, 767, 14])).
% 3.48/3.61 tff(1442,plain,
% 3.48/3.61 (X0!21 = n2),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[1316, 1441, 1367, 1429, 866, 853, 841, 828, 815, 802, 788])).
% 3.48/3.61 tff(1443,plain,
% 3.48/3.61 (succ(X0!21) = succ(n2)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1442])).
% 3.48/3.61 tff(1444,plain,
% 3.48/3.61 (succ(X0!21) = n3),
% 3.48/3.61 inference(transitivity,[status(thm)],[1443, 89])).
% 3.48/3.61 tff(1445,plain,
% 3.48/3.61 (pred(X0!21) = pred(n2)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1442])).
% 3.48/3.61 tff(1446,plain,
% 3.48/3.61 (pred(X0!21) = n1),
% 3.48/3.61 inference(transitivity,[status(thm)],[1445, 93])).
% 3.48/3.61 tff(1447,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(X0!21)) = sum(n1, n3)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1446, 1444])).
% 3.48/3.61 tff(1448,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(X0!21)) = n4),
% 3.48/3.61 inference(transitivity,[status(thm)],[1447, 88])).
% 3.48/3.61 tff(1449,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n8)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1448, 773])).
% 3.48/3.61 tff(1450,plain,
% 3.48/3.61 (sum(n4, n8) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.61 inference(symmetry,[status(thm)],[1449])).
% 3.48/3.61 tff(1451,plain,
% 3.48/3.61 (n1 = sum(n4, n8)),
% 3.48/3.61 inference(symmetry,[status(thm)],[628])).
% 3.48/3.61 tff(1452,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n3, n3)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[771, 1444])).
% 3.48/3.61 tff(1453,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.48/3.61 inference(transitivity,[status(thm)],[1452, 426])).
% 3.48/3.61 tff(1454,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n5)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1446, 769])).
% 3.48/3.61 tff(1455,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.48/3.61 inference(transitivity,[status(thm)],[1454, 423])).
% 3.48/3.61 tff(1456,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1455, 1453])).
% 3.48/3.61 tff(1457,plain,
% 3.48/3.61 (X1!19 = Y1!18),
% 3.48/3.61 inference(transitivity,[status(thm)],[49, 1456, 215, 1451, 1450, 11])).
% 3.48/3.61 tff(1458,plain,
% 3.48/3.61 ($false),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[14, 1457])).
% 3.48/3.61 tff(1459,plain,((~(Y0!20 = n4)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.61 tff(1460,plain,
% 3.48/3.61 (~(Y0!20 = n4)),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[1459, 14])).
% 3.48/3.61 tff(1461,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n1)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[687, 440])).
% 3.48/3.61 tff(1462,plain,
% 3.48/3.61 (sum(n4, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.61 inference(symmetry,[status(thm)],[1461])).
% 3.48/3.61 tff(1463,plain,
% 3.48/3.61 (n5 = sum(n4, n1)),
% 3.48/3.61 inference(symmetry,[status(thm)],[260])).
% 3.48/3.61 tff(1464,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n3)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[438, 683])).
% 3.48/3.61 tff(1465,plain,
% 3.48/3.61 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.48/3.61 inference(transitivity,[status(thm)],[1464, 127])).
% 3.48/3.61 tff(1466,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n7)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[685, 436])).
% 3.48/3.61 tff(1467,plain,
% 3.48/3.61 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.48/3.61 inference(transitivity,[status(thm)],[1466, 39])).
% 3.48/3.61 tff(1468,plain,
% 3.48/3.61 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.48/3.61 inference(monotonicity,[status(thm)],[1467, 1465])).
% 3.48/3.61 tff(1469,plain,
% 3.48/3.61 (X1!19 = Y1!18),
% 3.48/3.61 inference(transitivity,[status(thm)],[49, 1468, 76, 1463, 1462, 11])).
% 3.48/3.61 tff(1470,plain,
% 3.48/3.61 ($false),
% 3.48/3.61 inference(unit_resolution,[status(thm)],[14, 1469])).
% 3.48/3.62 tff(1471,plain,((~(Y0!20 = n6)) | (X1!19 = Y1!18) | (~(X0!21 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1472,plain,
% 3.48/3.62 (~(Y0!20 = n6)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1471, 681, 14])).
% 3.48/3.62 tff(1473,plain,
% 3.48/3.62 (Y0!20 = n5),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1348, 1472, 1335, 1398, 1460, 766, 754, 740, 727, 715, 701])).
% 3.48/3.62 tff(1474,plain,
% 3.48/3.62 (succ(Y0!20) = succ(n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1473])).
% 3.48/3.62 tff(1475,plain,
% 3.48/3.62 (succ(Y0!20) = n6),
% 3.48/3.62 inference(transitivity,[status(thm)],[1474, 245])).
% 3.48/3.62 tff(1476,plain,
% 3.48/3.62 (pred(Y0!20) = pred(n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1473])).
% 3.48/3.62 tff(1477,plain,
% 3.48/3.62 (pred(Y0!20) = n4),
% 3.48/3.62 inference(transitivity,[status(thm)],[1476, 248])).
% 3.48/3.62 tff(1478,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = sum(n4, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1477, 1475])).
% 3.48/3.62 tff(1479,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1478, 244])).
% 3.48/3.62 tff(1480,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n4, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[687, 1479])).
% 3.48/3.62 tff(1481,plain,
% 3.48/3.62 (sum(n4, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1480])).
% 3.48/3.62 tff(1482,plain,
% 3.48/3.62 (n3 = sum(n4, n10)),
% 3.48/3.62 inference(symmetry,[status(thm)],[655])).
% 3.48/3.62 tff(1483,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1477, 683])).
% 3.48/3.62 tff(1484,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.48/3.62 inference(transitivity,[status(thm)],[1483, 290])).
% 3.48/3.62 tff(1485,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n1, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[685, 1475])).
% 3.48/3.62 tff(1486,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.48/3.62 inference(transitivity,[status(thm)],[1485, 287])).
% 3.48/3.62 tff(1487,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1486, 1484])).
% 3.48/3.62 tff(1488,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1487, 231, 1482, 1481, 11])).
% 3.48/3.62 tff(1489,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1488])).
% 3.48/3.62 tff(1490,plain,((~(X0!21 = n2)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1491,plain,
% 3.48/3.62 (~(X0!21 = n2)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1490, 14])).
% 3.48/3.62 tff(1492,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[374, 595])).
% 3.48/3.62 tff(1493,plain,
% 3.48/3.62 (sum(n8, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1492])).
% 3.48/3.62 tff(1494,plain,
% 3.48/3.62 (n7 = sum(n8, n10)),
% 3.48/3.62 inference(symmetry,[status(thm)],[15])).
% 3.48/3.62 tff(1495,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[593, 369])).
% 3.48/3.62 tff(1496,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.48/3.62 inference(transitivity,[status(thm)],[1495, 704])).
% 3.48/3.62 tff(1497,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[372, 591])).
% 3.48/3.62 tff(1498,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.48/3.62 inference(transitivity,[status(thm)],[1497, 793])).
% 3.48/3.62 tff(1499,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1498, 1496])).
% 3.48/3.62 tff(1500,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1499, 235, 1494, 1493, 11])).
% 3.48/3.62 tff(1501,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1500])).
% 3.48/3.62 tff(1502,plain,((~(X0!21 = n4)) | (X1!19 = Y1!18) | (~(Y0!20 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1503,plain,
% 3.48/3.62 (~(X0!21 = n4)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1502, 589, 14])).
% 3.48/3.62 tff(1504,plain,
% 3.48/3.62 (X0!21 = n3),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1316, 1503, 1367, 1429, 1491, 680, 665, 651, 637, 624, 610])).
% 3.48/3.62 tff(1505,plain,
% 3.48/3.62 (succ(X0!21) = succ(n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1504])).
% 3.48/3.62 tff(1506,plain,
% 3.48/3.62 (succ(X0!21) = n4),
% 3.48/3.62 inference(transitivity,[status(thm)],[1505, 513])).
% 3.48/3.62 tff(1507,plain,
% 3.48/3.62 (pred(X0!21) = pred(n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1504])).
% 3.48/3.62 tff(1508,plain,
% 3.48/3.62 (pred(X0!21) = n2),
% 3.48/3.62 inference(transitivity,[status(thm)],[1507, 516])).
% 3.48/3.62 tff(1509,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = sum(n2, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1508, 1506])).
% 3.48/3.62 tff(1510,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = n6),
% 3.48/3.62 inference(transitivity,[status(thm)],[1509, 512])).
% 3.48/3.62 tff(1511,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1510, 595])).
% 3.48/3.62 tff(1512,plain,
% 3.48/3.62 (sum(n6, n10) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1511])).
% 3.48/3.62 tff(1513,plain,
% 3.48/3.62 (n5 = sum(n6, n10)),
% 3.48/3.62 inference(symmetry,[status(thm)],[340])).
% 3.48/3.62 tff(1514,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n4, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[593, 1506])).
% 3.48/3.62 tff(1515,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.48/3.62 inference(transitivity,[status(thm)],[1514, 41])).
% 3.48/3.62 tff(1516,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1508, 591])).
% 3.48/3.62 tff(1517,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.48/3.62 inference(transitivity,[status(thm)],[1516, 1005])).
% 3.48/3.62 tff(1518,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1517, 1515])).
% 3.48/3.62 tff(1519,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1518, 76, 1513, 1512, 11])).
% 3.48/3.62 tff(1520,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1519])).
% 3.48/3.62 tff(1521,plain,((~(Y0!20 = n5)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1522,plain,
% 3.48/3.62 (~(Y0!20 = n5)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1521, 14])).
% 3.48/3.62 tff(1523,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[520, 304])).
% 3.48/3.62 tff(1524,plain,
% 3.48/3.62 (sum(n6, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1523])).
% 3.48/3.62 tff(1525,plain,
% 3.48/3.62 (n9 = sum(n6, n3)),
% 3.48/3.62 inference(symmetry,[status(thm)],[691])).
% 3.48/3.62 tff(1526,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[302, 515])).
% 3.48/3.62 tff(1527,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1526, 577])).
% 3.48/3.62 tff(1528,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[518, 300])).
% 3.48/3.62 tff(1529,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1528, 1031])).
% 3.48/3.62 tff(1530,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1529, 1527])).
% 3.48/3.62 tff(1531,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1530, 158, 1525, 1524, 11])).
% 3.48/3.62 tff(1532,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1531])).
% 3.48/3.62 tff(1533,plain,((~(Y0!20 = n7)) | (X1!19 = Y1!18) | (~(X0!21 = n3))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1534,plain,
% 3.48/3.62 (~(Y0!20 = n7)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1533, 511, 14])).
% 3.48/3.62 tff(1535,plain,
% 3.48/3.62 (Y0!20 = n6),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1348, 1534, 1335, 1398, 1460, 1522, 588, 574, 561, 548, 534])).
% 3.48/3.62 tff(1536,plain,
% 3.48/3.62 (succ(Y0!20) = succ(n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1535])).
% 3.48/3.62 tff(1537,plain,
% 3.48/3.62 (succ(Y0!20) = n7),
% 3.48/3.62 inference(transitivity,[status(thm)],[1536, 28])).
% 3.48/3.62 tff(1538,plain,
% 3.48/3.62 (pred(Y0!20) = pred(n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1535])).
% 3.48/3.62 tff(1539,plain,
% 3.48/3.62 (pred(Y0!20) = n5),
% 3.48/3.62 inference(transitivity,[status(thm)],[1538, 32])).
% 3.48/3.62 tff(1540,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = sum(n5, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1539, 1537])).
% 3.48/3.62 tff(1541,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1540, 27])).
% 3.48/3.62 tff(1542,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n6, n1)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[520, 1541])).
% 3.48/3.62 tff(1543,plain,
% 3.48/3.62 (sum(n6, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1542])).
% 3.48/3.62 tff(1544,plain,
% 3.48/3.62 (n7 = sum(n6, n1)),
% 3.48/3.62 inference(symmetry,[status(thm)],[1113])).
% 3.48/3.62 tff(1545,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1539, 515])).
% 3.48/3.62 tff(1546,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.48/3.62 inference(transitivity,[status(thm)],[1545, 1020])).
% 3.48/3.62 tff(1547,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n2, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[518, 1537])).
% 3.48/3.62 tff(1548,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.48/3.62 inference(transitivity,[status(thm)],[1547, 917])).
% 3.48/3.62 tff(1549,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1548, 1546])).
% 3.48/3.62 tff(1550,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1549, 235, 1544, 1543, 11])).
% 3.48/3.62 tff(1551,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1550])).
% 3.48/3.62 tff(1552,plain,((~(X0!21 = n3)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1553,plain,
% 3.48/3.62 (~(X0!21 = n3)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1552, 14])).
% 3.48/3.62 tff(1554,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n1)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[252, 440])).
% 3.48/3.62 tff(1555,plain,
% 3.48/3.62 (sum(n10, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1554])).
% 3.48/3.62 tff(1556,plain,
% 3.48/3.62 (n0 = sum(n10, n1)),
% 3.48/3.62 inference(symmetry,[status(thm)],[136])).
% 3.48/3.62 tff(1557,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[438, 247])).
% 3.48/3.62 tff(1558,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.48/3.62 inference(transitivity,[status(thm)],[1557, 617])).
% 3.48/3.62 tff(1559,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[250, 436])).
% 3.48/3.62 tff(1560,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.48/3.62 inference(transitivity,[status(thm)],[1559, 614])).
% 3.48/3.62 tff(1561,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1560, 1558])).
% 3.48/3.62 tff(1562,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1561, 109, 1556, 1555, 11])).
% 3.48/3.62 tff(1563,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1562])).
% 3.48/3.62 tff(1564,plain,((~(X0!21 = n5)) | (X1!19 = Y1!18) | (~(Y0!20 = n6))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1565,plain,
% 3.48/3.62 (~(X0!21 = n5)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1564, 434, 14])).
% 3.48/3.62 tff(1566,plain,
% 3.48/3.62 (X0!21 = n4),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1316, 1565, 1367, 1429, 1491, 1553, 510, 496, 483, 469, 455])).
% 3.48/3.62 tff(1567,plain,
% 3.48/3.62 (succ(X0!21) = succ(n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1566])).
% 3.48/3.62 tff(1568,plain,
% 3.48/3.62 (succ(X0!21) = n5),
% 3.48/3.62 inference(transitivity,[status(thm)],[1567, 367])).
% 3.48/3.62 tff(1569,plain,
% 3.48/3.62 (pred(X0!21) = pred(n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1566])).
% 3.48/3.62 tff(1570,plain,
% 3.48/3.62 (pred(X0!21) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1569, 370])).
% 3.48/3.62 tff(1571,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = sum(n3, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1570, 1568])).
% 3.48/3.62 tff(1572,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = n8),
% 3.48/3.62 inference(transitivity,[status(thm)],[1571, 366])).
% 3.48/3.62 tff(1573,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n1)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1572, 440])).
% 3.48/3.62 tff(1574,plain,
% 3.48/3.62 (sum(n8, n1) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1573])).
% 3.48/3.62 tff(1575,plain,
% 3.48/3.62 (n9 = sum(n8, n1)),
% 3.48/3.62 inference(symmetry,[status(thm)],[1139])).
% 3.48/3.62 tff(1576,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n5, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[438, 1568])).
% 3.48/3.62 tff(1577,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1576, 256])).
% 3.48/3.62 tff(1578,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1570, 436])).
% 3.48/3.62 tff(1579,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1578, 806])).
% 3.48/3.62 tff(1580,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1579, 1577])).
% 3.48/3.62 tff(1581,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1580, 158, 1575, 1574, 11])).
% 3.48/3.62 tff(1582,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1581])).
% 3.48/3.62 tff(1583,plain,((~(Y0!20 = n6)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1584,plain,
% 3.48/3.62 (~(Y0!20 = n6)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1583, 14])).
% 3.48/3.62 tff(1585,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[374, 190])).
% 3.48/3.62 tff(1586,plain,
% 3.48/3.62 (sum(n8, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1585])).
% 3.48/3.62 tff(1587,plain,
% 3.48/3.62 (n2 = sum(n8, n5)),
% 3.48/3.62 inference(symmetry,[status(thm)],[379])).
% 3.48/3.62 tff(1588,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[188, 369])).
% 3.48/3.62 tff(1589,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1588, 213])).
% 3.48/3.62 tff(1590,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[372, 185])).
% 3.48/3.62 tff(1591,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1590, 832])).
% 3.48/3.62 tff(1592,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1591, 1589])).
% 3.48/3.62 tff(1593,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1592, 538, 1587, 1586, 11])).
% 3.48/3.62 tff(1594,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1593])).
% 3.48/3.62 tff(1595,plain,((~(Y0!20 = n8)) | (X1!19 = Y1!18) | (~(X0!21 = n4))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1596,plain,
% 3.48/3.62 (~(Y0!20 = n8)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1595, 365, 14])).
% 3.48/3.62 tff(1597,plain,
% 3.48/3.62 (Y0!20 = n7),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1348, 1596, 1335, 1398, 1460, 1522, 1584, 433, 418, 404, 389])).
% 3.48/3.62 tff(1598,plain,
% 3.48/3.62 (succ(Y0!20) = succ(n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1597])).
% 3.48/3.62 tff(1599,plain,
% 3.48/3.62 (succ(Y0!20) = n8),
% 3.48/3.62 inference(transitivity,[status(thm)],[1598, 64])).
% 3.48/3.62 tff(1600,plain,
% 3.48/3.62 (pred(Y0!20) = pred(n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1597])).
% 3.48/3.62 tff(1601,plain,
% 3.48/3.62 (pred(Y0!20) = n6),
% 3.48/3.62 inference(transitivity,[status(thm)],[1600, 67])).
% 3.48/3.62 tff(1602,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = sum(n6, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1601, 1599])).
% 3.48/3.62 tff(1603,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1602, 63])).
% 3.48/3.62 tff(1604,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n8, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[374, 1603])).
% 3.48/3.62 tff(1605,plain,
% 3.48/3.62 (sum(n8, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1604])).
% 3.48/3.62 tff(1606,plain,
% 3.48/3.62 (n0 = sum(n8, n3)),
% 3.48/3.62 inference(symmetry,[status(thm)],[113])).
% 3.48/3.62 tff(1607,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1601, 369])).
% 3.48/3.62 tff(1608,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n0),
% 3.48/3.62 inference(transitivity,[status(thm)],[1607, 523])).
% 3.48/3.62 tff(1609,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n3, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[372, 1599])).
% 3.48/3.62 tff(1610,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n0),
% 3.48/3.62 inference(transitivity,[status(thm)],[1609, 818])).
% 3.48/3.62 tff(1611,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n0, n0)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1610, 1608])).
% 3.48/3.62 tff(1612,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1611, 109, 1606, 1605, 11])).
% 3.48/3.62 tff(1613,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1612])).
% 3.48/3.62 tff(1614,plain,((~(X0!21 = n4)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1615,plain,
% 3.48/3.62 (~(X0!21 = n4)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1614, 14])).
% 3.48/3.62 tff(1616,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[36, 304])).
% 3.48/3.62 tff(1617,plain,
% 3.48/3.62 (sum(n1, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1616])).
% 3.48/3.62 tff(1618,plain,
% 3.48/3.62 (n4 = sum(n1, n3)),
% 3.48/3.62 inference(symmetry,[status(thm)],[88])).
% 3.48/3.62 tff(1619,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[302, 31])).
% 3.48/3.62 tff(1620,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.48/3.62 inference(transitivity,[status(thm)],[1619, 462])).
% 3.48/3.62 tff(1621,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[34, 300])).
% 3.48/3.62 tff(1622,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.48/3.62 inference(transitivity,[status(thm)],[1621, 459])).
% 3.48/3.62 tff(1623,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1622, 1620])).
% 3.48/3.62 tff(1624,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1623, 378, 1618, 1617, 11])).
% 3.48/3.62 tff(1625,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1624])).
% 3.48/3.62 tff(1626,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1627,plain,
% 3.48/3.62 (~(X0!21 = n6)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1626, 298, 14])).
% 3.48/3.62 tff(1628,plain,
% 3.48/3.62 (X0!21 = n5),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1316, 1627, 1367, 1429, 1491, 1553, 1615, 364, 349, 335, 319])).
% 3.48/3.62 tff(1629,plain,
% 3.48/3.62 (succ(X0!21) = succ(n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1628])).
% 3.48/3.62 tff(1630,plain,
% 3.48/3.62 (succ(X0!21) = n6),
% 3.48/3.62 inference(transitivity,[status(thm)],[1629, 245])).
% 3.48/3.62 tff(1631,plain,
% 3.48/3.62 (pred(X0!21) = pred(n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1628])).
% 3.48/3.62 tff(1632,plain,
% 3.48/3.62 (pred(X0!21) = n4),
% 3.48/3.62 inference(transitivity,[status(thm)],[1631, 248])).
% 3.48/3.62 tff(1633,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = sum(n4, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1632, 1630])).
% 3.48/3.62 tff(1634,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1633, 244])).
% 3.48/3.62 tff(1635,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1634, 304])).
% 3.48/3.62 tff(1636,plain,
% 3.48/3.62 (sum(n10, n3) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1635])).
% 3.48/3.62 tff(1637,plain,
% 3.48/3.62 (n2 = sum(n10, n3)),
% 3.48/3.62 inference(symmetry,[status(thm)],[731])).
% 3.48/3.62 tff(1638,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n6, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[302, 1630])).
% 3.48/3.62 tff(1639,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1638, 215])).
% 3.48/3.62 tff(1640,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1632, 300])).
% 3.48/3.62 tff(1641,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1640, 628])).
% 3.48/3.62 tff(1642,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1641, 1639])).
% 3.48/3.62 tff(1643,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1642, 538, 1637, 1636, 11])).
% 3.48/3.62 tff(1644,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1643])).
% 3.48/3.62 tff(1645,plain,((~(Y0!20 = n7)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1646,plain,
% 3.48/3.62 (~(Y0!20 = n7)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1645, 14])).
% 3.48/3.62 tff(1647,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[252, 24])).
% 3.48/3.62 tff(1648,plain,
% 3.48/3.62 (sum(n10, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1647])).
% 3.48/3.62 tff(1649,plain,
% 3.48/3.62 (n6 = sum(n10, n7)),
% 3.48/3.62 inference(symmetry,[status(thm)],[1102])).
% 3.48/3.62 tff(1650,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[22, 247])).
% 3.48/3.62 tff(1651,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1650, 658])).
% 3.48/3.62 tff(1652,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[250, 19])).
% 3.48/3.62 tff(1653,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1652, 655])).
% 3.48/3.62 tff(1654,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1653, 1651])).
% 3.48/3.62 tff(1655,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1654, 426, 1649, 1648, 11])).
% 3.48/3.62 tff(1656,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1655])).
% 3.48/3.62 tff(1657,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n5))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1658,plain,
% 3.48/3.62 (~(Y0!20 = n9)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1657, 243, 14])).
% 3.48/3.62 tff(1659,plain,
% 3.48/3.62 (Y0!20 = n8),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1348, 1658, 1335, 1398, 1460, 1522, 1584, 1646, 297, 282, 267])).
% 3.48/3.62 tff(1660,plain,
% 3.48/3.62 (succ(Y0!20) = succ(n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1659])).
% 3.48/3.62 tff(1661,plain,
% 3.48/3.62 (succ(Y0!20) = n9),
% 3.48/3.62 inference(transitivity,[status(thm)],[1660, 26])).
% 3.48/3.62 tff(1662,plain,
% 3.48/3.62 (pred(Y0!20) = pred(n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1659])).
% 3.48/3.62 tff(1663,plain,
% 3.48/3.62 (pred(Y0!20) = n7),
% 3.48/3.62 inference(transitivity,[status(thm)],[1662, 186])).
% 3.48/3.62 tff(1664,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = sum(n7, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1663, 1661])).
% 3.48/3.62 tff(1665,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = n5),
% 3.48/3.62 inference(transitivity,[status(thm)],[1664, 25])).
% 3.48/3.62 tff(1666,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n10, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[252, 1665])).
% 3.48/3.62 tff(1667,plain,
% 3.48/3.62 (sum(n10, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1666])).
% 3.48/3.62 tff(1668,plain,
% 3.48/3.62 (n4 = sum(n10, n5)),
% 3.48/3.62 inference(symmetry,[status(thm)],[394])).
% 3.48/3.62 tff(1669,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1663, 247])).
% 3.48/3.62 tff(1670,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n2),
% 3.48/3.62 inference(transitivity,[status(thm)],[1669, 644])).
% 3.48/3.62 tff(1671,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n4, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[250, 1661])).
% 3.48/3.62 tff(1672,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n2),
% 3.48/3.62 inference(transitivity,[status(thm)],[1671, 641])).
% 3.48/3.62 tff(1673,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n2, n2)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1672, 1670])).
% 3.48/3.62 tff(1674,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1673, 378, 1668, 1667, 11])).
% 3.48/3.62 tff(1675,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1674])).
% 3.48/3.62 tff(1676,plain,((~(X0!21 = n5)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1677,plain,
% 3.48/3.62 (~(X0!21 = n5)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1676, 14])).
% 3.48/3.62 tff(1678,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[71, 190])).
% 3.48/3.62 tff(1679,plain,
% 3.48/3.62 (sum(n3, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1678])).
% 3.48/3.62 tff(1680,plain,
% 3.48/3.62 (n8 = sum(n3, n5)),
% 3.48/3.62 inference(symmetry,[status(thm)],[366])).
% 3.48/3.62 tff(1681,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[188, 66])).
% 3.48/3.62 tff(1682,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n4),
% 3.48/3.62 inference(transitivity,[status(thm)],[1681, 328])).
% 3.48/3.62 tff(1683,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[69, 185])).
% 3.48/3.62 tff(1684,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n4),
% 3.48/3.62 inference(transitivity,[status(thm)],[1683, 325])).
% 3.48/3.62 tff(1685,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n4, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1684, 1682])).
% 3.48/3.62 tff(1686,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1685, 41, 1680, 1679, 11])).
% 3.48/3.62 tff(1687,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1686])).
% 3.48/3.62 tff(1688,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18) | (~(Y0!20 = n8))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1689,plain,
% 3.48/3.62 (~(X0!21 = n7)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1688, 183, 14])).
% 3.48/3.62 tff(1690,plain,
% 3.48/3.62 (X0!21 = n6),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1316, 1689, 1367, 1429, 1491, 1553, 1615, 1677, 242, 226, 210])).
% 3.48/3.62 tff(1691,plain,
% 3.48/3.62 (succ(X0!21) = succ(n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1690])).
% 3.48/3.62 tff(1692,plain,
% 3.48/3.62 (succ(X0!21) = n7),
% 3.48/3.62 inference(transitivity,[status(thm)],[1691, 28])).
% 3.48/3.62 tff(1693,plain,
% 3.48/3.62 (pred(X0!21) = pred(n6)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1690])).
% 3.48/3.62 tff(1694,plain,
% 3.48/3.62 (pred(X0!21) = n5),
% 3.48/3.62 inference(transitivity,[status(thm)],[1693, 32])).
% 3.48/3.62 tff(1695,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = sum(n5, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1694, 1692])).
% 3.48/3.62 tff(1696,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(X0!21)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1695, 27])).
% 3.48/3.62 tff(1697,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n5)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1696, 190])).
% 3.48/3.62 tff(1698,plain,
% 3.48/3.62 (sum(n1, n5) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1697])).
% 3.48/3.62 tff(1699,plain,
% 3.48/3.62 (n6 = sum(n1, n5)),
% 3.48/3.62 inference(symmetry,[status(thm)],[423])).
% 3.48/3.62 tff(1700,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n7, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[188, 1692])).
% 3.48/3.62 tff(1701,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1700, 231])).
% 3.48/3.62 tff(1702,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1694, 185])).
% 3.48/3.62 tff(1703,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1702, 474])).
% 3.48/3.62 tff(1704,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n3, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1703, 1701])).
% 3.48/3.62 tff(1705,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1704, 426, 1699, 1698, 11])).
% 3.48/3.62 tff(1706,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1705])).
% 3.48/3.62 tff(1707,plain,((~(Y0!20 = n8)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1708,plain,
% 3.48/3.62 (~(Y0!20 = n8)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1707, 14])).
% 3.48/3.62 tff(1709,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n7)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[154, 24])).
% 3.48/3.62 tff(1710,plain,
% 3.48/3.62 (sum(n9, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1709])).
% 3.48/3.62 tff(1711,plain,
% 3.48/3.62 (n5 = sum(n9, n7)),
% 3.48/3.62 inference(symmetry,[status(thm)],[503])).
% 3.48/3.62 tff(1712,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n0)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[22, 149])).
% 3.48/3.62 tff(1713,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.48/3.62 inference(transitivity,[status(thm)],[1712, 392])).
% 3.48/3.62 tff(1714,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[152, 19])).
% 3.48/3.62 tff(1715,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.48/3.62 inference(transitivity,[status(thm)],[1714, 668])).
% 3.48/3.62 tff(1716,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1715, 1713])).
% 3.48/3.62 tff(1717,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1716, 76, 1711, 1710, 11])).
% 3.48/3.62 tff(1718,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1717])).
% 3.48/3.62 tff(1719,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18) | (~(X0!21 = n10))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1720,plain,
% 3.48/3.62 (~(Y0!20 = n9)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1719, 135, 14])).
% 3.48/3.62 tff(1721,plain,
% 3.48/3.62 (Y0!20 = n2),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1348, 1720, 1335, 1398, 1460, 1522, 1584, 1646, 1708, 182, 169])).
% 3.48/3.62 tff(1722,plain,
% 3.48/3.62 (succ(Y0!20) = succ(n2)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1721])).
% 3.48/3.62 tff(1723,plain,
% 3.48/3.62 (succ(Y0!20) = n3),
% 3.48/3.62 inference(transitivity,[status(thm)],[1722, 89])).
% 3.48/3.62 tff(1724,plain,
% 3.48/3.62 (pred(Y0!20) = pred(n2)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1721])).
% 3.48/3.62 tff(1725,plain,
% 3.48/3.62 (pred(Y0!20) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1724, 93])).
% 3.48/3.62 tff(1726,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = sum(n1, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1725, 1723])).
% 3.48/3.62 tff(1727,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(Y0!20)) = n4),
% 3.48/3.62 inference(transitivity,[status(thm)],[1726, 88])).
% 3.48/3.62 tff(1728,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n9, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[154, 1727])).
% 3.48/3.62 tff(1729,plain,
% 3.48/3.62 (sum(n9, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1728])).
% 3.48/3.62 tff(1730,plain,
% 3.48/3.62 (n2 = sum(n9, n4)),
% 3.48/3.62 inference(symmetry,[status(thm)],[1070])).
% 3.48/3.62 tff(1731,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n0)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1725, 149])).
% 3.48/3.62 tff(1732,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1731, 1197])).
% 3.48/3.62 tff(1733,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n9, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[152, 1723])).
% 3.48/3.62 tff(1734,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n1),
% 3.48/3.62 inference(transitivity,[status(thm)],[1733, 352])).
% 3.48/3.62 tff(1735,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n1, n1)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1734, 1732])).
% 3.48/3.62 tff(1736,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1735, 538, 1730, 1729, 11])).
% 3.48/3.62 tff(1737,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1736])).
% 3.48/3.62 tff(1738,plain,((~(X0!21 = n10)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1739,plain,
% 3.48/3.62 (~(X0!21 = n10)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1738, 14])).
% 3.48/3.62 tff(1740,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n4)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[321, 97])).
% 3.48/3.62 tff(1741,plain,
% 3.48/3.62 (sum(n5, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.62 inference(symmetry,[status(thm)],[1740])).
% 3.48/3.62 tff(1742,plain,
% 3.48/3.62 (n9 = sum(n5, n4)),
% 3.48/3.62 inference(symmetry,[status(thm)],[1020])).
% 3.48/3.62 tff(1743,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n9)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[95, 193])).
% 3.48/3.62 tff(1744,plain,
% 3.48/3.62 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1743, 708])).
% 3.48/3.62 tff(1745,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n3)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[203, 92])).
% 3.48/3.62 tff(1746,plain,
% 3.48/3.62 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.48/3.62 inference(transitivity,[status(thm)],[1745, 338])).
% 3.48/3.62 tff(1747,plain,
% 3.48/3.62 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.48/3.62 inference(monotonicity,[status(thm)],[1746, 1744])).
% 3.48/3.62 tff(1748,plain,
% 3.48/3.62 (X1!19 = Y1!18),
% 3.48/3.62 inference(transitivity,[status(thm)],[49, 1747, 158, 1742, 1741, 11])).
% 3.48/3.62 tff(1749,plain,
% 3.48/3.62 ($false),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[14, 1748])).
% 3.48/3.62 tff(1750,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18) | (~(Y0!20 = n2))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.62 tff(1751,plain,
% 3.48/3.62 (~(X0!21 = n8)),
% 3.48/3.62 inference(unit_resolution,[status(thm)],[1750, 90, 14])).
% 3.48/3.63 tff(1752,plain,
% 3.48/3.63 (X0!21 = n7),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1316, 1751, 1367, 1429, 1491, 1553, 1615, 1677, 1739, 134, 120])).
% 3.48/3.63 tff(1753,plain,
% 3.48/3.63 (succ(X0!21) = succ(n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1752])).
% 3.48/3.63 tff(1754,plain,
% 3.48/3.63 (succ(X0!21) = n8),
% 3.48/3.63 inference(transitivity,[status(thm)],[1753, 64])).
% 3.48/3.63 tff(1755,plain,
% 3.48/3.63 (pred(X0!21) = pred(n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1752])).
% 3.48/3.63 tff(1756,plain,
% 3.48/3.63 (pred(X0!21) = n6),
% 3.48/3.63 inference(transitivity,[status(thm)],[1755, 67])).
% 3.48/3.63 tff(1757,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = sum(n6, n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1756, 1754])).
% 3.48/3.63 tff(1758,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = n3),
% 3.48/3.63 inference(transitivity,[status(thm)],[1757, 63])).
% 3.48/3.63 tff(1759,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n4)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1758, 97])).
% 3.48/3.63 tff(1760,plain,
% 3.48/3.63 (sum(n3, n4) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1759])).
% 3.48/3.63 tff(1761,plain,
% 3.48/3.63 (n7 = sum(n3, n4)),
% 3.48/3.63 inference(symmetry,[status(thm)],[994])).
% 3.48/3.63 tff(1762,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n1, n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[95, 1754])).
% 3.48/3.63 tff(1763,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1762, 694])).
% 3.48/3.63 tff(1764,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n3)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1756, 92])).
% 3.48/3.63 tff(1765,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1764, 691])).
% 3.48/3.63 tff(1766,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1765, 1763])).
% 3.48/3.63 tff(1767,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1766, 235, 1761, 1760, 11])).
% 3.48/3.63 tff(1768,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1767])).
% 3.48/3.63 tff(1769,plain,((~(Y0!20 = n2)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1770,plain,
% 3.48/3.63 (~(Y0!20 = n2)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1769, 14])).
% 3.48/3.63 tff(1771,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n0)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[71, 145])).
% 3.48/3.63 tff(1772,plain,
% 3.48/3.63 (sum(n3, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1771])).
% 3.48/3.63 tff(1773,plain,
% 3.48/3.63 (n3 = sum(n3, n0)),
% 3.48/3.63 inference(symmetry,[status(thm)],[857])).
% 3.48/3.63 tff(1774,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[143, 66])).
% 3.48/3.63 tff(1775,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1774, 791])).
% 3.48/3.63 tff(1776,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[69, 140])).
% 3.48/3.63 tff(1777,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1776, 1113])).
% 3.48/3.63 tff(1778,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1777, 1775])).
% 3.48/3.63 tff(1779,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1778, 231, 1773, 1772, 11])).
% 3.48/3.63 tff(1780,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1779])).
% 3.48/3.63 tff(1781,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18) | (~(X0!21 = n7))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1782,plain,
% 3.48/3.63 (~(Y0!20 = n0)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1781, 54, 14])).
% 3.48/3.63 tff(1783,plain,
% 3.48/3.63 (Y0!20 = n9),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1348, 1782, 1335, 1398, 1460, 1522, 1584, 1646, 1708, 1770, 87])).
% 3.48/3.63 tff(1784,plain,
% 3.48/3.63 (succ(Y0!20) = succ(n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1783])).
% 3.48/3.63 tff(1785,plain,
% 3.48/3.63 (succ(Y0!20) = n10),
% 3.48/3.63 inference(transitivity,[status(thm)],[1784, 16])).
% 3.48/3.63 tff(1786,plain,
% 3.48/3.63 (pred(Y0!20) = pred(n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1783])).
% 3.48/3.63 tff(1787,plain,
% 3.48/3.63 (pred(Y0!20) = n8),
% 3.48/3.63 inference(transitivity,[status(thm)],[1786, 20])).
% 3.48/3.63 tff(1788,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(Y0!20)) = sum(n8, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1787, 1785])).
% 3.48/3.63 tff(1789,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(Y0!20)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1788, 15])).
% 3.48/3.63 tff(1790,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n3, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[71, 1789])).
% 3.48/3.63 tff(1791,plain,
% 3.48/3.63 (sum(n3, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1790])).
% 3.48/3.63 tff(1792,plain,
% 3.48/3.63 (n10 = sum(n3, n7)),
% 3.48/3.63 inference(symmetry,[status(thm)],[806])).
% 3.48/3.63 tff(1793,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1787, 66])).
% 3.48/3.63 tff(1794,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n5),
% 3.48/3.63 inference(transitivity,[status(thm)],[1793, 76])).
% 3.48/3.63 tff(1795,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n6, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[69, 1785])).
% 3.48/3.63 tff(1796,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n5),
% 3.48/3.63 inference(transitivity,[status(thm)],[1795, 340])).
% 3.48/3.63 tff(1797,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n5, n5)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1796, 1794])).
% 3.48/3.63 tff(1798,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1797, 256, 1792, 1791, 11])).
% 3.48/3.63 tff(1799,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1798])).
% 3.48/3.63 tff(1800,plain,((~(X0!21 = n7)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1801,plain,
% 3.48/3.63 (~(X0!21 = n7)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1800, 14])).
% 3.48/3.63 tff(1802,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[22, 100])).
% 3.48/3.63 tff(1803,plain,
% 3.48/3.63 (pred(n9) = pred(Y0!20)),
% 3.48/3.63 inference(symmetry,[status(thm)],[21])).
% 3.48/3.63 tff(1804,plain,
% 3.48/3.63 (pred(X0!21) = pred(Y0!20)),
% 3.48/3.63 inference(transitivity,[status(thm)],[101, 1803])).
% 3.48/3.63 tff(1805,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = sum(pred(Y0!20), succ(X0!21))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1804])).
% 3.48/3.63 tff(1806,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1805, 1802, 15])).
% 3.48/3.63 tff(1807,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1806, 24])).
% 3.48/3.63 tff(1808,plain,
% 3.48/3.63 (sum(n7, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1807])).
% 3.48/3.63 tff(1809,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1802, 15])).
% 3.48/3.63 tff(1810,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[102, 19])).
% 3.48/3.63 tff(1811,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1810, 15])).
% 3.48/3.63 tff(1812,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1811, 1809])).
% 3.48/3.63 tff(1813,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1812, 1808, 11])).
% 3.48/3.63 tff(1814,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1813])).
% 3.48/3.63 tff(1815,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18) | (~(Y0!20 = n9))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1816,plain,
% 3.48/3.63 (~(X0!21 = n9)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1815, 17, 14])).
% 3.48/3.63 tff(1817,plain,
% 3.48/3.63 (X0!21 = n8),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1316, 1816, 1367, 1429, 1491, 1553, 1615, 1677, 1739, 1801, 53])).
% 3.48/3.63 tff(1818,plain,
% 3.48/3.63 (succ(X0!21) = succ(n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1817])).
% 3.48/3.63 tff(1819,plain,
% 3.48/3.63 (succ(X0!21) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1818, 26])).
% 3.48/3.63 tff(1820,plain,
% 3.48/3.63 (pred(X0!21) = pred(n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1817])).
% 3.48/3.63 tff(1821,plain,
% 3.48/3.63 (pred(X0!21) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1820, 186])).
% 3.48/3.63 tff(1822,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = sum(n7, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1821, 1819])).
% 3.48/3.63 tff(1823,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = n5),
% 3.48/3.63 inference(transitivity,[status(thm)],[1822, 25])).
% 3.48/3.63 tff(1824,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1823, 24])).
% 3.48/3.63 tff(1825,plain,
% 3.48/3.63 (sum(n5, n7) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1824])).
% 3.48/3.63 tff(1826,plain,
% 3.48/3.63 (n1 = sum(n5, n7)),
% 3.48/3.63 inference(symmetry,[status(thm)],[27])).
% 3.48/3.63 tff(1827,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n8, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[22, 1819])).
% 3.48/3.63 tff(1828,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.48/3.63 inference(transitivity,[status(thm)],[1827, 219])).
% 3.48/3.63 tff(1829,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1821, 19])).
% 3.48/3.63 tff(1830,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.48/3.63 inference(transitivity,[status(thm)],[1829, 216])).
% 3.48/3.63 tff(1831,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1830, 1828])).
% 3.48/3.63 tff(1832,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1831, 215, 1826, 1825, 11])).
% 3.48/3.63 tff(1833,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1832])).
% 3.48/3.63 tff(1834,plain,((~(Y0!20 = n9)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1835,plain,
% 3.48/3.63 (~(Y0!20 = n9)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1834, 14])).
% 3.48/3.63 tff(1836,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[321, 62])).
% 3.48/3.63 tff(1837,plain,
% 3.48/3.63 (sum(n5, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1836])).
% 3.48/3.63 tff(1838,plain,
% 3.48/3.63 (n7 = sum(n5, n2)),
% 3.48/3.63 inference(symmetry,[status(thm)],[877])).
% 3.48/3.63 tff(1839,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[60, 193])).
% 3.48/3.63 tff(1840,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1839, 907])).
% 3.48/3.63 tff(1841,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[203, 57])).
% 3.48/3.63 tff(1842,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1841, 904])).
% 3.48/3.63 tff(1843,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1842, 1840])).
% 3.48/3.63 tff(1844,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1843, 235, 1838, 1837, 11])).
% 3.48/3.63 tff(1845,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1844])).
% 3.48/3.63 tff(1846,plain,((~(Y0!20 = n1)) | (X1!19 = Y1!18) | (~(X0!21 = n8))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1847,plain,
% 3.48/3.63 (~(Y0!20 = n1)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1846, 191, 14])).
% 3.48/3.63 tff(1848,plain,
% 3.48/3.63 (Y0!20 = n0),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1348, 1847, 1335, 1398, 1460, 1522, 1584, 1646, 1708, 1770, 1835])).
% 3.48/3.63 tff(1849,plain,
% 3.48/3.63 (succ(Y0!20) = succ(n0)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1848])).
% 3.48/3.63 tff(1850,plain,
% 3.48/3.63 (succ(Y0!20) = n1),
% 3.48/3.63 inference(transitivity,[status(thm)],[1849, 137])).
% 3.48/3.63 tff(1851,plain,
% 3.48/3.63 (pred(Y0!20) = pred(n0)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1848])).
% 3.48/3.63 tff(1852,plain,
% 3.48/3.63 (pred(Y0!20) = n10),
% 3.48/3.63 inference(transitivity,[status(thm)],[1851, 141])).
% 3.48/3.63 tff(1853,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(Y0!20)) = sum(n10, n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1852, 1850])).
% 3.48/3.63 tff(1854,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(Y0!20)) = n0),
% 3.48/3.63 inference(transitivity,[status(thm)],[1853, 136])).
% 3.48/3.63 tff(1855,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n5, n0)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[321, 1854])).
% 3.48/3.63 tff(1856,plain,
% 3.48/3.63 (sum(n5, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1855])).
% 3.48/3.63 tff(1857,plain,
% 3.48/3.63 (n5 = sum(n5, n0)),
% 3.48/3.63 inference(symmetry,[status(thm)],[500])).
% 3.48/3.63 tff(1858,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1852, 193])).
% 3.48/3.63 tff(1859,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n8),
% 3.48/3.63 inference(transitivity,[status(thm)],[1858, 1128])).
% 3.48/3.63 tff(1860,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n7, n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[203, 1850])).
% 3.48/3.63 tff(1861,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n8),
% 3.48/3.63 inference(transitivity,[status(thm)],[1860, 486])).
% 3.48/3.63 tff(1862,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n8, n8)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1861, 1859])).
% 3.48/3.63 tff(1863,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1862, 76, 1857, 1856, 11])).
% 3.48/3.63 tff(1864,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1863])).
% 3.48/3.63 tff(1865,plain,((~(X0!21 = n8)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1866,plain,
% 3.48/3.63 (~(X0!21 = n8)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1865, 14])).
% 3.48/3.63 tff(1867,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n0)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[36, 145])).
% 3.48/3.63 tff(1868,plain,
% 3.48/3.63 (sum(n1, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1867])).
% 3.48/3.63 tff(1869,plain,
% 3.48/3.63 (n1 = sum(n1, n0)),
% 3.48/3.63 inference(symmetry,[status(thm)],[1197])).
% 3.48/3.63 tff(1870,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[143, 31])).
% 3.48/3.63 tff(1871,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n6),
% 3.48/3.63 inference(transitivity,[status(thm)],[1870, 1102])).
% 3.48/3.63 tff(1872,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[34, 140])).
% 3.48/3.63 tff(1873,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n6),
% 3.48/3.63 inference(transitivity,[status(thm)],[1872, 472])).
% 3.48/3.63 tff(1874,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n6, n6)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1873, 1871])).
% 3.48/3.63 tff(1875,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1874, 215, 1869, 1868, 11])).
% 3.48/3.63 tff(1876,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1875])).
% 3.48/3.63 tff(1877,plain,((~(X0!21 = n6)) | (X1!19 = Y1!18) | (~(Y0!20 = n0))), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1878,plain,
% 3.48/3.63 (~(X0!21 = n6)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1877, 138, 14])).
% 3.48/3.63 tff(1879,plain,
% 3.48/3.63 (X0!21 = n9),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1316, 1878, 1367, 1429, 1491, 1553, 1615, 1677, 1739, 1801, 1866])).
% 3.48/3.63 tff(1880,plain,
% 3.48/3.63 (succ(X0!21) = succ(n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1879])).
% 3.48/3.63 tff(1881,plain,
% 3.48/3.63 (succ(X0!21) = n10),
% 3.48/3.63 inference(transitivity,[status(thm)],[1880, 16])).
% 3.48/3.63 tff(1882,plain,
% 3.48/3.63 (pred(X0!21) = pred(n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1879])).
% 3.48/3.63 tff(1883,plain,
% 3.48/3.63 (pred(X0!21) = n8),
% 3.48/3.63 inference(transitivity,[status(thm)],[1882, 20])).
% 3.48/3.63 tff(1884,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = sum(n8, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1883, 1881])).
% 3.48/3.63 tff(1885,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1884, 15])).
% 3.48/3.63 tff(1886,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n0)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1885, 145])).
% 3.48/3.63 tff(1887,plain,
% 3.48/3.63 (sum(n7, n0) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1886])).
% 3.48/3.63 tff(1888,plain,
% 3.48/3.63 (n7 = sum(n7, n0)),
% 3.48/3.63 inference(symmetry,[status(thm)],[232])).
% 3.48/3.63 tff(1889,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n10, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[143, 1881])).
% 3.48/3.63 tff(1890,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1889, 158])).
% 3.48/3.63 tff(1891,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1883, 140])).
% 3.48/3.63 tff(1892,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1891, 1139])).
% 3.48/3.63 tff(1893,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n9, n9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1892, 1890])).
% 3.48/3.63 tff(1894,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1893, 235, 1888, 1887, 11])).
% 3.48/3.63 tff(1895,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1894])).
% 3.48/3.63 tff(1896,plain,((~(Y0!20 = n0)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1897,plain,
% 3.48/3.63 (~(Y0!20 = n0)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1896, 14])).
% 3.48/3.63 tff(1898,plain,
% 3.48/3.63 (Y0!20 = n1),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1348, 1897, 1335, 1398, 1460, 1522, 1584, 1646, 1708, 1770, 1835])).
% 3.48/3.63 tff(1899,plain,
% 3.48/3.63 (succ(Y0!20) = succ(n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1898])).
% 3.48/3.63 tff(1900,plain,
% 3.48/3.63 (succ(Y0!20) = n2),
% 3.48/3.63 inference(transitivity,[status(thm)],[1899, 13])).
% 3.48/3.63 tff(1901,plain,
% 3.48/3.63 (pred(Y0!20) = pred(n1)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1898])).
% 3.48/3.63 tff(1902,plain,
% 3.48/3.63 (pred(Y0!20) = n0),
% 3.48/3.63 inference(transitivity,[status(thm)],[1901, 58])).
% 3.48/3.63 tff(1903,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(Y0!20)) = sum(n0, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1902, 1900])).
% 3.48/3.63 tff(1904,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(Y0!20)) = n2),
% 3.48/3.63 inference(transitivity,[status(thm)],[1903, 12])).
% 3.48/3.63 tff(1905,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n7, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[104, 1904])).
% 3.48/3.63 tff(1906,plain,
% 3.48/3.63 (sum(n7, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1905])).
% 3.48/3.63 tff(1907,plain,
% 3.48/3.63 (n9 = sum(n7, n2)),
% 3.48/3.63 inference(symmetry,[status(thm)],[904])).
% 3.48/3.63 tff(1908,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1902, 100])).
% 3.48/3.63 tff(1909,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n10),
% 3.48/3.63 inference(transitivity,[status(thm)],[1908, 921])).
% 3.48/3.63 tff(1910,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n8, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[102, 1900])).
% 3.48/3.63 tff(1911,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n10),
% 3.48/3.63 inference(transitivity,[status(thm)],[1910, 407])).
% 3.48/3.63 tff(1912,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n10, n10)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1911, 1909])).
% 3.48/3.63 tff(1913,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1912, 158, 1907, 1906, 11])).
% 3.48/3.63 tff(1914,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1913])).
% 3.48/3.63 tff(1915,plain,((~(X0!21 = n9)) | (X1!19 = Y1!18)), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1916,plain,
% 3.48/3.63 (~(X0!21 = n9)),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1915, 14])).
% 3.48/3.63 tff(1917,plain,
% 3.48/3.63 (X0!21 = n6),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[1316, 1916, 1367, 1429, 1491, 1553, 1615, 1677, 1739, 1801, 1866])).
% 3.48/3.63 tff(1918,plain,
% 3.48/3.63 (succ(X0!21) = succ(n6)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1917])).
% 3.48/3.63 tff(1919,plain,
% 3.48/3.63 (succ(X0!21) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1918, 28])).
% 3.48/3.63 tff(1920,plain,
% 3.48/3.63 (pred(X0!21) = pred(n6)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1917])).
% 3.48/3.63 tff(1921,plain,
% 3.48/3.63 (pred(X0!21) = n5),
% 3.48/3.63 inference(transitivity,[status(thm)],[1920, 32])).
% 3.48/3.63 tff(1922,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = sum(n5, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1921, 1919])).
% 3.48/3.63 tff(1923,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(X0!21)) = n1),
% 3.48/3.63 inference(transitivity,[status(thm)],[1922, 27])).
% 3.48/3.63 tff(1924,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20))) = sum(n1, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1923, 1904])).
% 3.48/3.63 tff(1925,plain,
% 3.48/3.63 (sum(n1, n2) = sum(sum(pred(X0!21), succ(X0!21)), sum(pred(Y0!20), succ(Y0!20)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1924])).
% 3.48/3.63 tff(1926,plain,
% 3.48/3.63 (n3 = sum(n1, n2)),
% 3.48/3.63 inference(symmetry,[status(thm)],[747])).
% 3.48/3.63 tff(1927,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = sum(n0, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1902, 1919])).
% 3.48/3.63 tff(1928,plain,
% 3.48/3.63 (sum(pred(Y0!20), succ(X0!21)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1927, 880])).
% 3.48/3.63 tff(1929,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = sum(n5, n2)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1921, 1900])).
% 3.48/3.63 tff(1930,plain,
% 3.48/3.63 (sum(pred(X0!21), succ(Y0!20)) = n7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1929, 877])).
% 3.48/3.63 tff(1931,plain,
% 3.48/3.63 (sum(sum(pred(X0!21), succ(Y0!20)), sum(pred(Y0!20), succ(X0!21))) = sum(n7, n7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1930, 1928])).
% 3.48/3.63 tff(1932,plain,
% 3.48/3.63 (X1!19 = Y1!18),
% 3.48/3.63 inference(transitivity,[status(thm)],[49, 1931, 231, 1926, 1925, 11])).
% 3.48/3.63 tff(1933,plain,
% 3.48/3.63 ($false),
% 3.48/3.63 inference(unit_resolution,[status(thm)],[14, 1932])).
% 3.48/3.63 tff(1934,plain,(X1!19 = Y1!18), inference(lemma,lemma(discharge,[]))).
% 3.48/3.63 tff(1935,plain,
% 3.48/3.63 (Y2!16 = sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1936,plain,
% 3.48/3.63 (sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18))) = Y2!16),
% 3.48/3.63 inference(symmetry,[status(thm)],[1935])).
% 3.48/3.63 tff(1937,plain,
% 3.48/3.63 (succ(X1!19) = succ(Y1!18)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1934])).
% 3.48/3.63 tff(1938,plain,
% 3.48/3.63 (sum(pred(Y1!18), succ(X1!19)) = sum(pred(Y1!18), succ(Y1!18))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1937])).
% 3.48/3.63 tff(1939,plain,
% 3.48/3.63 (sum(pred(Y1!18), succ(Y1!18)) = sum(pred(Y1!18), succ(X1!19))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1938])).
% 3.48/3.63 tff(1940,plain,
% 3.48/3.63 (pred(X1!19) = pred(Y1!18)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1934])).
% 3.48/3.63 tff(1941,plain,
% 3.48/3.63 (sum(pred(X1!19), succ(Y1!18)) = sum(pred(Y1!18), succ(Y1!18))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1940])).
% 3.48/3.63 tff(1942,plain,
% 3.48/3.63 (sum(pred(Y1!18), succ(Y1!18)) = sum(pred(X1!19), succ(Y1!18))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1941])).
% 3.48/3.63 tff(1943,plain,
% 3.48/3.63 (sum(pred(X1!19), succ(X1!19)) = sum(pred(Y1!18), succ(X1!19))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1940])).
% 3.48/3.63 tff(1944,plain,
% 3.48/3.63 (sum(pred(X1!19), succ(X1!19)) = sum(pred(X1!19), succ(Y1!18))),
% 3.48/3.63 inference(transitivity,[status(thm)],[1943, 1938, 1942])).
% 3.48/3.63 tff(1945,plain,
% 3.48/3.63 (sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18))) = sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19)))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1944, 1939])).
% 3.48/3.63 tff(1946,plain,
% 3.48/3.63 (sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19))) = sum(sum(pred(X1!19), succ(X1!19)), sum(pred(Y1!18), succ(Y1!18)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1945])).
% 3.48/3.63 tff(1947,plain,
% 3.48/3.63 (X2!17 = sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1948,plain,
% 3.48/3.63 (X2!17 = Y2!16),
% 3.48/3.63 inference(transitivity,[status(thm)],[1947, 1946, 1936])).
% 3.48/3.63 tff(1949,plain,
% 3.48/3.63 (Y3!14 = sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1950,plain,
% 3.48/3.63 (sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16))) = Y3!14),
% 3.48/3.63 inference(symmetry,[status(thm)],[1949])).
% 3.48/3.63 tff(1951,plain,
% 3.48/3.63 (sum(sum(pred(X1!19), succ(Y1!18)), sum(pred(Y1!18), succ(X1!19))) = X2!17),
% 3.48/3.63 inference(symmetry,[status(thm)],[1947])).
% 3.48/3.63 tff(1952,plain,
% 3.48/3.63 (Y2!16 = X2!17),
% 3.48/3.63 inference(transitivity,[status(thm)],[1935, 1945, 1951])).
% 3.48/3.63 tff(1953,plain,
% 3.48/3.63 (succ(Y2!16) = succ(X2!17)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1952])).
% 3.48/3.63 tff(1954,plain,
% 3.48/3.63 (sum(pred(Y2!16), succ(Y2!16)) = sum(pred(Y2!16), succ(X2!17))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1953])).
% 3.48/3.63 tff(1955,plain,
% 3.48/3.63 (sum(pred(X2!17), succ(Y2!16)) = sum(pred(X2!17), succ(X2!17))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1953])).
% 3.48/3.63 tff(1956,plain,
% 3.48/3.63 (sum(pred(X2!17), succ(X2!17)) = sum(pred(X2!17), succ(Y2!16))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1955])).
% 3.48/3.63 tff(1957,plain,
% 3.48/3.63 (sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16))) = sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17)))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1956, 1954])).
% 3.48/3.63 tff(1958,plain,
% 3.48/3.63 (sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17))) = sum(sum(pred(X2!17), succ(X2!17)), sum(pred(Y2!16), succ(Y2!16)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1957])).
% 3.48/3.63 tff(1959,plain,
% 3.48/3.63 (X3!15 = sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1960,plain,
% 3.48/3.63 (X3!15 = Y3!14),
% 3.48/3.63 inference(transitivity,[status(thm)],[1959, 1958, 1950])).
% 3.48/3.63 tff(1961,plain,
% 3.48/3.63 (Y4!12 = sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1962,plain,
% 3.48/3.63 (sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14))) = Y4!12),
% 3.48/3.63 inference(symmetry,[status(thm)],[1961])).
% 3.48/3.63 tff(1963,plain,
% 3.48/3.63 (sum(sum(pred(X2!17), succ(Y2!16)), sum(pred(Y2!16), succ(X2!17))) = X3!15),
% 3.48/3.63 inference(symmetry,[status(thm)],[1959])).
% 3.48/3.63 tff(1964,plain,
% 3.48/3.63 (Y3!14 = X3!15),
% 3.48/3.63 inference(transitivity,[status(thm)],[1949, 1957, 1963])).
% 3.48/3.63 tff(1965,plain,
% 3.48/3.63 (succ(Y3!14) = succ(X3!15)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1964])).
% 3.48/3.63 tff(1966,plain,
% 3.48/3.63 (sum(pred(Y3!14), succ(Y3!14)) = sum(pred(Y3!14), succ(X3!15))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1965])).
% 3.48/3.63 tff(1967,plain,
% 3.48/3.63 (sum(pred(X3!15), succ(Y3!14)) = sum(pred(X3!15), succ(X3!15))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1965])).
% 3.48/3.63 tff(1968,plain,
% 3.48/3.63 (sum(pred(X3!15), succ(X3!15)) = sum(pred(X3!15), succ(Y3!14))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1967])).
% 3.48/3.63 tff(1969,plain,
% 3.48/3.63 (sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14))) = sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15)))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1968, 1966])).
% 3.48/3.63 tff(1970,plain,
% 3.48/3.63 (sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15))) = sum(sum(pred(X3!15), succ(X3!15)), sum(pred(Y3!14), succ(Y3!14)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1969])).
% 3.48/3.63 tff(1971,plain,
% 3.48/3.63 (X4!13 = sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1972,plain,
% 3.48/3.63 (X4!13 = Y4!12),
% 3.48/3.63 inference(transitivity,[status(thm)],[1971, 1970, 1962])).
% 3.48/3.63 tff(1973,plain,
% 3.48/3.63 (Y5!10 = sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1974,plain,
% 3.48/3.63 (sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12))) = Y5!10),
% 3.48/3.63 inference(symmetry,[status(thm)],[1973])).
% 3.48/3.63 tff(1975,plain,
% 3.48/3.63 (sum(sum(pred(X3!15), succ(Y3!14)), sum(pred(Y3!14), succ(X3!15))) = X4!13),
% 3.48/3.63 inference(symmetry,[status(thm)],[1971])).
% 3.48/3.63 tff(1976,plain,
% 3.48/3.63 (Y4!12 = X4!13),
% 3.48/3.63 inference(transitivity,[status(thm)],[1961, 1969, 1975])).
% 3.48/3.63 tff(1977,plain,
% 3.48/3.63 (succ(Y4!12) = succ(X4!13)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1976])).
% 3.48/3.63 tff(1978,plain,
% 3.48/3.63 (sum(pred(Y4!12), succ(Y4!12)) = sum(pred(Y4!12), succ(X4!13))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1977])).
% 3.48/3.63 tff(1979,plain,
% 3.48/3.63 (sum(pred(X4!13), succ(Y4!12)) = sum(pred(X4!13), succ(X4!13))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1977])).
% 3.48/3.63 tff(1980,plain,
% 3.48/3.63 (sum(pred(X4!13), succ(X4!13)) = sum(pred(X4!13), succ(Y4!12))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1979])).
% 3.48/3.63 tff(1981,plain,
% 3.48/3.63 (sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12))) = sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13)))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1980, 1978])).
% 3.48/3.63 tff(1982,plain,
% 3.48/3.63 (sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13))) = sum(sum(pred(X4!13), succ(X4!13)), sum(pred(Y4!12), succ(Y4!12)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1981])).
% 3.48/3.63 tff(1983,plain,
% 3.48/3.63 (X5!11 = sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1984,plain,
% 3.48/3.63 (X5!11 = Y5!10),
% 3.48/3.63 inference(transitivity,[status(thm)],[1983, 1982, 1974])).
% 3.48/3.63 tff(1985,plain,
% 3.48/3.63 (Y6!8 = sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1986,plain,
% 3.48/3.63 (sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10))) = Y6!8),
% 3.48/3.63 inference(symmetry,[status(thm)],[1985])).
% 3.48/3.63 tff(1987,plain,
% 3.48/3.63 (sum(sum(pred(X4!13), succ(Y4!12)), sum(pred(Y4!12), succ(X4!13))) = X5!11),
% 3.48/3.63 inference(symmetry,[status(thm)],[1983])).
% 3.48/3.63 tff(1988,plain,
% 3.48/3.63 (Y5!10 = X5!11),
% 3.48/3.63 inference(transitivity,[status(thm)],[1973, 1981, 1987])).
% 3.48/3.63 tff(1989,plain,
% 3.48/3.63 (succ(Y5!10) = succ(X5!11)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1988])).
% 3.48/3.63 tff(1990,plain,
% 3.48/3.63 (sum(pred(Y5!10), succ(Y5!10)) = sum(pred(Y5!10), succ(X5!11))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1989])).
% 3.48/3.63 tff(1991,plain,
% 3.48/3.63 (sum(pred(X5!11), succ(Y5!10)) = sum(pred(X5!11), succ(X5!11))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1989])).
% 3.48/3.63 tff(1992,plain,
% 3.48/3.63 (sum(pred(X5!11), succ(X5!11)) = sum(pred(X5!11), succ(Y5!10))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1991])).
% 3.48/3.63 tff(1993,plain,
% 3.48/3.63 (sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10))) = sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11)))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[1992, 1990])).
% 3.48/3.63 tff(1994,plain,
% 3.48/3.63 (sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11))) = sum(sum(pred(X5!11), succ(X5!11)), sum(pred(Y5!10), succ(Y5!10)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[1993])).
% 3.48/3.63 tff(1995,plain,
% 3.48/3.63 (X6!9 = sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1996,plain,
% 3.48/3.63 (X6!9 = Y6!8),
% 3.48/3.63 inference(transitivity,[status(thm)],[1995, 1994, 1986])).
% 3.48/3.63 tff(1997,plain,
% 3.48/3.63 (Y7!6 = sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(1998,plain,
% 3.48/3.63 (sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8))) = Y7!6),
% 3.48/3.63 inference(symmetry,[status(thm)],[1997])).
% 3.48/3.63 tff(1999,plain,
% 3.48/3.63 (sum(sum(pred(X5!11), succ(Y5!10)), sum(pred(Y5!10), succ(X5!11))) = X6!9),
% 3.48/3.63 inference(symmetry,[status(thm)],[1995])).
% 3.48/3.63 tff(2000,plain,
% 3.48/3.63 (Y6!8 = X6!9),
% 3.48/3.63 inference(transitivity,[status(thm)],[1985, 1993, 1999])).
% 3.48/3.63 tff(2001,plain,
% 3.48/3.63 (succ(Y6!8) = succ(X6!9)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2000])).
% 3.48/3.63 tff(2002,plain,
% 3.48/3.63 (sum(pred(Y6!8), succ(Y6!8)) = sum(pred(Y6!8), succ(X6!9))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2001])).
% 3.48/3.63 tff(2003,plain,
% 3.48/3.63 (sum(pred(X6!9), succ(Y6!8)) = sum(pred(X6!9), succ(X6!9))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2001])).
% 3.48/3.63 tff(2004,plain,
% 3.48/3.63 (sum(pred(X6!9), succ(X6!9)) = sum(pred(X6!9), succ(Y6!8))),
% 3.48/3.63 inference(symmetry,[status(thm)],[2003])).
% 3.48/3.63 tff(2005,plain,
% 3.48/3.63 (sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8))) = sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9)))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2004, 2002])).
% 3.48/3.63 tff(2006,plain,
% 3.48/3.63 (sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9))) = sum(sum(pred(X6!9), succ(X6!9)), sum(pred(Y6!8), succ(Y6!8)))),
% 3.48/3.63 inference(symmetry,[status(thm)],[2005])).
% 3.48/3.63 tff(2007,plain,
% 3.48/3.63 (X7!7 = sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(2008,plain,
% 3.48/3.63 (X7!7 = Y7!6),
% 3.48/3.63 inference(transitivity,[status(thm)],[2007, 2006, 1998])).
% 3.48/3.63 tff(2009,plain,
% 3.48/3.63 (Y8!4 = sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6)))),
% 3.48/3.63 inference(and_elim,[status(thm)],[9])).
% 3.48/3.63 tff(2010,plain,
% 3.48/3.63 (sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6))) = Y8!4),
% 3.48/3.63 inference(symmetry,[status(thm)],[2009])).
% 3.48/3.63 tff(2011,plain,
% 3.48/3.63 (sum(sum(pred(X6!9), succ(Y6!8)), sum(pred(Y6!8), succ(X6!9))) = X7!7),
% 3.48/3.63 inference(symmetry,[status(thm)],[2007])).
% 3.48/3.63 tff(2012,plain,
% 3.48/3.63 (Y7!6 = X7!7),
% 3.48/3.63 inference(transitivity,[status(thm)],[1997, 2005, 2011])).
% 3.48/3.63 tff(2013,plain,
% 3.48/3.63 (succ(Y7!6) = succ(X7!7)),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2012])).
% 3.48/3.63 tff(2014,plain,
% 3.48/3.63 (sum(pred(Y7!6), succ(Y7!6)) = sum(pred(Y7!6), succ(X7!7))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2013])).
% 3.48/3.63 tff(2015,plain,
% 3.48/3.63 (sum(pred(X7!7), succ(Y7!6)) = sum(pred(X7!7), succ(X7!7))),
% 3.48/3.63 inference(monotonicity,[status(thm)],[2013])).
% 3.48/3.63 tff(2016,plain,
% 3.48/3.63 (sum(pred(X7!7), succ(X7!7)) = sum(pred(X7!7), succ(Y7!6))),
% 3.48/3.63 inference(symmetry,[status(thm)],[2015])).
% 3.48/3.63 tff(2017,plain,
% 3.48/3.63 (sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6))) = sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7)))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2016, 2014])).
% 3.48/3.64 tff(2018,plain,
% 3.48/3.64 (sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7))) = sum(sum(pred(X7!7), succ(X7!7)), sum(pred(Y7!6), succ(Y7!6)))),
% 3.48/3.64 inference(symmetry,[status(thm)],[2017])).
% 3.48/3.64 tff(2019,plain,
% 3.48/3.64 (X8!5 = sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7)))),
% 3.48/3.64 inference(and_elim,[status(thm)],[9])).
% 3.48/3.64 tff(2020,plain,
% 3.48/3.64 (X8!5 = Y8!4),
% 3.48/3.64 inference(transitivity,[status(thm)],[2019, 2018, 2010])).
% 3.48/3.64 tff(2021,plain,
% 3.48/3.64 (Y9!2 = sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4)))),
% 3.48/3.64 inference(and_elim,[status(thm)],[9])).
% 3.48/3.64 tff(2022,plain,
% 3.48/3.64 (sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4))) = Y9!2),
% 3.48/3.64 inference(symmetry,[status(thm)],[2021])).
% 3.48/3.64 tff(2023,plain,
% 3.48/3.64 (sum(sum(pred(X7!7), succ(Y7!6)), sum(pred(Y7!6), succ(X7!7))) = X8!5),
% 3.48/3.64 inference(symmetry,[status(thm)],[2019])).
% 3.48/3.64 tff(2024,plain,
% 3.48/3.64 (Y8!4 = X8!5),
% 3.48/3.64 inference(transitivity,[status(thm)],[2009, 2017, 2023])).
% 3.48/3.64 tff(2025,plain,
% 3.48/3.64 (succ(Y8!4) = succ(X8!5)),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2024])).
% 3.48/3.64 tff(2026,plain,
% 3.48/3.64 (sum(pred(Y8!4), succ(Y8!4)) = sum(pred(Y8!4), succ(X8!5))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2025])).
% 3.48/3.64 tff(2027,plain,
% 3.48/3.64 (sum(pred(X8!5), succ(Y8!4)) = sum(pred(X8!5), succ(X8!5))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2025])).
% 3.48/3.64 tff(2028,plain,
% 3.48/3.64 (sum(pred(X8!5), succ(X8!5)) = sum(pred(X8!5), succ(Y8!4))),
% 3.48/3.64 inference(symmetry,[status(thm)],[2027])).
% 3.48/3.64 tff(2029,plain,
% 3.48/3.64 (sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4))) = sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5)))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2028, 2026])).
% 3.48/3.64 tff(2030,plain,
% 3.48/3.64 (sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5))) = sum(sum(pred(X8!5), succ(X8!5)), sum(pred(Y8!4), succ(Y8!4)))),
% 3.48/3.64 inference(symmetry,[status(thm)],[2029])).
% 3.48/3.64 tff(2031,plain,
% 3.48/3.64 (X9!3 = sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5)))),
% 3.48/3.64 inference(and_elim,[status(thm)],[9])).
% 3.48/3.64 tff(2032,plain,
% 3.48/3.64 (X9!3 = Y9!2),
% 3.48/3.64 inference(transitivity,[status(thm)],[2031, 2030, 2022])).
% 3.48/3.64 tff(2033,plain,
% 3.48/3.64 (Y10!0 = sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2)))),
% 3.48/3.64 inference(and_elim,[status(thm)],[9])).
% 3.48/3.64 tff(2034,plain,
% 3.48/3.64 (sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2))) = Y10!0),
% 3.48/3.64 inference(symmetry,[status(thm)],[2033])).
% 3.48/3.64 tff(2035,plain,
% 3.48/3.64 (sum(sum(pred(X8!5), succ(Y8!4)), sum(pred(Y8!4), succ(X8!5))) = X9!3),
% 3.48/3.64 inference(symmetry,[status(thm)],[2031])).
% 3.48/3.64 tff(2036,plain,
% 3.48/3.64 (Y9!2 = X9!3),
% 3.48/3.64 inference(transitivity,[status(thm)],[2021, 2029, 2035])).
% 3.48/3.64 tff(2037,plain,
% 3.48/3.64 (succ(Y9!2) = succ(X9!3)),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2036])).
% 3.48/3.64 tff(2038,plain,
% 3.48/3.64 (sum(pred(Y9!2), succ(Y9!2)) = sum(pred(Y9!2), succ(X9!3))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2037])).
% 3.48/3.64 tff(2039,plain,
% 3.48/3.64 (sum(pred(X9!3), succ(Y9!2)) = sum(pred(X9!3), succ(X9!3))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2037])).
% 3.48/3.64 tff(2040,plain,
% 3.48/3.64 (sum(pred(X9!3), succ(X9!3)) = sum(pred(X9!3), succ(Y9!2))),
% 3.48/3.64 inference(symmetry,[status(thm)],[2039])).
% 3.48/3.64 tff(2041,plain,
% 3.48/3.64 (sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2))) = sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3)))),
% 3.48/3.64 inference(monotonicity,[status(thm)],[2040, 2038])).
% 3.48/3.64 tff(2042,plain,
% 3.48/3.64 (sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3))) = sum(sum(pred(X9!3), succ(X9!3)), sum(pred(Y9!2), succ(Y9!2)))),
% 3.48/3.64 inference(symmetry,[status(thm)],[2041])).
% 3.48/3.64 tff(2043,plain,
% 3.48/3.64 (X10!1 = sum(sum(pred(X9!3), succ(Y9!2)), sum(pred(Y9!2), succ(X9!3)))),
% 3.48/3.64 inference(and_elim,[status(thm)],[9])).
% 3.48/3.64 tff(2044,plain,
% 3.48/3.64 (X10!1 = Y10!0),
% 3.48/3.64 inference(transitivity,[status(thm)],[2043, 2042, 2034])).
% 3.48/3.64 tff(2045,plain,
% 3.48/3.64 ((~(X10!1 = Y10!0)) | (~(X9!3 = Y9!2)) | (~(X8!5 = Y8!4)) | (~(X7!7 = Y7!6)) | (~(X6!9 = Y6!8)) | (~(X5!11 = Y5!10)) | (~(X4!13 = Y4!12)) | (~(X3!15 = Y3!14)) | (~(X2!17 = Y2!16)) | (~(X1!19 = Y1!18))),
% 3.48/3.64 inference(and_elim,[status(thm)],[9])).
% 3.48/3.64 tff(2046,plain,
% 3.48/3.64 ($false),
% 3.48/3.64 inference(unit_resolution,[status(thm)],[2045, 2044, 2032, 2020, 2008, 1996, 1984, 1972, 1960, 1948, 1934])).
% 3.48/3.64 % SZS output end Proof
%------------------------------------------------------------------------------