TPTP Problem File: SWC519_1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWC519_1 : TPTP v9.0.0. Released v9.0.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 1 501 Group s164 Tag s163
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0012-00023-1-501.tptp [Deh24]
% Status : Theorem
% Rating : 0.00 v9.0.0
% Syntax : Number of formulae : 486 ( 141 unt; 208 typ; 0 def)
% Number of atoms : 899 ( 145 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 655 ( 32 ~; 20 |; 320 &)
% ( 83 <=>; 200 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 12 ( 0 fml; 12 var)
% Number arithmetic : 1046 ( 290 atm; 82 fun; 201 num; 473 var)
% Number of types : 11 ( 8 usr; 2 ari)
% Number of type conns : 42 ( 21 >; 21 *; 0 +; 0 <<)
% Number of predicates : 15 ( 8 usr; 2 prp; 0-4 aty)
% Number of functors : 207 ( 192 usr; 189 con; 0-2 aty)
% Number of variables : 518 ( 428 !; 90 ?; 518 :)
% SPC : TX0_THM_EQU_ARI
% Comments : Autogenerated by PPTRANS-TPTP - github.com/CLEARSY/pptranspog
%------------------------------------------------------------------------------
tff(set_0_type,type,
set_0: $tType ).
tff(mem0_type,type,
mem0: ( $int * set_0 ) > $o ).
tff(set_1_type,type,
set_1: $tType ).
tff(mem1_type,type,
mem1: ( $real * set_1 ) > $o ).
tff(b_division_type,type,
divB: ( $int * $int ) > $int ).
tff(b_division_def_1,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(0,Y) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_2,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(0,Y) )
=> ( divB(X,Y) = $uminus($quotient_f($uminus(X),Y)) ) ) ).
tff(b_division_def_3,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_4,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f($uminus(X),$uminus(Y)) ) ) ).
tff(exp_type,type,
exp: ( $int * $int ) > $int ).
tff(exp_def_1,axiom,
! [X: $int] : ( exp(X,0) = 1 ) ).
tff(exp_def_2,axiom,
! [X: $int,Y: $int] :
( $greatereq(Y,1)
=> ( exp(X,Y) = $sum(X,exp(X,$difference(Y,1))) ) ) ).
tff(rexp_type,type,
rexp: ( $real * $int ) > $real ).
tff(rexp_def_1,axiom,
! [X: $real] :
( ( X != 0.0 )
=> ( rexp(X,0) = 1.0 ) ) ).
tff(rexp_def_2,axiom,
! [X: $real,Y: $int] :
( $greatereq(Y,1)
=> ( rexp(X,Y) = $sum(X,rexp(X,$difference(Y,1))) ) ) ).
tff(isum_type,type,
isum: set_0 > $int ).
tff(isum_def_1,axiom,
! [S: set_0] :
( ! [X: $int] : ~ mem0(X,S)
=> ( isum(S) = 0 ) ) ).
tff(isum_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( isum(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( mem0(X,S1)
=> mem0(X,S2) ) )
=> ( isum(S2) = $sum(N,E) ) ) ).
tff(rsum_type,type,
rsum: set_1 > $real ).
tff(rsum_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rsum(S) = 0.0 ) ) ).
tff(rsum_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rsum(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( mem1(X,S1)
=> mem1(X,S2) ) )
=> ( rsum(S2) = $sum(N,E) ) ) ).
tff(iprod_type,type,
iprod: set_0 > $int ).
tff(iprod_def_1,axiom,
! [S: set_0,X: $int] :
( ~ mem0(X,S)
=> ( iprod(S) = 1 ) ) ).
tff(iprod_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( iprod(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( ( ( X = E )
| mem0(X,S1) )
=> mem0(X,S2) ) )
=> ( isum(S2) = $product(N,E) ) ) ).
tff(rprod_type,type,
rprod: set_1 > $real ).
tff(rprod_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rprod(S) = 1.0 ) ) ).
tff(rprod_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rprod(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( ( ( X = E )
| mem1(X,S1) )
=> mem1(X,S2) ) )
=> ( rprod(S2) = $sum(N,E) ) ) ).
tff(min_int_type,type,
min_int: $int ).
tff(max_int_type,type,
max_int: $int ).
tff(min_int_axiom,axiom,
min_int = $uminus(2147483648) ).
tff(max_int_axiom,axiom,
max_int = 2147483647 ).
%--------------------------------------------------------------------------
%----Global declarations
tff(g_s0_0_type,type,
g_s0_0: set_0 ).
tff(g_s100_100_type,type,
g_s100_100: $int ).
tff(g_s101_101_type,type,
g_s101_101: $int ).
tff(g_s102_102_type,type,
g_s102_102: $int ).
tff(g_s103_103_type,type,
g_s103_103: $int ).
tff(g_s104_104_type,type,
g_s104_104: $int ).
tff(g_s105_105_type,type,
g_s105_105: $int ).
tff(g_s106_106_type,type,
g_s106_106: $int ).
tff(g_s107_107_type,type,
g_s107_107: $int ).
tff(g_s108_108_type,type,
g_s108_108: $int ).
tff(g_s109_109_type,type,
g_s109_109: $int ).
tff(g_s10_10_type,type,
g_s10_10: $int ).
tff(g_s110_110_type,type,
g_s110_110: $int ).
tff(g_s111_111_type,type,
g_s111_111: $int ).
tff(g_s112_112_type,type,
g_s112_112: $int ).
tff(g_s113_113_type,type,
g_s113_113: $int ).
tff(g_s114_114_type,type,
g_s114_114: $int ).
tff(g_s115_115_type,type,
g_s115_115: $int ).
tff(g_s116_116_type,type,
g_s116_116: $int ).
tff(g_s117_117_type,type,
g_s117_117: $int ).
tff(g_s118_118_type,type,
g_s118_118: $int ).
tff(g_s119_119_type,type,
g_s119_119: $int ).
tff(g_s11_11_type,type,
g_s11_11: $int ).
tff(g_s120_120_type,type,
g_s120_120: $int ).
tff(g_s121_121_type,type,
g_s121_121: $int ).
tff(g_s122_123_type,type,
g_s122_123: set_0 ).
tff(g_s122_1_143_type,type,
g_s122_1_143: set_0 ).
tff(g_s123_124_type,type,
g_s123_124: set_3 ).
tff(g_s124_125_type,type,
g_s124_125: set_3 ).
tff(g_s125_126_type,type,
g_s125_126: set_3 ).
tff(g_s126_127_type,type,
g_s126_127: set_3 ).
tff(g_s127_128_type,type,
g_s127_128: set_3 ).
tff(g_s128_129_type,type,
g_s128_129: set_3 ).
tff(g_s129_130_type,type,
g_s129_130: set_3 ).
tff(g_s12_12_type,type,
g_s12_12: $int ).
tff(g_s130_131_type,type,
g_s130_131: set_3 ).
tff(g_s131_132_type,type,
g_s131_132: set_3 ).
tff(g_s132_133_type,type,
g_s132_133: set_3 ).
tff(g_s133_134_type,type,
g_s133_134: set_3 ).
tff(g_s134_135_type,type,
g_s134_135: set_4 ).
tff(g_s135_136_type,type,
g_s135_136: set_3 ).
tff(g_s136_137_type,type,
g_s136_137: set_3 ).
tff(g_s136_1_147_type,type,
g_s136_1_147: set_3 ).
tff(g_s137_138_type,type,
g_s137_138: set_0 ).
tff(g_s137_1_145_type,type,
g_s137_1_145: set_0 ).
tff(g_s138_139_type,type,
g_s138_139: set_0 ).
tff(g_s138_1_146_type,type,
g_s138_1_146: set_0 ).
tff(g_s139_140_type,type,
g_s139_140: set_0 ).
tff(g_s139_1_144_type,type,
g_s139_1_144: set_0 ).
tff(g_s13_13_type,type,
g_s13_13: $int ).
tff(g_s140_141_type,type,
g_s140_141: set_0 ).
tff(g_s141_142_type,type,
g_s141_142: set_0 ).
tff(g_s142_122_type,type,
g_s142_122: $int ).
tff(g_s143_1_148_type,type,
g_s143_1_148: set_0 ).
tff(g_s144_1_149_type,type,
g_s144_1_149: set_0 ).
tff(g_s145_1_150_type,type,
g_s145_1_150: set_0 ).
tff(g_s146_1_151_type,type,
g_s146_1_151: set_0 ).
tff(g_s147_1_152_type,type,
g_s147_1_152: set_0 ).
tff(g_s148_1_153_type,type,
g_s148_1_153: set_0 ).
tff(g_s149_1_154_type,type,
g_s149_1_154: set_0 ).
tff(g_s14_14_type,type,
g_s14_14: $int ).
tff(g_s150_1_155_type,type,
g_s150_1_155: set_0 ).
tff(g_s151_1_156_type,type,
g_s151_1_156: set_0 ).
tff(g_s152_1_157_type,type,
g_s152_1_157: set_0 ).
tff(g_s153_1_158_type,type,
g_s153_1_158: set_0 ).
tff(g_s154_1_159_type,type,
g_s154_1_159: set_3 ).
tff(g_s155_1_160_type,type,
g_s155_1_160: set_3 ).
tff(g_s156_1_161_type,type,
g_s156_1_161: set_3 ).
tff(g_s157_1_162_type,type,
g_s157_1_162: set_3 ).
tff(g_s158_1_163_type,type,
g_s158_1_163: set_3 ).
tff(g_s159_1_164_type,type,
g_s159_1_164: set_3 ).
tff(g_s15_15_type,type,
g_s15_15: $int ).
tff(g_s160_1_165_type,type,
g_s160_1_165: set_3 ).
tff(g_s161_1_166_type,type,
g_s161_1_166: set_3 ).
tff(g_s165_167_type,type,
g_s165_167: $int ).
tff(g_s166_168_type,type,
g_s166_168: $int ).
tff(g_s167_169_type,type,
g_s167_169: $int ).
tff(g_s168_170_type,type,
g_s168_170: $int ).
tff(g_s16_16_type,type,
g_s16_16: $int ).
tff(g_s17_17_type,type,
g_s17_17: $int ).
tff(g_s18_18_type,type,
g_s18_18: $int ).
tff(g_s19_20_type,type,
g_s19_20: $int ).
tff(g_s1_1_type,type,
g_s1_1: $int ).
tff(g_s20_19_type,type,
g_s20_19: set_0 ).
tff(g_s21_22_type,type,
g_s21_22: $int ).
tff(g_s22_21_type,type,
g_s22_21: set_0 ).
tff(g_s23_24_type,type,
g_s23_24: $int ).
tff(g_s24_23_type,type,
g_s24_23: set_0 ).
tff(g_s25_25_type,type,
g_s25_25: $int ).
tff(g_s26_26_type,type,
g_s26_26: $int ).
tff(g_s27_27_type,type,
g_s27_27: set_0 ).
tff(g_s28_28_type,type,
g_s28_28: set_2 ).
tff(g_s29_29_type,type,
g_s29_29: $int ).
tff(g_s2_2_type,type,
g_s2_2: $int ).
tff(g_s30_30_type,type,
g_s30_30: $int ).
tff(g_s31_31_type,type,
g_s31_31: $int ).
tff(g_s32_32_type,type,
g_s32_32: $int ).
tff(g_s33_33_type,type,
g_s33_33: $int ).
tff(g_s34_34_type,type,
g_s34_34: $int ).
tff(g_s35_35_type,type,
g_s35_35: $int ).
tff(g_s36_36_type,type,
g_s36_36: $int ).
tff(g_s37_37_type,type,
g_s37_37: $int ).
tff(g_s38_38_type,type,
g_s38_38: $int ).
tff(g_s39_39_type,type,
g_s39_39: $int ).
tff(g_s3_3_type,type,
g_s3_3: set_0 ).
tff(g_s40_40_type,type,
g_s40_40: $int ).
tff(g_s41_41_type,type,
g_s41_41: $int ).
tff(g_s42_42_type,type,
g_s42_42: $int ).
tff(g_s43_43_type,type,
g_s43_43: $int ).
tff(g_s44_44_type,type,
g_s44_44: $int ).
tff(g_s45_45_type,type,
g_s45_45: $int ).
tff(g_s46_46_type,type,
g_s46_46: $int ).
tff(g_s47_47_type,type,
g_s47_47: $int ).
tff(g_s48_48_type,type,
g_s48_48: $int ).
tff(g_s49_49_type,type,
g_s49_49: $int ).
tff(g_s4_4_type,type,
g_s4_4: $int ).
tff(g_s50_50_type,type,
g_s50_50: $int ).
tff(g_s51_51_type,type,
g_s51_51: $int ).
tff(g_s52_52_type,type,
g_s52_52: $int ).
tff(g_s53_53_type,type,
g_s53_53: $int ).
tff(g_s54_54_type,type,
g_s54_54: $int ).
tff(g_s55_55_type,type,
g_s55_55: $int ).
tff(g_s56_56_type,type,
g_s56_56: $int ).
tff(g_s57_57_type,type,
g_s57_57: $int ).
tff(g_s58_58_type,type,
g_s58_58: $int ).
tff(g_s59_59_type,type,
g_s59_59: $int ).
tff(g_s5_5_type,type,
g_s5_5: $int ).
tff(g_s60_60_type,type,
g_s60_60: $int ).
tff(g_s61_61_type,type,
g_s61_61: $int ).
tff(g_s62_62_type,type,
g_s62_62: $int ).
tff(g_s63_63_type,type,
g_s63_63: $int ).
tff(g_s64_64_type,type,
g_s64_64: $int ).
tff(g_s65_65_type,type,
g_s65_65: $int ).
tff(g_s66_66_type,type,
g_s66_66: $int ).
tff(g_s67_67_type,type,
g_s67_67: $int ).
tff(g_s68_68_type,type,
g_s68_68: $int ).
tff(g_s69_69_type,type,
g_s69_69: $int ).
tff(g_s6_6_type,type,
g_s6_6: set_0 ).
tff(g_s70_70_type,type,
g_s70_70: $int ).
tff(g_s71_71_type,type,
g_s71_71: $int ).
tff(g_s72_72_type,type,
g_s72_72: $int ).
tff(g_s73_73_type,type,
g_s73_73: $int ).
tff(g_s74_74_type,type,
g_s74_74: $int ).
tff(g_s75_75_type,type,
g_s75_75: $int ).
tff(g_s76_76_type,type,
g_s76_76: $int ).
tff(g_s77_77_type,type,
g_s77_77: $int ).
tff(g_s78_78_type,type,
g_s78_78: $int ).
tff(g_s79_79_type,type,
g_s79_79: $int ).
tff(g_s7_7_type,type,
g_s7_7: $int ).
tff(g_s80_80_type,type,
g_s80_80: $int ).
tff(g_s81_81_type,type,
g_s81_81: $int ).
tff(g_s82_82_type,type,
g_s82_82: $int ).
tff(g_s83_83_type,type,
g_s83_83: $int ).
tff(g_s84_84_type,type,
g_s84_84: $int ).
tff(g_s85_85_type,type,
g_s85_85: $int ).
tff(g_s86_86_type,type,
g_s86_86: $int ).
tff(g_s87_87_type,type,
g_s87_87: $int ).
tff(g_s88_88_type,type,
g_s88_88: $int ).
tff(g_s89_89_type,type,
g_s89_89: $int ).
tff(g_s8_8_type,type,
g_s8_8: $int ).
tff(g_s90_90_type,type,
g_s90_90: $int ).
tff(g_s91_91_type,type,
g_s91_91: $int ).
tff(g_s92_92_type,type,
g_s92_92: $int ).
tff(g_s93_93_type,type,
g_s93_93: $int ).
tff(g_s94_94_type,type,
g_s94_94: $int ).
tff(g_s95_95_type,type,
g_s95_95: $int ).
tff(g_s96_96_type,type,
g_s96_96: $int ).
tff(g_s97_97_type,type,
g_s97_97: $int ).
tff(g_s98_98_type,type,
g_s98_98: $int ).
tff(g_s99_99_type,type,
g_s99_99: $int ).
tff(g_s9_9_type,type,
g_s9_9: set_0 ).
tff(mem2_type,type,
mem2: ( $o * $int * set_2 ) > $o ).
tff(mem3_type,type,
mem3: ( $int * $int * set_3 ) > $o ).
tff(mem4_type,type,
mem4: ( $int * $int * $int * set_4 ) > $o ).
tff(prod_0_type,type,
prod_0: $tType ).
tff(prod_0_empty,type,
prod_0_empty: prod_0 ).
tff(prod_0_insert,type,
prod_0: ( $o * $int ) > prod_0 ).
tff(prod_0_in,type,
prod_0_in: ( $o * $int * prod_0 ) > $o ).
tff(prod_1_type,type,
prod_1: $tType ).
tff(prod_1_empty,type,
prod_1_empty: prod_1 ).
tff(prod_1_insert,type,
prod_1: ( $int * $int ) > prod_1 ).
tff(prod_1_in,type,
prod_1_in: ( $int * $int * prod_1 ) > $o ).
tff(prod_2_type,type,
prod_2: $tType ).
tff(prod_2_empty,type,
prod_2_empty: prod_2 ).
tff(prod_2_insert,type,
prod_2: ( prod_1 * $int ) > prod_2 ).
tff(prod_2_in,type,
prod_2_in: ( prod_1 * $int * prod_2 ) > $o ).
tff(set_2_type,type,
set_2: $tType ).
tff(set_2_empty,type,
set_2_empty: set_2 ).
tff(set_2_insert,type,
set_2: prod_0 > set_2 ).
tff(set_3_type,type,
set_3: $tType ).
tff(set_3_empty,type,
set_3_empty: set_3 ).
tff(set_3_insert,type,
set_3: prod_1 > set_3 ).
tff(set_4_type,type,
set_4: $tType ).
tff(set_4_empty,type,
set_4_empty: set_4 ).
tff(set_4_insert,type,
set_4: prod_2 > set_4 ).
%----Defines
tff('Define:B definitions:0',axiom,
! [X_3: $int] :
( ( $greatereq(X_3,0)
& $lesseq(X_3,max_int) )
<=> ( $greatereq(X_3,0)
& $lesseq(X_3,max_int) ) ) ).
tff('Define:B definitions:1',axiom,
! [X_4: $int] :
( ( $greatereq(X_4,min_int)
& $lesseq(X_4,max_int) )
<=> ( $greatereq(X_4,min_int)
& $lesseq(X_4,max_int) ) ) ).
tff('Define:abs:0',axiom,
! [X_140: $int] :
( mem0(X_140,g_s122_123)
=> ( $greatereq(X_140,0)
& $lesseq(X_140,g_s51_51) ) ) ).
tff('Define:abs:1',axiom,
? [X_141: set_3] :
( ! [X_142: $int,X_143: $int] :
( mem3(X_143,X_142,X_141)
<=> mem3(X_143,X_142,g_s123_124) )
& ! [X_144: $int,X_145: $int,X_146: $int] :
( ( mem3(X_144,X_145,X_141)
& mem3(X_144,X_146,X_141) )
=> ( X_145 = X_146 ) )
& ! [X_147: $int] :
( ( $greatereq(X_147,0)
& $lesseq(X_147,g_s51_51) )
<=> ? [X_148: $int] : mem3(X_147,X_148,X_141) )
& ! [X_149: $int] :
( ? [X_150: $int] : mem3(X_150,X_149,X_141)
=> $greatereq(X_149,0) ) ) ).
tff('Define:abs:10',axiom,
! [X_215: $int,X_216: $int] :
( mem3(X_216,X_215,g_s132_133)
=> ( $greatereq(X_216,0)
& $lesseq(X_216,g_s51_51)
& $greatereq(X_215,0) ) ) ).
tff('Define:abs:11',axiom,
! [X_217: $int,X_218: $int] :
( mem3(X_218,X_217,g_s133_134)
=> ( $greatereq(X_218,0)
& $lesseq(X_218,g_s51_51)
& $greatereq(X_217,0) ) ) ).
tff('Define:abs:12',axiom,
! [X_219: $int,X_220: $int,X_221: $int] :
( mem4(X_221,X_220,X_219,g_s134_135)
=> ( $greatereq(X_221,0)
& $lesseq(X_221,g_s51_51)
& $greatereq(X_220,0)
& mem0(X_219,g_s3_3) ) ) ).
tff('Define:abs:13',axiom,
? [X_222: set_3] :
( ! [X_223: $int,X_224: $int] :
( mem3(X_224,X_223,X_222)
<=> mem3(X_224,X_223,g_s135_136) )
& ! [X_225: $int,X_226: $int,X_227: $int] :
( ( mem3(X_225,X_226,X_222)
& mem3(X_225,X_227,X_222) )
=> ( X_226 = X_227 ) )
& ! [X_228: $int] :
( ( $greatereq(X_228,0)
& $lesseq(X_228,g_s51_51) )
<=> ? [X_229: $int] : mem3(X_228,X_229,X_222) )
& ! [X_230: $int] :
( ? [X_231: $int] : mem3(X_231,X_230,X_222)
=> $greatereq(X_230,0) ) ) ).
tff('Define:abs:14',axiom,
? [X_232: set_3] :
( ! [X_233: $int,X_234: $int] :
( mem3(X_234,X_233,X_232)
<=> mem3(X_234,X_233,g_s136_137) )
& ! [X_235: $int,X_236: $int,X_237: $int] :
( ( mem3(X_235,X_236,X_232)
& mem3(X_235,X_237,X_232) )
=> ( X_236 = X_237 ) )
& ! [X_238: $int] :
( ( $greatereq(X_238,0)
& $lesseq(X_238,g_s51_51) )
<=> ? [X_239: $int] : mem3(X_238,X_239,X_232) )
& ! [X_240: $int] :
( ? [X_241: $int] : mem3(X_241,X_240,X_232)
=> $greatereq(X_240,0) ) ) ).
tff('Define:abs:15',axiom,
! [X_242: $int] :
( mem0(X_242,g_s137_138)
=> ( $greatereq(X_242,0)
& $lesseq(X_242,g_s51_51) ) ) ).
tff('Define:abs:16',axiom,
! [X_243: $int] :
( mem0(X_243,g_s138_139)
=> ( $greatereq(X_243,0)
& $lesseq(X_243,g_s51_51) ) ) ).
tff('Define:abs:17',axiom,
! [X_244: $int] :
( mem0(X_244,g_s139_140)
=> ( $greatereq(X_244,0)
& $lesseq(X_244,g_s51_51) ) ) ).
tff('Define:abs:18',axiom,
! [X_245: $int] :
( mem0(X_245,g_s140_141)
=> ( $greatereq(X_245,0)
& $lesseq(X_245,g_s51_51) ) ) ).
tff('Define:abs:19',axiom,
! [X_246: $int] :
( mem0(X_246,g_s141_142)
=> ( $greatereq(X_246,0)
& $lesseq(X_246,g_s51_51) ) ) ).
tff('Define:abs:2',axiom,
? [X_151: set_3] :
( ! [X_152: $int,X_153: $int] :
( mem3(X_153,X_152,X_151)
<=> mem3(X_153,X_152,g_s124_125) )
& ! [X_154: $int,X_155: $int,X_156: $int] :
( ( mem3(X_154,X_155,X_151)
& mem3(X_154,X_156,X_151) )
=> ( X_155 = X_156 ) )
& ! [X_157: $int] :
( ( $greatereq(X_157,0)
& $lesseq(X_157,g_s51_51) )
<=> ? [X_158: $int] : mem3(X_157,X_158,X_151) )
& ! [X_159: $int] :
( ? [X_160: $int] : mem3(X_160,X_159,X_151)
=> $greatereq(X_159,0) ) ) ).
tff('Define:abs:20',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_247: $int] :
( ? [X_248: $int] :
( ( X_248 = L_s142 )
& mem3(X_248,X_247,g_s133_134) )
=> ! [X_249: $int] :
( mem3(L_s142,X_249,g_s123_124)
=> ( $greatereq(X_247,1)
& $lesseq(X_247,X_249) ) ) ) ) ).
tff('Define:abs:21',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_250: $int] :
( ? [X_251: $int] :
( ( X_251 = L_s142 )
& ? [X_252: $int] : mem4(X_251,X_250,X_252,g_s134_135) )
=> ! [X_253: $int] :
( mem3(L_s142,X_253,g_s123_124)
=> ( $greatereq(X_250,1)
& $lesseq(X_250,X_253) ) ) ) ) ).
tff('Define:abs:22',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_254: $int] :
( ? [X_255: $int] :
( ( X_255 = L_s142 )
& mem3(X_255,X_254,g_s131_132) )
=> ! [X_256: $int] :
( mem3(L_s142,X_256,g_s127_128)
=> ( $greatereq(X_254,1)
& $lesseq(X_254,X_256) ) ) ) ) ).
tff('Define:abs:23',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_257: $int] :
( ? [X_258: $int] :
( ( X_258 = L_s142 )
& mem3(X_258,X_257,g_s132_133) )
=> ! [X_259: $int] :
( mem3(L_s142,X_259,g_s124_125)
=> ( $greatereq(X_257,1)
& $lesseq(X_257,X_259) ) ) ) ) ).
tff('Define:abs:24',axiom,
? [X_260: set_3] :
( ! [X_261: $int,X_262: $int] :
( mem3(X_262,X_261,X_260)
<=> mem3(X_262,X_261,g_s123_124) )
& ! [X_263: $int,X_264: $int,X_265: $int] :
( ( mem3(X_263,X_264,X_260)
& mem3(X_263,X_265,X_260) )
=> ( X_264 = X_265 ) )
& ! [X_266: $int] :
( ( $greatereq(X_266,0)
& $lesseq(X_266,g_s51_51) )
<=> ? [X_267: $int] : mem3(X_266,X_267,X_260) )
& ! [X_268: $int] :
( ? [X_269: $int] : mem3(X_269,X_268,X_260)
=> $greatereq(X_268,0) ) ) ).
tff('Define:abs:25',axiom,
? [X_270: set_3] :
( ! [X_271: $int,X_272: $int] :
( mem3(X_272,X_271,X_270)
<=> mem3(X_272,X_271,g_s124_125) )
& ! [X_273: $int,X_274: $int,X_275: $int] :
( ( mem3(X_273,X_274,X_270)
& mem3(X_273,X_275,X_270) )
=> ( X_274 = X_275 ) )
& ! [X_276: $int] :
( ( $greatereq(X_276,0)
& $lesseq(X_276,g_s51_51) )
<=> ? [X_277: $int] : mem3(X_276,X_277,X_270) )
& ! [X_278: $int] :
( ? [X_279: $int] : mem3(X_279,X_278,X_270)
=> $greatereq(X_278,0) ) ) ).
tff('Define:abs:26',axiom,
? [X_280: set_3] :
( ! [X_281: $int,X_282: $int] :
( mem3(X_282,X_281,X_280)
<=> mem3(X_282,X_281,g_s125_126) )
& ! [X_283: $int,X_284: $int,X_285: $int] :
( ( mem3(X_283,X_284,X_280)
& mem3(X_283,X_285,X_280) )
=> ( X_284 = X_285 ) )
& ! [X_286: $int] :
( ( $greatereq(X_286,0)
& $lesseq(X_286,g_s51_51) )
<=> ? [X_287: $int] : mem3(X_286,X_287,X_280) )
& ! [X_288: $int] :
( ? [X_289: $int] : mem3(X_289,X_288,X_280)
=> $greatereq(X_288,0) ) ) ).
tff('Define:abs:27',axiom,
? [X_290: set_3] :
( ! [X_291: $int,X_292: $int] :
( mem3(X_292,X_291,X_290)
<=> mem3(X_292,X_291,g_s126_127) )
& ! [X_293: $int,X_294: $int,X_295: $int] :
( ( mem3(X_293,X_294,X_290)
& mem3(X_293,X_295,X_290) )
=> ( X_294 = X_295 ) )
& ! [X_296: $int] :
( ( $greatereq(X_296,0)
& $lesseq(X_296,g_s51_51) )
<=> ? [X_297: $int] : mem3(X_296,X_297,X_290) )
& ! [X_298: $int] :
( ? [X_299: $int] : mem3(X_299,X_298,X_290)
=> $greatereq(X_298,0) ) ) ).
tff('Define:abs:28',axiom,
? [X_300: set_3] :
( ! [X_301: $int,X_302: $int] :
( mem3(X_302,X_301,X_300)
<=> mem3(X_302,X_301,g_s127_128) )
& ! [X_303: $int,X_304: $int,X_305: $int] :
( ( mem3(X_303,X_304,X_300)
& mem3(X_303,X_305,X_300) )
=> ( X_304 = X_305 ) )
& ! [X_306: $int] :
( ( $greatereq(X_306,0)
& $lesseq(X_306,g_s51_51) )
<=> ? [X_307: $int] : mem3(X_306,X_307,X_300) )
& ! [X_308: $int] :
( ? [X_309: $int] : mem3(X_309,X_308,X_300)
=> $greatereq(X_308,0) ) ) ).
tff('Define:abs:29',axiom,
? [X_310: set_3] :
( ! [X_311: $int,X_312: $int] :
( mem3(X_312,X_311,X_310)
<=> mem3(X_312,X_311,g_s128_129) )
& ! [X_313: $int,X_314: $int,X_315: $int] :
( ( mem3(X_313,X_314,X_310)
& mem3(X_313,X_315,X_310) )
=> ( X_314 = X_315 ) )
& ! [X_316: $int] :
( ( $greatereq(X_316,0)
& $lesseq(X_316,g_s51_51) )
<=> ? [X_317: $int] : mem3(X_316,X_317,X_310) )
& ! [X_318: $int] :
( ? [X_319: $int] : mem3(X_319,X_318,X_310)
=> $greatereq(X_318,0) ) ) ).
tff('Define:abs:3',axiom,
? [X_161: set_3] :
( ! [X_162: $int,X_163: $int] :
( mem3(X_163,X_162,X_161)
<=> mem3(X_163,X_162,g_s125_126) )
& ! [X_164: $int,X_165: $int,X_166: $int] :
( ( mem3(X_164,X_165,X_161)
& mem3(X_164,X_166,X_161) )
=> ( X_165 = X_166 ) )
& ! [X_167: $int] :
( ( $greatereq(X_167,0)
& $lesseq(X_167,g_s51_51) )
<=> ? [X_168: $int] : mem3(X_167,X_168,X_161) )
& ! [X_169: $int] :
( ? [X_170: $int] : mem3(X_170,X_169,X_161)
=> $greatereq(X_169,0) ) ) ).
tff('Define:abs:30',axiom,
? [X_320: set_3] :
( ! [X_321: $int,X_322: $int] :
( mem3(X_322,X_321,X_320)
<=> mem3(X_322,X_321,g_s129_130) )
& ! [X_323: $int,X_324: $int,X_325: $int] :
( ( mem3(X_323,X_324,X_320)
& mem3(X_323,X_325,X_320) )
=> ( X_324 = X_325 ) )
& ! [X_326: $int] :
( ( $greatereq(X_326,0)
& $lesseq(X_326,g_s51_51) )
<=> ? [X_327: $int] : mem3(X_326,X_327,X_320) )
& ! [X_328: $int] :
( ? [X_329: $int] : mem3(X_329,X_328,X_320)
=> $greatereq(X_328,0) ) ) ).
tff('Define:abs:31',axiom,
! [X_330: $int] :
( mem0(X_330,g_s122_123)
=> ( $greatereq(X_330,0)
& $lesseq(X_330,g_s51_51) ) ) ).
tff('Define:abs:32',axiom,
! [X_331: $int] :
( mem0(X_331,g_s137_138)
=> ( $greatereq(X_331,0)
& $lesseq(X_331,g_s51_51) ) ) ).
tff('Define:abs:33',axiom,
! [X_332: $int] :
( mem0(X_332,g_s138_139)
=> ( $greatereq(X_332,0)
& $lesseq(X_332,g_s51_51) ) ) ).
tff('Define:abs:34',axiom,
! [X_333: $int] :
( mem0(X_333,g_s139_140)
=> ( $greatereq(X_333,0)
& $lesseq(X_333,g_s51_51) ) ) ).
tff('Define:abs:35',axiom,
? [X_334: set_3] :
( ! [X_335: $int,X_336: $int] :
( mem3(X_336,X_335,X_334)
<=> mem3(X_336,X_335,g_s135_136) )
& ! [X_337: $int,X_338: $int,X_339: $int] :
( ( mem3(X_337,X_338,X_334)
& mem3(X_337,X_339,X_334) )
=> ( X_338 = X_339 ) )
& ! [X_340: $int] :
( ( $greatereq(X_340,0)
& $lesseq(X_340,g_s51_51) )
<=> ? [X_341: $int] : mem3(X_340,X_341,X_334) )
& ! [X_342: $int] :
( ? [X_343: $int] : mem3(X_343,X_342,X_334)
=> $greatereq(X_342,0) ) ) ).
tff('Define:abs:4',axiom,
? [X_171: set_3] :
( ! [X_172: $int,X_173: $int] :
( mem3(X_173,X_172,X_171)
<=> mem3(X_173,X_172,g_s126_127) )
& ! [X_174: $int,X_175: $int,X_176: $int] :
( ( mem3(X_174,X_175,X_171)
& mem3(X_174,X_176,X_171) )
=> ( X_175 = X_176 ) )
& ! [X_177: $int] :
( ( $greatereq(X_177,0)
& $lesseq(X_177,g_s51_51) )
<=> ? [X_178: $int] : mem3(X_177,X_178,X_171) )
& ! [X_179: $int] :
( ? [X_180: $int] : mem3(X_180,X_179,X_171)
=> $greatereq(X_179,0) ) ) ).
tff('Define:abs:5',axiom,
? [X_181: set_3] :
( ! [X_182: $int,X_183: $int] :
( mem3(X_183,X_182,X_181)
<=> mem3(X_183,X_182,g_s127_128) )
& ! [X_184: $int,X_185: $int,X_186: $int] :
( ( mem3(X_184,X_185,X_181)
& mem3(X_184,X_186,X_181) )
=> ( X_185 = X_186 ) )
& ! [X_187: $int] :
( ( $greatereq(X_187,0)
& $lesseq(X_187,g_s51_51) )
<=> ? [X_188: $int] : mem3(X_187,X_188,X_181) )
& ! [X_189: $int] :
( ? [X_190: $int] : mem3(X_190,X_189,X_181)
=> $greatereq(X_189,0) ) ) ).
tff('Define:abs:6',axiom,
? [X_191: set_3] :
( ! [X_192: $int,X_193: $int] :
( mem3(X_193,X_192,X_191)
<=> mem3(X_193,X_192,g_s128_129) )
& ! [X_194: $int,X_195: $int,X_196: $int] :
( ( mem3(X_194,X_195,X_191)
& mem3(X_194,X_196,X_191) )
=> ( X_195 = X_196 ) )
& ! [X_197: $int] :
( ( $greatereq(X_197,0)
& $lesseq(X_197,g_s51_51) )
<=> ? [X_198: $int] : mem3(X_197,X_198,X_191) )
& ! [X_199: $int] :
( ? [X_200: $int] : mem3(X_200,X_199,X_191)
=> $greatereq(X_199,0) ) ) ).
tff('Define:abs:7',axiom,
? [X_201: set_3] :
( ! [X_202: $int,X_203: $int] :
( mem3(X_203,X_202,X_201)
<=> mem3(X_203,X_202,g_s129_130) )
& ! [X_204: $int,X_205: $int,X_206: $int] :
( ( mem3(X_204,X_205,X_201)
& mem3(X_204,X_206,X_201) )
=> ( X_205 = X_206 ) )
& ! [X_207: $int] :
( ( $greatereq(X_207,0)
& $lesseq(X_207,g_s51_51) )
<=> ? [X_208: $int] : mem3(X_207,X_208,X_201) )
& ! [X_209: $int] :
( ? [X_210: $int] : mem3(X_210,X_209,X_201)
=> $greatereq(X_209,0) ) ) ).
tff('Define:abs:8',axiom,
! [X_211: $int,X_212: $int] :
( mem3(X_212,X_211,g_s130_131)
=> ( $greatereq(X_212,0)
& $lesseq(X_212,g_s51_51)
& $greatereq(X_211,0) ) ) ).
tff('Define:abs:9',axiom,
! [X_213: $int,X_214: $int] :
( mem3(X_214,X_213,g_s131_132)
=> ( $greatereq(X_214,0)
& $lesseq(X_214,g_s51_51)
& $greatereq(X_213,0) ) ) ).
tff('Define:ctx:0',axiom,
( ! [X_5: $int] :
( mem0(X_5,g_s0_0)
<=> ( ( X_5 = g_s1_1 )
| ( X_5 = g_s2_2 ) ) )
& ( g_s1_1 != g_s2_2 ) ) ).
tff('Define:ctx:1',axiom,
( ! [X_6: $int] :
( mem0(X_6,g_s3_3)
<=> ( ( X_6 = g_s4_4 )
| ( X_6 = g_s5_5 ) ) )
& ( g_s4_4 != g_s5_5 ) ) ).
tff('Define:ctx:10',axiom,
g_s21_22 = 65535 ).
tff('Define:ctx:100',axiom,
$lesseq(2,g_s89_89) ).
tff('Define:ctx:101',axiom,
mem0(g_s90_90,g_s24_23) ).
tff('Define:ctx:102',axiom,
g_s90_90 = $difference(g_s89_89,1) ).
tff('Define:ctx:103',axiom,
mem0(g_s91_91,g_s24_23) ).
tff('Define:ctx:104',axiom,
mem0(g_s92_92,g_s24_23) ).
tff('Define:ctx:105',axiom,
g_s92_92 = $difference(g_s91_91,1) ).
tff('Define:ctx:106',axiom,
mem0(g_s93_93,g_s24_23) ).
tff('Define:ctx:107',axiom,
mem0(g_s94_94,g_s24_23) ).
tff('Define:ctx:108',axiom,
g_s94_94 = $difference(g_s93_93,1) ).
tff('Define:ctx:109',axiom,
mem0(g_s95_95,g_s22_21) ).
tff('Define:ctx:11',axiom,
g_s23_24 = 255 ).
tff('Define:ctx:110',axiom,
mem0(g_s96_96,g_s22_21) ).
tff('Define:ctx:111',axiom,
mem0(g_s97_97,g_s22_21) ).
tff('Define:ctx:112',axiom,
mem0(g_s98_98,g_s22_21) ).
tff('Define:ctx:113',axiom,
g_s97_97 != g_s98_98 ).
tff('Define:ctx:114',axiom,
mem0(g_s99_99,g_s22_21) ).
tff('Define:ctx:115',axiom,
mem0(g_s100_100,g_s22_21) ).
tff('Define:ctx:116',axiom,
mem0(g_s101_101,g_s22_21) ).
tff('Define:ctx:117',axiom,
$greatereq(g_s102_102,0) ).
tff('Define:ctx:118',axiom,
g_s102_102 = $difference(g_s100_100,g_s101_101) ).
tff('Define:ctx:119',axiom,
mem0(g_s103_103,g_s22_21) ).
tff('Define:ctx:12',axiom,
( $greatereq(g_s25_25,0)
& $lesseq(g_s25_25,g_s23_24) ) ).
tff('Define:ctx:120',axiom,
mem0(g_s104_104,g_s22_21) ).
tff('Define:ctx:121',axiom,
mem0(g_s105_105,g_s22_21) ).
tff('Define:ctx:122',axiom,
mem0(g_s106_106,g_s22_21) ).
tff('Define:ctx:123',axiom,
mem0(g_s107_107,g_s24_23) ).
tff('Define:ctx:124',axiom,
mem0(g_s108_108,g_s24_23) ).
tff('Define:ctx:125',axiom,
g_s108_108 = $difference(g_s107_107,1) ).
tff('Define:ctx:126',axiom,
g_s93_93 = $product(g_s89_89,g_s107_107) ).
tff('Define:ctx:127',axiom,
$lesseq(1,g_s107_107) ).
tff('Define:ctx:128',axiom,
$less(g_s107_107,g_s23_24) ).
tff('Define:ctx:129',axiom,
mem0(g_s109_109,g_s24_23) ).
tff('Define:ctx:13',axiom,
( $greatereq(g_s26_26,0)
& $lesseq(g_s26_26,g_s23_24) ) ).
tff('Define:ctx:130',axiom,
mem0(g_s110_110,g_s24_23) ).
tff('Define:ctx:131',axiom,
mem0(g_s111_111,g_s20_19) ).
tff('Define:ctx:132',axiom,
mem0(g_s112_112,g_s20_19) ).
tff('Define:ctx:133',axiom,
mem0(g_s113_113,g_s20_19) ).
tff('Define:ctx:134',axiom,
mem0(g_s114_114,g_s20_19) ).
tff('Define:ctx:135',axiom,
mem0(g_s115_115,g_s20_19) ).
tff('Define:ctx:136',axiom,
mem0(g_s116_116,g_s20_19) ).
tff('Define:ctx:137',axiom,
g_s116_116 = $difference(g_s115_115,1) ).
tff('Define:ctx:138',axiom,
mem0(g_s117_117,g_s20_19) ).
tff('Define:ctx:139',axiom,
mem0(g_s118_118,g_s20_19) ).
tff('Define:ctx:14',axiom,
g_s25_25 != g_s26_26 ).
tff('Define:ctx:140',axiom,
g_s118_118 = $difference(g_s117_117,1) ).
tff('Define:ctx:141',axiom,
mem0(g_s119_119,g_s24_23) ).
tff('Define:ctx:142',axiom,
mem0(g_s120_120,g_s24_23) ).
tff('Define:ctx:143',axiom,
mem0(g_s121_121,g_s20_19) ).
tff('Define:ctx:15',axiom,
! [X_9: $int] :
( mem0(X_9,g_s27_27)
<=> ( ( X_9 = g_s25_25 )
| ( X_9 = g_s26_26 ) ) ) ).
tff('Define:ctx:16',axiom,
! [X_10: $int,X_11: $o] :
( mem2((X_11),X_10,g_s28_28)
<=> ( ( ( (X_11)
<=> $true )
& ( X_10 = g_s25_25 ) )
| ( ( (X_11)
<=> $false )
& ( X_10 = g_s26_26 ) ) ) ) ).
tff('Define:ctx:17',axiom,
! [X_12: $int] :
( mem0(X_12,g_s20_19)
<=> ( $greatereq(X_12,0)
& $lesseq(X_12,4294967295) ) ) ).
tff('Define:ctx:18',axiom,
! [X_13: $int] :
( mem0(X_13,g_s22_21)
<=> ( $greatereq(X_13,0)
& $lesseq(X_13,65535) ) ) ).
tff('Define:ctx:19',axiom,
! [X_14: $int] :
( mem0(X_14,g_s24_23)
<=> ( $greatereq(X_14,0)
& $lesseq(X_14,255) ) ) ).
tff('Define:ctx:2',axiom,
( ! [X_7: $int] :
( mem0(X_7,g_s6_6)
<=> ( ( X_7 = g_s7_7 )
| ( X_7 = g_s8_8 ) ) )
& ( g_s7_7 != g_s8_8 ) ) ).
tff('Define:ctx:20',axiom,
mem0(g_s29_29,g_s24_23) ).
tff('Define:ctx:21',axiom,
mem0(g_s30_30,g_s24_23) ).
tff('Define:ctx:22',axiom,
mem0(g_s31_31,g_s22_21) ).
tff('Define:ctx:23',axiom,
mem0(g_s32_32,g_s22_21) ).
tff('Define:ctx:24',axiom,
mem0(g_s33_33,g_s20_19) ).
tff('Define:ctx:25',axiom,
mem0(g_s34_34,g_s20_19) ).
tff('Define:ctx:26',axiom,
$greatereq(g_s35_35,0) ).
tff('Define:ctx:27',axiom,
$lesseq(2,g_s35_35) ).
tff('Define:ctx:28',axiom,
$greatereq(g_s36_36,0) ).
tff('Define:ctx:29',axiom,
$lesseq(2,g_s36_36) ).
tff('Define:ctx:3',axiom,
( ! [X_8: $int] :
( mem0(X_8,g_s9_9)
<=> ( ( X_8 = g_s10_10 )
| ( X_8 = g_s11_11 )
| ( X_8 = g_s12_12 )
| ( X_8 = g_s13_13 )
| ( X_8 = g_s14_14 )
| ( X_8 = g_s15_15 )
| ( X_8 = g_s16_16 )
| ( X_8 = g_s17_17 )
| ( X_8 = g_s18_18 ) ) )
& ( g_s10_10 != g_s11_11 )
& ( g_s11_11 != g_s12_12 )
& ( g_s12_12 != g_s13_13 )
& ( g_s13_13 != g_s14_14 )
& ( g_s14_14 != g_s15_15 )
& ( g_s15_15 != g_s16_16 )
& ( g_s16_16 != g_s17_17 )
& ( g_s17_17 != g_s18_18 ) ) ).
tff('Define:ctx:30',axiom,
$greatereq(g_s37_37,0) ).
tff('Define:ctx:31',axiom,
$lesseq(2,g_s37_37) ).
tff('Define:ctx:32',axiom,
$lesseq(g_s35_35,g_s37_37) ).
tff('Define:ctx:33',axiom,
mem0(g_s38_38,g_s24_23) ).
tff('Define:ctx:34',axiom,
mem0(g_s39_39,g_s24_23) ).
tff('Define:ctx:35',axiom,
g_s39_39 = $sum(g_s38_38,g_s35_35) ).
tff('Define:ctx:36',axiom,
mem0(g_s40_40,g_s24_23) ).
tff('Define:ctx:37',axiom,
g_s40_40 = $sum(g_s38_38,g_s36_36) ).
tff('Define:ctx:38',axiom,
mem0(g_s41_41,g_s24_23) ).
tff('Define:ctx:39',axiom,
g_s41_41 = $sum(g_s38_38,g_s37_37) ).
tff('Define:ctx:4',axiom,
mem0(g_s19_20,g_s20_19) ).
tff('Define:ctx:40',axiom,
mem0(g_s42_42,g_s22_21) ).
tff('Define:ctx:41',axiom,
mem0(g_s43_43,g_s22_21) ).
tff('Define:ctx:42',axiom,
mem0(g_s44_44,g_s24_23) ).
tff('Define:ctx:43',axiom,
$lesseq(g_s42_42,g_s43_43) ).
tff('Define:ctx:44',axiom,
mem0(g_s45_45,g_s20_19) ).
tff('Define:ctx:45',axiom,
mem0(g_s46_46,g_s20_19) ).
tff('Define:ctx:46',axiom,
mem0(g_s47_47,g_s20_19) ).
tff('Define:ctx:47',axiom,
mem0(g_s48_48,g_s20_19) ).
tff('Define:ctx:48',axiom,
mem0(g_s49_49,g_s20_19) ).
tff('Define:ctx:49',axiom,
mem0(g_s50_50,g_s24_23) ).
tff('Define:ctx:5',axiom,
mem0(g_s21_22,g_s22_21) ).
tff('Define:ctx:50',axiom,
$lesseq(2,g_s50_50) ).
tff('Define:ctx:51',axiom,
mem0(g_s51_51,g_s24_23) ).
tff('Define:ctx:52',axiom,
g_s51_51 = $difference(g_s50_50,1) ).
tff('Define:ctx:53',axiom,
$greatereq(g_s52_52,1) ).
tff('Define:ctx:54',axiom,
$greatereq(g_s53_53,1) ).
tff('Define:ctx:55',axiom,
$greatereq(g_s54_54,1) ).
tff('Define:ctx:56',axiom,
$greatereq(g_s55_55,1) ).
tff('Define:ctx:57',axiom,
$greatereq(g_s56_56,1) ).
tff('Define:ctx:58',axiom,
$greatereq(g_s57_57,1) ).
tff('Define:ctx:59',axiom,
$greatereq(g_s58_58,1) ).
tff('Define:ctx:6',axiom,
mem0(g_s23_24,g_s24_23) ).
tff('Define:ctx:60',axiom,
$greatereq(g_s59_59,1) ).
tff('Define:ctx:61',axiom,
mem0(g_s60_60,g_s24_23) ).
tff('Define:ctx:62',axiom,
mem0(g_s61_61,g_s24_23) ).
tff('Define:ctx:63',axiom,
g_s61_61 = $sum(g_s60_60,g_s52_52) ).
tff('Define:ctx:64',axiom,
mem0(g_s62_62,g_s24_23) ).
tff('Define:ctx:65',axiom,
mem0(g_s63_63,g_s24_23) ).
tff('Define:ctx:66',axiom,
g_s63_63 = $sum(g_s62_62,g_s53_53) ).
tff('Define:ctx:67',axiom,
mem0(g_s64_64,g_s24_23) ).
tff('Define:ctx:68',axiom,
g_s64_64 = $sum(g_s62_62,g_s54_54) ).
tff('Define:ctx:69',axiom,
mem0(g_s65_65,g_s24_23) ).
tff('Define:ctx:7',axiom,
mem0(g_s25_25,g_s24_23) ).
tff('Define:ctx:70',axiom,
g_s65_65 = $sum(g_s62_62,g_s55_55) ).
tff('Define:ctx:71',axiom,
mem0(g_s66_66,g_s24_23) ).
tff('Define:ctx:72',axiom,
g_s66_66 = $sum(g_s62_62,g_s56_56) ).
tff('Define:ctx:73',axiom,
mem0(g_s67_67,g_s24_23) ).
tff('Define:ctx:74',axiom,
g_s67_67 = $sum(g_s62_62,g_s57_57) ).
tff('Define:ctx:75',axiom,
mem0(g_s68_68,g_s24_23) ).
tff('Define:ctx:76',axiom,
g_s68_68 = $sum(g_s62_62,g_s58_58) ).
tff('Define:ctx:77',axiom,
mem0(g_s69_69,g_s24_23) ).
tff('Define:ctx:78',axiom,
g_s69_69 = $sum(g_s62_62,g_s59_59) ).
tff('Define:ctx:79',axiom,
mem0(g_s70_70,g_s20_19) ).
tff('Define:ctx:8',axiom,
mem0(g_s26_26,g_s24_23) ).
tff('Define:ctx:80',axiom,
mem0(g_s71_71,g_s20_19) ).
tff('Define:ctx:81',axiom,
mem0(g_s72_72,g_s20_19) ).
tff('Define:ctx:82',axiom,
mem0(g_s73_73,g_s20_19) ).
tff('Define:ctx:83',axiom,
mem0(g_s74_74,g_s20_19) ).
tff('Define:ctx:84',axiom,
mem0(g_s75_75,g_s20_19) ).
tff('Define:ctx:85',axiom,
mem0(g_s76_76,g_s20_19) ).
tff('Define:ctx:86',axiom,
mem0(g_s77_77,g_s20_19) ).
tff('Define:ctx:87',axiom,
mem0(g_s78_78,g_s20_19) ).
tff('Define:ctx:88',axiom,
mem0(g_s79_79,g_s20_19) ).
tff('Define:ctx:89',axiom,
mem0(g_s80_80,g_s20_19) ).
tff('Define:ctx:9',axiom,
g_s19_20 = 4294967295 ).
tff('Define:ctx:90',axiom,
mem0(g_s81_81,g_s20_19) ).
tff('Define:ctx:91',axiom,
mem0(g_s82_82,g_s20_19) ).
tff('Define:ctx:92',axiom,
mem0(g_s83_83,g_s20_19) ).
tff('Define:ctx:93',axiom,
mem0(g_s84_84,g_s20_19) ).
tff('Define:ctx:94',axiom,
mem0(g_s85_85,g_s20_19) ).
tff('Define:ctx:95',axiom,
mem0(g_s86_86,g_s20_19) ).
tff('Define:ctx:96',axiom,
mem0(g_s87_87,g_s20_19) ).
tff('Define:ctx:97',axiom,
mem0(g_s88_88,g_s20_19) ).
tff('Define:ctx:98',axiom,
mem0(g_s89_89,g_s24_23) ).
tff('Define:ctx:99',axiom,
$lesseq(0,g_s89_89) ).
tff('Define:inv:0',axiom,
! [X_344: $int] :
( mem0(X_344,g_s122_123)
<=> mem0(X_344,g_s122_1_143) ) ).
tff('Define:inv:1',axiom,
! [X_345: $int] :
( mem0(X_345,g_s139_140)
<=> mem0(X_345,g_s139_1_144) ) ).
tff('Define:inv:10',axiom,
! [X_355: $int] :
( mem0(X_355,g_s148_1_153)
=> ( $greatereq(X_355,0)
& $lesseq(X_355,g_s51_51) ) ) ).
tff('Define:inv:11',axiom,
! [X_356: $int] :
( mem0(X_356,g_s149_1_154)
=> ( $greatereq(X_356,0)
& $lesseq(X_356,g_s51_51) ) ) ).
tff('Define:inv:12',axiom,
! [X_357: $int] :
( mem0(X_357,g_s150_1_155)
=> ( $greatereq(X_357,0)
& $lesseq(X_357,g_s51_51) ) ) ).
tff('Define:inv:13',axiom,
! [X_358: $int] :
( mem0(X_358,g_s151_1_156)
=> ( $greatereq(X_358,0)
& $lesseq(X_358,g_s51_51) ) ) ).
tff('Define:inv:14',axiom,
! [X_359: $int] :
( mem0(X_359,g_s152_1_157)
=> ( $greatereq(X_359,0)
& $lesseq(X_359,g_s51_51) ) ) ).
tff('Define:inv:15',axiom,
! [X_360: $int] :
( mem0(X_360,g_s122_1_143)
=> ( $greatereq(X_360,0)
& $lesseq(X_360,g_s51_51) ) ) ).
tff('Define:inv:16',axiom,
! [X_361: $int] :
( mem0(X_361,g_s139_1_144)
=> ( $greatereq(X_361,0)
& $lesseq(X_361,g_s51_51) ) ) ).
tff('Define:inv:17',axiom,
! [X_362: $int] :
( mem0(X_362,g_s137_1_145)
=> ( $greatereq(X_362,0)
& $lesseq(X_362,g_s51_51) ) ) ).
tff('Define:inv:18',axiom,
! [X_363: $int] :
( mem0(X_363,g_s138_1_146)
=> ( $greatereq(X_363,0)
& $lesseq(X_363,g_s51_51) ) ) ).
tff('Define:inv:19',axiom,
! [X_364: $int] :
( mem0(X_364,g_s153_1_158)
=> ( $greatereq(X_364,0)
& $lesseq(X_364,g_s51_51) ) ) ).
tff('Define:inv:2',axiom,
! [X_346: $int] :
( mem0(X_346,g_s137_138)
<=> mem0(X_346,g_s137_1_145) ) ).
tff('Define:inv:20',axiom,
? [X_365: set_3] :
( ! [X_366: $int,X_367: $int] :
( mem3(X_367,X_366,X_365)
<=> mem3(X_367,X_366,g_s154_1_159) )
& ! [X_368: $int,X_369: $int,X_370: $int] :
( ( mem3(X_368,X_369,X_365)
& mem3(X_368,X_370,X_365) )
=> ( X_369 = X_370 ) )
& ! [X_371: $int] :
( ( $greatereq(X_371,0)
& $lesseq(X_371,g_s51_51) )
<=> ? [X_372: $int] : mem3(X_371,X_372,X_365) )
& ! [X_373: $int] :
( ? [X_374: $int] : mem3(X_374,X_373,X_365)
=> $true ) ) ).
tff('Define:inv:21',axiom,
? [X_375: set_3] :
( ! [X_376: $int,X_377: $int] :
( mem3(X_377,X_376,X_375)
<=> mem3(X_377,X_376,g_s155_1_160) )
& ! [X_378: $int,X_379: $int,X_380: $int] :
( ( mem3(X_378,X_379,X_375)
& mem3(X_378,X_380,X_375) )
=> ( X_379 = X_380 ) )
& ! [X_381: $int] :
( ( $greatereq(X_381,0)
& $lesseq(X_381,g_s51_51) )
<=> ? [X_382: $int] : mem3(X_381,X_382,X_375) )
& ! [X_383: $int] :
( ? [X_384: $int] : mem3(X_384,X_383,X_375)
=> $true ) ) ).
tff('Define:inv:22',axiom,
? [X_385: set_3] :
( ! [X_386: $int,X_387: $int] :
( mem3(X_387,X_386,X_385)
<=> mem3(X_387,X_386,g_s156_1_161) )
& ! [X_388: $int,X_389: $int,X_390: $int] :
( ( mem3(X_388,X_389,X_385)
& mem3(X_388,X_390,X_385) )
=> ( X_389 = X_390 ) )
& ! [X_391: $int] :
( ( $greatereq(X_391,0)
& $lesseq(X_391,g_s51_51) )
<=> ? [X_392: $int] : mem3(X_391,X_392,X_385) )
& ! [X_393: $int] :
( ? [X_394: $int] : mem3(X_394,X_393,X_385)
=> $true ) ) ).
tff('Define:inv:23',axiom,
? [X_395: set_3] :
( ! [X_396: $int,X_397: $int] :
( mem3(X_397,X_396,X_395)
<=> mem3(X_397,X_396,g_s157_1_162) )
& ! [X_398: $int,X_399: $int,X_400: $int] :
( ( mem3(X_398,X_399,X_395)
& mem3(X_398,X_400,X_395) )
=> ( X_399 = X_400 ) )
& ! [X_401: $int] :
( ( $greatereq(X_401,0)
& $lesseq(X_401,g_s51_51) )
<=> ? [X_402: $int] : mem3(X_401,X_402,X_395) )
& ! [X_403: $int] :
( ? [X_404: $int] : mem3(X_404,X_403,X_395)
=> $true ) ) ).
tff('Define:inv:24',axiom,
? [X_405: set_3] :
( ! [X_406: $int,X_407: $int] :
( mem3(X_407,X_406,X_405)
<=> mem3(X_407,X_406,g_s158_1_163) )
& ! [X_408: $int,X_409: $int,X_410: $int] :
( ( mem3(X_408,X_409,X_405)
& mem3(X_408,X_410,X_405) )
=> ( X_409 = X_410 ) )
& ! [X_411: $int] :
( ( $greatereq(X_411,0)
& $lesseq(X_411,g_s51_51) )
<=> ? [X_412: $int] : mem3(X_411,X_412,X_405) )
& ! [X_413: $int] :
( ? [X_414: $int] : mem3(X_414,X_413,X_405)
=> $true ) ) ).
tff('Define:inv:25',axiom,
? [X_415: set_3] :
( ! [X_416: $int,X_417: $int] :
( mem3(X_417,X_416,X_415)
<=> mem3(X_417,X_416,g_s159_1_164) )
& ! [X_418: $int,X_419: $int,X_420: $int] :
( ( mem3(X_418,X_419,X_415)
& mem3(X_418,X_420,X_415) )
=> ( X_419 = X_420 ) )
& ! [X_421: $int] :
( ( $greatereq(X_421,0)
& $lesseq(X_421,g_s51_51) )
<=> ? [X_422: $int] : mem3(X_421,X_422,X_415) )
& ! [X_423: $int] :
( ? [X_424: $int] : mem3(X_424,X_423,X_415)
=> $true ) ) ).
tff('Define:inv:26',axiom,
? [X_425: set_3] :
( ! [X_426: $int,X_427: $int] :
( mem3(X_427,X_426,X_425)
<=> mem3(X_427,X_426,g_s136_1_147) )
& ! [X_428: $int,X_429: $int,X_430: $int] :
( ( mem3(X_428,X_429,X_425)
& mem3(X_428,X_430,X_425) )
=> ( X_429 = X_430 ) )
& ! [X_431: $int] :
( ( $greatereq(X_431,0)
& $lesseq(X_431,g_s51_51) )
<=> ? [X_432: $int] : mem3(X_431,X_432,X_425) )
& ! [X_433: $int] :
( ? [X_434: $int] : mem3(X_434,X_433,X_425)
=> $greatereq(X_433,0) ) ) ).
tff('Define:inv:27',axiom,
? [X_435: set_3] :
( ! [X_436: $int,X_437: $int] :
( mem3(X_437,X_436,X_435)
<=> mem3(X_437,X_436,g_s160_1_165) )
& ! [X_438: $int,X_439: $int,X_440: $int] :
( ( mem3(X_438,X_439,X_435)
& mem3(X_438,X_440,X_435) )
=> ( X_439 = X_440 ) )
& ! [X_441: $int] :
( ( $greatereq(X_441,0)
& $lesseq(X_441,g_s51_51) )
<=> ? [X_442: $int] : mem3(X_441,X_442,X_435) )
& ! [X_443: $int] :
( ? [X_444: $int] : mem3(X_444,X_443,X_435)
=> $greatereq(X_443,0) ) ) ).
tff('Define:inv:28',axiom,
? [X_445: set_3] :
( ! [X_446: $int,X_447: $int] :
( mem3(X_447,X_446,X_445)
<=> mem3(X_447,X_446,g_s161_1_166) )
& ! [X_448: $int,X_449: $int,X_450: $int] :
( ( mem3(X_448,X_449,X_445)
& mem3(X_448,X_450,X_445) )
=> ( X_449 = X_450 ) )
& ! [X_451: $int] :
( ( $greatereq(X_451,0)
& $lesseq(X_451,g_s51_51) )
<=> ? [X_452: $int] : mem3(X_451,X_452,X_445) )
& ! [X_453: $int] :
( ? [X_454: $int] : mem3(X_454,X_453,X_445)
=> $true ) ) ).
tff('Define:inv:29',axiom,
! [X_455: $int,X_456: $int] :
( mem3(X_456,X_455,g_s160_1_165)
<=> mem3(X_456,X_455,g_s135_136) ) ).
tff('Define:inv:3',axiom,
! [X_347: $int] :
( mem0(X_347,g_s138_139)
<=> mem0(X_347,g_s138_1_146) ) ).
tff('Define:inv:30',axiom,
! [X_457: $int] :
( mem0(X_457,g_s144_1_149)
=> mem0(X_457,g_s146_1_151) ) ).
tff('Define:inv:31',axiom,
! [X_458: $int] :
( mem0(X_458,g_s144_1_149)
=> mem0(X_458,g_s147_1_152) ) ).
tff('Define:inv:32',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_459: $int] :
( mem3(L_s142,X_459,g_s158_1_163)
=> $lesseq(X_459,g_s54_54) ) ) ).
tff('Define:inv:33',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_460: $int] :
( mem3(L_s142,X_460,g_s157_1_162)
=> $lesseq(X_460,g_s57_57) ) ) ).
tff('Define:inv:34',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_461: $int] :
( mem3(L_s142,X_461,g_s155_1_160)
=> $lesseq(X_461,g_s53_53) ) ) ).
tff('Define:inv:35',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_462: $int] :
( mem3(L_s142,X_462,g_s154_1_159)
=> $lesseq(X_462,g_s58_58) ) ) ).
tff('Define:inv:36',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_463: $int] :
( mem3(L_s142,X_463,g_s156_1_161)
=> $lesseq(X_463,g_s56_56) ) ) ).
tff('Define:inv:37',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_464: $int] :
( mem3(L_s142,X_464,g_s159_1_164)
=> $lesseq(X_464,g_s59_59) ) ) ).
tff('Define:inv:38',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_465: $int] :
( mem3(L_s142,X_465,g_s161_1_166)
=> $lesseq(X_465,g_s55_55) ) ) ).
tff('Define:inv:39',axiom,
! [X_466: $int] :
( mem0(X_466,g_s143_1_148)
<=> ( $greatereq(X_466,0)
& $lesseq(X_466,g_s51_51)
& ! [X_467: $int] :
( mem3(X_466,X_467,g_s124_125)
=> mem3(X_466,X_467,g_s132_133) ) ) ) ).
tff('Define:inv:4',axiom,
! [X_348: $int,X_349: $int] :
( mem3(X_349,X_348,g_s136_137)
<=> mem3(X_349,X_348,g_s136_1_147) ) ).
tff('Define:inv:40',axiom,
! [X_468: $int] :
( mem0(X_468,g_s144_1_149)
<=> ( $greatereq(X_468,0)
& $lesseq(X_468,g_s51_51)
& ! [X_469: $int] :
( mem3(X_468,X_469,g_s123_124)
=> mem3(X_468,X_469,g_s133_134) ) ) ) ).
tff('Define:inv:41',axiom,
! [X_470: $int] :
( mem0(X_470,g_s145_1_150)
<=> ( $greatereq(X_470,0)
& $lesseq(X_470,g_s51_51)
& ! [X_471: $int] :
( ! [X_472: $int] :
( mem3(X_470,X_472,g_s123_124)
=> ( X_471 = $difference(X_472,1) ) )
=> mem3(X_470,X_471,g_s133_134) ) ) ) ).
tff('Define:inv:42',axiom,
! [X_473: $int] :
( mem0(X_473,g_s146_1_151)
<=> ( $greatereq(X_473,0)
& $lesseq(X_473,g_s51_51)
& ? [X_474: $int,X_475: $int] :
( ( X_475 = X_473 )
& mem3(X_473,X_474,g_s123_124)
& mem4(X_475,X_474,g_s4_4,g_s134_135) ) ) ) ).
tff('Define:inv:43',axiom,
! [X_476: $int] :
( mem0(X_476,g_s147_1_152)
<=> ( $greatereq(X_476,0)
& $lesseq(X_476,g_s51_51)
& ? [X_477: $int,X_478: $int] :
( ( X_478 = X_476 )
& mem3(X_476,X_477,g_s123_124)
& mem4(X_478,X_477,g_s5_5,g_s134_135) ) ) ) ).
tff('Define:inv:44',axiom,
! [X_479: $int] :
( mem0(X_479,g_s152_1_157)
<=> ( $greatereq(X_479,0)
& $lesseq(X_479,g_s51_51)
& ? [X_480: $int,X_481: $int] :
( ( X_481 = X_479 )
& ! [X_482: $int] :
( mem3(X_479,X_482,g_s123_124)
=> ( X_480 = $difference(X_482,1) ) )
& mem4(X_481,X_480,g_s5_5,g_s134_135) ) ) ) ).
tff('Define:inv:45',axiom,
! [X_483: $int] :
( mem0(X_483,g_s151_1_156)
<=> ( $greatereq(X_483,0)
& $lesseq(X_483,g_s51_51)
& ! [X_484: $int] :
( mem3(X_483,X_484,g_s127_128)
=> mem3(X_483,X_484,g_s131_132) ) ) ) ).
tff('Define:inv:46',axiom,
! [X_485: $int] :
( mem0(X_485,g_s150_1_155)
<=> ( $greatereq(X_485,0)
& $lesseq(X_485,g_s51_51)
& ! [X_486: $int] :
( ! [X_487: $int] :
( mem3(X_485,X_487,g_s127_128)
=> ( X_486 = $difference(X_487,1) ) )
=> mem3(X_485,X_486,g_s131_132) ) ) ) ).
tff('Define:inv:47',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_488: $int,X_489: $int] :
( ( ( X_489 = L_s142 )
& ! [X_490: $int,X_491: $int,X_492: $int] :
( ( mem3(L_s142,X_490,g_s123_124)
& mem3(L_s142,X_491,g_s157_1_162)
& mem3(L_s142,X_492,g_s123_124) )
=> ( $greatereq(X_488,$sum($sum($difference(X_490,g_s57_57),1),X_491))
& $lesseq(X_488,X_492) ) )
& mem3(X_489,X_488,g_s133_134) )
<=> $false ) ) ).
tff('Define:inv:48',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51)
& ! [X_493: $int] :
( mem3(L_s142,X_493,g_s157_1_162)
=> $greater(X_493,0) ) )
=> ! [X_494: $int] :
( ! [X_495: $int,X_496: $int] :
( ( mem3(L_s142,X_495,g_s123_124)
& mem3(L_s142,X_496,g_s157_1_162) )
=> ( X_494 = $sum($difference(X_495,g_s57_57),X_496) ) )
=> mem3(L_s142,X_494,g_s133_134) ) ) ).
tff('Define:inv:49',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_497: $int,X_498: $int] :
( ( ( X_498 = L_s142 )
& ! [X_499: $int,X_500: $int,X_501: $int] :
( ( mem3(L_s142,X_499,g_s123_124)
& mem3(L_s142,X_500,g_s156_1_161)
& mem3(L_s142,X_501,g_s123_124) )
=> ( $greatereq(X_497,$sum($sum($difference(X_499,g_s56_56),1),X_500))
& $lesseq(X_497,X_501) ) )
& mem3(X_498,X_497,g_s133_134) )
<=> $false ) ) ).
tff('Define:inv:5',axiom,
! [X_350: $int] :
( mem0(X_350,g_s143_1_148)
=> ( $greatereq(X_350,0)
& $lesseq(X_350,g_s51_51) ) ) ).
tff('Define:inv:50',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51)
& ! [X_502: $int] :
( mem3(L_s142,X_502,g_s156_1_161)
=> $greater(X_502,0) ) )
=> ! [X_503: $int] :
( ! [X_504: $int,X_505: $int] :
( ( mem3(L_s142,X_504,g_s123_124)
& mem3(L_s142,X_505,g_s156_1_161) )
=> ( X_503 = $sum($difference(X_504,g_s56_56),X_505) ) )
=> mem3(L_s142,X_503,g_s133_134) ) ) ).
tff('Define:inv:51',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_506: $int,X_507: $int] :
( ( ( X_507 = L_s142 )
& ! [X_508: $int,X_509: $int,X_510: $int] :
( ( mem3(L_s142,X_508,g_s124_125)
& mem3(L_s142,X_509,g_s154_1_159)
& mem3(L_s142,X_510,g_s124_125) )
=> ( $greatereq(X_506,$sum($sum($difference(X_508,g_s58_58),1),X_509))
& $lesseq(X_506,X_510) ) ) )
=> mem3(X_507,X_506,g_s132_133) ) ) ).
tff('Define:inv:52',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ~ ! [X_511: $int] :
( ! [X_512: $int,X_513: $int] :
( ( mem3(L_s142,X_512,g_s124_125)
& mem3(L_s142,X_513,g_s154_1_159) )
=> ( X_511 = $sum($difference(X_512,g_s58_58),X_513) ) )
=> mem3(L_s142,X_511,g_s132_133) ) ) ).
tff('Define:inv:53',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_514: $int,X_515: $int] :
( ( ( X_515 = L_s142 )
& ! [X_516: $int,X_517: $int,X_518: $int] :
( ( mem3(L_s142,X_516,g_s128_129)
& mem3(L_s142,X_517,g_s155_1_160)
& mem3(L_s142,X_518,g_s128_129) )
=> ( $greatereq(X_514,$sum($sum($difference(X_516,g_s53_53),1),X_517))
& $lesseq(X_514,X_518) ) ) )
=> mem3(X_515,X_514,g_s133_134) ) ) ).
tff('Define:inv:54',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ~ ! [X_519: $int] :
( ! [X_520: $int,X_521: $int] :
( ( mem3(L_s142,X_520,g_s128_129)
& mem3(L_s142,X_521,g_s155_1_160) )
=> ( X_519 = $sum($difference(X_520,g_s53_53),X_521) ) )
=> mem3(L_s142,X_519,g_s133_134) ) ) ).
tff('Define:inv:55',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_522: $int,X_523: $int] :
( ( ( X_523 = L_s142 )
& ! [X_524: $int,X_525: $int,X_526: $int] :
( ( mem3(L_s142,X_524,g_s123_124)
& mem3(L_s142,X_525,g_s158_1_163)
& mem3(L_s142,X_526,g_s123_124) )
=> ( $greatereq(X_522,$sum($sum($difference(X_524,g_s54_54),1),X_525))
& $lesseq(X_522,X_526) ) )
& mem3(X_523,X_522,g_s133_134) )
<=> $false ) ) ).
tff('Define:inv:56',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51)
& ! [X_527: $int] :
( mem3(L_s142,X_527,g_s158_1_163)
=> $greater(X_527,0) ) )
=> ! [X_528: $int] :
( ! [X_529: $int,X_530: $int] :
( ( mem3(L_s142,X_529,g_s123_124)
& mem3(L_s142,X_530,g_s158_1_163) )
=> ( X_528 = $sum($difference(X_529,g_s54_54),X_530) ) )
=> mem3(L_s142,X_528,g_s133_134) ) ) ).
tff('Define:inv:57',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_531: $int,X_532: $int] :
( ( ( X_532 = L_s142 )
& ! [X_533: $int,X_534: $int,X_535: $int] :
( ( mem3(L_s142,X_533,g_s129_130)
& mem3(L_s142,X_534,g_s161_1_166)
& mem3(L_s142,X_535,g_s129_130) )
=> ( $greatereq(X_531,$sum($sum($difference(X_533,g_s55_55),1),X_534))
& $lesseq(X_531,X_535) ) ) )
=> ( mem3(X_532,X_531,g_s133_134)
& mem3(X_532,X_531,g_s132_133)
& ~ mem3(X_532,X_531,g_s131_132) ) ) ) ).
tff('Define:inv:58',axiom,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ~ ( ! [X_536: $int] :
( ! [X_537: $int,X_538: $int] :
( ( mem3(L_s142,X_537,g_s129_130)
& mem3(L_s142,X_538,g_s161_1_166) )
=> ( X_536 = $sum($difference(X_537,g_s55_55),X_538) ) )
=> mem3(L_s142,X_536,g_s133_134) )
& ! [X_539: $int] :
( ! [X_540: $int,X_541: $int] :
( ( mem3(L_s142,X_540,g_s129_130)
& mem3(L_s142,X_541,g_s161_1_166) )
=> ( X_539 = $sum($difference(X_540,g_s55_55),X_541) ) )
=> mem3(L_s142,X_539,g_s132_133) )
& ~ ! [X_542: $int] :
( ! [X_543: $int,X_544: $int] :
( ( mem3(L_s142,X_543,g_s129_130)
& mem3(L_s142,X_544,g_s161_1_166) )
=> ( X_542 = $sum($difference(X_543,g_s55_55),X_544) ) )
=> mem3(L_s142,X_542,g_s131_132) ) ) ) ).
tff('Define:inv:6',axiom,
! [X_351: $int] :
( mem0(X_351,g_s144_1_149)
=> ( $greatereq(X_351,0)
& $lesseq(X_351,g_s51_51) ) ) ).
tff('Define:inv:7',axiom,
! [X_352: $int] :
( mem0(X_352,g_s145_1_150)
=> ( $greatereq(X_352,0)
& $lesseq(X_352,g_s51_51) ) ) ).
tff('Define:inv:8',axiom,
! [X_353: $int] :
( mem0(X_353,g_s146_1_151)
=> ( $greatereq(X_353,0)
& $lesseq(X_353,g_s51_51) ) ) ).
tff('Define:inv:9',axiom,
! [X_354: $int] :
( mem0(X_354,g_s147_1_152)
=> ( $greatereq(X_354,0)
& $lesseq(X_354,g_s51_51) ) ) ).
tff('Define:seext:0',axiom,
( ! [X_15: $int,X_16: $o] :
( mem2((X_16),X_15,g_s28_28)
=> ( $true
& mem0(X_15,g_s24_23) ) )
& ! [X_17: $o,X_18: $int,X_19: $int] :
( ( mem2((X_17),X_18,g_s28_28)
& mem2((X_17),X_19,g_s28_28) )
=> ( X_18 = X_19 ) ) ) ).
tff('Define:seext:1',axiom,
( ! [X_20: $int,X_21: $o] :
( mem2((X_21),X_20,g_s28_28)
=> ( $true
& mem0(X_20,g_s22_21) ) )
& ! [X_22: $o,X_23: $int,X_24: $int] :
( ( mem2((X_22),X_23,g_s28_28)
& mem2((X_22),X_24,g_s28_28) )
=> ( X_23 = X_24 ) ) ) ).
tff('Define:seext:2',axiom,
( ! [X_25: $int,X_26: $o] :
( mem2((X_26),X_25,g_s28_28)
=> ( $true
& mem0(X_25,g_s20_19) ) )
& ! [X_27: $o,X_28: $int,X_29: $int] :
( ( mem2((X_27),X_28,g_s28_28)
& mem2((X_27),X_29,g_s28_28) )
=> ( X_28 = X_29 ) ) ) ).
%Global hypotheses
tff(gh_0_def,hypothesis,
mem0(g_s165_167,g_s24_23) ).
tff(gh_1_def,hypothesis,
( $greatereq(g_s165_167,0)
& $lesseq(g_s165_167,g_s51_51) ) ).
tff(gh_2_def,hypothesis,
mem0(g_s166_168,g_s24_23) ).
tff(gh_3_def,hypothesis,
mem0(g_s167_169,g_s24_23) ).
tff(gh_4_def,hypothesis,
mem0(g_s168_170,g_s24_23) ).
tff(gh_5_def,hypothesis,
! [X_545: $int] :
( mem3(g_s165_167,X_545,g_s123_124)
=> mem3(g_s165_167,X_545,g_s128_129) ) ).
tff(gh_6_def,hypothesis,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_546: $int] :
( mem3(L_s142,X_546,g_s128_129)
=> mem3(L_s142,X_546,g_s123_124) ) ) ).
tff(gh_7_def,hypothesis,
! [X_547: $int] :
( mem3(g_s165_167,X_547,g_s123_124)
=> mem3(g_s165_167,X_547,g_s129_130) ) ).
tff(gh_8_def,hypothesis,
! [L_s142: $int] :
( ( $greatereq(L_s142,0)
& $lesseq(L_s142,g_s51_51) )
=> ! [X_548: $int] :
( mem3(L_s142,X_548,g_s129_130)
=> mem3(L_s142,X_548,g_s123_124) ) ) ).
%----Local hypotheses
tff('Local_Hyp:6',hypothesis,
~ ( ( g_s166_168 = g_s25_25 )
& ( g_s167_169 = g_s26_26 ) ) ).
tff('Local_Hyp:19',hypothesis,
~ mem0(g_s165_167,g_s144_1_149) ).
tff('Local_Hyp:20',hypothesis,
! [X_3313: $int] :
( mem3(g_s165_167,X_3313,g_s156_1_161)
=> $lesseq(X_3313,0) ) ).
tff('Local_Hyp:10',hypothesis,
~ ! [X_1050: $int] :
( ! [X_1051: $int] :
( mem3(g_s165_167,X_1051,g_s123_124)
=> ( X_1050 = $difference($sum(X_1051,1),1) ) )
=> mem3(g_s165_167,X_1050,g_s133_134) ) ).
tff('Local_Hyp:12',hypothesis,
~ ! [X_1192: $int,X_1193: $int] :
( ( ( X_1193 = g_s165_167 )
& ! [X_1194: $int,X_1195: $int] :
( ( mem3(g_s165_167,X_1194,g_s123_124)
& mem3(g_s165_167,X_1195,g_s123_124) )
=> ( $greatereq(X_1192,$difference($sum(X_1194,1),g_s56_56))
& $lesseq(X_1192,$difference($sum(X_1195,1),1)) ) )
& mem3(X_1193,X_1192,g_s133_134) )
<=> $false ) ).
tff('Local_Hyp:2',hypothesis,
( $greatereq(g_s142_122,0)
& $lesseq(g_s142_122,g_s51_51) ) ).
%----Goal
tff('Goal',conjecture,
! [X_4092: $int] :
( ( ( ( g_s142_122 = g_s165_167 )
& ! [X_4093: $int] :
( mem3(g_s165_167,X_4093,g_s156_1_161)
=> ( X_4092 = $difference(X_4093,1) ) ) )
| ( mem3(g_s142_122,X_4092,g_s156_1_161)
& ~ ? [X_4094: $int] :
( ( g_s142_122 = g_s165_167 )
& ! [X_4095: $int] :
( mem3(g_s165_167,X_4095,g_s156_1_161)
=> ( X_4094 = $difference(X_4095,1) ) ) ) ) )
=> $lesseq(X_4092,g_s56_56) ) ).
%------------------------------------------------------------------------------