TPTP Problem File: SWC543_1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWC543_1 : TPTP v9.1.0. Bugfixed v9.1.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 10 0 Group s264 Tag s251
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0015-00333-10-0.tptp [Deh24]
% Status : Theorem
% Rating : ? v9.1.0
% Syntax : Number of formulae : 639 ( 169 unt; 264 typ; 0 def)
% Number of atoms : 1006 ( 138 equ)
% Maximal formula atoms : 34 ( 2 avg)
% Number of connectives : 656 ( 23 ~; 4 |; 406 &)
% ( 93 <=>; 130 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 9 ( 0 fml; 9 var)
% Number arithmetic : 1194 ( 465 atm; 24 fun; 264 num; 441 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 19 ( 9 >; 10 *; 0 +; 0 <<)
% Number of predicates : 15 ( 8 usr; 6 prp; 0-4 aty)
% Number of functors : 319 ( 252 usr; 309 con; 0-2 aty)
% Number of variables : 486 ( 359 !; 127 ?; 486 :)
% SPC : TX0_THM_EQU_ARI
% Comments : Autogenerated by PPTRANS-TPTP - github.com/CLEARSY/pptranspog
% Bugfixes : v9.1.0 - Added missing types, and maybe more.
%------------------------------------------------------------------------------
tff(set_0_type,type,
set_0: $tType ).
tff(mem0_type,type,
mem0: ( $int * set_0 ) > $o ).
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 ).
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(iexp_type,type,
iexp: ( $int * $int ) > $int ).
tff(iexp_def_1,axiom,
! [X: $int] : ( iexp(X,0) = 1 ) ).
tff(iexp_def_2,axiom,
! [X: $int,Y: $int] :
( $greatereq(Y,1)
=> ( iexp(X,Y) = $sum(X,iexp(X,$difference(Y,1))) ) ) ).
%----Global declarations
tff(g_s0_0_type,type,
g_s0_0: set_0 ).
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_insert: set_2 > set_2 ).
tff(mem2_type,type,
mem2: ( $int * $int * set_2 ) > $o ).
tff(g_s1_1_type,type,
g_s1_1: set_0 ).
tff(g_s2_2_type,type,
g_s2_2: set_0 ).
tff(g_s3_3_type,type,
g_s3_3: set_0 ).
tff(g_s4_4_type,type,
g_s4_4: set_0 ).
tff(g_s5_5_type,type,
g_s5_5: set_0 ).
tff(g_s6_6_type,type,
g_s6_6: set_0 ).
tff(g_s7_7_type,type,
g_s7_7: set_0 ).
tff(g_s8_8_type,type,
g_s8_8: set_0 ).
tff(g_s9_9_type,type,
g_s9_9: set_0 ).
tff(g_s10_10_type,type,
g_s10_10: $int ).
tff(g_s11_11_type,type,
g_s11_11: $int ).
tff(g_s12_12_type,type,
g_s12_12: $int ).
tff(g_s13_13_type,type,
g_s13_13: $int ).
tff(g_s14_14_type,type,
g_s14_14: $int ).
tff(g_s15_15_type,type,
g_s15_15: $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_19_type,type,
g_s19_19: $int ).
tff(g_s20_20_type,type,
g_s20_20: $int ).
tff(g_s21_21_type,type,
g_s21_21: $int ).
tff(g_s22_22_type,type,
g_s22_22: $int ).
tff(g_s23_23_type,type,
g_s23_23: $int ).
tff(g_s24_24_type,type,
g_s24_24: $int ).
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: $int ).
tff(g_s28_28_type,type,
g_s28_28: $int ).
tff(g_s29_29_type,type,
g_s29_29: $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_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_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_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_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_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_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_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_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_s120_120_type,type,
g_s120_120: $int ).
tff(g_s121_121_type,type,
g_s121_121: $int ).
tff(g_s122_122_type,type,
g_s122_122: $int ).
tff(g_s123_123_type,type,
g_s123_123: $int ).
tff(g_s124_124_type,type,
g_s124_124: $int ).
tff(g_s125_125_type,type,
g_s125_125: $int ).
tff(g_s126_126_type,type,
g_s126_126: $int ).
tff(g_s127_127_type,type,
g_s127_127: $int ).
tff(g_s128_128_type,type,
g_s128_128: $int ).
tff(g_s129_129_type,type,
g_s129_129: $int ).
tff(g_s130_130_type,type,
g_s130_130: $int ).
tff(g_s131_131_type,type,
g_s131_131: $int ).
tff(g_s132_132_type,type,
g_s132_132: $int ).
tff(g_s133_133_type,type,
g_s133_133: $int ).
tff(g_s134_134_type,type,
g_s134_134: $int ).
tff(g_s135_135_type,type,
g_s135_135: $int ).
tff(g_s136_136_type,type,
g_s136_136: $int ).
tff(g_s137_137_type,type,
g_s137_137: $int ).
tff(g_s138_138_type,type,
g_s138_138: $int ).
tff(g_s139_139_type,type,
g_s139_139: $int ).
tff(g_s140_140_type,type,
g_s140_140: $int ).
tff(g_s141_141_type,type,
g_s141_141: $int ).
tff(g_s142_142_type,type,
g_s142_142: set_0 ).
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_insert: set_3 > set_3 ).
tff(mem3_type,type,
mem3: ( $int * $int * $int * set_3 ) > $o ).
tff(g_s143_143_type,type,
g_s143_143: 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_insert: set_4 > set_4 ).
tff(mem4_type,type,
mem4: ( $o * $int * set_4 ) > $o ).
tff(g_s146_144_type,type,
g_s146_144: set_4 ).
tff(g_s147_145_type,type,
g_s147_145: set_2 ).
tff(g_s149_146_type,type,
g_s149_146: set_2 ).
tff(g_s151_147_type,type,
g_s151_147: $int ).
tff(g_s152_148_type,type,
g_s152_148: $int ).
tff(g_s153_149_type,type,
g_s153_149: $int ).
tff(g_s154_150_type,type,
g_s154_150: $int ).
tff(g_s155_151_type,type,
g_s155_151: $int ).
tff(g_s219_160_type,type,
g_s219_160: set_0 ).
tff(g_s220_161_type,type,
g_s220_161: set_0 ).
tff(g_s221_162_type,type,
g_s221_162: set_0 ).
tff(g_s222_163_type,type,
g_s222_163: set_0 ).
tff(g_s223_164_type,type,
g_s223_164: set_0 ).
tff(g_s224_157_type,type,
g_s224_157: set_0 ).
tff(g_s225_165_type,type,
g_s225_165: $int ).
tff(g_s226_156_type,type,
g_s226_156: set_2 ).
tff(g_s227_159_type,type,
g_s227_159: set_0 ).
tff(g_s228_166_type,type,
g_s228_166: $int ).
tff(g_s229_158_type,type,
g_s229_158: set_2 ).
tff(g_s230_153_type,type,
g_s230_153: set_0 ).
tff(g_s231_167_type,type,
g_s231_167: $int ).
tff(g_s232_152_type,type,
g_s232_152: set_2 ).
tff(g_s233_155_type,type,
g_s233_155: set_0 ).
tff(g_s234_168_type,type,
g_s234_168: $int ).
tff(g_s235_154_type,type,
g_s235_154: set_2 ).
tff(g_s236_169_type,type,
g_s236_169: $int ).
tff(g_s237_170_type,type,
g_s237_170: set_0 ).
tff(g_s238_171_type,type,
g_s238_171: set_0 ).
tff(g_s239_172_type,type,
g_s239_172: $int ).
tff(g_s240_173_type,type,
g_s240_173: set_0 ).
tff(g_s241_174_type,type,
g_s241_174: set_0 ).
tff(g_s242_175_type,type,
g_s242_175: $int ).
tff(g_s243_176_type,type,
g_s243_176: set_0 ).
tff(g_s244_177_type,type,
g_s244_177: set_0 ).
tff(g_s245_178_type,type,
g_s245_178: $int ).
tff(g_s156_179_type,type,
g_s156_179: $o ).
tff(g_s157_180_type,type,
g_s157_180: $o ).
tff(g_s158_181_type,type,
g_s158_181: $int ).
tff(g_s159_182_type,type,
g_s159_182: $int ).
tff(g_s160_183_type,type,
g_s160_183: $int ).
tff(g_s161_184_type,type,
g_s161_184: $int ).
tff(g_s162_185_type,type,
g_s162_185: $int ).
tff(g_s163_186_type,type,
g_s163_186: $int ).
tff(g_s164_187_type,type,
g_s164_187: $int ).
tff(g_s165_188_type,type,
g_s165_188: $int ).
tff(g_s166_189_type,type,
g_s166_189: $int ).
tff(g_s167_190_type,type,
g_s167_190: $int ).
tff(g_s168_191_type,type,
g_s168_191: $int ).
tff(g_s169_192_type,type,
g_s169_192: $int ).
tff(g_s170_193_type,type,
g_s170_193: $int ).
tff(g_s171_194_type,type,
g_s171_194: $int ).
tff(g_s172_195_type,type,
g_s172_195: $int ).
tff(g_s173_196_type,type,
g_s173_196: $int ).
tff(g_s174_197_type,type,
g_s174_197: $int ).
tff(g_s175_198_type,type,
g_s175_198: $int ).
tff(g_s176_199_type,type,
g_s176_199: $int ).
tff(g_s177_200_type,type,
g_s177_200: $int ).
tff(g_s178_201_type,type,
g_s178_201: $int ).
tff(g_s179_202_type,type,
g_s179_202: $int ).
tff(g_s180_203_type,type,
g_s180_203: $int ).
tff(g_s181_204_type,type,
g_s181_204: $int ).
tff(g_s182_205_type,type,
g_s182_205: $int ).
tff(g_s183_206_type,type,
g_s183_206: $int ).
tff(g_s184_207_type,type,
g_s184_207: $int ).
tff(g_s185_208_type,type,
g_s185_208: $int ).
tff(g_s186_209_type,type,
g_s186_209: $int ).
tff(g_s187_210_type,type,
g_s187_210: $int ).
tff(g_s188_211_type,type,
g_s188_211: $int ).
tff(g_s189_212_type,type,
g_s189_212: $int ).
tff(g_s190_213_type,type,
g_s190_213: $int ).
tff(g_s191_214_type,type,
g_s191_214: $int ).
tff(g_s192_215_type,type,
g_s192_215: $int ).
tff(g_s193_216_type,type,
g_s193_216: $int ).
tff(g_s194_217_type,type,
g_s194_217: $int ).
tff(g_s195_218_type,type,
g_s195_218: $int ).
tff(g_s196_219_type,type,
g_s196_219: $int ).
tff(g_s197_220_type,type,
g_s197_220: $int ).
tff(g_s198_221_type,type,
g_s198_221: $int ).
tff(g_s199_222_type,type,
g_s199_222: $int ).
tff(g_s200_223_type,type,
g_s200_223: $int ).
tff(g_s201_224_type,type,
g_s201_224: $int ).
tff(g_s202_225_type,type,
g_s202_225: $int ).
tff(g_s203_226_type,type,
g_s203_226: $int ).
tff(g_s204_227_type,type,
g_s204_227: $int ).
tff(g_s205_228_type,type,
g_s205_228: $int ).
tff(g_s206_229_type,type,
g_s206_229: $int ).
tff(g_s207_230_type,type,
g_s207_230: $int ).
tff(g_s208_231_type,type,
g_s208_231: $int ).
tff(g_s209_232_type,type,
g_s209_232: $int ).
tff(g_s210_233_type,type,
g_s210_233: $int ).
tff(g_s211_234_type,type,
g_s211_234: $int ).
tff(g_s212_235_type,type,
g_s212_235: $int ).
tff(g_s213_236_type,type,
g_s213_236: $int ).
tff(g_s214_237_type,type,
g_s214_237: $int ).
tff(g_s215_238_type,type,
g_s215_238: $int ).
tff(g_s216_239_type,type,
g_s216_239: $int ).
tff(g_s217_240_type,type,
g_s217_240: $int ).
tff(g_s218_241_type,type,
g_s218_241: $int ).
tff(g_s246_1_242_type,type,
g_s246_1_242: $int ).
tff(g_s250_1_245_type,type,
g_s250_1_245: $o ).
tff(g_s250_246_type,type,
g_s250_246: $o ).
tff(g_s253_247_type,type,
g_s253_247: $int ).
%----Defines
tff('Define:aprp:0',axiom,
( ~ ! [X_469: $int] :
( mem0(X_469,g_s219_160)
<=> $false )
& ! [X_472: $int] :
( mem0(X_472,g_s219_160)
=> $true )
& ? [X_470: $int,X_471: set_2] :
( ? [X_473: set_2] :
( ! [X_474: $int,X_475: $int] :
( mem2(X_475,X_474,X_473)
<=> mem2(X_475,X_474,X_471) )
& ! [X_476: $int,X_477: $int,X_478: $int] :
( ( mem2(X_476,X_477,X_473)
& mem2(X_476,X_478,X_473) )
=> ( X_477 = X_478 ) )
& ! [X_479: $int] :
( ( $greatereq(X_479,1)
& $lesseq(X_479,X_470) )
<=> ? [X_480: $int] : mem2(X_479,X_480,X_473) )
& ! [X_481: $int] :
( ? [X_482: $int] : mem2(X_482,X_481,X_473)
=> mem0(X_481,g_s219_160) ) )
& ! [X_483: $int] :
( mem0(X_483,g_s219_160)
=> ? [X_484: $int] : mem2(X_484,X_483,X_471) )
& ! [X_485: $int,X_486: $int,X_487: $int] :
( ( mem2(X_486,X_485,X_471)
& mem2(X_487,X_485,X_471) )
=> ( X_486 = X_487 ) ) ) ) ).
tff('Define:aprp:1',axiom,
( ~ ! [X_488: $int] :
( mem0(X_488,g_s220_161)
<=> $false )
& ! [X_491: $int] :
( mem0(X_491,g_s220_161)
=> $true )
& ? [X_489: $int,X_490: set_2] :
( ? [X_492: set_2] :
( ! [X_493: $int,X_494: $int] :
( mem2(X_494,X_493,X_492)
<=> mem2(X_494,X_493,X_490) )
& ! [X_495: $int,X_496: $int,X_497: $int] :
( ( mem2(X_495,X_496,X_492)
& mem2(X_495,X_497,X_492) )
=> ( X_496 = X_497 ) )
& ! [X_498: $int] :
( ( $greatereq(X_498,1)
& $lesseq(X_498,X_489) )
<=> ? [X_499: $int] : mem2(X_498,X_499,X_492) )
& ! [X_500: $int] :
( ? [X_501: $int] : mem2(X_501,X_500,X_492)
=> mem0(X_500,g_s220_161) ) )
& ! [X_502: $int] :
( mem0(X_502,g_s220_161)
=> ? [X_503: $int] : mem2(X_503,X_502,X_490) )
& ! [X_504: $int,X_505: $int,X_506: $int] :
( ( mem2(X_505,X_504,X_490)
& mem2(X_506,X_504,X_490) )
=> ( X_505 = X_506 ) ) ) ) ).
tff('Define:aprp:10',axiom,
! [X_586: $int,X_587: $int] :
( ( ? [X_588: set_2] :
( ? [X_589: set_2] :
( ! [X_590: $int,X_591: $int] :
( mem2(X_591,X_590,X_589)
<=> mem2(X_591,X_590,X_588) )
& ! [X_592: $int,X_593: $int,X_594: $int] :
( ( mem2(X_592,X_593,X_589)
& mem2(X_592,X_594,X_589) )
=> ( X_593 = X_594 ) )
& ! [X_595: $int] :
( mem0(X_595,g_s224_157)
<=> ? [X_596: $int] : mem2(X_595,X_596,X_589) )
& ! [X_597: $int] :
( ? [X_598: $int] : mem2(X_598,X_597,X_589)
=> ( $greatereq(X_597,1)
& $lesseq(X_597,X_586) ) ) )
& ! [X_599: $int] :
( ( $greatereq(X_599,1)
& $lesseq(X_599,X_586) )
=> ? [X_600: $int] : mem2(X_600,X_599,X_588) )
& ! [X_601: $int,X_602: $int,X_603: $int] :
( ( mem2(X_602,X_601,X_588)
& mem2(X_603,X_601,X_588) )
=> ( X_602 = X_603 ) ) )
& ? [X_604: set_2] :
( ? [X_605: set_2] :
( ! [X_606: $int,X_607: $int] :
( mem2(X_607,X_606,X_605)
<=> mem2(X_607,X_606,X_604) )
& ! [X_608: $int,X_609: $int,X_610: $int] :
( ( mem2(X_608,X_609,X_605)
& mem2(X_608,X_610,X_605) )
=> ( X_609 = X_610 ) )
& ! [X_611: $int] :
( mem0(X_611,g_s224_157)
<=> ? [X_612: $int] : mem2(X_611,X_612,X_605) )
& ! [X_613: $int] :
( ? [X_614: $int] : mem2(X_614,X_613,X_605)
=> ( $greatereq(X_613,1)
& $lesseq(X_613,X_587) ) ) )
& ! [X_615: $int] :
( ( $greatereq(X_615,1)
& $lesseq(X_615,X_587) )
=> ? [X_616: $int] : mem2(X_616,X_615,X_604) )
& ! [X_617: $int,X_618: $int,X_619: $int] :
( ( mem2(X_618,X_617,X_604)
& mem2(X_619,X_617,X_604) )
=> ( X_618 = X_619 ) ) ) )
=> ( $greatereq(X_586,0)
& $lesseq(X_587,max_int) ) ) ).
tff('Define:aprp:11',axiom,
! [X_620: $int] :
( mem0(X_620,g_s227_159)
=> mem0(X_620,g_s220_161) ) ).
tff('Define:aprp:12',axiom,
mem0(g_s228_166,g_s220_161) ).
tff('Define:aprp:13',axiom,
~ mem0(g_s228_166,g_s227_159) ).
tff('Define:aprp:14',axiom,
( ! [X_621: $int,X_622: $int] :
( mem2(X_622,X_621,g_s229_158)
=> ( $greatereq(X_622,0)
& $lesseq(X_622,max_int)
& mem0(X_621,g_s220_161) ) )
& ! [X_623: $int,X_624: $int,X_625: $int] :
( ( mem2(X_623,X_624,g_s229_158)
& mem2(X_623,X_625,g_s229_158) )
=> ( X_624 = X_625 ) ) ) ).
tff('Define:aprp:15',axiom,
? [X_626: $int] :
( ? [X_627: set_2] :
( ! [X_628: $int,X_629: $int] :
( mem2(X_629,X_628,X_627)
<=> mem2(X_629,X_628,g_s229_158) )
& ! [X_630: $int,X_631: $int,X_632: $int] :
( ( mem2(X_630,X_631,X_627)
& mem2(X_630,X_632,X_627) )
=> ( X_631 = X_632 ) )
& ! [X_633: $int] :
( ( $greatereq(X_633,1)
& $lesseq(X_633,X_626) )
<=> ? [X_634: $int] : mem2(X_633,X_634,X_627) )
& ! [X_635: $int] :
( ? [X_636: $int] : mem2(X_636,X_635,X_627)
=> mem0(X_635,g_s227_159) ) )
& ! [X_637: $int] :
( mem0(X_637,g_s227_159)
=> ? [X_638: $int] : mem2(X_638,X_637,g_s229_158) )
& ! [X_639: $int,X_640: $int,X_641: $int] :
( ( mem2(X_640,X_639,g_s229_158)
& mem2(X_641,X_639,g_s229_158) )
=> ( X_640 = X_641 ) ) ) ).
tff('Define:aprp:16',axiom,
! [X_642: $int] :
( mem0(X_642,g_s230_153)
=> mem0(X_642,g_s221_162) ) ).
tff('Define:aprp:17',axiom,
mem0(g_s231_167,g_s221_162) ).
tff('Define:aprp:18',axiom,
~ mem0(g_s231_167,g_s230_153) ).
tff('Define:aprp:19',axiom,
( ! [X_643: $int,X_644: $int] :
( mem2(X_644,X_643,g_s232_152)
=> ( $greatereq(X_644,0)
& $lesseq(X_644,max_int)
& mem0(X_643,g_s221_162) ) )
& ! [X_645: $int,X_646: $int,X_647: $int] :
( ( mem2(X_645,X_646,g_s232_152)
& mem2(X_645,X_647,g_s232_152) )
=> ( X_646 = X_647 ) ) ) ).
tff('Define:aprp:2',axiom,
( ~ ! [X_507: $int] :
( mem0(X_507,g_s221_162)
<=> $false )
& ! [X_510: $int] :
( mem0(X_510,g_s221_162)
=> $true )
& ? [X_508: $int,X_509: set_2] :
( ? [X_511: set_2] :
( ! [X_512: $int,X_513: $int] :
( mem2(X_513,X_512,X_511)
<=> mem2(X_513,X_512,X_509) )
& ! [X_514: $int,X_515: $int,X_516: $int] :
( ( mem2(X_514,X_515,X_511)
& mem2(X_514,X_516,X_511) )
=> ( X_515 = X_516 ) )
& ! [X_517: $int] :
( ( $greatereq(X_517,1)
& $lesseq(X_517,X_508) )
<=> ? [X_518: $int] : mem2(X_517,X_518,X_511) )
& ! [X_519: $int] :
( ? [X_520: $int] : mem2(X_520,X_519,X_511)
=> mem0(X_519,g_s221_162) ) )
& ! [X_521: $int] :
( mem0(X_521,g_s221_162)
=> ? [X_522: $int] : mem2(X_522,X_521,X_509) )
& ! [X_523: $int,X_524: $int,X_525: $int] :
( ( mem2(X_524,X_523,X_509)
& mem2(X_525,X_523,X_509) )
=> ( X_524 = X_525 ) ) ) ) ).
tff('Define:aprp:20',axiom,
? [X_648: $int] :
( ? [X_649: set_2] :
( ! [X_650: $int,X_651: $int] :
( mem2(X_651,X_650,X_649)
<=> mem2(X_651,X_650,g_s232_152) )
& ! [X_652: $int,X_653: $int,X_654: $int] :
( ( mem2(X_652,X_653,X_649)
& mem2(X_652,X_654,X_649) )
=> ( X_653 = X_654 ) )
& ! [X_655: $int] :
( ( $greatereq(X_655,1)
& $lesseq(X_655,X_648) )
<=> ? [X_656: $int] : mem2(X_655,X_656,X_649) )
& ! [X_657: $int] :
( ? [X_658: $int] : mem2(X_658,X_657,X_649)
=> mem0(X_657,g_s230_153) ) )
& ! [X_659: $int] :
( mem0(X_659,g_s230_153)
=> ? [X_660: $int] : mem2(X_660,X_659,g_s232_152) )
& ! [X_661: $int,X_662: $int,X_663: $int] :
( ( mem2(X_662,X_661,g_s232_152)
& mem2(X_663,X_661,g_s232_152) )
=> ( X_662 = X_663 ) ) ) ).
tff('Define:aprp:21',axiom,
! [X_664: $int] :
( mem0(X_664,g_s233_155)
=> mem0(X_664,g_s222_163) ) ).
tff('Define:aprp:22',axiom,
mem0(g_s234_168,g_s222_163) ).
tff('Define:aprp:23',axiom,
~ mem0(g_s234_168,g_s233_155) ).
tff('Define:aprp:24',axiom,
( ! [X_665: $int,X_666: $int] :
( mem2(X_666,X_665,g_s235_154)
=> ( $greatereq(X_666,0)
& $lesseq(X_666,max_int)
& mem0(X_665,g_s222_163) ) )
& ! [X_667: $int,X_668: $int,X_669: $int] :
( ( mem2(X_667,X_668,g_s235_154)
& mem2(X_667,X_669,g_s235_154) )
=> ( X_668 = X_669 ) ) ) ).
tff('Define:aprp:25',axiom,
? [X_670: $int] :
( ? [X_671: set_2] :
( ! [X_672: $int,X_673: $int] :
( mem2(X_673,X_672,X_671)
<=> mem2(X_673,X_672,g_s235_154) )
& ! [X_674: $int,X_675: $int,X_676: $int] :
( ( mem2(X_674,X_675,X_671)
& mem2(X_674,X_676,X_671) )
=> ( X_675 = X_676 ) )
& ! [X_677: $int] :
( ( $greatereq(X_677,1)
& $lesseq(X_677,X_670) )
<=> ? [X_678: $int] : mem2(X_677,X_678,X_671) )
& ! [X_679: $int] :
( ? [X_680: $int] : mem2(X_680,X_679,X_671)
=> mem0(X_679,g_s233_155) ) )
& ! [X_681: $int] :
( mem0(X_681,g_s233_155)
=> ? [X_682: $int] : mem2(X_682,X_681,g_s235_154) )
& ! [X_683: $int,X_684: $int,X_685: $int] :
( ( mem2(X_684,X_683,g_s235_154)
& mem2(X_685,X_683,g_s235_154) )
=> ( X_684 = X_685 ) ) ) ).
tff('Define:aprp:26',axiom,
mem0(g_s236_169,g_s223_164) ).
tff('Define:aprp:27',axiom,
! [X_686: $int] :
( mem0(X_686,g_s237_170)
=> ( $greatereq(X_686,min_int)
& $lesseq(X_686,max_int) ) ) ).
tff('Define:aprp:28',axiom,
! [X_687: $int] :
( mem0(X_687,g_s237_170)
<=> ( $greatereq(X_687,0)
& $lesseq(X_687,g_s74_74) ) ) ).
tff('Define:aprp:29',axiom,
! [X_688: $int] :
( mem0(X_688,g_s238_171)
=> mem0(X_688,g_s237_170) ) ).
tff('Define:aprp:3',axiom,
( ~ ! [X_526: $int] :
( mem0(X_526,g_s222_163)
<=> $false )
& ! [X_529: $int] :
( mem0(X_529,g_s222_163)
=> $true )
& ? [X_527: $int,X_528: set_2] :
( ? [X_530: set_2] :
( ! [X_531: $int,X_532: $int] :
( mem2(X_532,X_531,X_530)
<=> mem2(X_532,X_531,X_528) )
& ! [X_533: $int,X_534: $int,X_535: $int] :
( ( mem2(X_533,X_534,X_530)
& mem2(X_533,X_535,X_530) )
=> ( X_534 = X_535 ) )
& ! [X_536: $int] :
( ( $greatereq(X_536,1)
& $lesseq(X_536,X_527) )
<=> ? [X_537: $int] : mem2(X_536,X_537,X_530) )
& ! [X_538: $int] :
( ? [X_539: $int] : mem2(X_539,X_538,X_530)
=> mem0(X_538,g_s222_163) ) )
& ! [X_540: $int] :
( mem0(X_540,g_s222_163)
=> ? [X_541: $int] : mem2(X_541,X_540,X_528) )
& ! [X_542: $int,X_543: $int,X_544: $int] :
( ( mem2(X_543,X_542,X_528)
& mem2(X_544,X_542,X_528) )
=> ( X_543 = X_544 ) ) ) ) ).
tff('Define:aprp:30',axiom,
! [X_689: $int] :
( mem0(X_689,g_s238_171)
=> ( $greatereq(X_689,0)
& $lesseq(X_689,max_int) ) ) ).
tff('Define:aprp:31',axiom,
mem0(g_s239_172,g_s237_170) ).
tff('Define:aprp:32',axiom,
~ mem0(g_s239_172,g_s238_171) ).
tff('Define:aprp:33',axiom,
! [X_690: $int] :
( mem0(X_690,g_s240_173)
<=> ( $greatereq(X_690,min_int)
& $lesseq(X_690,max_int) ) ) ).
tff('Define:aprp:34',axiom,
! [X_691: $int] :
( mem0(X_691,g_s241_174)
=> ( $greatereq(X_691,0)
& $lesseq(X_691,max_int) ) ) ).
tff('Define:aprp:35',axiom,
! [X_692: $int] :
( mem0(X_692,g_s241_174)
=> mem0(X_692,g_s240_173) ) ).
tff('Define:aprp:36',axiom,
mem0(g_s242_175,g_s240_173) ).
tff('Define:aprp:37',axiom,
~ mem0(g_s242_175,g_s241_174) ).
tff('Define:aprp:38',axiom,
! [X_693: $int] :
( mem0(X_693,g_s243_176)
<=> ( $greatereq(X_693,min_int)
& $lesseq(X_693,max_int) ) ) ).
tff('Define:aprp:39',axiom,
! [X_694: $int] :
( mem0(X_694,g_s244_177)
=> ( $greatereq(X_694,min_int)
& $lesseq(X_694,max_int) ) ) ).
tff('Define:aprp:4',axiom,
( ~ ! [X_545: $int] :
( mem0(X_545,g_s223_164)
<=> $false )
& ! [X_548: $int] :
( mem0(X_548,g_s223_164)
=> $true )
& ? [X_546: $int,X_547: set_2] :
( ? [X_549: set_2] :
( ! [X_550: $int,X_551: $int] :
( mem2(X_551,X_550,X_549)
<=> mem2(X_551,X_550,X_547) )
& ! [X_552: $int,X_553: $int,X_554: $int] :
( ( mem2(X_552,X_553,X_549)
& mem2(X_552,X_554,X_549) )
=> ( X_553 = X_554 ) )
& ! [X_555: $int] :
( ( $greatereq(X_555,1)
& $lesseq(X_555,X_546) )
<=> ? [X_556: $int] : mem2(X_555,X_556,X_549) )
& ! [X_557: $int] :
( ? [X_558: $int] : mem2(X_558,X_557,X_549)
=> mem0(X_557,g_s223_164) ) )
& ! [X_559: $int] :
( mem0(X_559,g_s223_164)
=> ? [X_560: $int] : mem2(X_560,X_559,X_547) )
& ! [X_561: $int,X_562: $int,X_563: $int] :
( ( mem2(X_562,X_561,X_547)
& mem2(X_563,X_561,X_547) )
=> ( X_562 = X_563 ) ) ) ) ).
tff('Define:aprp:40',axiom,
! [X_695: $int] :
( mem0(X_695,g_s244_177)
=> mem0(X_695,g_s243_176) ) ).
tff('Define:aprp:41',axiom,
mem0(g_s245_178,g_s243_176) ).
tff('Define:aprp:42',axiom,
~ mem0(g_s245_178,g_s244_177) ).
tff('Define:aprp:5',axiom,
! [X_564: $int] :
( mem0(X_564,g_s224_157)
=> mem0(X_564,g_s219_160) ) ).
tff('Define:aprp:6',axiom,
mem0(g_s225_165,g_s219_160) ).
tff('Define:aprp:7',axiom,
~ mem0(g_s225_165,g_s224_157) ).
tff('Define:aprp:8',axiom,
( ! [X_565: $int,X_566: $int] :
( mem2(X_566,X_565,g_s226_156)
=> ( $greatereq(X_566,0)
& $lesseq(X_566,max_int)
& mem0(X_565,g_s219_160) ) )
& ! [X_567: $int,X_568: $int,X_569: $int] :
( ( mem2(X_567,X_568,g_s226_156)
& mem2(X_567,X_569,g_s226_156) )
=> ( X_568 = X_569 ) ) ) ).
tff('Define:aprp:9',axiom,
? [X_570: $int] :
( ? [X_571: set_2] :
( ! [X_572: $int,X_573: $int] :
( mem2(X_573,X_572,X_571)
<=> mem2(X_573,X_572,g_s226_156) )
& ! [X_574: $int,X_575: $int,X_576: $int] :
( ( mem2(X_574,X_575,X_571)
& mem2(X_574,X_576,X_571) )
=> ( X_575 = X_576 ) )
& ! [X_577: $int] :
( ( $greatereq(X_577,1)
& $lesseq(X_577,X_570) )
<=> ? [X_578: $int] : mem2(X_577,X_578,X_571) )
& ! [X_579: $int] :
( ? [X_580: $int] : mem2(X_580,X_579,X_571)
=> mem0(X_579,g_s224_157) ) )
& ! [X_581: $int] :
( mem0(X_581,g_s224_157)
=> ? [X_582: $int] : mem2(X_582,X_581,g_s226_156) )
& ! [X_583: $int,X_584: $int,X_585: $int] :
( ( mem2(X_584,X_583,g_s226_156)
& mem2(X_585,X_583,g_s226_156) )
=> ( X_584 = X_585 ) ) ) ).
tff('Define:ctx:0',axiom,
( ~ ! [X_5: $int] :
( mem0(X_5,g_s0_0)
<=> $false )
& ! [X_8: $int] :
( mem0(X_8,g_s0_0)
=> $true )
& ? [X_6: $int,X_7: set_2] :
( ? [X_9: set_2] :
( ! [X_10: $int,X_11: $int] :
( mem2(X_11,X_10,X_9)
<=> mem2(X_11,X_10,X_7) )
& ! [X_12: $int,X_13: $int,X_14: $int] :
( ( mem2(X_12,X_13,X_9)
& mem2(X_12,X_14,X_9) )
=> ( X_13 = X_14 ) )
& ! [X_15: $int] :
( ( $greatereq(X_15,1)
& $lesseq(X_15,X_6) )
<=> ? [X_16: $int] : mem2(X_15,X_16,X_9) )
& ! [X_17: $int] :
( ? [X_18: $int] : mem2(X_18,X_17,X_9)
=> mem0(X_17,g_s0_0) ) )
& ! [X_19: $int] :
( mem0(X_19,g_s0_0)
=> ? [X_20: $int] : mem2(X_20,X_19,X_7) )
& ! [X_21: $int,X_22: $int,X_23: $int] :
( ( mem2(X_22,X_21,X_7)
& mem2(X_23,X_21,X_7) )
=> ( X_22 = X_23 ) ) ) ) ).
tff('Define:ctx:1',axiom,
( ~ ! [X_24: $int] :
( mem0(X_24,g_s1_1)
<=> $false )
& ! [X_27: $int] :
( mem0(X_27,g_s1_1)
=> $true )
& ? [X_25: $int,X_26: set_2] :
( ? [X_28: set_2] :
( ! [X_29: $int,X_30: $int] :
( mem2(X_30,X_29,X_28)
<=> mem2(X_30,X_29,X_26) )
& ! [X_31: $int,X_32: $int,X_33: $int] :
( ( mem2(X_31,X_32,X_28)
& mem2(X_31,X_33,X_28) )
=> ( X_32 = X_33 ) )
& ! [X_34: $int] :
( ( $greatereq(X_34,1)
& $lesseq(X_34,X_25) )
<=> ? [X_35: $int] : mem2(X_34,X_35,X_28) )
& ! [X_36: $int] :
( ? [X_37: $int] : mem2(X_37,X_36,X_28)
=> mem0(X_36,g_s1_1) ) )
& ! [X_38: $int] :
( mem0(X_38,g_s1_1)
=> ? [X_39: $int] : mem2(X_39,X_38,X_26) )
& ! [X_40: $int,X_41: $int,X_42: $int] :
( ( mem2(X_41,X_40,X_26)
& mem2(X_42,X_40,X_26) )
=> ( X_41 = X_42 ) ) ) ) ).
tff('Define:ctx:10',axiom,
$less(g_s10_10,max_int) ).
tff('Define:ctx:100',axiom,
$lesseq(g_s89_89,g_s31_31) ).
tff('Define:ctx:101',axiom,
$lesseq(g_s90_90,g_s32_32) ).
tff('Define:ctx:102',axiom,
$lesseq(g_s91_91,g_s38_38) ).
tff('Define:ctx:103',axiom,
$lesseq(g_s92_92,g_s37_37) ).
tff('Define:ctx:104',axiom,
$lesseq(g_s93_93,g_s39_39) ).
tff('Define:ctx:105',axiom,
$lesseq(g_s94_94,g_s40_40) ).
tff('Define:ctx:106',axiom,
$lesseq(g_s95_95,g_s41_41) ).
tff('Define:ctx:107',axiom,
$lesseq(g_s96_96,g_s42_42) ).
tff('Define:ctx:108',axiom,
$lesseq(g_s96_96,1) ).
tff('Define:ctx:109',axiom,
$lesseq(g_s97_97,g_s43_43) ).
tff('Define:ctx:11',axiom,
$less(g_s11_11,max_int) ).
tff('Define:ctx:110',axiom,
$lesseq(g_s98_98,g_s44_44) ).
tff('Define:ctx:111',axiom,
$lesseq(g_s99_99,g_s15_15) ).
tff('Define:ctx:112',axiom,
$lesseq(g_s100_100,g_s64_64) ).
tff('Define:ctx:113',axiom,
$lesseq(g_s101_101,g_s65_65) ).
tff('Define:ctx:114',axiom,
$lesseq(g_s102_102,g_s62_62) ).
tff('Define:ctx:115',axiom,
$lesseq(g_s103_103,g_s63_63) ).
tff('Define:ctx:116',axiom,
$lesseq(g_s104_104,g_s46_46) ).
tff('Define:ctx:117',axiom,
$lesseq(g_s105_105,g_s14_14) ).
tff('Define:ctx:118',axiom,
$lesseq(g_s106_106,g_s13_13) ).
tff('Define:ctx:119',axiom,
$lesseq(g_s107_107,g_s58_58) ).
tff('Define:ctx:12',axiom,
$less(g_s12_12,max_int) ).
tff('Define:ctx:120',axiom,
$lesseq(g_s108_108,g_s59_59) ).
tff('Define:ctx:121',axiom,
$lesseq(g_s109_109,g_s61_61) ).
tff('Define:ctx:122',axiom,
$lesseq(g_s110_110,g_s69_69) ).
tff('Define:ctx:123',axiom,
$lesseq(g_s111_111,g_s70_70) ).
tff('Define:ctx:124',axiom,
$lesseq(g_s112_112,g_s48_48) ).
tff('Define:ctx:125',axiom,
$lesseq(g_s113_113,g_s49_49) ).
tff('Define:ctx:126',axiom,
$lesseq(g_s114_114,g_s52_52) ).
tff('Define:ctx:127',axiom,
$lesseq(g_s115_115,g_s53_53) ).
tff('Define:ctx:128',axiom,
$lesseq(g_s116_116,g_s54_54) ).
tff('Define:ctx:129',axiom,
$lesseq(g_s117_117,g_s55_55) ).
tff('Define:ctx:13',axiom,
$lesseq(g_s13_13,g_s14_14) ).
tff('Define:ctx:130',axiom,
$lesseq(g_s118_118,g_s47_47) ).
tff('Define:ctx:131',axiom,
$lesseq(g_s119_119,g_s56_56) ).
tff('Define:ctx:132',axiom,
$lesseq(g_s120_120,g_s71_71) ).
tff('Define:ctx:133',axiom,
$lesseq(g_s121_121,g_s72_72) ).
tff('Define:ctx:134',axiom,
$lesseq(g_s122_122,g_s73_73) ).
tff('Define:ctx:135',axiom,
$lesseq(g_s123_123,g_s33_33) ).
tff('Define:ctx:136',axiom,
$lesseq(g_s124_124,g_s34_34) ).
tff('Define:ctx:137',axiom,
$lesseq(g_s125_125,g_s35_35) ).
tff('Define:ctx:138',axiom,
$lesseq(g_s126_126,g_s36_36) ).
tff('Define:ctx:139',axiom,
$lesseq(g_s127_127,g_s16_16) ).
tff('Define:ctx:14',axiom,
$lesseq(g_s15_15,g_s16_16) ).
tff('Define:ctx:140',axiom,
$lesseq(g_s128_128,g_s66_66) ).
tff('Define:ctx:141',axiom,
$lesseq(g_s129_129,g_s67_67) ).
tff('Define:ctx:142',axiom,
$lesseq(g_s130_130,g_s131_131) ).
tff('Define:ctx:143',axiom,
$lesseq(g_s106_106,g_s105_105) ).
tff('Define:ctx:144',axiom,
$lesseq(g_s132_132,g_s75_75) ).
tff('Define:ctx:145',axiom,
$lesseq(g_s133_133,g_s76_76) ).
tff('Define:ctx:146',axiom,
$lesseq(g_s134_134,g_s77_77) ).
tff('Define:ctx:147',axiom,
$lesseq(g_s135_135,g_s78_78) ).
tff('Define:ctx:148',axiom,
$lesseq(g_s136_136,g_s79_79) ).
tff('Define:ctx:149',axiom,
$lesseq(g_s137_137,g_s18_18) ).
tff('Define:ctx:15',axiom,
$lesseq(g_s17_17,g_s18_18) ).
tff('Define:ctx:150',axiom,
$lesseq(g_s138_138,g_s17_17) ).
tff('Define:ctx:151',axiom,
$lesseq(g_s138_138,g_s137_137) ).
tff('Define:ctx:152',axiom,
$lesseq(g_s139_139,g_s19_19) ).
tff('Define:ctx:153',axiom,
$lesseq(g_s139_139,g_s137_137) ).
tff('Define:ctx:154',axiom,
$lesseq(g_s83_83,g_s140_140) ).
tff('Define:ctx:155',axiom,
$lesseq(g_s94_94,g_s141_141) ).
tff('Define:ctx:156',axiom,
$lesseq(g_s95_95,g_s141_141) ).
tff('Define:ctx:157',axiom,
$lesseq(g_s96_96,g_s141_141) ).
tff('Define:ctx:158',axiom,
$lesseq(g_s97_97,g_s141_141) ).
tff('Define:ctx:159',axiom,
$lesseq($sum($sum($sum(g_s95_95,g_s94_94),g_s97_97),g_s96_96),g_s141_141) ).
tff('Define:ctx:16',axiom,
$lesseq(g_s19_19,g_s18_18) ).
tff('Define:ctx:160',axiom,
( $greatereq(g_s83_83,0)
& $lesseq(g_s83_83,max_int) ) ).
tff('Define:ctx:161',axiom,
( $greatereq(g_s84_84,0)
& $lesseq(g_s84_84,max_int) ) ).
tff('Define:ctx:162',axiom,
( $greatereq(g_s85_85,0)
& $lesseq(g_s85_85,max_int) ) ).
tff('Define:ctx:163',axiom,
( $greatereq(g_s86_86,0)
& $lesseq(g_s86_86,max_int) ) ).
tff('Define:ctx:164',axiom,
( $greatereq(g_s87_87,0)
& $lesseq(g_s87_87,max_int) ) ).
tff('Define:ctx:165',axiom,
( $greatereq(g_s88_88,0)
& $lesseq(g_s88_88,max_int) ) ).
tff('Define:ctx:166',axiom,
( $greatereq(g_s89_89,0)
& $lesseq(g_s89_89,max_int) ) ).
tff('Define:ctx:167',axiom,
( $greatereq(g_s90_90,0)
& $lesseq(g_s90_90,max_int) ) ).
tff('Define:ctx:168',axiom,
( $greatereq(g_s91_91,0)
& $lesseq(g_s91_91,max_int) ) ).
tff('Define:ctx:169',axiom,
( $greatereq(g_s92_92,0)
& $lesseq(g_s92_92,max_int) ) ).
tff('Define:ctx:17',axiom,
$less(g_s20_20,g_s21_21) ).
tff('Define:ctx:170',axiom,
( $greatereq(g_s93_93,0)
& $lesseq(g_s93_93,max_int) ) ).
tff('Define:ctx:171',axiom,
( $greatereq(g_s94_94,0)
& $lesseq(g_s94_94,max_int) ) ).
tff('Define:ctx:172',axiom,
( $greatereq(g_s95_95,0)
& $lesseq(g_s95_95,max_int) ) ).
tff('Define:ctx:173',axiom,
( $greatereq(g_s96_96,0)
& $lesseq(g_s96_96,max_int) ) ).
tff('Define:ctx:174',axiom,
( $greatereq(g_s97_97,0)
& $lesseq(g_s97_97,max_int) ) ).
tff('Define:ctx:175',axiom,
( $greater(g_s98_98,0)
& $lesseq(g_s98_98,max_int) ) ).
tff('Define:ctx:176',axiom,
( $greatereq(g_s99_99,0)
& $lesseq(g_s99_99,max_int) ) ).
tff('Define:ctx:177',axiom,
( $greatereq(g_s100_100,0)
& $lesseq(g_s100_100,max_int) ) ).
tff('Define:ctx:178',axiom,
( $greatereq(g_s101_101,0)
& $lesseq(g_s101_101,max_int) ) ).
tff('Define:ctx:179',axiom,
( $greatereq(g_s102_102,0)
& $lesseq(g_s102_102,max_int) ) ).
tff('Define:ctx:18',axiom,
~ ( $greatereq(g_s22_22,g_s20_20)
& $lesseq(g_s22_22,g_s21_21) ) ).
tff('Define:ctx:180',axiom,
( $greatereq(g_s103_103,0)
& $lesseq(g_s103_103,max_int) ) ).
tff('Define:ctx:181',axiom,
( $greatereq(g_s104_104,0)
& $lesseq(g_s104_104,max_int) ) ).
tff('Define:ctx:182',axiom,
( $greatereq(g_s105_105,0)
& $lesseq(g_s105_105,max_int) ) ).
tff('Define:ctx:183',axiom,
( $greatereq(g_s106_106,0)
& $lesseq(g_s106_106,max_int) ) ).
tff('Define:ctx:184',axiom,
( $greatereq(g_s107_107,0)
& $lesseq(g_s107_107,max_int) ) ).
tff('Define:ctx:185',axiom,
( $greatereq(g_s108_108,0)
& $lesseq(g_s108_108,max_int) ) ).
tff('Define:ctx:186',axiom,
( $greatereq(g_s109_109,0)
& $lesseq(g_s109_109,max_int) ) ).
tff('Define:ctx:187',axiom,
( $greatereq(g_s128_128,0)
& $lesseq(g_s128_128,max_int) ) ).
tff('Define:ctx:188',axiom,
( $greatereq(g_s129_129,0)
& $lesseq(g_s129_129,max_int) ) ).
tff('Define:ctx:189',axiom,
mem0(g_s130_130,g_s142_142) ).
tff('Define:ctx:19',axiom,
g_s23_23 = max_int ).
tff('Define:ctx:190',axiom,
( $greatereq(g_s111_111,0)
& $lesseq(g_s111_111,max_int) ) ).
tff('Define:ctx:191',axiom,
( $greatereq(g_s112_112,0)
& $lesseq(g_s112_112,max_int) ) ).
tff('Define:ctx:192',axiom,
( $greatereq(g_s113_113,0)
& $lesseq(g_s113_113,max_int) ) ).
tff('Define:ctx:193',axiom,
( $greatereq(g_s114_114,0)
& $lesseq(g_s114_114,max_int) ) ).
tff('Define:ctx:194',axiom,
( $greatereq(g_s115_115,0)
& $lesseq(g_s115_115,max_int) ) ).
tff('Define:ctx:195',axiom,
( $greatereq(g_s116_116,0)
& $lesseq(g_s116_116,max_int) ) ).
tff('Define:ctx:196',axiom,
( $greatereq(g_s117_117,0)
& $lesseq(g_s117_117,max_int) ) ).
tff('Define:ctx:197',axiom,
( $greatereq(g_s118_118,0)
& $lesseq(g_s118_118,max_int) ) ).
tff('Define:ctx:198',axiom,
( $greatereq(g_s119_119,0)
& $lesseq(g_s119_119,max_int) ) ).
tff('Define:ctx:199',axiom,
( $greatereq(g_s120_120,0)
& $lesseq(g_s120_120,max_int) ) ).
tff('Define:ctx:2',axiom,
( ~ ! [X_43: $int] :
( mem0(X_43,g_s2_2)
<=> $false )
& ! [X_46: $int] :
( mem0(X_46,g_s2_2)
=> $true )
& ? [X_44: $int,X_45: set_2] :
( ? [X_47: set_2] :
( ! [X_48: $int,X_49: $int] :
( mem2(X_49,X_48,X_47)
<=> mem2(X_49,X_48,X_45) )
& ! [X_50: $int,X_51: $int,X_52: $int] :
( ( mem2(X_50,X_51,X_47)
& mem2(X_50,X_52,X_47) )
=> ( X_51 = X_52 ) )
& ! [X_53: $int] :
( ( $greatereq(X_53,1)
& $lesseq(X_53,X_44) )
<=> ? [X_54: $int] : mem2(X_53,X_54,X_47) )
& ! [X_55: $int] :
( ? [X_56: $int] : mem2(X_56,X_55,X_47)
=> mem0(X_55,g_s2_2) ) )
& ! [X_57: $int] :
( mem0(X_57,g_s2_2)
=> ? [X_58: $int] : mem2(X_58,X_57,X_45) )
& ! [X_59: $int,X_60: $int,X_61: $int] :
( ( mem2(X_60,X_59,X_45)
& mem2(X_61,X_59,X_45) )
=> ( X_60 = X_61 ) ) ) ) ).
tff('Define:ctx:20',axiom,
g_s24_24 = $product(g_s25_25,50) ).
tff('Define:ctx:200',axiom,
( $greatereq(g_s121_121,0)
& $lesseq(g_s121_121,max_int) ) ).
tff('Define:ctx:201',axiom,
( $greatereq(g_s122_122,0)
& $lesseq(g_s122_122,max_int) ) ).
tff('Define:ctx:202',axiom,
( $greatereq(g_s123_123,0)
& $lesseq(g_s123_123,max_int) ) ).
tff('Define:ctx:203',axiom,
( $greatereq(g_s124_124,0)
& $lesseq(g_s124_124,max_int) ) ).
tff('Define:ctx:204',axiom,
( $greatereq(g_s125_125,0)
& $lesseq(g_s125_125,max_int) ) ).
tff('Define:ctx:205',axiom,
( $greatereq(g_s126_126,0)
& $lesseq(g_s126_126,max_int) ) ).
tff('Define:ctx:206',axiom,
( $greatereq(g_s127_127,0)
& $lesseq(g_s127_127,max_int) ) ).
tff('Define:ctx:207',axiom,
( $greatereq(g_s110_110,0)
& $lesseq(g_s110_110,max_int) ) ).
tff('Define:ctx:208',axiom,
( $greatereq(g_s132_132,0)
& $lesseq(g_s132_132,max_int) ) ).
tff('Define:ctx:209',axiom,
( $greatereq(g_s133_133,0)
& $lesseq(g_s133_133,max_int) ) ).
tff('Define:ctx:21',axiom,
( $greatereq(g_s10_10,0)
& $lesseq(g_s10_10,max_int) ) ).
tff('Define:ctx:210',axiom,
( $greatereq(g_s134_134,0)
& $lesseq(g_s134_134,max_int) ) ).
tff('Define:ctx:211',axiom,
( $greatereq(g_s135_135,0)
& $lesseq(g_s135_135,max_int) ) ).
tff('Define:ctx:212',axiom,
( $greatereq(g_s136_136,0)
& $lesseq(g_s136_136,max_int) ) ).
tff('Define:ctx:213',axiom,
( $greatereq(g_s137_137,0)
& $lesseq(g_s137_137,max_int) ) ).
tff('Define:ctx:214',axiom,
( $greatereq(g_s138_138,0)
& $lesseq(g_s138_138,max_int) ) ).
tff('Define:ctx:215',axiom,
( $greatereq(g_s139_139,0)
& $lesseq(g_s139_139,max_int) ) ).
tff('Define:ctx:216',axiom,
? [X_195: set_3] :
( ! [X_196: $int,X_197: $int,X_198: $int] :
( mem3(X_198,X_197,X_196,X_195)
<=> mem3(X_198,X_197,X_196,g_s143_143) )
& ! [X_199: $int,X_200: $int,X_201: $int,X_202: $int] :
( ( mem3(X_200,X_199,X_201,X_195)
& mem3(X_200,X_199,X_202,X_195) )
=> ( X_201 = X_202 ) )
& ! [X_203: $int,X_204: $int] :
( ( $true
& $greatereq(X_203,0) )
<=> ? [X_205: $int] : mem3(X_204,X_203,X_205,X_195) )
& ! [X_206: $int] :
( ? [X_207: $int,X_208: $int] : mem3(X_208,X_207,X_206,X_195)
=> $true ) ) ).
tff('Define:ctx:217',axiom,
! [X_209: $int,X_210: $int,X_211: $int] :
( mem3(X_211,X_210,X_209,g_s143_143)
<=> ( ( $greatereq(X_211,0)
& $greatereq(X_210,0)
& ( X_209 = divB(X_211,iexp(2,X_210)) ) )
| ( $true
& $greatereq(X_210,0)
& $less(X_211,0)
& ( X_209 = $uminus(divB($difference($sum($uminus(X_211),iexp(2,X_210)),1),iexp(2,X_210))) ) ) ) ) ).
tff('Define:ctx:218',axiom,
? [X_212: set_4] :
( ! [X_213: $int,X_214: $o] :
( mem4((X_214),X_213,X_212)
<=> mem4((X_214),X_213,g_s146_144) )
& ! [X_215: $o,X_216: $int,X_217: $int] :
( ( mem4((X_215),X_216,X_212)
& mem4((X_215),X_217,X_212) )
=> ( X_216 = X_217 ) )
& ! [X_218: $o] :
( $true
<=> ? [X_219: $int] : mem4((X_218),X_219,X_212) )
& ! [X_220: $int] :
( ? [X_221: $o] : mem4((X_221),X_220,X_212)
=> ( $greatereq(X_220,0)
& $lesseq(X_220,max_int) ) ) ) ).
tff('Define:ctx:219',axiom,
! [X_222: $int,X_223: $o] :
( mem4((X_223),X_222,g_s146_144)
<=> ( ( ( (X_223)
<=> $true )
& ( X_222 = 1 ) )
| ( ( (X_223)
<=> $false )
& ( X_222 = 0 ) ) ) ) ).
tff('Define:ctx:22',axiom,
( $greatereq(g_s11_11,0)
& $lesseq(g_s11_11,max_int) ) ).
tff('Define:ctx:220',axiom,
! [X_224: $int,X_225: $int] :
( mem2(X_225,X_224,g_s147_145)
<=> ( $true
& ( ( X_224 = X_225 )
| ( X_224 = $uminus(X_225) ) )
& ! [X_226: $int] :
( ( ( X_226 = X_225 )
| ( X_226 = $uminus(X_225) ) )
=> $greatereq(X_224,X_226) ) ) ) ).
tff('Define:ctx:221',axiom,
! [X_227: $int,X_228: $int] :
( mem2(X_228,X_227,g_s149_146)
<=> ( $greatereq(X_228,0)
& $true
& $lesseq($product(X_227,X_227),X_228)
& ! [X_229: $int] :
( ( $true
& $lesseq($product(X_229,X_229),X_228) )
=> $greatereq(X_227,X_229) ) ) ) ).
tff('Define:ctx:222',axiom,
( $greatereq(g_s151_147,min_int)
& $lesseq(g_s151_147,max_int) ) ).
tff('Define:ctx:223',axiom,
( $greatereq(g_s152_148,min_int)
& $lesseq(g_s152_148,max_int) ) ).
tff('Define:ctx:224',axiom,
( $greatereq(g_s153_149,min_int)
& $lesseq(g_s153_149,max_int) ) ).
tff('Define:ctx:225',axiom,
( $greatereq(g_s154_150,min_int)
& $lesseq(g_s154_150,max_int) ) ).
tff('Define:ctx:226',axiom,
( $greatereq(g_s155_151,min_int)
& $lesseq(g_s155_151,max_int) ) ).
tff('Define:ctx:23',axiom,
( $greatereq(g_s12_12,0)
& $lesseq(g_s12_12,max_int) ) ).
tff('Define:ctx:24',axiom,
( $greatereq(g_s26_26,0)
& $lesseq(g_s26_26,max_int) ) ).
tff('Define:ctx:25',axiom,
( $greatereq(g_s27_27,0)
& $lesseq(g_s27_27,max_int) ) ).
tff('Define:ctx:26',axiom,
( $greatereq(g_s28_28,0)
& $lesseq(g_s28_28,max_int) ) ).
tff('Define:ctx:27',axiom,
( $greatereq(g_s29_29,0)
& $lesseq(g_s29_29,max_int) ) ).
tff('Define:ctx:28',axiom,
( $greatereq(g_s30_30,0)
& $lesseq(g_s30_30,max_int) ) ).
tff('Define:ctx:29',axiom,
( $greatereq(g_s31_31,0)
& $lesseq(g_s31_31,max_int) ) ).
tff('Define:ctx:3',axiom,
( ~ ! [X_62: $int] :
( mem0(X_62,g_s3_3)
<=> $false )
& ! [X_65: $int] :
( mem0(X_65,g_s3_3)
=> $true )
& ? [X_63: $int,X_64: set_2] :
( ? [X_66: set_2] :
( ! [X_67: $int,X_68: $int] :
( mem2(X_68,X_67,X_66)
<=> mem2(X_68,X_67,X_64) )
& ! [X_69: $int,X_70: $int,X_71: $int] :
( ( mem2(X_69,X_70,X_66)
& mem2(X_69,X_71,X_66) )
=> ( X_70 = X_71 ) )
& ! [X_72: $int] :
( ( $greatereq(X_72,1)
& $lesseq(X_72,X_63) )
<=> ? [X_73: $int] : mem2(X_72,X_73,X_66) )
& ! [X_74: $int] :
( ? [X_75: $int] : mem2(X_75,X_74,X_66)
=> mem0(X_74,g_s3_3) ) )
& ! [X_76: $int] :
( mem0(X_76,g_s3_3)
=> ? [X_77: $int] : mem2(X_77,X_76,X_64) )
& ! [X_78: $int,X_79: $int,X_80: $int] :
( ( mem2(X_79,X_78,X_64)
& mem2(X_80,X_78,X_64) )
=> ( X_79 = X_80 ) ) ) ) ).
tff('Define:ctx:30',axiom,
( $greatereq(g_s32_32,0)
& $lesseq(g_s32_32,max_int) ) ).
tff('Define:ctx:31',axiom,
( $greatereq(g_s33_33,0)
& $lesseq(g_s33_33,max_int) ) ).
tff('Define:ctx:32',axiom,
( $greatereq(g_s34_34,0)
& $lesseq(g_s34_34,max_int) ) ).
tff('Define:ctx:33',axiom,
( $greatereq(g_s35_35,0)
& $lesseq(g_s35_35,max_int) ) ).
tff('Define:ctx:34',axiom,
( $greatereq(g_s36_36,0)
& $lesseq(g_s36_36,max_int) ) ).
tff('Define:ctx:35',axiom,
( $greatereq(g_s16_16,0)
& $lesseq(g_s16_16,max_int) ) ).
tff('Define:ctx:36',axiom,
( $greatereq(g_s37_37,0)
& $lesseq(g_s37_37,max_int) ) ).
tff('Define:ctx:37',axiom,
( $greatereq(g_s38_38,0)
& $lesseq(g_s38_38,max_int) ) ).
tff('Define:ctx:38',axiom,
( $greatereq(g_s39_39,0)
& $lesseq(g_s39_39,max_int) ) ).
tff('Define:ctx:39',axiom,
( $greatereq(g_s40_40,0)
& $lesseq(g_s40_40,max_int) ) ).
tff('Define:ctx:4',axiom,
( ~ ! [X_81: $int] :
( mem0(X_81,g_s4_4)
<=> $false )
& ! [X_84: $int] :
( mem0(X_84,g_s4_4)
=> $true )
& ? [X_82: $int,X_83: set_2] :
( ? [X_85: set_2] :
( ! [X_86: $int,X_87: $int] :
( mem2(X_87,X_86,X_85)
<=> mem2(X_87,X_86,X_83) )
& ! [X_88: $int,X_89: $int,X_90: $int] :
( ( mem2(X_88,X_89,X_85)
& mem2(X_88,X_90,X_85) )
=> ( X_89 = X_90 ) )
& ! [X_91: $int] :
( ( $greatereq(X_91,1)
& $lesseq(X_91,X_82) )
<=> ? [X_92: $int] : mem2(X_91,X_92,X_85) )
& ! [X_93: $int] :
( ? [X_94: $int] : mem2(X_94,X_93,X_85)
=> mem0(X_93,g_s4_4) ) )
& ! [X_95: $int] :
( mem0(X_95,g_s4_4)
=> ? [X_96: $int] : mem2(X_96,X_95,X_83) )
& ! [X_97: $int,X_98: $int,X_99: $int] :
( ( mem2(X_98,X_97,X_83)
& mem2(X_99,X_97,X_83) )
=> ( X_98 = X_99 ) ) ) ) ).
tff('Define:ctx:40',axiom,
( $greatereq(g_s41_41,0)
& $lesseq(g_s41_41,max_int) ) ).
tff('Define:ctx:41',axiom,
( $greatereq(g_s42_42,0)
& $lesseq(g_s42_42,max_int) ) ).
tff('Define:ctx:42',axiom,
( $greatereq(g_s43_43,0)
& $lesseq(g_s43_43,max_int) ) ).
tff('Define:ctx:43',axiom,
( $greater(g_s44_44,0)
& $lesseq(g_s44_44,max_int) ) ).
tff('Define:ctx:44',axiom,
( $greatereq(g_s45_45,0)
& $lesseq(g_s45_45,max_int) ) ).
tff('Define:ctx:45',axiom,
( $greatereq(g_s15_15,0)
& $lesseq(g_s15_15,max_int) ) ).
tff('Define:ctx:46',axiom,
( $greatereq(g_s46_46,0)
& $lesseq(g_s46_46,max_int) ) ).
tff('Define:ctx:47',axiom,
( $greatereq(g_s47_47,0)
& $lesseq(g_s47_47,max_int) ) ).
tff('Define:ctx:48',axiom,
( $greatereq(g_s48_48,0)
& $lesseq(g_s48_48,max_int) ) ).
tff('Define:ctx:49',axiom,
( $greatereq(g_s49_49,0)
& $lesseq(g_s49_49,max_int) ) ).
tff('Define:ctx:5',axiom,
( ~ ! [X_100: $int] :
( mem0(X_100,g_s5_5)
<=> $false )
& ! [X_103: $int] :
( mem0(X_103,g_s5_5)
=> $true )
& ? [X_101: $int,X_102: set_2] :
( ? [X_104: set_2] :
( ! [X_105: $int,X_106: $int] :
( mem2(X_106,X_105,X_104)
<=> mem2(X_106,X_105,X_102) )
& ! [X_107: $int,X_108: $int,X_109: $int] :
( ( mem2(X_107,X_108,X_104)
& mem2(X_107,X_109,X_104) )
=> ( X_108 = X_109 ) )
& ! [X_110: $int] :
( ( $greatereq(X_110,1)
& $lesseq(X_110,X_101) )
<=> ? [X_111: $int] : mem2(X_110,X_111,X_104) )
& ! [X_112: $int] :
( ? [X_113: $int] : mem2(X_113,X_112,X_104)
=> mem0(X_112,g_s5_5) ) )
& ! [X_114: $int] :
( mem0(X_114,g_s5_5)
=> ? [X_115: $int] : mem2(X_115,X_114,X_102) )
& ! [X_116: $int,X_117: $int,X_118: $int] :
( ( mem2(X_117,X_116,X_102)
& mem2(X_118,X_116,X_102) )
=> ( X_117 = X_118 ) ) ) ) ).
tff('Define:ctx:50',axiom,
( $greatereq(g_s50_50,0)
& $lesseq(g_s50_50,max_int) ) ).
tff('Define:ctx:51',axiom,
( $greatereq(g_s51_51,0)
& $lesseq(g_s51_51,max_int) ) ).
tff('Define:ctx:52',axiom,
( $greatereq(g_s52_52,0)
& $lesseq(g_s52_52,max_int) ) ).
tff('Define:ctx:53',axiom,
( $greatereq(g_s53_53,0)
& $lesseq(g_s53_53,max_int) ) ).
tff('Define:ctx:54',axiom,
( $greatereq(g_s54_54,0)
& $lesseq(g_s54_54,max_int) ) ).
tff('Define:ctx:55',axiom,
( $greatereq(g_s55_55,0)
& $lesseq(g_s55_55,max_int) ) ).
tff('Define:ctx:56',axiom,
( $greatereq(g_s56_56,0)
& $lesseq(g_s56_56,max_int) ) ).
tff('Define:ctx:57',axiom,
( $greatereq(g_s57_57,0)
& $lesseq(g_s57_57,max_int) ) ).
tff('Define:ctx:58',axiom,
( $greatereq(g_s14_14,0)
& $lesseq(g_s14_14,max_int) ) ).
tff('Define:ctx:59',axiom,
( $greatereq(g_s13_13,0)
& $lesseq(g_s13_13,max_int) ) ).
tff('Define:ctx:6',axiom,
( ~ ! [X_119: $int] :
( mem0(X_119,g_s6_6)
<=> $false )
& ! [X_122: $int] :
( mem0(X_122,g_s6_6)
=> $true )
& ? [X_120: $int,X_121: set_2] :
( ? [X_123: set_2] :
( ! [X_124: $int,X_125: $int] :
( mem2(X_125,X_124,X_123)
<=> mem2(X_125,X_124,X_121) )
& ! [X_126: $int,X_127: $int,X_128: $int] :
( ( mem2(X_126,X_127,X_123)
& mem2(X_126,X_128,X_123) )
=> ( X_127 = X_128 ) )
& ! [X_129: $int] :
( ( $greatereq(X_129,1)
& $lesseq(X_129,X_120) )
<=> ? [X_130: $int] : mem2(X_129,X_130,X_123) )
& ! [X_131: $int] :
( ? [X_132: $int] : mem2(X_132,X_131,X_123)
=> mem0(X_131,g_s6_6) ) )
& ! [X_133: $int] :
( mem0(X_133,g_s6_6)
=> ? [X_134: $int] : mem2(X_134,X_133,X_121) )
& ! [X_135: $int,X_136: $int,X_137: $int] :
( ( mem2(X_136,X_135,X_121)
& mem2(X_137,X_135,X_121) )
=> ( X_136 = X_137 ) ) ) ) ).
tff('Define:ctx:60',axiom,
( $greatereq(g_s58_58,0)
& $lesseq(g_s58_58,max_int) ) ).
tff('Define:ctx:61',axiom,
( $greatereq(g_s59_59,0)
& $lesseq(g_s59_59,max_int) ) ).
tff('Define:ctx:62',axiom,
( $greatereq(g_s60_60,0)
& $lesseq(g_s60_60,max_int) ) ).
tff('Define:ctx:63',axiom,
( $greatereq(g_s61_61,0)
& $lesseq(g_s61_61,max_int) ) ).
tff('Define:ctx:64',axiom,
( $greatereq(g_s62_62,0)
& $lesseq(g_s62_62,max_int) ) ).
tff('Define:ctx:65',axiom,
( $greatereq(g_s63_63,0)
& $lesseq(g_s63_63,max_int) ) ).
tff('Define:ctx:66',axiom,
( $greatereq(g_s64_64,0)
& $lesseq(g_s64_64,max_int) ) ).
tff('Define:ctx:67',axiom,
( $greatereq(g_s65_65,0)
& $lesseq(g_s65_65,max_int) ) ).
tff('Define:ctx:68',axiom,
( $greatereq(g_s66_66,0)
& $lesseq(g_s66_66,max_int) ) ).
tff('Define:ctx:69',axiom,
( $greatereq(g_s67_67,0)
& $lesseq(g_s67_67,max_int) ) ).
tff('Define:ctx:7',axiom,
( ~ ! [X_138: $int] :
( mem0(X_138,g_s7_7)
<=> $false )
& ! [X_141: $int] :
( mem0(X_141,g_s7_7)
=> $true )
& ? [X_139: $int,X_140: set_2] :
( ? [X_142: set_2] :
( ! [X_143: $int,X_144: $int] :
( mem2(X_144,X_143,X_142)
<=> mem2(X_144,X_143,X_140) )
& ! [X_145: $int,X_146: $int,X_147: $int] :
( ( mem2(X_145,X_146,X_142)
& mem2(X_145,X_147,X_142) )
=> ( X_146 = X_147 ) )
& ! [X_148: $int] :
( ( $greatereq(X_148,1)
& $lesseq(X_148,X_139) )
<=> ? [X_149: $int] : mem2(X_148,X_149,X_142) )
& ! [X_150: $int] :
( ? [X_151: $int] : mem2(X_151,X_150,X_142)
=> mem0(X_150,g_s7_7) ) )
& ! [X_152: $int] :
( mem0(X_152,g_s7_7)
=> ? [X_153: $int] : mem2(X_153,X_152,X_140) )
& ! [X_154: $int,X_155: $int,X_156: $int] :
( ( mem2(X_155,X_154,X_140)
& mem2(X_156,X_154,X_140) )
=> ( X_155 = X_156 ) ) ) ) ).
tff('Define:ctx:70',axiom,
( $greatereq(g_s68_68,0)
& $lesseq(g_s68_68,max_int) ) ).
tff('Define:ctx:71',axiom,
( $greatereq(g_s69_69,0)
& $lesseq(g_s69_69,max_int) ) ).
tff('Define:ctx:72',axiom,
( $greatereq(g_s70_70,0)
& $lesseq(g_s70_70,max_int) ) ).
tff('Define:ctx:73',axiom,
( $greatereq(g_s71_71,0)
& $lesseq(g_s71_71,max_int) ) ).
tff('Define:ctx:74',axiom,
( $greatereq(g_s72_72,0)
& $lesseq(g_s72_72,max_int) ) ).
tff('Define:ctx:75',axiom,
( $greatereq(g_s73_73,0)
& $lesseq(g_s73_73,max_int) ) ).
tff('Define:ctx:76',axiom,
( $greater(g_s74_74,0)
& $lesseq(g_s74_74,max_int) ) ).
tff('Define:ctx:77',axiom,
( $greatereq(g_s75_75,0)
& $lesseq(g_s75_75,max_int) ) ).
tff('Define:ctx:78',axiom,
( $greatereq(g_s76_76,0)
& $lesseq(g_s76_76,max_int) ) ).
tff('Define:ctx:79',axiom,
( $greatereq(g_s77_77,0)
& $lesseq(g_s77_77,max_int) ) ).
tff('Define:ctx:8',axiom,
( ~ ! [X_157: $int] :
( mem0(X_157,g_s8_8)
<=> $false )
& ! [X_160: $int] :
( mem0(X_160,g_s8_8)
=> $true )
& ? [X_158: $int,X_159: set_2] :
( ? [X_161: set_2] :
( ! [X_162: $int,X_163: $int] :
( mem2(X_163,X_162,X_161)
<=> mem2(X_163,X_162,X_159) )
& ! [X_164: $int,X_165: $int,X_166: $int] :
( ( mem2(X_164,X_165,X_161)
& mem2(X_164,X_166,X_161) )
=> ( X_165 = X_166 ) )
& ! [X_167: $int] :
( ( $greatereq(X_167,1)
& $lesseq(X_167,X_158) )
<=> ? [X_168: $int] : mem2(X_167,X_168,X_161) )
& ! [X_169: $int] :
( ? [X_170: $int] : mem2(X_170,X_169,X_161)
=> mem0(X_169,g_s8_8) ) )
& ! [X_171: $int] :
( mem0(X_171,g_s8_8)
=> ? [X_172: $int] : mem2(X_172,X_171,X_159) )
& ! [X_173: $int,X_174: $int,X_175: $int] :
( ( mem2(X_174,X_173,X_159)
& mem2(X_175,X_173,X_159) )
=> ( X_174 = X_175 ) ) ) ) ).
tff('Define:ctx:80',axiom,
( $greatereq(g_s78_78,0)
& $lesseq(g_s78_78,max_int) ) ).
tff('Define:ctx:81',axiom,
( $greatereq(g_s79_79,0)
& $lesseq(g_s79_79,max_int) ) ).
tff('Define:ctx:82',axiom,
( $greatereq(g_s18_18,0)
& $lesseq(g_s18_18,max_int) ) ).
tff('Define:ctx:83',axiom,
( $greatereq(g_s17_17,0)
& $lesseq(g_s17_17,max_int) ) ).
tff('Define:ctx:84',axiom,
( $greatereq(g_s19_19,0)
& $lesseq(g_s19_19,max_int) ) ).
tff('Define:ctx:85',axiom,
( $greatereq(g_s24_24,0)
& $lesseq(g_s24_24,max_int) ) ).
tff('Define:ctx:86',axiom,
( $greatereq(g_s25_25,0)
& $lesseq(g_s25_25,max_int) ) ).
tff('Define:ctx:87',axiom,
( $greatereq(g_s80_80,0)
& $lesseq(g_s80_80,max_int) ) ).
tff('Define:ctx:88',axiom,
( $greatereq(g_s23_23,0)
& $lesseq(g_s23_23,max_int) ) ).
tff('Define:ctx:89',axiom,
( $greatereq(g_s81_81,0)
& $lesseq(g_s81_81,max_int) ) ).
tff('Define:ctx:9',axiom,
( ~ ! [X_176: $int] :
( mem0(X_176,g_s9_9)
<=> $false )
& ! [X_179: $int] :
( mem0(X_179,g_s9_9)
=> $true )
& ? [X_177: $int,X_178: set_2] :
( ? [X_180: set_2] :
( ! [X_181: $int,X_182: $int] :
( mem2(X_182,X_181,X_180)
<=> mem2(X_182,X_181,X_178) )
& ! [X_183: $int,X_184: $int,X_185: $int] :
( ( mem2(X_183,X_184,X_180)
& mem2(X_183,X_185,X_180) )
=> ( X_184 = X_185 ) )
& ! [X_186: $int] :
( ( $greatereq(X_186,1)
& $lesseq(X_186,X_177) )
<=> ? [X_187: $int] : mem2(X_186,X_187,X_180) )
& ! [X_188: $int] :
( ? [X_189: $int] : mem2(X_189,X_188,X_180)
=> mem0(X_188,g_s9_9) ) )
& ! [X_190: $int] :
( mem0(X_190,g_s9_9)
=> ? [X_191: $int] : mem2(X_191,X_190,X_178) )
& ! [X_192: $int,X_193: $int,X_194: $int] :
( ( mem2(X_193,X_192,X_178)
& mem2(X_194,X_192,X_178) )
=> ( X_193 = X_194 ) ) ) ) ).
tff('Define:ctx:90',axiom,
( $greatereq(g_s82_82,0)
& $lesseq(g_s82_82,max_int) ) ).
tff('Define:ctx:91',axiom,
( $greatereq(g_s20_20,min_int)
& $lesseq(g_s20_20,max_int) ) ).
tff('Define:ctx:92',axiom,
( $greatereq(g_s21_21,0)
& $lesseq(g_s21_21,max_int) ) ).
tff('Define:ctx:93',axiom,
( $greatereq(g_s22_22,min_int)
& $lesseq(g_s22_22,max_int) ) ).
tff('Define:ctx:94',axiom,
$lesseq(g_s83_83,g_s60_60) ).
tff('Define:ctx:95',axiom,
$lesseq(g_s84_84,g_s26_26) ).
tff('Define:ctx:96',axiom,
$lesseq(g_s85_85,g_s27_27) ).
tff('Define:ctx:97',axiom,
$lesseq(g_s86_86,g_s28_28) ).
tff('Define:ctx:98',axiom,
$lesseq(g_s87_87,g_s29_29) ).
tff('Define:ctx:99',axiom,
$lesseq(g_s88_88,g_s30_30) ).
tff('Define:imlprp:0',axiom,
! [X_696: $int] :
( mem0(X_696,g_s224_157)
<=> ( $greatereq(X_696,1)
& $lesseq(X_696,g_s107_107) ) ) ).
tff('Define:imlprp:1',axiom,
! [X_697: $int,X_698: $int] :
( mem2(X_698,X_697,g_s226_156)
<=> ( ( X_698 = X_697 )
& mem0(X_698,g_s224_157) ) ) ).
tff('Define:imlprp:10',axiom,
! [X_710: $int] :
( mem0(X_710,g_s244_177)
<=> ( $greatereq(X_710,g_s20_20)
& $lesseq(X_710,g_s21_21) ) ) ).
tff('Define:imlprp:11',axiom,
g_s225_165 = 0 ).
tff('Define:imlprp:12',axiom,
! [X_711: $int] :
( mem0(X_711,g_s219_160)
<=> ( $greatereq(X_711,0)
& $lesseq(X_711,g_s58_58) ) ) ).
tff('Define:imlprp:13',axiom,
g_s228_166 = 0 ).
tff('Define:imlprp:14',axiom,
! [X_712: $int] :
( mem0(X_712,g_s220_161)
<=> ( $greatereq(X_712,0)
& $lesseq(X_712,g_s59_59) ) ) ).
tff('Define:imlprp:15',axiom,
g_s231_167 = 0 ).
tff('Define:imlprp:16',axiom,
! [X_713: $int] :
( mem0(X_713,g_s221_162)
<=> ( $greatereq(X_713,0)
& $lesseq(X_713,g_s71_71) ) ) ).
tff('Define:imlprp:17',axiom,
g_s234_168 = 0 ).
tff('Define:imlprp:18',axiom,
! [X_714: $int] :
( mem0(X_714,g_s222_163)
<=> ( $greatereq(X_714,0)
& $lesseq(X_714,g_s72_72) ) ) ).
tff('Define:imlprp:19',axiom,
g_s236_169 = 0 ).
tff('Define:imlprp:2',axiom,
! [X_699: $int] :
( mem0(X_699,g_s227_159)
<=> ( $greatereq(X_699,1)
& $lesseq(X_699,g_s108_108) ) ) ).
tff('Define:imlprp:20',axiom,
! [X_715: $int] :
( mem0(X_715,g_s223_164)
<=> ( $greatereq(X_715,0)
& $lesseq(X_715,g_s73_73) ) ) ).
tff('Define:imlprp:21',axiom,
g_s239_172 = 0 ).
tff('Define:imlprp:22',axiom,
! [X_716: $int] :
( mem0(X_716,g_s237_170)
<=> ( $greatereq(X_716,0)
& $lesseq(X_716,g_s74_74) ) ) ).
tff('Define:imlprp:23',axiom,
g_s242_175 = $uminus(1) ).
tff('Define:imlprp:24',axiom,
! [X_717: $int] :
( mem0(X_717,g_s240_173)
<=> ( $greatereq(X_717,min_int)
& $lesseq(X_717,max_int) ) ) ).
tff('Define:imlprp:25',axiom,
g_s245_178 = g_s22_22 ).
tff('Define:imlprp:26',axiom,
! [X_718: $int] :
( mem0(X_718,g_s243_176)
<=> ( $greatereq(X_718,min_int)
& $lesseq(X_718,max_int) ) ) ).
tff('Define:imlprp:3',axiom,
! [X_700: $int,X_701: $int] :
( mem2(X_701,X_700,g_s229_158)
<=> ( ( X_701 = X_700 )
& mem0(X_701,g_s227_159) ) ) ).
tff('Define:imlprp:4',axiom,
! [X_702: $int] :
( mem0(X_702,g_s230_153)
<=> ( $greatereq(X_702,1)
& $lesseq(X_702,g_s120_120) ) ) ).
tff('Define:imlprp:5',axiom,
! [X_703: $int,X_704: $int] :
( mem2(X_704,X_703,g_s232_152)
<=> ( ( X_704 = X_703 )
& mem0(X_704,g_s230_153) ) ) ).
tff('Define:imlprp:6',axiom,
! [X_705: $int] :
( mem0(X_705,g_s233_155)
<=> ( $greatereq(X_705,1)
& $lesseq(X_705,g_s121_121) ) ) ).
tff('Define:imlprp:7',axiom,
! [X_706: $int,X_707: $int] :
( mem2(X_707,X_706,g_s235_154)
<=> ( ( X_707 = X_706 )
& mem0(X_707,g_s233_155) ) ) ).
tff('Define:imlprp:8',axiom,
! [X_708: $int] :
( mem0(X_708,g_s238_171)
<=> ( $greatereq(X_708,1)
& $lesseq(X_708,g_s74_74) ) ) ).
tff('Define:imlprp:9',axiom,
! [X_709: $int] :
( mem0(X_709,g_s241_174)
<=> ( $greatereq(X_709,g_s81_81)
& $lesseq(X_709,g_s82_82) ) ) ).
tff('Define:inv:0',axiom,
mem0(g_s246_1_242,g_s221_162) ).
tff('Define:seext:0',axiom,
( g_s156_179
<=> $true ) ).
tff('Define:seext:1',axiom,
( g_s157_180
<=> $false ) ).
tff('Define:seext:10',axiom,
g_s166_189 = 8 ).
tff('Define:seext:11',axiom,
g_s167_190 = 9 ).
tff('Define:seext:12',axiom,
g_s168_191 = 10 ).
tff('Define:seext:13',axiom,
g_s169_192 = 11 ).
tff('Define:seext:14',axiom,
g_s170_193 = 12 ).
tff('Define:seext:15',axiom,
g_s171_194 = 13 ).
tff('Define:seext:16',axiom,
g_s172_195 = 14 ).
tff('Define:seext:17',axiom,
g_s173_196 = 15 ).
tff('Define:seext:18',axiom,
g_s174_197 = 16 ).
tff('Define:seext:19',axiom,
g_s175_198 = 17 ).
tff('Define:seext:2',axiom,
g_s158_181 = 0 ).
tff('Define:seext:20',axiom,
g_s176_199 = 18 ).
tff('Define:seext:21',axiom,
g_s177_200 = 19 ).
tff('Define:seext:22',axiom,
g_s178_201 = 20 ).
tff('Define:seext:23',axiom,
g_s179_202 = 21 ).
tff('Define:seext:24',axiom,
g_s180_203 = 22 ).
tff('Define:seext:25',axiom,
g_s181_204 = 23 ).
tff('Define:seext:26',axiom,
g_s182_205 = 24 ).
tff('Define:seext:27',axiom,
g_s183_206 = 25 ).
tff('Define:seext:28',axiom,
g_s184_207 = 26 ).
tff('Define:seext:29',axiom,
g_s185_208 = 27 ).
tff('Define:seext:3',axiom,
g_s159_182 = 1 ).
tff('Define:seext:30',axiom,
g_s186_209 = 28 ).
tff('Define:seext:31',axiom,
g_s187_210 = 29 ).
tff('Define:seext:32',axiom,
g_s188_211 = 30 ).
tff('Define:seext:33',axiom,
g_s189_212 = 31 ).
tff('Define:seext:34',axiom,
g_s190_213 = 32 ).
tff('Define:seext:35',axiom,
g_s191_214 = 33 ).
tff('Define:seext:36',axiom,
g_s192_215 = 34 ).
tff('Define:seext:37',axiom,
g_s193_216 = 35 ).
tff('Define:seext:38',axiom,
g_s194_217 = 36 ).
tff('Define:seext:39',axiom,
g_s195_218 = 37 ).
tff('Define:seext:4',axiom,
g_s160_183 = 2 ).
tff('Define:seext:40',axiom,
g_s196_219 = 38 ).
tff('Define:seext:41',axiom,
g_s197_220 = 39 ).
tff('Define:seext:42',axiom,
g_s198_221 = 40 ).
tff('Define:seext:43',axiom,
g_s199_222 = 41 ).
tff('Define:seext:44',axiom,
g_s200_223 = 42 ).
tff('Define:seext:45',axiom,
g_s201_224 = 43 ).
tff('Define:seext:46',axiom,
g_s202_225 = 44 ).
tff('Define:seext:47',axiom,
g_s203_226 = 45 ).
tff('Define:seext:48',axiom,
g_s204_227 = 46 ).
tff('Define:seext:49',axiom,
g_s205_228 = 47 ).
tff('Define:seext:5',axiom,
g_s161_184 = 3 ).
tff('Define:seext:50',axiom,
g_s206_229 = 48 ).
tff('Define:seext:51',axiom,
g_s207_230 = 49 ).
tff('Define:seext:52',axiom,
g_s208_231 = 50 ).
tff('Define:seext:53',axiom,
g_s209_232 = 51 ).
tff('Define:seext:54',axiom,
g_s210_233 = 52 ).
tff('Define:seext:55',axiom,
g_s211_234 = 53 ).
tff('Define:seext:56',axiom,
g_s212_235 = 54 ).
tff('Define:seext:57',axiom,
g_s213_236 = 55 ).
tff('Define:seext:58',axiom,
g_s214_237 = 56 ).
tff('Define:seext:59',axiom,
g_s215_238 = 57 ).
tff('Define:seext:6',axiom,
g_s162_185 = 4 ).
tff('Define:seext:60',axiom,
g_s216_239 = 58 ).
tff('Define:seext:61',axiom,
g_s217_240 = 59 ).
tff('Define:seext:62',axiom,
mem0(g_s218_241,g_s8_8) ).
tff('Define:seext:7',axiom,
g_s163_186 = 5 ).
tff('Define:seext:8',axiom,
g_s164_187 = 6 ).
tff('Define:seext:9',axiom,
g_s165_188 = 7 ).
%Global hypotheses
tff(gh_0_def,hypothesis,
( g_s250_1_245
<=> g_s250_246 ) ).
%----Local hypotheses
tff('Local_Hyp:0',hypothesis,
mem0(g_s253_247,g_s221_162) ).
tff('Local_Hyp:1',hypothesis,
$true ).
tff('Local_Hyp:2',hypothesis,
$true ).
tff('Local_Hyp:3',hypothesis,
$true ).
%----Goal
tff('Goal',conjecture,
( ( $greatereq(g_s253_247,g_s159_182)
& $lesseq(g_s253_247,g_s120_120) )
<=> mem0(g_s253_247,g_s230_153) ) ).
%------------------------------------------------------------------------------