TPTP Problem File: SWC522_1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWC522_1 : TPTP v9.0.0. Released v9.0.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 29 10 Group s408 Tag s384
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0012-00055-29-10.tptp [Deh24]
% Status : Theorem
% Rating : 0.00 v9.0.0
% Syntax : Number of formulae : 910 ( 373 unt; 390 typ; 0 def)
% Number of atoms : 1241 ( 233 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 767 ( 40 ~; 34 |; 390 &)
% ( 139 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 20 ( 0 fml; 20 var)
% Number arithmetic : 1331 ( 260 atm; 131 fun; 224 num; 716 var)
% Number of types : 11 ( 8 usr; 2 ari)
% Number of type conns : 42 ( 21 >; 21 *; 0 +; 0 <<)
% Number of predicates : 22 ( 16 usr; 10 prp; 0-4 aty)
% Number of functors : 384 ( 366 usr; 365 con; 0-2 aty)
% Number of variables : 785 ( 611 !; 174 ?; 785 :)
% 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_95_type,type,
g_s100_95: $int ).
tff(g_s101_96_type,type,
g_s101_96: $int ).
tff(g_s102_97_type,type,
g_s102_97: $int ).
tff(g_s103_98_type,type,
g_s103_98: $int ).
tff(g_s104_99_type,type,
g_s104_99: $int ).
tff(g_s105_100_type,type,
g_s105_100: $int ).
tff(g_s106_101_type,type,
g_s106_101: $int ).
tff(g_s107_102_type,type,
g_s107_102: $int ).
tff(g_s108_103_type,type,
g_s108_103: $int ).
tff(g_s109_104_type,type,
g_s109_104: $int ).
tff(g_s10_10_type,type,
g_s10_10: $int ).
tff(g_s110_105_type,type,
g_s110_105: $int ).
tff(g_s111_106_type,type,
g_s111_106: $int ).
tff(g_s112_107_type,type,
g_s112_107: $int ).
tff(g_s113_108_type,type,
g_s113_108: $int ).
tff(g_s114_109_type,type,
g_s114_109: $int ).
tff(g_s115_110_type,type,
g_s115_110: $int ).
tff(g_s116_111_type,type,
g_s116_111: $int ).
tff(g_s117_112_type,type,
g_s117_112: $int ).
tff(g_s118_113_type,type,
g_s118_113: $int ).
tff(g_s119_114_type,type,
g_s119_114: $int ).
tff(g_s11_11_type,type,
g_s11_11: $int ).
tff(g_s120_115_type,type,
g_s120_115: $int ).
tff(g_s121_116_type,type,
g_s121_116: $int ).
tff(g_s122_117_type,type,
g_s122_117: $int ).
tff(g_s123_118_type,type,
g_s123_118: $int ).
tff(g_s124_119_type,type,
g_s124_119: $int ).
tff(g_s125_120_type,type,
g_s125_120: $int ).
tff(g_s126_121_type,type,
g_s126_121: $int ).
tff(g_s127_122_type,type,
g_s127_122: $int ).
tff(g_s128_123_type,type,
g_s128_123: $int ).
tff(g_s129_124_type,type,
g_s129_124: $int ).
tff(g_s12_12_type,type,
g_s12_12: $int ).
tff(g_s130_125_type,type,
g_s130_125: $int ).
tff(g_s131_126_type,type,
g_s131_126: $int ).
tff(g_s132_127_type,type,
g_s132_127: $int ).
tff(g_s133_128_type,type,
g_s133_128: $int ).
tff(g_s134_129_type,type,
g_s134_129: $int ).
tff(g_s135_130_type,type,
g_s135_130: $int ).
tff(g_s136_131_type,type,
g_s136_131: $int ).
tff(g_s137_132_type,type,
g_s137_132: $int ).
tff(g_s138_133_type,type,
g_s138_133: $int ).
tff(g_s139_134_type,type,
g_s139_134: $int ).
tff(g_s13_13_type,type,
g_s13_13: $int ).
tff(g_s140_135_type,type,
g_s140_135: $int ).
tff(g_s141_136_type,type,
g_s141_136: $int ).
tff(g_s142_137_type,type,
g_s142_137: $int ).
tff(g_s143_138_type,type,
g_s143_138: $int ).
tff(g_s144_139_type,type,
g_s144_139: $int ).
tff(g_s145_140_type,type,
g_s145_140: $int ).
tff(g_s146_141_type,type,
g_s146_141: $int ).
tff(g_s147_142_type,type,
g_s147_142: $int ).
tff(g_s148_143_type,type,
g_s148_143: $int ).
tff(g_s149_144_type,type,
g_s149_144: $int ).
tff(g_s14_14_type,type,
g_s14_14: $int ).
tff(g_s150_145_type,type,
g_s150_145: $int ).
tff(g_s151_146_type,type,
g_s151_146: $int ).
tff(g_s152_147_type,type,
g_s152_147: $int ).
tff(g_s153_148_type,type,
g_s153_148: $int ).
tff(g_s154_149_type,type,
g_s154_149: $int ).
tff(g_s155_150_type,type,
g_s155_150: $int ).
tff(g_s156_151_type,type,
g_s156_151: $int ).
tff(g_s157_152_type,type,
g_s157_152: $int ).
tff(g_s158_153_type,type,
g_s158_153: $int ).
tff(g_s159_154_type,type,
g_s159_154: $int ).
tff(g_s15_15_type,type,
g_s15_15: $int ).
tff(g_s160_155_type,type,
g_s160_155: $int ).
tff(g_s161_156_type,type,
g_s161_156: $int ).
tff(g_s162_157_type,type,
g_s162_157: $int ).
tff(g_s163_158_type,type,
g_s163_158: $int ).
tff(g_s164_159_type,type,
g_s164_159: $int ).
tff(g_s165_160_type,type,
g_s165_160: $int ).
tff(g_s166_161_type,type,
g_s166_161: $int ).
tff(g_s167_162_type,type,
g_s167_162: $int ).
tff(g_s168_163_type,type,
g_s168_163: $int ).
tff(g_s169_164_type,type,
g_s169_164: $int ).
tff(g_s16_16_type,type,
g_s16_16: $int ).
tff(g_s170_165_type,type,
g_s170_165: $int ).
tff(g_s171_166_type,type,
g_s171_166: $int ).
tff(g_s172_167_type,type,
g_s172_167: $int ).
tff(g_s173_168_type,type,
g_s173_168: $int ).
tff(g_s174_169_type,type,
g_s174_169: $int ).
tff(g_s175_170_type,type,
g_s175_170: $int ).
tff(g_s176_171_type,type,
g_s176_171: $int ).
tff(g_s177_172_type,type,
g_s177_172: $int ).
tff(g_s178_173_type,type,
g_s178_173: $int ).
tff(g_s179_174_type,type,
g_s179_174: $int ).
tff(g_s17_17_type,type,
g_s17_17: $int ).
tff(g_s180_175_type,type,
g_s180_175: $int ).
tff(g_s181_176_type,type,
g_s181_176: $int ).
tff(g_s182_177_type,type,
g_s182_177: $int ).
tff(g_s183_178_type,type,
g_s183_178: $int ).
tff(g_s184_179_type,type,
g_s184_179: $int ).
tff(g_s185_180_type,type,
g_s185_180: set_0 ).
tff(g_s186_181_type,type,
g_s186_181: set_0 ).
tff(g_s187_182_type,type,
g_s187_182: $int ).
tff(g_s188_183_type,type,
g_s188_183: $int ).
tff(g_s189_184_type,type,
g_s189_184: $int ).
tff(g_s18_18_type,type,
g_s18_18: $int ).
tff(g_s190_185_type,type,
g_s190_185: $int ).
tff(g_s191_186_type,type,
g_s191_186: $int ).
tff(g_s192_187_type,type,
g_s192_187: $int ).
tff(g_s193_188_type,type,
g_s193_188: $int ).
tff(g_s194_189_type,type,
g_s194_189: $int ).
tff(g_s195_190_type,type,
g_s195_190: $int ).
tff(g_s196_191_type,type,
g_s196_191: $int ).
tff(g_s197_192_type,type,
g_s197_192: $int ).
tff(g_s198_193_type,type,
g_s198_193: $int ).
tff(g_s199_194_type,type,
g_s199_194: $int ).
tff(g_s19_19_type,type,
g_s19_19: set_0 ).
tff(g_s1_1_type,type,
g_s1_1: $int ).
tff(g_s200_195_type,type,
g_s200_195: $int ).
tff(g_s201_196_type,type,
g_s201_196: $int ).
tff(g_s202_197_type,type,
g_s202_197: $int ).
tff(g_s203_198_type,type,
g_s203_198: $int ).
tff(g_s204_199_type,type,
g_s204_199: $int ).
tff(g_s205_200_type,type,
g_s205_200: $int ).
tff(g_s206_201_type,type,
g_s206_201: $int ).
tff(g_s207_202_type,type,
g_s207_202: $int ).
tff(g_s208_203_type,type,
g_s208_203: $int ).
tff(g_s209_204_type,type,
g_s209_204: $int ).
tff(g_s20_20_type,type,
g_s20_20: $int ).
tff(g_s210_205_type,type,
g_s210_205: $int ).
tff(g_s211_206_type,type,
g_s211_206: $int ).
tff(g_s212_207_type,type,
g_s212_207: $int ).
tff(g_s213_208_type,type,
g_s213_208: $int ).
tff(g_s214_209_type,type,
g_s214_209: $int ).
tff(g_s215_210_type,type,
g_s215_210: $int ).
tff(g_s216_211_type,type,
g_s216_211: $int ).
tff(g_s217_212_type,type,
g_s217_212: $int ).
tff(g_s218_213_type,type,
g_s218_213: $int ).
tff(g_s219_214_type,type,
g_s219_214: $int ).
tff(g_s21_21_type,type,
g_s21_21: $int ).
tff(g_s220_215_type,type,
g_s220_215: $int ).
tff(g_s221_216_type,type,
g_s221_216: $int ).
tff(g_s222_217_type,type,
g_s222_217: $int ).
tff(g_s223_218_type,type,
g_s223_218: $int ).
tff(g_s224_219_type,type,
g_s224_219: $int ).
tff(g_s225_220_type,type,
g_s225_220: $int ).
tff(g_s226_221_type,type,
g_s226_221: $int ).
tff(g_s227_222_type,type,
g_s227_222: $int ).
tff(g_s228_223_type,type,
g_s228_223: $int ).
tff(g_s229_224_type,type,
g_s229_224: $int ).
tff(g_s22_22_type,type,
g_s22_22: set_0 ).
tff(g_s230_225_type,type,
g_s230_225: $int ).
tff(g_s231_226_type,type,
g_s231_226: $int ).
tff(g_s232_227_type,type,
g_s232_227: $int ).
tff(g_s233_228_type,type,
g_s233_228: $int ).
tff(g_s234_229_type,type,
g_s234_229: $int ).
tff(g_s235_230_type,type,
g_s235_230: $int ).
tff(g_s236_231_type,type,
g_s236_231: $int ).
tff(g_s237_232_type,type,
g_s237_232: $int ).
tff(g_s238_233_type,type,
g_s238_233: $int ).
tff(g_s239_234_type,type,
g_s239_234: $int ).
tff(g_s23_23_type,type,
g_s23_23: $int ).
tff(g_s240_235_type,type,
g_s240_235: $int ).
tff(g_s241_236_type,type,
g_s241_236: $int ).
tff(g_s242_237_type,type,
g_s242_237: $int ).
tff(g_s243_238_type,type,
g_s243_238: $int ).
tff(g_s244_239_type,type,
g_s244_239: $int ).
tff(g_s245_240_type,type,
g_s245_240: $int ).
tff(g_s246_241_type,type,
g_s246_241: $int ).
tff(g_s247_242_type,type,
g_s247_242: $int ).
tff(g_s248_243_type,type,
g_s248_243: $int ).
tff(g_s249_244_type,type,
g_s249_244: $int ).
tff(g_s24_24_type,type,
g_s24_24: $int ).
tff(g_s250_245_type,type,
g_s250_245: $int ).
tff(g_s251_246_type,type,
g_s251_246: $int ).
tff(g_s252_247_type,type,
g_s252_247: $int ).
tff(g_s253_248_type,type,
g_s253_248: $int ).
tff(g_s254_249_type,type,
g_s254_249: $int ).
tff(g_s255_250_type,type,
g_s255_250: $int ).
tff(g_s256_251_type,type,
g_s256_251: $int ).
tff(g_s257_252_type,type,
g_s257_252: $int ).
tff(g_s258_253_type,type,
g_s258_253: $int ).
tff(g_s259_254_type,type,
g_s259_254: $int ).
tff(g_s25_25_type,type,
g_s25_25: $int ).
tff(g_s260_255_type,type,
g_s260_255: $int ).
tff(g_s261_256_type,type,
g_s261_256: $int ).
tff(g_s262_257_type,type,
g_s262_257: $int ).
tff(g_s263_258_type,type,
g_s263_258: $int ).
tff(g_s264_259_type,type,
g_s264_259: $int ).
tff(g_s265_260_type,type,
g_s265_260: $int ).
tff(g_s266_261_type,type,
g_s266_261: $int ).
tff(g_s267_262_type,type,
g_s267_262: $int ).
tff(g_s268_263_type,type,
g_s268_263: $int ).
tff(g_s269_264_type,type,
g_s269_264: $int ).
tff(g_s26_26_type,type,
g_s26_26: $int ).
tff(g_s270_265_type,type,
g_s270_265: $int ).
tff(g_s271_266_type,type,
g_s271_266: $int ).
tff(g_s272_267_type,type,
g_s272_267: $int ).
tff(g_s273_268_type,type,
g_s273_268: $int ).
tff(g_s274_269_type,type,
g_s274_269: $int ).
tff(g_s275_270_type,type,
g_s275_270: $int ).
tff(g_s276_271_type,type,
g_s276_271: $int ).
tff(g_s277_272_type,type,
g_s277_272: $int ).
tff(g_s278_273_type,type,
g_s278_273: $int ).
tff(g_s279_274_type,type,
g_s279_274: $int ).
tff(g_s27_27_type,type,
g_s27_27: $int ).
tff(g_s280_275_type,type,
g_s280_275: $int ).
tff(g_s281_276_type,type,
g_s281_276: $int ).
tff(g_s282_277_type,type,
g_s282_277: $int ).
tff(g_s283_278_type,type,
g_s283_278: $int ).
tff(g_s284_279_type,type,
g_s284_279: $int ).
tff(g_s285_280_type,type,
g_s285_280: $int ).
tff(g_s286_281_type,type,
g_s286_281: $int ).
tff(g_s287_282_type,type,
g_s287_282: $int ).
tff(g_s288_283_type,type,
g_s288_283: $int ).
tff(g_s289_284_type,type,
g_s289_284: $int ).
tff(g_s28_28_type,type,
g_s28_28: $int ).
tff(g_s290_285_type,type,
g_s290_285: $int ).
tff(g_s291_286_type,type,
g_s291_286: $int ).
tff(g_s292_287_type,type,
g_s292_287: $int ).
tff(g_s293_288_type,type,
g_s293_288: $int ).
tff(g_s294_289_type,type,
g_s294_289: $int ).
tff(g_s295_290_type,type,
g_s295_290: $int ).
tff(g_s296_291_type,type,
g_s296_291: $int ).
tff(g_s297_292_type,type,
g_s297_292: $int ).
tff(g_s298_293_type,type,
g_s298_293: $int ).
tff(g_s299_294_type,type,
g_s299_294: $int ).
tff(g_s29_29_type,type,
g_s29_29: $int ).
tff(g_s2_2_type,type,
g_s2_2: $int ).
tff(g_s300_295_type,type,
g_s300_295: $int ).
tff(g_s301_296_type,type,
g_s301_296: set_4 ).
tff(g_s302_297_type,type,
g_s302_297: set_3 ).
tff(g_s303_298_type,type,
g_s303_298: set_4 ).
tff(g_s304_299_type,type,
g_s304_299: set_3 ).
tff(g_s305_300_type,type,
g_s305_300: set_4 ).
tff(g_s306_303_type,type,
g_s306_303: set_0 ).
tff(g_s307_304_type,type,
g_s307_304: set_0 ).
tff(g_s308_305_type,type,
g_s308_305: set_0 ).
tff(g_s309_306_type,type,
g_s309_306: set_0 ).
tff(g_s30_30_type,type,
g_s30_30: $int ).
tff(g_s310_307_type,type,
g_s310_307: set_3 ).
tff(g_s311_308_type,type,
g_s311_308: set_3 ).
tff(g_s312_309_type,type,
g_s312_309: set_3 ).
tff(g_s313_310_type,type,
g_s313_310: set_3 ).
tff(g_s314_311_type,type,
g_s314_311: set_0 ).
tff(g_s315_312_type,type,
g_s315_312: set_0 ).
tff(g_s316_313_type,type,
g_s316_313: set_0 ).
tff(g_s317_314_type,type,
g_s317_314: set_0 ).
tff(g_s318_315_type,type,
g_s318_315: set_3 ).
tff(g_s319_316_type,type,
g_s319_316: set_3 ).
tff(g_s31_31_type,type,
g_s31_31: $int ).
tff(g_s320_317_type,type,
g_s320_317: set_0 ).
tff(g_s321_318_type,type,
g_s321_318: set_3 ).
tff(g_s322_301_type,type,
g_s322_301: set_4 ).
tff(g_s323_302_type,type,
g_s323_302: set_4 ).
tff(g_s326_1_342_type,type,
g_s326_1_342: $int ).
tff(g_s326_325_type,type,
g_s326_325: $int ).
tff(g_s327_1_348_type,type,
g_s327_1_348: $o ).
tff(g_s327_347_type,type,
g_s327_347: $o ).
tff(g_s328_1_336_type,type,
g_s328_1_336: set_4 ).
tff(g_s328_319_type,type,
g_s328_319: set_4 ).
tff(g_s329_1_337_type,type,
g_s329_1_337: set_4 ).
tff(g_s329_320_type,type,
g_s329_320: set_4 ).
tff(g_s32_33_type,type,
g_s32_33: $int ).
tff(g_s330_1_350_type,type,
g_s330_1_350: $o ).
tff(g_s330_349_type,type,
g_s330_349: $o ).
tff(g_s331_1_338_type,type,
g_s331_1_338: set_4 ).
tff(g_s331_321_type,type,
g_s331_321: set_4 ).
tff(g_s332_1_339_type,type,
g_s332_1_339: set_4 ).
tff(g_s332_322_type,type,
g_s332_322: set_4 ).
tff(g_s333_1_352_type,type,
g_s333_1_352: $o ).
tff(g_s333_351_type,type,
g_s333_351: $o ).
tff(g_s334_1_354_type,type,
g_s334_1_354: $o ).
tff(g_s334_353_type,type,
g_s334_353: $o ).
tff(g_s335_1_343_type,type,
g_s335_1_343: set_3 ).
tff(g_s335_326_type,type,
g_s335_326: set_3 ).
tff(g_s336_1_344_type,type,
g_s336_1_344: set_3 ).
tff(g_s336_327_type,type,
g_s336_327: set_3 ).
tff(g_s337_1_345_type,type,
g_s337_1_345: set_3 ).
tff(g_s337_328_type,type,
g_s337_328: set_3 ).
tff(g_s338_1_346_type,type,
g_s338_1_346: set_3 ).
tff(g_s338_329_type,type,
g_s338_329: set_3 ).
tff(g_s339_1_340_type,type,
g_s339_1_340: set_0 ).
tff(g_s339_323_type,type,
g_s339_323: set_0 ).
tff(g_s33_32_type,type,
g_s33_32: set_0 ).
tff(g_s340_1_341_type,type,
g_s340_1_341: set_0 ).
tff(g_s340_324_type,type,
g_s340_324: set_0 ).
tff(g_s34_35_type,type,
g_s34_35: $int ).
tff(g_s358_335_type,type,
g_s358_335: $int ).
tff(g_s35_34_type,type,
g_s35_34: set_0 ).
tff(g_s369_1_362_type,type,
g_s369_1_362: $int ).
tff(g_s369_361_type,type,
g_s369_361: $int ).
tff(g_s36_37_type,type,
g_s36_37: $int ).
tff(g_s375_364_type,type,
g_s375_364: $int ).
tff(g_s37_36_type,type,
g_s37_36: set_0 ).
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: set_0 ).
tff(g_s41_41_type,type,
g_s41_41: set_2 ).
tff(g_s42_42_type,type,
g_s42_42: set_3 ).
tff(g_s43_43_type,type,
g_s43_43: set_4 ).
tff(g_s44_44_type,type,
g_s44_44: set_4 ).
tff(g_s45_45_type,type,
g_s45_45: set_3 ).
tff(g_s46_46_type,type,
g_s46_46: set_4 ).
tff(g_s47_47_type,type,
g_s47_47: set_4 ).
tff(g_s48_48_type,type,
g_s48_48: set_3 ).
tff(g_s49_49_type,type,
g_s49_49: set_4 ).
tff(g_s4_4_type,type,
g_s4_4: $int ).
tff(g_s50_50_type,type,
g_s50_50: set_4 ).
tff(g_s51_51_type,type,
g_s51_51: set_4 ).
tff(g_s52_52_type,type,
g_s52_52: set_4 ).
tff(g_s53_53_type,type,
g_s53_53: set_4 ).
tff(g_s54_54_type,type,
g_s54_54: set_4 ).
tff(g_s55_55_type,type,
g_s55_55: set_4 ).
tff(g_s56_56_type,type,
g_s56_56: set_4 ).
tff(g_s57_57_type,type,
g_s57_57: set_4 ).
tff(g_s58_58_type,type,
g_s58_58: set_4 ).
tff(g_s59_59_type,type,
g_s59_59: set_4 ).
tff(g_s5_5_type,type,
g_s5_5: $int ).
tff(g_s60_60_type,type,
g_s60_60: set_4 ).
tff(g_s66_61_type,type,
g_s66_61: $int ).
tff(g_s67_62_type,type,
g_s67_62: $int ).
tff(g_s68_63_type,type,
g_s68_63: $int ).
tff(g_s69_64_type,type,
g_s69_64: $int ).
tff(g_s6_6_type,type,
g_s6_6: set_0 ).
tff(g_s70_65_type,type,
g_s70_65: $int ).
tff(g_s71_66_type,type,
g_s71_66: $int ).
tff(g_s72_67_type,type,
g_s72_67: $int ).
tff(g_s73_68_type,type,
g_s73_68: $int ).
tff(g_s74_69_type,type,
g_s74_69: $int ).
tff(g_s75_70_type,type,
g_s75_70: $int ).
tff(g_s76_71_type,type,
g_s76_71: $int ).
tff(g_s77_72_type,type,
g_s77_72: $int ).
tff(g_s78_73_type,type,
g_s78_73: $int ).
tff(g_s79_74_type,type,
g_s79_74: $int ).
tff(g_s7_7_type,type,
g_s7_7: $int ).
tff(g_s80_75_type,type,
g_s80_75: $int ).
tff(g_s81_76_type,type,
g_s81_76: $int ).
tff(g_s82_77_type,type,
g_s82_77: $int ).
tff(g_s83_78_type,type,
g_s83_78: $int ).
tff(g_s84_79_type,type,
g_s84_79: $int ).
tff(g_s85_80_type,type,
g_s85_80: $int ).
tff(g_s86_81_type,type,
g_s86_81: $int ).
tff(g_s87_82_type,type,
g_s87_82: $int ).
tff(g_s88_83_type,type,
g_s88_83: $int ).
tff(g_s89_84_type,type,
g_s89_84: $int ).
tff(g_s8_8_type,type,
g_s8_8: $int ).
tff(g_s90_85_type,type,
g_s90_85: $int ).
tff(g_s91_86_type,type,
g_s91_86: $int ).
tff(g_s92_87_type,type,
g_s92_87: $int ).
tff(g_s93_88_type,type,
g_s93_88: $int ).
tff(g_s94_89_type,type,
g_s94_89: $int ).
tff(g_s95_90_type,type,
g_s95_90: $int ).
tff(g_s96_91_type,type,
g_s96_91: $int ).
tff(g_s97_92_type,type,
g_s97_92: $int ).
tff(g_s98_93_type,type,
g_s98_93: $int ).
tff(g_s99_94_type,type,
g_s99_94: $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,
$greatereq(g_s326_325,0) ).
tff('Define:abs:1',axiom,
$true ).
tff('Define:abs:10',axiom,
? [X_1984: set_3] :
( ! [X_1985: $int,X_1986: $int] :
( mem3(X_1986,X_1985,X_1984)
<=> mem3(X_1986,X_1985,g_s336_327) )
& ! [X_1987: $int,X_1988: $int,X_1989: $int] :
( ( mem3(X_1987,X_1988,X_1984)
& mem3(X_1987,X_1989,X_1984) )
=> ( X_1988 = X_1989 ) )
& ! [X_1990: $int] :
( ( $greatereq(X_1990,1)
& $lesseq(X_1990,g_s326_325) )
<=> ? [X_1991: $int] : mem3(X_1990,X_1991,X_1984) )
& ! [X_1992: $int] :
( ? [X_1993: $int] : mem3(X_1993,X_1992,X_1984)
=> ( $greatereq(X_1992,0)
& $lesseq(X_1992,g_s126_121) ) ) ) ).
tff('Define:abs:11',axiom,
? [X_1994: set_3] :
( ! [X_1995: $int,X_1996: $int] :
( mem3(X_1996,X_1995,X_1994)
<=> mem3(X_1996,X_1995,g_s337_328) )
& ! [X_1997: $int,X_1998: $int,X_1999: $int] :
( ( mem3(X_1997,X_1998,X_1994)
& mem3(X_1997,X_1999,X_1994) )
=> ( X_1998 = X_1999 ) )
& ! [X_2000: $int] :
( ( $greatereq(X_2000,1)
& $lesseq(X_2000,g_s326_325) )
<=> ? [X_2001: $int] : mem3(X_2000,X_2001,X_1994) )
& ! [X_2002: $int] :
( ? [X_2003: $int] : mem3(X_2003,X_2002,X_1994)
=> ( $greatereq(X_2002,0)
& $lesseq(X_2002,g_s126_121) ) ) ) ).
tff('Define:abs:12',axiom,
! [X_2004: $int,X_2005: $int] :
( mem3(X_2005,X_2004,g_s338_329)
=> ( mem0(X_2005,g_s186_181)
& $greatereq(X_2004,1)
& $lesseq(X_2004,g_s326_325) ) ) ).
tff('Define:abs:13',axiom,
$true ).
tff('Define:abs:14',axiom,
$true ).
tff('Define:abs:15',axiom,
$true ).
tff('Define:abs:16',axiom,
! [X_2006: $int] :
( mem0(X_2006,g_s339_323)
=> ( $greatereq(X_2006,1)
& $lesseq(X_2006,g_s126_121) ) ) ).
tff('Define:abs:17',axiom,
! [X_2007: $int] :
( mem0(X_2007,g_s340_324)
=> ( $greatereq(X_2007,1)
& $lesseq(X_2007,g_s126_121) ) ) ).
tff('Define:abs:2',axiom,
? [X_1918: set_4] :
( ! [X_1919: $int,X_1920: $int,X_1921: $int] :
( mem4(X_1921,X_1920,X_1919,X_1918)
<=> mem4(X_1921,X_1920,X_1919,g_s328_319) )
& ! [X_1922: $int,X_1923: $int,X_1924: $int,X_1925: $int] :
( ( mem4(X_1923,X_1922,X_1924,X_1918)
& mem4(X_1923,X_1922,X_1925,X_1918) )
=> ( X_1924 = X_1925 ) )
& ! [X_1926: $int,X_1927: $int] :
( ( $greatereq(X_1927,1)
& $lesseq(X_1927,g_s126_121)
& $greatereq(X_1926,1)
& $lesseq(X_1926,g_s126_121) )
<=> ? [X_1928: $int] : mem4(X_1927,X_1926,X_1928,X_1918) )
& ! [X_1929: $int] :
( ? [X_1930: $int,X_1931: $int] : mem4(X_1931,X_1930,X_1929,X_1918)
=> $greatereq(X_1929,0) ) ) ).
tff('Define:abs:3',axiom,
? [X_1932: set_4] :
( ! [X_1933: $int,X_1934: $int,X_1935: $int] :
( mem4(X_1935,X_1934,X_1933,X_1932)
<=> mem4(X_1935,X_1934,X_1933,g_s329_320) )
& ! [X_1936: $int,X_1937: $int,X_1938: $int,X_1939: $int] :
( ( mem4(X_1937,X_1936,X_1938,X_1932)
& mem4(X_1937,X_1936,X_1939,X_1932) )
=> ( X_1938 = X_1939 ) )
& ! [X_1940: $int,X_1941: $int] :
( ( $greatereq(X_1941,1)
& $lesseq(X_1941,g_s126_121)
& $greatereq(X_1940,1)
& $lesseq(X_1940,g_s126_121) )
<=> ? [X_1942: $int] : mem4(X_1941,X_1940,X_1942,X_1932) )
& ! [X_1943: $int] :
( ? [X_1944: $int,X_1945: $int] : mem4(X_1945,X_1944,X_1943,X_1932)
=> $greatereq(X_1943,0) ) ) ).
tff('Define:abs:4',axiom,
$true ).
tff('Define:abs:5',axiom,
? [X_1946: set_4] :
( ! [X_1947: $int,X_1948: $int,X_1949: $int] :
( mem4(X_1949,X_1948,X_1947,X_1946)
<=> mem4(X_1949,X_1948,X_1947,g_s331_321) )
& ! [X_1950: $int,X_1951: $int,X_1952: $int,X_1953: $int] :
( ( mem4(X_1951,X_1950,X_1952,X_1946)
& mem4(X_1951,X_1950,X_1953,X_1946) )
=> ( X_1952 = X_1953 ) )
& ! [X_1954: $int,X_1955: $int] :
( ( $greatereq(X_1955,1)
& $lesseq(X_1955,g_s126_121)
& $greatereq(X_1954,1)
& $lesseq(X_1954,g_s126_121) )
<=> ? [X_1956: $int] : mem4(X_1955,X_1954,X_1956,X_1946) )
& ! [X_1957: $int] :
( ? [X_1958: $int,X_1959: $int] : mem4(X_1959,X_1958,X_1957,X_1946)
=> $greatereq(X_1957,0) ) ) ).
tff('Define:abs:6',axiom,
? [X_1960: set_4] :
( ! [X_1961: $int,X_1962: $int,X_1963: $int] :
( mem4(X_1963,X_1962,X_1961,X_1960)
<=> mem4(X_1963,X_1962,X_1961,g_s332_322) )
& ! [X_1964: $int,X_1965: $int,X_1966: $int,X_1967: $int] :
( ( mem4(X_1965,X_1964,X_1966,X_1960)
& mem4(X_1965,X_1964,X_1967,X_1960) )
=> ( X_1966 = X_1967 ) )
& ! [X_1968: $int,X_1969: $int] :
( ( $greatereq(X_1969,1)
& $lesseq(X_1969,g_s126_121)
& $greatereq(X_1968,1)
& $lesseq(X_1968,g_s126_121) )
<=> ? [X_1970: $int] : mem4(X_1969,X_1968,X_1970,X_1960) )
& ! [X_1971: $int] :
( ? [X_1972: $int,X_1973: $int] : mem4(X_1973,X_1972,X_1971,X_1960)
=> $greatereq(X_1971,0) ) ) ).
tff('Define:abs:7',axiom,
$true ).
tff('Define:abs:8',axiom,
$true ).
tff('Define:abs:9',axiom,
? [X_1974: set_3] :
( ! [X_1975: $int,X_1976: $int] :
( mem3(X_1976,X_1975,X_1974)
<=> mem3(X_1976,X_1975,g_s335_326) )
& ! [X_1977: $int,X_1978: $int,X_1979: $int] :
( ( mem3(X_1977,X_1978,X_1974)
& mem3(X_1977,X_1979,X_1974) )
=> ( X_1978 = X_1979 ) )
& ! [X_1980: $int] :
( ( $greatereq(X_1980,1)
& $lesseq(X_1980,g_s326_325) )
<=> ? [X_1981: $int] : mem3(X_1980,X_1981,X_1974) )
& ! [X_1982: $int] :
( ? [X_1983: $int] : mem3(X_1983,X_1982,X_1974)
=> ( $greatereq(X_1982,0)
& $lesseq(X_1982,g_s126_121) ) ) ) ).
tff('Define:aprp:0',axiom,
? [X_468: set_4] :
( ! [X_469: $int,X_470: $int,X_471: $int] :
( mem4(X_471,X_470,X_469,X_468)
<=> mem4(X_471,X_470,X_469,g_s322_301) )
& ! [X_472: $int,X_473: $int,X_474: $int,X_475: $int] :
( ( mem4(X_473,X_472,X_474,X_468)
& mem4(X_473,X_472,X_475,X_468) )
=> ( X_474 = X_475 ) )
& ! [X_476: $int,X_477: $int] :
( ( $greatereq(X_477,1)
& $lesseq(X_477,g_s126_121)
& $greatereq(X_476,1)
& $lesseq(X_476,g_s126_121) )
<=> ? [X_478: $int] : mem4(X_477,X_476,X_478,X_468) )
& ! [X_479: $int] :
( ? [X_480: $int,X_481: $int] : mem4(X_481,X_480,X_479,X_468)
=> mem0(X_479,g_s35_34) ) ) ).
tff('Define:aprp:1',axiom,
? [X_482: set_4] :
( ! [X_483: $int,X_484: $int,X_485: $int] :
( mem4(X_485,X_484,X_483,X_482)
<=> mem4(X_485,X_484,X_483,g_s323_302) )
& ! [X_486: $int,X_487: $int,X_488: $int,X_489: $int] :
( ( mem4(X_487,X_486,X_488,X_482)
& mem4(X_487,X_486,X_489,X_482) )
=> ( X_488 = X_489 ) )
& ! [X_490: $int,X_491: $int] :
( ( $greatereq(X_491,1)
& $lesseq(X_491,g_s126_121)
& $greatereq(X_490,1)
& $lesseq(X_490,g_s126_121) )
<=> ? [X_492: $int] : mem4(X_491,X_490,X_492,X_482) )
& ! [X_493: $int] :
( ? [X_494: $int,X_495: $int] : mem4(X_495,X_494,X_493,X_482)
=> mem0(X_493,g_s37_36) ) ) ).
tff('Define:aprp:2',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s185_180)
& mem0(L_s325,g_s185_180) )
=> ( mem4(L_s324,L_s325,g_s227_222,g_s322_301)
& mem4(L_s324,L_s325,g_s228_223,g_s323_302) ) ) ).
tff('Define:aprp:3',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s186_181)
& mem0(L_s325,g_s186_181) )
=> ( mem4(L_s324,L_s325,g_s229_224,g_s322_301)
& mem4(L_s324,L_s325,g_s230_225,g_s323_302) ) ) ).
tff('Define:aprp:4',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s186_181)
& mem0(L_s325,g_s185_180) )
=> ( mem4(L_s324,L_s325,g_s231_226,g_s322_301)
& mem4(L_s324,L_s325,g_s232_227,g_s323_302) ) ) ).
tff('Define:aprp:5',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s185_180)
& mem0(L_s325,g_s186_181) )
=> ( mem4(L_s324,L_s325,g_s231_226,g_s322_301)
& mem4(L_s324,L_s325,g_s232_227,g_s323_302) ) ) ).
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,
mem0(g_s39_39,g_s37_36) ).
tff('Define:ctx:100',axiom,
mem0(g_s102_97,g_s37_36) ).
tff('Define:ctx:101',axiom,
g_s102_97 = $sum(g_s99_94,g_s92_87) ).
tff('Define:ctx:102',axiom,
mem0(g_s103_98,g_s37_36) ).
tff('Define:ctx:103',axiom,
g_s103_98 = $sum(g_s99_94,g_s93_88) ).
tff('Define:ctx:104',axiom,
mem0(g_s104_99,g_s37_36) ).
tff('Define:ctx:105',axiom,
g_s104_99 = $sum(g_s99_94,g_s94_89) ).
tff('Define:ctx:106',axiom,
mem0(g_s105_100,g_s37_36) ).
tff('Define:ctx:107',axiom,
g_s105_100 = $sum(g_s99_94,g_s95_90) ).
tff('Define:ctx:108',axiom,
mem0(g_s106_101,g_s37_36) ).
tff('Define:ctx:109',axiom,
g_s106_101 = $sum(g_s99_94,g_s96_91) ).
tff('Define:ctx:11',axiom,
g_s32_33 = 4294967295 ).
tff('Define:ctx:110',axiom,
mem0(g_s107_102,g_s33_32) ).
tff('Define:ctx:111',axiom,
mem0(g_s108_103,g_s33_32) ).
tff('Define:ctx:112',axiom,
mem0(g_s109_104,g_s33_32) ).
tff('Define:ctx:113',axiom,
mem0(g_s110_105,g_s33_32) ).
tff('Define:ctx:114',axiom,
mem0(g_s111_106,g_s33_32) ).
tff('Define:ctx:115',axiom,
mem0(g_s112_107,g_s33_32) ).
tff('Define:ctx:116',axiom,
mem0(g_s113_108,g_s33_32) ).
tff('Define:ctx:117',axiom,
mem0(g_s114_109,g_s33_32) ).
tff('Define:ctx:118',axiom,
mem0(g_s115_110,g_s33_32) ).
tff('Define:ctx:119',axiom,
mem0(g_s116_111,g_s33_32) ).
tff('Define:ctx:12',axiom,
g_s34_35 = 65535 ).
tff('Define:ctx:120',axiom,
mem0(g_s117_112,g_s33_32) ).
tff('Define:ctx:121',axiom,
mem0(g_s118_113,g_s33_32) ).
tff('Define:ctx:122',axiom,
mem0(g_s119_114,g_s33_32) ).
tff('Define:ctx:123',axiom,
mem0(g_s120_115,g_s33_32) ).
tff('Define:ctx:124',axiom,
mem0(g_s121_116,g_s33_32) ).
tff('Define:ctx:125',axiom,
mem0(g_s122_117,g_s33_32) ).
tff('Define:ctx:126',axiom,
mem0(g_s123_118,g_s33_32) ).
tff('Define:ctx:127',axiom,
mem0(g_s124_119,g_s33_32) ).
tff('Define:ctx:128',axiom,
mem0(g_s125_120,g_s33_32) ).
tff('Define:ctx:129',axiom,
mem0(g_s126_121,g_s37_36) ).
tff('Define:ctx:13',axiom,
g_s36_37 = 255 ).
tff('Define:ctx:130',axiom,
$lesseq(0,g_s126_121) ).
tff('Define:ctx:131',axiom,
$lesseq(2,g_s126_121) ).
tff('Define:ctx:132',axiom,
mem0(g_s127_122,g_s37_36) ).
tff('Define:ctx:133',axiom,
g_s127_122 = $difference(g_s126_121,1) ).
tff('Define:ctx:134',axiom,
mem0(g_s128_123,g_s37_36) ).
tff('Define:ctx:135',axiom,
mem0(g_s129_124,g_s37_36) ).
tff('Define:ctx:136',axiom,
g_s129_124 = $difference(g_s128_123,1) ).
tff('Define:ctx:137',axiom,
mem0(g_s130_125,g_s37_36) ).
tff('Define:ctx:138',axiom,
mem0(g_s131_126,g_s37_36) ).
tff('Define:ctx:139',axiom,
g_s131_126 = $difference(g_s130_125,1) ).
tff('Define:ctx:14',axiom,
( $greatereq(g_s38_38,0)
& $lesseq(g_s38_38,g_s36_37) ) ).
tff('Define:ctx:140',axiom,
mem0(g_s132_127,g_s35_34) ).
tff('Define:ctx:141',axiom,
mem0(g_s133_128,g_s35_34) ).
tff('Define:ctx:142',axiom,
mem0(g_s134_129,g_s35_34) ).
tff('Define:ctx:143',axiom,
mem0(g_s135_130,g_s35_34) ).
tff('Define:ctx:144',axiom,
g_s134_129 != g_s135_130 ).
tff('Define:ctx:145',axiom,
mem0(g_s136_131,g_s35_34) ).
tff('Define:ctx:146',axiom,
mem0(g_s137_132,g_s35_34) ).
tff('Define:ctx:147',axiom,
mem0(g_s138_133,g_s35_34) ).
tff('Define:ctx:148',axiom,
$greatereq(g_s139_134,0) ).
tff('Define:ctx:149',axiom,
g_s139_134 = $difference(g_s137_132,g_s138_133) ).
tff('Define:ctx:15',axiom,
( $greatereq(g_s39_39,0)
& $lesseq(g_s39_39,g_s36_37) ) ).
tff('Define:ctx:150',axiom,
mem0(g_s140_135,g_s35_34) ).
tff('Define:ctx:151',axiom,
mem0(g_s141_136,g_s35_34) ).
tff('Define:ctx:152',axiom,
mem0(g_s142_137,g_s35_34) ).
tff('Define:ctx:153',axiom,
mem0(g_s143_138,g_s35_34) ).
tff('Define:ctx:154',axiom,
mem0(g_s144_139,g_s37_36) ).
tff('Define:ctx:155',axiom,
mem0(g_s145_140,g_s37_36) ).
tff('Define:ctx:156',axiom,
g_s145_140 = $difference(g_s144_139,1) ).
tff('Define:ctx:157',axiom,
g_s130_125 = $product(g_s126_121,g_s144_139) ).
tff('Define:ctx:158',axiom,
$lesseq(1,g_s144_139) ).
tff('Define:ctx:159',axiom,
$less(g_s144_139,g_s36_37) ).
tff('Define:ctx:16',axiom,
g_s38_38 != g_s39_39 ).
tff('Define:ctx:160',axiom,
mem0(g_s146_141,g_s37_36) ).
tff('Define:ctx:161',axiom,
mem0(g_s147_142,g_s37_36) ).
tff('Define:ctx:162',axiom,
mem0(g_s148_143,g_s33_32) ).
tff('Define:ctx:163',axiom,
mem0(g_s149_144,g_s33_32) ).
tff('Define:ctx:164',axiom,
mem0(g_s150_145,g_s33_32) ).
tff('Define:ctx:165',axiom,
mem0(g_s151_146,g_s33_32) ).
tff('Define:ctx:166',axiom,
mem0(g_s152_147,g_s33_32) ).
tff('Define:ctx:167',axiom,
mem0(g_s153_148,g_s33_32) ).
tff('Define:ctx:168',axiom,
g_s153_148 = $difference(g_s152_147,1) ).
tff('Define:ctx:169',axiom,
mem0(g_s154_149,g_s33_32) ).
tff('Define:ctx:17',axiom,
! [X_11: $int] :
( mem0(X_11,g_s40_40)
<=> ( ( X_11 = g_s38_38 )
| ( X_11 = g_s39_39 ) ) ) ).
tff('Define:ctx:170',axiom,
mem0(g_s155_150,g_s33_32) ).
tff('Define:ctx:171',axiom,
g_s155_150 = $difference(g_s154_149,1) ).
tff('Define:ctx:172',axiom,
mem0(g_s156_151,g_s37_36) ).
tff('Define:ctx:173',axiom,
mem0(g_s157_152,g_s37_36) ).
tff('Define:ctx:174',axiom,
mem0(g_s158_153,g_s33_32) ).
tff('Define:ctx:175',axiom,
mem0(g_s159_154,g_s37_36) ).
tff('Define:ctx:176',axiom,
$lesseq(g_s159_154,g_s88_83) ).
tff('Define:ctx:177',axiom,
mem0(g_s160_155,g_s37_36) ).
tff('Define:ctx:178',axiom,
$lesseq(g_s160_155,g_s88_83) ).
tff('Define:ctx:179',axiom,
mem0(g_s161_156,g_s37_36) ).
tff('Define:ctx:18',axiom,
! [X_12: $int,X_13: $o] :
( mem2((X_13),X_12,g_s41_41)
<=> ( ( ( (X_13)
<=> $true )
& ( X_12 = g_s38_38 ) )
| ( ( (X_13)
<=> $false )
& ( X_12 = g_s39_39 ) ) ) ) ).
tff('Define:ctx:180',axiom,
$lesseq(g_s161_156,g_s157_152) ).
tff('Define:ctx:181',axiom,
mem0(g_s162_157,g_s37_36) ).
tff('Define:ctx:182',axiom,
$lesseq(g_s162_157,g_s157_152) ).
tff('Define:ctx:183',axiom,
mem0(g_s163_158,g_s37_36) ).
tff('Define:ctx:184',axiom,
$lesseq(g_s163_158,g_s157_152) ).
tff('Define:ctx:185',axiom,
mem0(g_s164_159,g_s37_36) ).
tff('Define:ctx:186',axiom,
$lesseq(g_s164_159,g_s157_152) ).
tff('Define:ctx:187',axiom,
mem0(g_s165_160,g_s37_36) ).
tff('Define:ctx:188',axiom,
mem0(g_s166_161,g_s37_36) ).
tff('Define:ctx:189',axiom,
mem0(g_s167_162,g_s37_36) ).
tff('Define:ctx:19',axiom,
? [X_14: set_3] :
( ! [X_15: $int,X_16: $int] :
( mem3(X_16,X_15,X_14)
<=> mem3(X_16,X_15,g_s42_42) )
& ! [X_17: $int,X_18: $int,X_19: $int] :
( ( mem3(X_17,X_18,X_14)
& mem3(X_17,X_19,X_14) )
=> ( X_18 = X_19 ) )
& ! [X_20: $int] :
( mem0(X_20,g_s33_32)
<=> ? [X_21: $int] : mem3(X_20,X_21,X_14) )
& ! [X_22: $int] :
( ? [X_23: $int] : mem3(X_23,X_22,X_14)
=> mem0(X_22,g_s33_32) ) ) ).
tff('Define:ctx:190',axiom,
mem0(g_s168_163,g_s37_36) ).
tff('Define:ctx:191',axiom,
g_s165_160 != g_s166_161 ).
tff('Define:ctx:192',axiom,
g_s165_160 != g_s167_162 ).
tff('Define:ctx:193',axiom,
g_s165_160 != g_s168_163 ).
tff('Define:ctx:194',axiom,
g_s166_161 != g_s167_162 ).
tff('Define:ctx:195',axiom,
g_s166_161 != g_s168_163 ).
tff('Define:ctx:196',axiom,
g_s167_162 != g_s168_163 ).
tff('Define:ctx:197',axiom,
! [X_300: $int] :
( ( $greatereq(X_300,0)
& $lesseq(X_300,g_s127_122) )
<=> ( ( X_300 = g_s165_160 )
| ( X_300 = g_s166_161 )
| ( X_300 = g_s167_162 )
| ( X_300 = g_s168_163 ) ) ) ).
tff('Define:ctx:198',axiom,
mem0(g_s169_164,g_s37_36) ).
tff('Define:ctx:199',axiom,
g_s169_164 = $product(g_s126_121,g_s126_121) ).
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,
? [X_24: set_4] :
( ! [X_25: $int,X_26: $int,X_27: $int] :
( mem4(X_27,X_26,X_25,X_24)
<=> mem4(X_27,X_26,X_25,g_s43_43) )
& ! [X_28: $int,X_29: $int,X_30: $int,X_31: $int] :
( ( mem4(X_29,X_28,X_30,X_24)
& mem4(X_29,X_28,X_31,X_24) )
=> ( X_30 = X_31 ) )
& ! [X_32: $int,X_33: $int] :
( ( mem0(X_33,g_s33_32)
& mem0(X_32,g_s33_32) )
<=> ? [X_34: $int] : mem4(X_33,X_32,X_34,X_24) )
& ! [X_35: $int] :
( ? [X_36: $int,X_37: $int] : mem4(X_37,X_36,X_35,X_24)
=> mem0(X_35,g_s33_32) ) ) ).
tff('Define:ctx:200',axiom,
mem0(g_s170_165,g_s37_36) ).
tff('Define:ctx:201',axiom,
g_s170_165 = $difference(g_s169_164,1) ).
tff('Define:ctx:202',axiom,
mem0(g_s171_166,g_s33_32) ).
tff('Define:ctx:203',axiom,
mem0(g_s172_167,g_s33_32) ).
tff('Define:ctx:204',axiom,
mem0(g_s173_168,g_s33_32) ).
tff('Define:ctx:205',axiom,
mem0(g_s174_169,g_s33_32) ).
tff('Define:ctx:206',axiom,
mem0(g_s175_170,g_s37_36) ).
tff('Define:ctx:207',axiom,
mem0(g_s176_171,g_s37_36) ).
tff('Define:ctx:208',axiom,
mem0(g_s177_172,g_s37_36) ).
tff('Define:ctx:209',axiom,
mem0(g_s178_173,g_s37_36) ).
tff('Define:ctx:21',axiom,
? [X_38: set_4] :
( ! [X_39: $int,X_40: $int,X_41: $int] :
( mem4(X_41,X_40,X_39,X_38)
<=> mem4(X_41,X_40,X_39,g_s44_44) )
& ! [X_42: $int,X_43: $int,X_44: $int,X_45: $int] :
( ( mem4(X_43,X_42,X_44,X_38)
& mem4(X_43,X_42,X_45,X_38) )
=> ( X_44 = X_45 ) )
& ! [X_46: $int,X_47: $int] :
( ( mem0(X_47,g_s33_32)
& mem0(X_46,g_s33_32) )
<=> ? [X_48: $int] : mem4(X_47,X_46,X_48,X_38) )
& ! [X_49: $int] :
( ? [X_50: $int,X_51: $int] : mem4(X_51,X_50,X_49,X_38)
=> mem0(X_49,g_s33_32) ) ) ).
tff('Define:ctx:210',axiom,
mem0(g_s179_174,g_s37_36) ).
tff('Define:ctx:211',axiom,
mem0(g_s180_175,g_s37_36) ).
tff('Define:ctx:212',axiom,
mem0(g_s181_176,g_s37_36) ).
tff('Define:ctx:213',axiom,
mem0(g_s182_177,g_s37_36) ).
tff('Define:ctx:214',axiom,
mem0(g_s183_178,g_s37_36) ).
tff('Define:ctx:215',axiom,
mem0(g_s184_179,g_s37_36) ).
tff('Define:ctx:216',axiom,
! [X_301: $int] :
( mem0(X_301,g_s185_180)
<=> ( ( X_301 = $sum(g_s166_161,1) )
| ( X_301 = $sum(g_s167_162,1) ) ) ) ).
tff('Define:ctx:217',axiom,
! [X_302: $int] :
( mem0(X_302,g_s186_181)
<=> ( ( X_302 = $sum(g_s165_160,1) )
| ( X_302 = $sum(g_s168_163,1) ) ) ) ).
tff('Define:ctx:218',axiom,
mem0(g_s187_182,g_s37_36) ).
tff('Define:ctx:219',axiom,
$less($sum(g_s187_182,g_s126_121),g_s36_37) ).
tff('Define:ctx:22',axiom,
? [X_52: set_3] :
( ! [X_53: $int,X_54: $int] :
( mem3(X_54,X_53,X_52)
<=> mem3(X_54,X_53,g_s45_45) )
& ! [X_55: $int,X_56: $int,X_57: $int] :
( ( mem3(X_55,X_56,X_52)
& mem3(X_55,X_57,X_52) )
=> ( X_56 = X_57 ) )
& ! [X_58: $int] :
( mem0(X_58,g_s35_34)
<=> ? [X_59: $int] : mem3(X_58,X_59,X_52) )
& ! [X_60: $int] :
( ? [X_61: $int] : mem3(X_61,X_60,X_52)
=> mem0(X_60,g_s35_34) ) ) ).
tff('Define:ctx:220',axiom,
mem0(g_s188_183,g_s37_36) ).
tff('Define:ctx:221',axiom,
g_s188_183 = $sum(g_s187_182,g_s126_121) ).
tff('Define:ctx:222',axiom,
mem0(g_s189_184,g_s37_36) ).
tff('Define:ctx:223',axiom,
mem0(g_s190_185,g_s37_36) ).
tff('Define:ctx:224',axiom,
$less($sum(g_s190_185,g_s126_121),g_s36_37) ).
tff('Define:ctx:225',axiom,
mem0(g_s191_186,g_s37_36) ).
tff('Define:ctx:226',axiom,
g_s191_186 = $sum(g_s190_185,g_s126_121) ).
tff('Define:ctx:227',axiom,
mem0(g_s192_187,g_s37_36) ).
tff('Define:ctx:228',axiom,
g_s192_187 = $difference(g_s191_186,1) ).
tff('Define:ctx:229',axiom,
mem0(g_s193_188,g_s37_36) ).
tff('Define:ctx:23',axiom,
? [X_62: set_4] :
( ! [X_63: $int,X_64: $int,X_65: $int] :
( mem4(X_65,X_64,X_63,X_62)
<=> mem4(X_65,X_64,X_63,g_s46_46) )
& ! [X_66: $int,X_67: $int,X_68: $int,X_69: $int] :
( ( mem4(X_67,X_66,X_68,X_62)
& mem4(X_67,X_66,X_69,X_62) )
=> ( X_68 = X_69 ) )
& ! [X_70: $int,X_71: $int] :
( ( mem0(X_71,g_s35_34)
& mem0(X_70,g_s35_34) )
<=> ? [X_72: $int] : mem4(X_71,X_70,X_72,X_62) )
& ! [X_73: $int] :
( ? [X_74: $int,X_75: $int] : mem4(X_75,X_74,X_73,X_62)
=> mem0(X_73,g_s35_34) ) ) ).
tff('Define:ctx:230',axiom,
g_s193_188 = $difference(g_s191_186,2) ).
tff('Define:ctx:231',axiom,
mem0(g_s194_189,g_s37_36) ).
tff('Define:ctx:232',axiom,
$less($sum(g_s194_189,g_s126_121),g_s36_37) ).
tff('Define:ctx:233',axiom,
mem0(g_s195_190,g_s37_36) ).
tff('Define:ctx:234',axiom,
g_s195_190 = $sum(g_s194_189,g_s126_121) ).
tff('Define:ctx:235',axiom,
mem0(g_s196_191,g_s37_36) ).
tff('Define:ctx:236',axiom,
g_s196_191 = $difference(g_s195_190,1) ).
tff('Define:ctx:237',axiom,
mem0(g_s197_192,g_s37_36) ).
tff('Define:ctx:238',axiom,
g_s197_192 = $difference(g_s195_190,2) ).
tff('Define:ctx:239',axiom,
mem0(g_s198_193,g_s37_36) ).
tff('Define:ctx:24',axiom,
? [X_76: set_4] :
( ! [X_77: $int,X_78: $int,X_79: $int] :
( mem4(X_79,X_78,X_77,X_76)
<=> mem4(X_79,X_78,X_77,g_s47_47) )
& ! [X_80: $int,X_81: $int,X_82: $int,X_83: $int] :
( ( mem4(X_81,X_80,X_82,X_76)
& mem4(X_81,X_80,X_83,X_76) )
=> ( X_82 = X_83 ) )
& ! [X_84: $int,X_85: $int] :
( ( mem0(X_85,g_s35_34)
& mem0(X_84,g_s35_34) )
<=> ? [X_86: $int] : mem4(X_85,X_84,X_86,X_76) )
& ! [X_87: $int] :
( ? [X_88: $int,X_89: $int] : mem4(X_89,X_88,X_87,X_76)
=> mem0(X_87,g_s35_34) ) ) ).
tff('Define:ctx:240',axiom,
mem0(g_s199_194,g_s37_36) ).
tff('Define:ctx:241',axiom,
mem0(g_s200_195,g_s37_36) ).
tff('Define:ctx:242',axiom,
mem0(g_s201_196,g_s37_36) ).
tff('Define:ctx:243',axiom,
$greatereq(g_s202_197,1) ).
tff('Define:ctx:244',axiom,
$greatereq(g_s203_198,1) ).
tff('Define:ctx:245',axiom,
$greatereq(g_s204_199,1) ).
tff('Define:ctx:246',axiom,
mem0(g_s205_200,g_s37_36) ).
tff('Define:ctx:247',axiom,
$less(g_s205_200,g_s36_37) ).
tff('Define:ctx:248',axiom,
g_s205_200 = $sum(g_s201_196,g_s202_197) ).
tff('Define:ctx:249',axiom,
mem0(g_s206_201,g_s37_36) ).
tff('Define:ctx:25',axiom,
? [X_90: set_3] :
( ! [X_91: $int,X_92: $int] :
( mem3(X_92,X_91,X_90)
<=> mem3(X_92,X_91,g_s48_48) )
& ! [X_93: $int,X_94: $int,X_95: $int] :
( ( mem3(X_93,X_94,X_90)
& mem3(X_93,X_95,X_90) )
=> ( X_94 = X_95 ) )
& ! [X_96: $int] :
( mem0(X_96,g_s37_36)
<=> ? [X_97: $int] : mem3(X_96,X_97,X_90) )
& ! [X_98: $int] :
( ? [X_99: $int] : mem3(X_99,X_98,X_90)
=> mem0(X_98,g_s37_36) ) ) ).
tff('Define:ctx:250',axiom,
$less(g_s206_201,g_s36_37) ).
tff('Define:ctx:251',axiom,
g_s206_201 = $sum(g_s201_196,g_s203_198) ).
tff('Define:ctx:252',axiom,
mem0(g_s207_202,g_s37_36) ).
tff('Define:ctx:253',axiom,
$less(g_s207_202,g_s36_37) ).
tff('Define:ctx:254',axiom,
g_s207_202 = $sum(g_s201_196,g_s204_199) ).
tff('Define:ctx:255',axiom,
mem0(g_s208_203,g_s37_36) ).
tff('Define:ctx:256',axiom,
$greatereq(g_s209_204,1) ).
tff('Define:ctx:257',axiom,
$greatereq(g_s210_205,1) ).
tff('Define:ctx:258',axiom,
$greatereq(g_s211_206,1) ).
tff('Define:ctx:259',axiom,
mem0(g_s212_207,g_s37_36) ).
tff('Define:ctx:26',axiom,
? [X_100: set_4] :
( ! [X_101: $int,X_102: $int,X_103: $int] :
( mem4(X_103,X_102,X_101,X_100)
<=> mem4(X_103,X_102,X_101,g_s49_49) )
& ! [X_104: $int,X_105: $int,X_106: $int,X_107: $int] :
( ( mem4(X_105,X_104,X_106,X_100)
& mem4(X_105,X_104,X_107,X_100) )
=> ( X_106 = X_107 ) )
& ! [X_108: $int,X_109: $int] :
( ( mem0(X_109,g_s37_36)
& mem0(X_108,g_s37_36) )
<=> ? [X_110: $int] : mem4(X_109,X_108,X_110,X_100) )
& ! [X_111: $int] :
( ? [X_112: $int,X_113: $int] : mem4(X_113,X_112,X_111,X_100)
=> mem0(X_111,g_s37_36) ) ) ).
tff('Define:ctx:260',axiom,
$less(g_s212_207,g_s36_37) ).
tff('Define:ctx:261',axiom,
g_s212_207 = $sum(g_s208_203,g_s209_204) ).
tff('Define:ctx:262',axiom,
mem0(g_s213_208,g_s37_36) ).
tff('Define:ctx:263',axiom,
$less(g_s213_208,g_s36_37) ).
tff('Define:ctx:264',axiom,
g_s213_208 = $sum(g_s208_203,g_s210_205) ).
tff('Define:ctx:265',axiom,
mem0(g_s214_209,g_s37_36) ).
tff('Define:ctx:266',axiom,
$less(g_s214_209,g_s36_37) ).
tff('Define:ctx:267',axiom,
g_s214_209 = $sum(g_s208_203,g_s211_206) ).
tff('Define:ctx:268',axiom,
mem0(g_s215_210,g_s37_36) ).
tff('Define:ctx:269',axiom,
mem0(g_s216_211,g_s37_36) ).
tff('Define:ctx:27',axiom,
? [X_114: set_4] :
( ! [X_115: $int,X_116: $int,X_117: $int] :
( mem4(X_117,X_116,X_115,X_114)
<=> mem4(X_117,X_116,X_115,g_s50_50) )
& ! [X_118: $int,X_119: $int,X_120: $int,X_121: $int] :
( ( mem4(X_119,X_118,X_120,X_114)
& mem4(X_119,X_118,X_121,X_114) )
=> ( X_120 = X_121 ) )
& ! [X_122: $int,X_123: $int] :
( ( mem0(X_123,g_s37_36)
& mem0(X_122,g_s37_36) )
<=> ? [X_124: $int] : mem4(X_123,X_122,X_124,X_114) )
& ! [X_125: $int] :
( ? [X_126: $int,X_127: $int] : mem4(X_127,X_126,X_125,X_114)
=> mem0(X_125,g_s37_36) ) ) ).
tff('Define:ctx:270',axiom,
mem0(g_s217_212,g_s37_36) ).
tff('Define:ctx:271',axiom,
( $greatereq(g_s217_212,0)
& $lesseq(g_s217_212,100) ) ).
tff('Define:ctx:272',axiom,
mem0(g_s218_213,g_s35_34) ).
tff('Define:ctx:273',axiom,
$lesseq(g_s218_213,g_s34_35) ).
tff('Define:ctx:274',axiom,
mem0(g_s219_214,g_s37_36) ).
tff('Define:ctx:275',axiom,
( $greatereq(g_s219_214,0)
& $lesseq(g_s219_214,100) ) ).
tff('Define:ctx:276',axiom,
mem0(g_s220_215,g_s37_36) ).
tff('Define:ctx:277',axiom,
mem0(g_s221_216,g_s37_36) ).
tff('Define:ctx:278',axiom,
mem0(g_s222_217,g_s37_36) ).
tff('Define:ctx:279',axiom,
$greatereq(g_s223_218,0) ).
tff('Define:ctx:28',axiom,
? [X_128: set_4] :
( ! [X_129: $int,X_130: $int,X_131: $int] :
( mem4(X_131,X_130,X_129,X_128)
<=> mem4(X_131,X_130,X_129,g_s51_51) )
& ! [X_132: $int,X_133: $int,X_134: $int,X_135: $int] :
( ( mem4(X_133,X_132,X_134,X_128)
& mem4(X_133,X_132,X_135,X_128) )
=> ( X_134 = X_135 ) )
& ! [X_136: $int,X_137: $int] :
( ( mem0(X_137,g_s37_36)
& mem0(X_136,g_s37_36) )
<=> ? [X_138: $int] : mem4(X_137,X_136,X_138,X_128) )
& ! [X_139: $int] :
( ? [X_140: $int,X_141: $int] : mem4(X_141,X_140,X_139,X_128)
=> mem0(X_139,g_s37_36) ) ) ).
tff('Define:ctx:280',axiom,
$lesseq(1,g_s223_218) ).
tff('Define:ctx:281',axiom,
$greatereq(g_s224_219,0) ).
tff('Define:ctx:282',axiom,
$lesseq(1,g_s224_219) ).
tff('Define:ctx:283',axiom,
$greatereq(g_s225_220,0) ).
tff('Define:ctx:284',axiom,
$lesseq(1,g_s225_220) ).
tff('Define:ctx:285',axiom,
$greatereq(g_s226_221,0) ).
tff('Define:ctx:286',axiom,
$lesseq(1,g_s226_221) ).
tff('Define:ctx:287',axiom,
mem0(g_s227_222,g_s35_34) ).
tff('Define:ctx:288',axiom,
$lesseq(g_s227_222,g_s34_35) ).
tff('Define:ctx:289',axiom,
mem0(g_s228_223,g_s37_36) ).
tff('Define:ctx:29',axiom,
? [X_142: set_4] :
( ! [X_143: $int,X_144: $int,X_145: $int] :
( mem4(X_145,X_144,X_143,X_142)
<=> mem4(X_145,X_144,X_143,g_s52_52) )
& ! [X_146: $int,X_147: $int,X_148: $int,X_149: $int] :
( ( mem4(X_147,X_146,X_148,X_142)
& mem4(X_147,X_146,X_149,X_142) )
=> ( X_148 = X_149 ) )
& ! [X_150: $int,X_151: $int] :
( ( mem0(X_151,g_s33_32)
& mem0(X_150,g_s33_32) )
<=> ? [X_152: $int] : mem4(X_151,X_150,X_152,X_142) )
& ! [X_153: $int] :
( ? [X_154: $int,X_155: $int] : mem4(X_155,X_154,X_153,X_142)
=> mem0(X_153,g_s33_32) ) ) ).
tff('Define:ctx:290',axiom,
( $greatereq(g_s228_223,0)
& $lesseq(g_s228_223,100) ) ).
tff('Define:ctx:291',axiom,
mem0(g_s229_224,g_s35_34) ).
tff('Define:ctx:292',axiom,
$lesseq(g_s229_224,g_s34_35) ).
tff('Define:ctx:293',axiom,
mem0(g_s230_225,g_s37_36) ).
tff('Define:ctx:294',axiom,
( $greatereq(g_s230_225,0)
& $lesseq(g_s230_225,100) ) ).
tff('Define:ctx:295',axiom,
mem0(g_s231_226,g_s35_34) ).
tff('Define:ctx:296',axiom,
$lesseq(g_s231_226,g_s34_35) ).
tff('Define:ctx:297',axiom,
mem0(g_s232_227,g_s37_36) ).
tff('Define:ctx:298',axiom,
( $greatereq(g_s232_227,0)
& $lesseq(g_s232_227,100) ) ).
tff('Define:ctx:299',axiom,
mem0(g_s233_228,g_s37_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,
? [X_156: set_4] :
( ! [X_157: $int,X_158: $int,X_159: $int] :
( mem4(X_159,X_158,X_157,X_156)
<=> mem4(X_159,X_158,X_157,g_s53_53) )
& ! [X_160: $int,X_161: $int,X_162: $int,X_163: $int] :
( ( mem4(X_161,X_160,X_162,X_156)
& mem4(X_161,X_160,X_163,X_156) )
=> ( X_162 = X_163 ) )
& ! [X_164: $int,X_165: $int] :
( ( mem0(X_165,g_s33_32)
& mem0(X_164,g_s33_32) )
<=> ? [X_166: $int] : mem4(X_165,X_164,X_166,X_156) )
& ! [X_167: $int] :
( ? [X_168: $int,X_169: $int] : mem4(X_169,X_168,X_167,X_156)
=> mem0(X_167,g_s33_32) ) ) ).
tff('Define:ctx:300',axiom,
mem0(g_s234_229,g_s37_36) ).
tff('Define:ctx:301',axiom,
( $greatereq(g_s234_229,0)
& $lesseq(g_s234_229,100) ) ).
tff('Define:ctx:302',axiom,
mem0(g_s235_230,g_s35_34) ).
tff('Define:ctx:303',axiom,
mem0(g_s236_231,g_s37_36) ).
tff('Define:ctx:304',axiom,
mem0(g_s237_232,g_s35_34) ).
tff('Define:ctx:305',axiom,
mem0(g_s238_233,g_s35_34) ).
tff('Define:ctx:306',axiom,
mem0(g_s239_234,g_s35_34) ).
tff('Define:ctx:307',axiom,
mem0(g_s240_235,g_s35_34) ).
tff('Define:ctx:308',axiom,
mem0(g_s241_236,g_s37_36) ).
tff('Define:ctx:309',axiom,
mem0(g_s242_237,g_s37_36) ).
tff('Define:ctx:31',axiom,
? [X_170: set_4] :
( ! [X_171: $int,X_172: $int,X_173: $int] :
( mem4(X_173,X_172,X_171,X_170)
<=> mem4(X_173,X_172,X_171,g_s54_54) )
& ! [X_174: $int,X_175: $int,X_176: $int,X_177: $int] :
( ( mem4(X_175,X_174,X_176,X_170)
& mem4(X_175,X_174,X_177,X_170) )
=> ( X_176 = X_177 ) )
& ! [X_178: $int,X_179: $int] :
( ( mem0(X_179,g_s33_32)
& mem0(X_178,g_s33_32) )
<=> ? [X_180: $int] : mem4(X_179,X_178,X_180,X_170) )
& ! [X_181: $int] :
( ? [X_182: $int,X_183: $int] : mem4(X_183,X_182,X_181,X_170)
=> mem0(X_181,g_s33_32) ) ) ).
tff('Define:ctx:310',axiom,
g_s242_237 = $sum(g_s241_236,g_s126_121) ).
tff('Define:ctx:311',axiom,
$less(g_s242_237,g_s36_37) ).
tff('Define:ctx:312',axiom,
mem0(g_s243_238,g_s37_36) ).
tff('Define:ctx:313',axiom,
$lesseq($sum(g_s243_238,2),g_s36_37) ).
tff('Define:ctx:314',axiom,
mem0(g_s244_239,g_s37_36) ).
tff('Define:ctx:315',axiom,
g_s244_239 = $sum(g_s243_238,g_s126_121) ).
tff('Define:ctx:316',axiom,
$less(g_s244_239,g_s36_37) ).
tff('Define:ctx:317',axiom,
mem0(g_s245_240,g_s37_36) ).
tff('Define:ctx:318',axiom,
g_s245_240 = $difference(g_s244_239,1) ).
tff('Define:ctx:319',axiom,
mem0(g_s246_241,g_s37_36) ).
tff('Define:ctx:32',axiom,
? [X_184: set_4] :
( ! [X_185: $int,X_186: $int,X_187: $int] :
( mem4(X_187,X_186,X_185,X_184)
<=> mem4(X_187,X_186,X_185,g_s55_55) )
& ! [X_188: $int,X_189: $int,X_190: $int,X_191: $int] :
( ( mem4(X_189,X_188,X_190,X_184)
& mem4(X_189,X_188,X_191,X_184) )
=> ( X_190 = X_191 ) )
& ! [X_192: $int,X_193: $int] :
( ( mem0(X_193,g_s35_34)
& mem0(X_192,g_s35_34) )
<=> ? [X_194: $int] : mem4(X_193,X_192,X_194,X_184) )
& ! [X_195: $int] :
( ? [X_196: $int,X_197: $int] : mem4(X_197,X_196,X_195,X_184)
=> mem0(X_195,g_s35_34) ) ) ).
tff('Define:ctx:320',axiom,
mem0(g_s247_242,g_s37_36) ).
tff('Define:ctx:321',axiom,
g_s247_242 = $sum(g_s246_241,g_s223_218) ).
tff('Define:ctx:322',axiom,
mem0(g_s248_243,g_s37_36) ).
tff('Define:ctx:323',axiom,
g_s248_243 = $sum(g_s246_241,g_s224_219) ).
tff('Define:ctx:324',axiom,
mem0(g_s249_244,g_s37_36) ).
tff('Define:ctx:325',axiom,
g_s249_244 = $sum(g_s246_241,g_s225_220) ).
tff('Define:ctx:326',axiom,
mem0(g_s250_245,g_s37_36) ).
tff('Define:ctx:327',axiom,
g_s250_245 = $sum(g_s246_241,g_s226_221) ).
tff('Define:ctx:328',axiom,
mem0(g_s251_246,g_s37_36) ).
tff('Define:ctx:329',axiom,
mem0(g_s252_247,g_s37_36) ).
tff('Define:ctx:33',axiom,
? [X_198: set_4] :
( ! [X_199: $int,X_200: $int,X_201: $int] :
( mem4(X_201,X_200,X_199,X_198)
<=> mem4(X_201,X_200,X_199,g_s56_56) )
& ! [X_202: $int,X_203: $int,X_204: $int,X_205: $int] :
( ( mem4(X_203,X_202,X_204,X_198)
& mem4(X_203,X_202,X_205,X_198) )
=> ( X_204 = X_205 ) )
& ! [X_206: $int,X_207: $int] :
( ( mem0(X_207,g_s35_34)
& mem0(X_206,g_s35_34) )
<=> ? [X_208: $int] : mem4(X_207,X_206,X_208,X_198) )
& ! [X_209: $int] :
( ? [X_210: $int,X_211: $int] : mem4(X_211,X_210,X_209,X_198)
=> mem0(X_209,g_s35_34) ) ) ).
tff('Define:ctx:330',axiom,
mem0(g_s253_248,g_s37_36) ).
tff('Define:ctx:331',axiom,
$greatereq(g_s254_249,0) ).
tff('Define:ctx:332',axiom,
$greatereq(g_s255_250,1) ).
tff('Define:ctx:333',axiom,
$lesseq(1,g_s254_249) ).
tff('Define:ctx:334',axiom,
g_s254_249 = $difference(g_s252_247,g_s251_246) ).
tff('Define:ctx:335',axiom,
g_s255_250 = $difference(g_s253_248,g_s251_246) ).
tff('Define:ctx:336',axiom,
$greatereq(g_s256_251,0) ).
tff('Define:ctx:337',axiom,
$greatereq(g_s257_252,0) ).
tff('Define:ctx:338',axiom,
$greatereq(g_s258_253,0) ).
tff('Define:ctx:339',axiom,
$greatereq(g_s259_254,0) ).
tff('Define:ctx:34',axiom,
? [X_212: set_4] :
( ! [X_213: $int,X_214: $int,X_215: $int] :
( mem4(X_215,X_214,X_213,X_212)
<=> mem4(X_215,X_214,X_213,g_s57_57) )
& ! [X_216: $int,X_217: $int,X_218: $int,X_219: $int] :
( ( mem4(X_217,X_216,X_218,X_212)
& mem4(X_217,X_216,X_219,X_212) )
=> ( X_218 = X_219 ) )
& ! [X_220: $int,X_221: $int] :
( ( mem0(X_221,g_s35_34)
& mem0(X_220,g_s35_34) )
<=> ? [X_222: $int] : mem4(X_221,X_220,X_222,X_212) )
& ! [X_223: $int] :
( ? [X_224: $int,X_225: $int] : mem4(X_225,X_224,X_223,X_212)
=> mem0(X_223,g_s35_34) ) ) ).
tff('Define:ctx:340',axiom,
$lesseq(1,g_s258_253) ).
tff('Define:ctx:341',axiom,
mem0(g_s260_255,g_s37_36) ).
tff('Define:ctx:342',axiom,
mem0(g_s261_256,g_s37_36) ).
tff('Define:ctx:343',axiom,
mem0(g_s262_257,g_s37_36) ).
tff('Define:ctx:344',axiom,
mem0(g_s263_258,g_s37_36) ).
tff('Define:ctx:345',axiom,
mem0(g_s264_259,g_s37_36) ).
tff('Define:ctx:346',axiom,
g_s261_256 = $sum(g_s260_255,g_s256_251) ).
tff('Define:ctx:347',axiom,
g_s262_257 = $sum(g_s260_255,g_s257_252) ).
tff('Define:ctx:348',axiom,
g_s263_258 = $sum(g_s260_255,g_s258_253) ).
tff('Define:ctx:349',axiom,
g_s264_259 = $sum(g_s260_255,g_s259_254) ).
tff('Define:ctx:35',axiom,
? [X_226: set_4] :
( ! [X_227: $int,X_228: $int,X_229: $int] :
( mem4(X_229,X_228,X_227,X_226)
<=> mem4(X_229,X_228,X_227,g_s58_58) )
& ! [X_230: $int,X_231: $int,X_232: $int,X_233: $int] :
( ( mem4(X_231,X_230,X_232,X_226)
& mem4(X_231,X_230,X_233,X_226) )
=> ( X_232 = X_233 ) )
& ! [X_234: $int,X_235: $int] :
( ( mem0(X_235,g_s37_36)
& mem0(X_234,g_s37_36) )
<=> ? [X_236: $int] : mem4(X_235,X_234,X_236,X_226) )
& ! [X_237: $int] :
( ? [X_238: $int,X_239: $int] : mem4(X_239,X_238,X_237,X_226)
=> mem0(X_237,g_s37_36) ) ) ).
tff('Define:ctx:350',axiom,
mem0(g_s265_260,g_s37_36) ).
tff('Define:ctx:351',axiom,
mem0(g_s266_261,g_s37_36) ).
tff('Define:ctx:352',axiom,
mem0(g_s267_262,g_s37_36) ).
tff('Define:ctx:353',axiom,
$greatereq(g_s268_263,1) ).
tff('Define:ctx:354',axiom,
$greatereq(g_s269_264,1) ).
tff('Define:ctx:355',axiom,
g_s268_263 = $difference($difference(g_s266_261,g_s265_260),1) ).
tff('Define:ctx:356',axiom,
g_s269_264 = $difference($difference(g_s267_262,g_s265_260),1) ).
tff('Define:ctx:357',axiom,
mem0(g_s270_265,g_s33_32) ).
tff('Define:ctx:358',axiom,
mem0(g_s271_266,g_s37_36) ).
tff('Define:ctx:359',axiom,
mem0(g_s272_267,g_s37_36) ).
tff('Define:ctx:36',axiom,
? [X_240: set_4] :
( ! [X_241: $int,X_242: $int,X_243: $int] :
( mem4(X_243,X_242,X_241,X_240)
<=> mem4(X_243,X_242,X_241,g_s59_59) )
& ! [X_244: $int,X_245: $int,X_246: $int,X_247: $int] :
( ( mem4(X_245,X_244,X_246,X_240)
& mem4(X_245,X_244,X_247,X_240) )
=> ( X_246 = X_247 ) )
& ! [X_248: $int,X_249: $int] :
( ( mem0(X_249,g_s37_36)
& mem0(X_248,g_s37_36) )
<=> ? [X_250: $int] : mem4(X_249,X_248,X_250,X_240) )
& ! [X_251: $int] :
( ? [X_252: $int,X_253: $int] : mem4(X_253,X_252,X_251,X_240)
=> mem0(X_251,g_s37_36) ) ) ).
tff('Define:ctx:360',axiom,
$greatereq(g_s273_268,1) ).
tff('Define:ctx:361',axiom,
$greatereq(g_s274_269,1) ).
tff('Define:ctx:362',axiom,
$greatereq(g_s275_270,1) ).
tff('Define:ctx:363',axiom,
g_s273_268 = $difference(g_s270_265,g_s265_260) ).
tff('Define:ctx:364',axiom,
g_s274_269 = $difference(g_s271_266,g_s265_260) ).
tff('Define:ctx:365',axiom,
g_s275_270 = $difference($difference(g_s272_267,g_s265_260),1) ).
tff('Define:ctx:366',axiom,
$greatereq(g_s276_271,1) ).
tff('Define:ctx:367',axiom,
mem0(g_s277_272,g_s37_36) ).
tff('Define:ctx:368',axiom,
mem0(g_s278_273,g_s37_36) ).
tff('Define:ctx:369',axiom,
mem0(g_s279_274,g_s33_32) ).
tff('Define:ctx:37',axiom,
? [X_254: set_4] :
( ! [X_255: $int,X_256: $int,X_257: $int] :
( mem4(X_257,X_256,X_255,X_254)
<=> mem4(X_257,X_256,X_255,g_s60_60) )
& ! [X_258: $int,X_259: $int,X_260: $int,X_261: $int] :
( ( mem4(X_259,X_258,X_260,X_254)
& mem4(X_259,X_258,X_261,X_254) )
=> ( X_260 = X_261 ) )
& ! [X_262: $int,X_263: $int] :
( ( mem0(X_263,g_s37_36)
& mem0(X_262,g_s37_36) )
<=> ? [X_264: $int] : mem4(X_263,X_262,X_264,X_254) )
& ! [X_265: $int] :
( ? [X_266: $int,X_267: $int] : mem4(X_267,X_266,X_265,X_254)
=> mem0(X_265,g_s37_36) ) ) ).
tff('Define:ctx:370',axiom,
g_s276_271 = $difference($difference(g_s279_274,g_s277_272),1) ).
tff('Define:ctx:371',axiom,
$greatereq(g_s280_275,0) ).
tff('Define:ctx:372',axiom,
$greatereq(g_s281_276,1) ).
tff('Define:ctx:373',axiom,
$greatereq(g_s282_277,0) ).
tff('Define:ctx:374',axiom,
$greatereq(g_s283_278,0) ).
tff('Define:ctx:375',axiom,
$greatereq(g_s284_279,0) ).
tff('Define:ctx:376',axiom,
$greatereq(g_s285_280,0) ).
tff('Define:ctx:377',axiom,
$greatereq(g_s286_281,0) ).
tff('Define:ctx:378',axiom,
$greatereq(g_s287_282,0) ).
tff('Define:ctx:379',axiom,
$greatereq(g_s288_283,0) ).
tff('Define:ctx:38',axiom,
! [X_268: $int,X_269: $int,X_270: $int] :
( mem4(X_270,X_269,X_268,g_s52_52)
<=> ( mem0(X_270,g_s33_32)
& mem0(X_269,g_s33_32)
& ( X_268 = $remainder_f($sum(X_270,X_269),$sum(g_s32_33,1)) ) ) ) ).
tff('Define:ctx:380',axiom,
$greatereq(g_s289_284,0) ).
tff('Define:ctx:381',axiom,
mem0(g_s290_285,g_s37_36) ).
tff('Define:ctx:382',axiom,
$lesseq(1,g_s290_285) ).
tff('Define:ctx:383',axiom,
mem0(g_s291_286,g_s37_36) ).
tff('Define:ctx:384',axiom,
g_s291_286 = $sum(g_s290_285,g_s288_283) ).
tff('Define:ctx:385',axiom,
mem0(g_s292_287,g_s37_36) ).
tff('Define:ctx:386',axiom,
g_s292_287 = $sum(g_s290_285,g_s289_284) ).
tff('Define:ctx:387',axiom,
mem0(g_s293_288,g_s37_36) ).
tff('Define:ctx:388',axiom,
g_s293_288 = $sum(g_s290_285,g_s283_278) ).
tff('Define:ctx:389',axiom,
mem0(g_s294_289,g_s37_36) ).
tff('Define:ctx:39',axiom,
! [X_271: $int,X_272: $int,X_273: $int] :
( mem4(X_273,X_272,X_271,g_s53_53)
<=> ( mem0(X_273,g_s33_32)
& mem0(X_272,g_s33_32)
& ( X_271 = $remainder_f($sum($sum($difference(X_273,X_272),g_s32_33),1),$sum(g_s32_33,1)) ) ) ) ).
tff('Define:ctx:390',axiom,
g_s294_289 = $sum(g_s290_285,g_s282_277) ).
tff('Define:ctx:391',axiom,
mem0(g_s295_290,g_s37_36) ).
tff('Define:ctx:392',axiom,
g_s295_290 = $sum(g_s290_285,g_s284_279) ).
tff('Define:ctx:393',axiom,
mem0(g_s296_291,g_s37_36) ).
tff('Define:ctx:394',axiom,
g_s296_291 = $sum(g_s290_285,g_s287_282) ).
tff('Define:ctx:395',axiom,
mem0(g_s297_292,g_s37_36) ).
tff('Define:ctx:396',axiom,
g_s297_292 = $sum(g_s290_285,g_s285_280) ).
tff('Define:ctx:397',axiom,
mem0(g_s298_293,g_s37_36) ).
tff('Define:ctx:398',axiom,
g_s298_293 = $sum(g_s290_285,g_s286_281) ).
tff('Define:ctx:399',axiom,
mem0(g_s299_294,g_s33_32) ).
tff('Define:ctx:4',axiom,
( ! [X_9: $int] :
( mem0(X_9,g_s19_19)
<=> ( ( X_9 = g_s20_20 )
| ( X_9 = g_s21_21 ) ) )
& ( g_s20_20 != g_s21_21 ) ) ).
tff('Define:ctx:40',axiom,
! [X_274: $int,X_275: $int,X_276: $int] :
( mem4(X_276,X_275,X_274,g_s54_54)
<=> ( mem0(X_276,g_s33_32)
& mem0(X_275,g_s33_32)
& ( X_274 = $remainder_f($product(X_276,X_275),$sum(g_s32_33,1)) ) ) ) ).
tff('Define:ctx:400',axiom,
g_s299_294 = $sum(g_s290_285,g_s280_275) ).
tff('Define:ctx:401',axiom,
mem0(g_s300_295,g_s37_36) ).
tff('Define:ctx:402',axiom,
g_s300_295 = $sum(g_s290_285,g_s281_276) ).
tff('Define:ctx:403',axiom,
? [X_303: set_4] :
( ! [X_304: $int,X_305: $int,X_306: $int] :
( mem4(X_306,X_305,X_304,X_303)
<=> mem4(X_306,X_305,X_304,g_s301_296) )
& ! [X_307: $int,X_308: $int,X_309: $int,X_310: $int] :
( ( mem4(X_308,X_307,X_309,X_303)
& mem4(X_308,X_307,X_310,X_303) )
=> ( X_309 = X_310 ) )
& ! [X_311: $int,X_312: $int] :
( ( mem0(X_312,g_s22_22)
& mem0(X_311,g_s22_22) )
<=> ? [X_313: $int] : mem4(X_312,X_311,X_313,X_303) )
& ! [X_314: $int] :
( ? [X_315: $int,X_316: $int] : mem4(X_316,X_315,X_314,X_303)
=> mem0(X_314,g_s37_36) ) ) ).
tff('Define:ctx:404',axiom,
! [X_317: $int,X_318: $int] :
( mem3(X_318,X_317,g_s302_297)
<=> ? [X_319: $int] :
( ( X_319 = g_s38_38 )
& mem4(X_318,X_317,X_319,g_s301_296) ) ) ).
tff('Define:ctx:405',axiom,
? [X_320: set_4] :
( ! [X_321: $int,X_322: $int,X_323: $int] :
( mem4(X_323,X_322,X_321,X_320)
<=> mem4(X_323,X_322,X_321,g_s303_298) )
& ! [X_324: $int,X_325: $int,X_326: $int,X_327: $int] :
( ( mem4(X_325,X_324,X_326,X_320)
& mem4(X_325,X_324,X_327,X_320) )
=> ( X_326 = X_327 ) )
& ! [X_328: $int,X_329: $int] :
( ( mem0(X_329,g_s22_22)
& mem0(X_328,g_s22_22) )
<=> ? [X_330: $int] : mem4(X_329,X_328,X_330,X_320) )
& ! [X_331: $int] :
( ? [X_332: $int,X_333: $int] : mem4(X_333,X_332,X_331,X_320)
=> ( mem0(X_331,g_s35_34)
& ( X_331 != 65535 ) ) ) ) ).
tff('Define:ctx:406',axiom,
! [X_334: $int,X_335: $int] :
( mem3(X_335,X_334,g_s304_299)
=> ( mem0(X_335,g_s22_22)
& mem0(X_334,g_s22_22) ) ) ).
tff('Define:ctx:407',axiom,
? [X_336: set_4] :
( ! [X_337: $int,X_338: $int,X_339: $int] :
( mem4(X_339,X_338,X_337,X_336)
<=> mem4(X_339,X_338,X_337,g_s305_300) )
& ! [X_340: $int,X_341: $int,X_342: $int,X_343: $int] :
( ( mem4(X_341,X_340,X_342,X_336)
& mem4(X_341,X_340,X_343,X_336) )
=> ( X_342 = X_343 ) )
& ! [X_344: $int,X_345: $int] :
( ( mem0(X_345,g_s22_22)
& mem0(X_344,g_s22_22) )
<=> ? [X_346: $int] : mem4(X_345,X_344,X_346,X_336) )
& ! [X_347: $int] :
( ? [X_348: $int,X_349: $int] : mem4(X_349,X_348,X_347,X_336)
=> mem0(X_347,g_s35_34) ) ) ).
tff('Define:ctx:408',axiom,
! [X_350: $int,X_351: $int,X_352: $int] :
( mem4(X_352,X_351,X_350,g_s305_300)
<=> ( ( mem3(X_352,X_351,g_s304_299)
& ( X_350 = 65535 ) )
| ( mem4(X_352,X_351,X_350,g_s303_298)
& ~ ? [X_353: $int] :
( mem3(X_352,X_351,g_s304_299)
& ( X_353 = 65535 ) ) ) ) ) ).
tff('Define:ctx:409',axiom,
! [X_354: $int,X_355: $int] :
( mem3(X_355,X_354,g_s302_297)
=> ( mem0(X_355,g_s22_22)
& mem0(X_354,g_s22_22) ) ) ).
tff('Define:ctx:41',axiom,
! [X_277: $int,X_278: $int,X_279: $int] :
( mem4(X_279,X_278,X_277,g_s55_55)
<=> ( mem0(X_279,g_s35_34)
& mem0(X_278,g_s35_34)
& ( X_277 = $remainder_f($sum(X_279,X_278),$sum(g_s34_35,1)) ) ) ) ).
tff('Define:ctx:42',axiom,
! [X_280: $int,X_281: $int,X_282: $int] :
( mem4(X_282,X_281,X_280,g_s56_56)
<=> ( mem0(X_282,g_s35_34)
& mem0(X_281,g_s35_34)
& ( X_280 = $remainder_f($sum($sum($difference(X_282,X_281),g_s34_35),1),$sum(g_s34_35,1)) ) ) ) ).
tff('Define:ctx:43',axiom,
! [X_283: $int,X_284: $int,X_285: $int] :
( mem4(X_285,X_284,X_283,g_s57_57)
<=> ( mem0(X_285,g_s35_34)
& mem0(X_284,g_s35_34)
& ( X_283 = $remainder_f($product(X_285,X_284),$sum(g_s34_35,1)) ) ) ) ).
tff('Define:ctx:44',axiom,
! [X_286: $int,X_287: $int,X_288: $int] :
( mem4(X_288,X_287,X_286,g_s58_58)
<=> ( mem0(X_288,g_s37_36)
& mem0(X_287,g_s37_36)
& ( X_286 = $remainder_f($sum(X_288,X_287),$sum(g_s36_37,1)) ) ) ) ).
tff('Define:ctx:45',axiom,
! [X_289: $int,X_290: $int,X_291: $int] :
( mem4(X_291,X_290,X_289,g_s59_59)
<=> ( mem0(X_291,g_s37_36)
& mem0(X_290,g_s37_36)
& ( X_289 = $remainder_f($sum($sum($difference(X_291,X_290),g_s36_37),1),$sum(g_s36_37,1)) ) ) ) ).
tff('Define:ctx:46',axiom,
! [X_292: $int,X_293: $int,X_294: $int] :
( mem4(X_294,X_293,X_292,g_s60_60)
<=> ( mem0(X_294,g_s37_36)
& mem0(X_293,g_s37_36)
& ( X_292 = $remainder_f($product(X_294,X_293),$sum(g_s36_37,1)) ) ) ) ).
tff('Define:ctx:47',axiom,
! [L_s65: $int] :
( mem0(L_s65,g_s33_32)
=> ! [X_295: $int] :
( ! [X_296: $int] :
( ( X_296 = 1023 )
=> mem4(L_s65,X_296,X_295,g_s43_43) )
=> $lesseq(X_295,1023) ) ) ).
tff('Define:ctx:48',axiom,
! [X_297: $int] :
( mem0(X_297,g_s33_32)
<=> ( $greatereq(X_297,0)
& $lesseq(X_297,4294967295) ) ) ).
tff('Define:ctx:49',axiom,
! [X_298: $int] :
( mem0(X_298,g_s35_34)
<=> ( $greatereq(X_298,0)
& $lesseq(X_298,65535) ) ) ).
tff('Define:ctx:5',axiom,
( ! [X_10: $int] :
( mem0(X_10,g_s22_22)
<=> ( ( X_10 = g_s23_23 )
| ( X_10 = g_s24_24 )
| ( X_10 = g_s25_25 )
| ( X_10 = g_s26_26 )
| ( X_10 = g_s27_27 )
| ( X_10 = g_s28_28 )
| ( X_10 = g_s29_29 )
| ( X_10 = g_s30_30 )
| ( X_10 = g_s31_31 ) ) )
& ( g_s23_23 != g_s24_24 )
& ( g_s24_24 != g_s25_25 )
& ( g_s25_25 != g_s26_26 )
& ( g_s26_26 != g_s27_27 )
& ( g_s27_27 != g_s28_28 )
& ( g_s28_28 != g_s29_29 )
& ( g_s29_29 != g_s30_30 )
& ( g_s30_30 != g_s31_31 ) ) ).
tff('Define:ctx:50',axiom,
! [X_299: $int] :
( mem0(X_299,g_s37_36)
<=> ( $greatereq(X_299,0)
& $lesseq(X_299,255) ) ) ).
tff('Define:ctx:51',axiom,
mem0(g_s66_61,g_s37_36) ).
tff('Define:ctx:52',axiom,
mem0(g_s67_62,g_s37_36) ).
tff('Define:ctx:53',axiom,
mem0(g_s68_63,g_s35_34) ).
tff('Define:ctx:54',axiom,
mem0(g_s69_64,g_s35_34) ).
tff('Define:ctx:55',axiom,
mem0(g_s70_65,g_s33_32) ).
tff('Define:ctx:56',axiom,
mem0(g_s71_66,g_s33_32) ).
tff('Define:ctx:57',axiom,
$greatereq(g_s72_67,0) ).
tff('Define:ctx:58',axiom,
$lesseq(2,g_s72_67) ).
tff('Define:ctx:59',axiom,
$greatereq(g_s73_68,0) ).
tff('Define:ctx:6',axiom,
mem0(g_s32_33,g_s33_32) ).
tff('Define:ctx:60',axiom,
$lesseq(2,g_s73_68) ).
tff('Define:ctx:61',axiom,
$greatereq(g_s74_69,0) ).
tff('Define:ctx:62',axiom,
$lesseq(2,g_s74_69) ).
tff('Define:ctx:63',axiom,
$lesseq(g_s72_67,g_s74_69) ).
tff('Define:ctx:64',axiom,
mem0(g_s75_70,g_s37_36) ).
tff('Define:ctx:65',axiom,
mem0(g_s76_71,g_s37_36) ).
tff('Define:ctx:66',axiom,
g_s76_71 = $sum(g_s75_70,g_s72_67) ).
tff('Define:ctx:67',axiom,
mem0(g_s77_72,g_s37_36) ).
tff('Define:ctx:68',axiom,
g_s77_72 = $sum(g_s75_70,g_s73_68) ).
tff('Define:ctx:69',axiom,
mem0(g_s78_73,g_s37_36) ).
tff('Define:ctx:7',axiom,
mem0(g_s34_35,g_s35_34) ).
tff('Define:ctx:70',axiom,
g_s78_73 = $sum(g_s75_70,g_s74_69) ).
tff('Define:ctx:71',axiom,
mem0(g_s79_74,g_s35_34) ).
tff('Define:ctx:72',axiom,
mem0(g_s80_75,g_s35_34) ).
tff('Define:ctx:73',axiom,
mem0(g_s81_76,g_s37_36) ).
tff('Define:ctx:74',axiom,
$lesseq(g_s79_74,g_s80_75) ).
tff('Define:ctx:75',axiom,
mem0(g_s82_77,g_s33_32) ).
tff('Define:ctx:76',axiom,
mem0(g_s83_78,g_s33_32) ).
tff('Define:ctx:77',axiom,
mem0(g_s84_79,g_s33_32) ).
tff('Define:ctx:78',axiom,
mem0(g_s85_80,g_s33_32) ).
tff('Define:ctx:79',axiom,
mem0(g_s86_81,g_s33_32) ).
tff('Define:ctx:8',axiom,
mem0(g_s36_37,g_s37_36) ).
tff('Define:ctx:80',axiom,
mem0(g_s87_82,g_s37_36) ).
tff('Define:ctx:81',axiom,
$lesseq(2,g_s87_82) ).
tff('Define:ctx:82',axiom,
mem0(g_s88_83,g_s37_36) ).
tff('Define:ctx:83',axiom,
g_s88_83 = $difference(g_s87_82,1) ).
tff('Define:ctx:84',axiom,
$greatereq(g_s89_84,1) ).
tff('Define:ctx:85',axiom,
$greatereq(g_s90_85,1) ).
tff('Define:ctx:86',axiom,
$greatereq(g_s91_86,1) ).
tff('Define:ctx:87',axiom,
$greatereq(g_s92_87,1) ).
tff('Define:ctx:88',axiom,
$greatereq(g_s93_88,1) ).
tff('Define:ctx:89',axiom,
$greatereq(g_s94_89,1) ).
tff('Define:ctx:9',axiom,
mem0(g_s38_38,g_s37_36) ).
tff('Define:ctx:90',axiom,
$greatereq(g_s95_90,1) ).
tff('Define:ctx:91',axiom,
$greatereq(g_s96_91,1) ).
tff('Define:ctx:92',axiom,
mem0(g_s97_92,g_s37_36) ).
tff('Define:ctx:93',axiom,
mem0(g_s98_93,g_s37_36) ).
tff('Define:ctx:94',axiom,
g_s98_93 = $sum(g_s97_92,g_s89_84) ).
tff('Define:ctx:95',axiom,
mem0(g_s99_94,g_s37_36) ).
tff('Define:ctx:96',axiom,
mem0(g_s100_95,g_s37_36) ).
tff('Define:ctx:97',axiom,
g_s100_95 = $sum(g_s99_94,g_s90_85) ).
tff('Define:ctx:98',axiom,
mem0(g_s101_96,g_s37_36) ).
tff('Define:ctx:99',axiom,
g_s101_96 = $sum(g_s99_94,g_s91_86) ).
tff('Define:imext:0',axiom,
$true ).
tff('Define:imext:1',axiom,
$true ).
tff('Define:imext:10',axiom,
$true ).
tff('Define:imext:11',axiom,
? [X_1886: set_3] :
( ! [X_1887: $int,X_1888: $int] :
( mem3(X_1888,X_1887,X_1886)
<=> mem3(X_1888,X_1887,g_s335_1_343) )
& ! [X_1889: $int,X_1890: $int,X_1891: $int] :
( ( mem3(X_1889,X_1890,X_1886)
& mem3(X_1889,X_1891,X_1886) )
=> ( X_1890 = X_1891 ) )
& ! [X_1892: $int] :
( ( $greatereq(X_1892,1)
& $lesseq(X_1892,g_s326_1_342) )
<=> ? [X_1893: $int] : mem3(X_1892,X_1893,X_1886) )
& ! [X_1894: $int] :
( ? [X_1895: $int] : mem3(X_1895,X_1894,X_1886)
=> ( $greatereq(X_1894,0)
& $lesseq(X_1894,g_s126_121) ) ) ) ).
tff('Define:imext:12',axiom,
? [X_1896: set_3] :
( ! [X_1897: $int,X_1898: $int] :
( mem3(X_1898,X_1897,X_1896)
<=> mem3(X_1898,X_1897,g_s336_1_344) )
& ! [X_1899: $int,X_1900: $int,X_1901: $int] :
( ( mem3(X_1899,X_1900,X_1896)
& mem3(X_1899,X_1901,X_1896) )
=> ( X_1900 = X_1901 ) )
& ! [X_1902: $int] :
( ( $greatereq(X_1902,1)
& $lesseq(X_1902,g_s326_1_342) )
<=> ? [X_1903: $int] : mem3(X_1902,X_1903,X_1896) )
& ! [X_1904: $int] :
( ? [X_1905: $int] : mem3(X_1905,X_1904,X_1896)
=> ( $greatereq(X_1904,0)
& $lesseq(X_1904,g_s126_121) ) ) ) ).
tff('Define:imext:13',axiom,
? [X_1906: set_3] :
( ! [X_1907: $int,X_1908: $int] :
( mem3(X_1908,X_1907,X_1906)
<=> mem3(X_1908,X_1907,g_s337_1_345) )
& ! [X_1909: $int,X_1910: $int,X_1911: $int] :
( ( mem3(X_1909,X_1910,X_1906)
& mem3(X_1909,X_1911,X_1906) )
=> ( X_1910 = X_1911 ) )
& ! [X_1912: $int] :
( ( $greatereq(X_1912,1)
& $lesseq(X_1912,g_s326_1_342) )
<=> ? [X_1913: $int] : mem3(X_1912,X_1913,X_1906) )
& ! [X_1914: $int] :
( ? [X_1915: $int] : mem3(X_1915,X_1914,X_1906)
=> ( $greatereq(X_1914,0)
& $lesseq(X_1914,g_s126_121) ) ) ) ).
tff('Define:imext:14',axiom,
! [X_1916: $int,X_1917: $int] :
( mem3(X_1917,X_1916,g_s338_1_346)
=> ( mem0(X_1917,g_s186_181)
& $greatereq(X_1916,1)
& $lesseq(X_1916,g_s326_1_342) ) ) ).
tff('Define:imext:2',axiom,
? [X_1828: set_4] :
( ! [X_1829: $int,X_1830: $int,X_1831: $int] :
( mem4(X_1831,X_1830,X_1829,X_1828)
<=> mem4(X_1831,X_1830,X_1829,g_s328_1_336) )
& ! [X_1832: $int,X_1833: $int,X_1834: $int,X_1835: $int] :
( ( mem4(X_1833,X_1832,X_1834,X_1828)
& mem4(X_1833,X_1832,X_1835,X_1828) )
=> ( X_1834 = X_1835 ) )
& ! [X_1836: $int,X_1837: $int] :
( ( $greatereq(X_1837,1)
& $lesseq(X_1837,g_s126_121)
& $greatereq(X_1836,1)
& $lesseq(X_1836,g_s126_121) )
<=> ? [X_1838: $int] : mem4(X_1837,X_1836,X_1838,X_1828) )
& ! [X_1839: $int] :
( ? [X_1840: $int,X_1841: $int] : mem4(X_1841,X_1840,X_1839,X_1828)
=> $greatereq(X_1839,0) ) ) ).
tff('Define:imext:3',axiom,
? [X_1842: set_4] :
( ! [X_1843: $int,X_1844: $int,X_1845: $int] :
( mem4(X_1845,X_1844,X_1843,X_1842)
<=> mem4(X_1845,X_1844,X_1843,g_s329_1_337) )
& ! [X_1846: $int,X_1847: $int,X_1848: $int,X_1849: $int] :
( ( mem4(X_1847,X_1846,X_1848,X_1842)
& mem4(X_1847,X_1846,X_1849,X_1842) )
=> ( X_1848 = X_1849 ) )
& ! [X_1850: $int,X_1851: $int] :
( ( $greatereq(X_1851,1)
& $lesseq(X_1851,g_s126_121)
& $greatereq(X_1850,1)
& $lesseq(X_1850,g_s126_121) )
<=> ? [X_1852: $int] : mem4(X_1851,X_1850,X_1852,X_1842) )
& ! [X_1853: $int] :
( ? [X_1854: $int,X_1855: $int] : mem4(X_1855,X_1854,X_1853,X_1842)
=> $greatereq(X_1853,0) ) ) ).
tff('Define:imext:4',axiom,
? [X_1856: set_4] :
( ! [X_1857: $int,X_1858: $int,X_1859: $int] :
( mem4(X_1859,X_1858,X_1857,X_1856)
<=> mem4(X_1859,X_1858,X_1857,g_s331_1_338) )
& ! [X_1860: $int,X_1861: $int,X_1862: $int,X_1863: $int] :
( ( mem4(X_1861,X_1860,X_1862,X_1856)
& mem4(X_1861,X_1860,X_1863,X_1856) )
=> ( X_1862 = X_1863 ) )
& ! [X_1864: $int,X_1865: $int] :
( ( $greatereq(X_1865,1)
& $lesseq(X_1865,g_s126_121)
& $greatereq(X_1864,1)
& $lesseq(X_1864,g_s126_121) )
<=> ? [X_1866: $int] : mem4(X_1865,X_1864,X_1866,X_1856) )
& ! [X_1867: $int] :
( ? [X_1868: $int,X_1869: $int] : mem4(X_1869,X_1868,X_1867,X_1856)
=> $greatereq(X_1867,0) ) ) ).
tff('Define:imext:5',axiom,
? [X_1870: set_4] :
( ! [X_1871: $int,X_1872: $int,X_1873: $int] :
( mem4(X_1873,X_1872,X_1871,X_1870)
<=> mem4(X_1873,X_1872,X_1871,g_s332_1_339) )
& ! [X_1874: $int,X_1875: $int,X_1876: $int,X_1877: $int] :
( ( mem4(X_1875,X_1874,X_1876,X_1870)
& mem4(X_1875,X_1874,X_1877,X_1870) )
=> ( X_1876 = X_1877 ) )
& ! [X_1878: $int,X_1879: $int] :
( ( $greatereq(X_1879,1)
& $lesseq(X_1879,g_s126_121)
& $greatereq(X_1878,1)
& $lesseq(X_1878,g_s126_121) )
<=> ? [X_1880: $int] : mem4(X_1879,X_1878,X_1880,X_1870) )
& ! [X_1881: $int] :
( ? [X_1882: $int,X_1883: $int] : mem4(X_1883,X_1882,X_1881,X_1870)
=> $greatereq(X_1881,0) ) ) ).
tff('Define:imext:6',axiom,
! [X_1884: $int] :
( mem0(X_1884,g_s339_1_340)
=> ( $greatereq(X_1884,1)
& $lesseq(X_1884,g_s126_121) ) ) ).
tff('Define:imext:7',axiom,
! [X_1885: $int] :
( mem0(X_1885,g_s340_1_341)
=> ( $greatereq(X_1885,1)
& $lesseq(X_1885,g_s126_121) ) ) ).
tff('Define:imext:8',axiom,
$greatereq(g_s326_1_342,0) ).
tff('Define:imext:9',axiom,
$true ).
tff('Define:imprp:0',axiom,
? [X_356: set_4] :
( ! [X_357: $int,X_358: $int,X_359: $int] :
( mem4(X_359,X_358,X_357,X_356)
<=> mem4(X_359,X_358,X_357,g_s322_301) )
& ! [X_360: $int,X_361: $int,X_362: $int,X_363: $int] :
( ( mem4(X_361,X_360,X_362,X_356)
& mem4(X_361,X_360,X_363,X_356) )
=> ( X_362 = X_363 ) )
& ! [X_364: $int,X_365: $int] :
( ( $greatereq(X_365,1)
& $lesseq(X_365,g_s126_121)
& $greatereq(X_364,1)
& $lesseq(X_364,g_s126_121) )
<=> ? [X_366: $int] : mem4(X_365,X_364,X_366,X_356) )
& ! [X_367: $int] :
( ? [X_368: $int,X_369: $int] : mem4(X_369,X_368,X_367,X_356)
=> mem0(X_367,g_s35_34) ) ) ).
tff('Define:imprp:1',axiom,
? [X_370: set_4] :
( ! [X_371: $int,X_372: $int,X_373: $int] :
( mem4(X_373,X_372,X_371,X_370)
<=> mem4(X_373,X_372,X_371,g_s323_302) )
& ! [X_374: $int,X_375: $int,X_376: $int,X_377: $int] :
( ( mem4(X_375,X_374,X_376,X_370)
& mem4(X_375,X_374,X_377,X_370) )
=> ( X_376 = X_377 ) )
& ! [X_378: $int,X_379: $int] :
( ( $greatereq(X_379,1)
& $lesseq(X_379,g_s126_121)
& $greatereq(X_378,1)
& $lesseq(X_378,g_s126_121) )
<=> ? [X_380: $int] : mem4(X_379,X_378,X_380,X_370) )
& ! [X_381: $int] :
( ? [X_382: $int,X_383: $int] : mem4(X_383,X_382,X_381,X_370)
=> mem0(X_381,g_s37_36) ) ) ).
tff('Define:imprp:2',axiom,
? [X_384: set_4] :
( ! [X_385: $int,X_386: $int,X_387: $int] :
( mem4(X_387,X_386,X_385,X_384)
<=> mem4(X_387,X_386,X_385,g_s323_302) )
& ! [X_388: $int,X_389: $int,X_390: $int,X_391: $int] :
( ( mem4(X_389,X_388,X_390,X_384)
& mem4(X_389,X_388,X_391,X_384) )
=> ( X_390 = X_391 ) )
& ! [X_392: $int,X_393: $int] :
( ( $greatereq(X_393,1)
& $lesseq(X_393,g_s126_121)
& $greatereq(X_392,1)
& $lesseq(X_392,g_s126_121) )
<=> ? [X_394: $int] : mem4(X_393,X_392,X_394,X_384) )
& ! [X_395: $int] :
( ? [X_396: $int,X_397: $int] : mem4(X_397,X_396,X_395,X_384)
=> ( $greatereq(X_395,0)
& $lesseq(X_395,100) ) ) ) ).
tff('Define:imprp:3',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s185_180)
& mem0(L_s325,g_s185_180) )
=> ( mem4(L_s324,L_s325,g_s227_222,g_s322_301)
& mem4(L_s324,L_s325,g_s228_223,g_s323_302) ) ) ).
tff('Define:imprp:4',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s186_181)
& mem0(L_s325,g_s186_181) )
=> ( mem4(L_s324,L_s325,g_s229_224,g_s322_301)
& mem4(L_s324,L_s325,g_s230_225,g_s323_302) ) ) ).
tff('Define:imprp:5',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s186_181)
& mem0(L_s325,g_s185_180) )
=> ( mem4(L_s324,L_s325,g_s231_226,g_s322_301)
& mem4(L_s324,L_s325,g_s232_227,g_s323_302) ) ) ).
tff('Define:imprp:6',axiom,
! [L_s324: $int,L_s325: $int] :
( ( mem0(L_s324,g_s185_180)
& mem0(L_s325,g_s186_181) )
=> ( mem4(L_s324,L_s325,g_s231_226,g_s322_301)
& mem4(L_s324,L_s325,g_s232_227,g_s323_302) ) ) ).
tff('Define:seext:0',axiom,
! [X_496: $int] :
( mem0(X_496,g_s306_303)
=> ( $greatereq(X_496,1)
& $lesseq(X_496,g_s126_121) ) ) ).
tff('Define:seext:1',axiom,
! [X_497: $int] :
( mem0(X_497,g_s307_304)
=> ( $greatereq(X_497,1)
& $lesseq(X_497,g_s126_121) ) ) ).
tff('Define:seext:10',axiom,
! [X_542: $int] :
( mem0(X_542,g_s316_313)
=> ( $greatereq(X_542,1)
& $lesseq(X_542,g_s126_121) ) ) ).
tff('Define:seext:11',axiom,
! [X_543: $int] :
( mem0(X_543,g_s317_314)
=> ( $greatereq(X_543,1)
& $lesseq(X_543,g_s126_121) ) ) ).
tff('Define:seext:12',axiom,
( ! [X_544: $int,X_545: $int] :
( mem3(X_545,X_544,g_s318_315)
=> ( $greatereq(X_545,1)
& $lesseq(X_545,g_s126_121)
& mem0(X_544,g_s35_34) ) )
& ! [X_546: $int,X_547: $int,X_548: $int] :
( ( mem3(X_546,X_547,g_s318_315)
& mem3(X_546,X_548,g_s318_315) )
=> ( X_547 = X_548 ) ) ) ).
tff('Define:seext:13',axiom,
( ! [X_549: $int,X_550: $int] :
( mem3(X_550,X_549,g_s319_316)
=> ( $greatereq(X_550,1)
& $lesseq(X_550,g_s126_121)
& mem0(X_549,g_s35_34) ) )
& ! [X_551: $int,X_552: $int,X_553: $int] :
( ( mem3(X_551,X_552,g_s319_316)
& mem3(X_551,X_553,g_s319_316) )
=> ( X_552 = X_553 ) ) ) ).
tff('Define:seext:14',axiom,
! [X_554: $int] :
( mem0(X_554,g_s320_317)
=> ( $greatereq(X_554,1)
& $lesseq(X_554,g_s126_121) ) ) ).
tff('Define:seext:15',axiom,
? [X_555: set_3] :
( ! [X_556: $int,X_557: $int] :
( mem3(X_557,X_556,X_555)
<=> mem3(X_557,X_556,g_s321_318) )
& ! [X_558: $int,X_559: $int,X_560: $int] :
( ( mem3(X_558,X_559,X_555)
& mem3(X_558,X_560,X_555) )
=> ( X_559 = X_560 ) )
& ! [X_561: $int] :
( ( $greatereq(X_561,0)
& $lesseq(X_561,g_s127_122) )
<=> ? [X_562: $int] : mem3(X_561,X_562,X_555) )
& ! [X_563: $int] :
( ? [X_564: $int] : mem3(X_564,X_563,X_555)
=> mem0(X_563,g_s35_34) ) ) ).
tff('Define:seext:16',axiom,
( ! [X_565: $int,X_566: $o] :
( mem2((X_566),X_565,g_s41_41)
=> ( $true
& mem0(X_565,g_s37_36) ) )
& ! [X_567: $o,X_568: $int,X_569: $int] :
( ( mem2((X_567),X_568,g_s41_41)
& mem2((X_567),X_569,g_s41_41) )
=> ( X_568 = X_569 ) ) ) ).
tff('Define:seext:17',axiom,
( ! [X_570: $int,X_571: $o] :
( mem2((X_571),X_570,g_s41_41)
=> ( $true
& mem0(X_570,g_s35_34) ) )
& ! [X_572: $o,X_573: $int,X_574: $int] :
( ( mem2((X_572),X_573,g_s41_41)
& mem2((X_572),X_574,g_s41_41) )
=> ( X_573 = X_574 ) ) ) ).
tff('Define:seext:18',axiom,
( ! [X_575: $int,X_576: $o] :
( mem2((X_576),X_575,g_s41_41)
=> ( $true
& mem0(X_575,g_s33_32) ) )
& ! [X_577: $o,X_578: $int,X_579: $int] :
( ( mem2((X_577),X_578,g_s41_41)
& mem2((X_577),X_579,g_s41_41) )
=> ( X_578 = X_579 ) ) ) ).
tff('Define:seext:2',axiom,
! [X_498: $int] :
( mem0(X_498,g_s308_305)
=> ( $greatereq(X_498,1)
& $lesseq(X_498,g_s126_121) ) ) ).
tff('Define:seext:3',axiom,
! [X_499: $int] :
( mem0(X_499,g_s309_306)
=> ( $greatereq(X_499,1)
& $lesseq(X_499,g_s126_121) ) ) ).
tff('Define:seext:4',axiom,
? [X_500: set_3] :
( ! [X_501: $int,X_502: $int] :
( mem3(X_502,X_501,X_500)
<=> mem3(X_502,X_501,g_s310_307) )
& ! [X_503: $int,X_504: $int,X_505: $int] :
( ( mem3(X_503,X_504,X_500)
& mem3(X_503,X_505,X_500) )
=> ( X_504 = X_505 ) )
& ! [X_506: $int] :
( ( $greatereq(X_506,1)
& $lesseq(X_506,g_s126_121) )
<=> ? [X_507: $int] : mem3(X_506,X_507,X_500) )
& ! [X_508: $int] :
( ? [X_509: $int] : mem3(X_509,X_508,X_500)
=> mem0(X_508,g_s37_36) ) ) ).
tff('Define:seext:5',axiom,
? [X_510: set_3] :
( ! [X_511: $int,X_512: $int] :
( mem3(X_512,X_511,X_510)
<=> mem3(X_512,X_511,g_s311_308) )
& ! [X_513: $int,X_514: $int,X_515: $int] :
( ( mem3(X_513,X_514,X_510)
& mem3(X_513,X_515,X_510) )
=> ( X_514 = X_515 ) )
& ! [X_516: $int] :
( ( $greatereq(X_516,1)
& $lesseq(X_516,g_s126_121) )
<=> ? [X_517: $int] : mem3(X_516,X_517,X_510) )
& ! [X_518: $int] :
( ? [X_519: $int] : mem3(X_519,X_518,X_510)
=> mem0(X_518,g_s37_36) ) ) ).
tff('Define:seext:6',axiom,
? [X_520: set_3] :
( ! [X_521: $int,X_522: $int] :
( mem3(X_522,X_521,X_520)
<=> mem3(X_522,X_521,g_s312_309) )
& ! [X_523: $int,X_524: $int,X_525: $int] :
( ( mem3(X_523,X_524,X_520)
& mem3(X_523,X_525,X_520) )
=> ( X_524 = X_525 ) )
& ! [X_526: $int] :
( ( $greatereq(X_526,1)
& $lesseq(X_526,g_s126_121) )
<=> ? [X_527: $int] : mem3(X_526,X_527,X_520) )
& ! [X_528: $int] :
( ? [X_529: $int] : mem3(X_529,X_528,X_520)
=> mem0(X_528,g_s37_36) ) ) ).
tff('Define:seext:7',axiom,
? [X_530: set_3] :
( ! [X_531: $int,X_532: $int] :
( mem3(X_532,X_531,X_530)
<=> mem3(X_532,X_531,g_s313_310) )
& ! [X_533: $int,X_534: $int,X_535: $int] :
( ( mem3(X_533,X_534,X_530)
& mem3(X_533,X_535,X_530) )
=> ( X_534 = X_535 ) )
& ! [X_536: $int] :
( ( $greatereq(X_536,1)
& $lesseq(X_536,g_s126_121) )
<=> ? [X_537: $int] : mem3(X_536,X_537,X_530) )
& ! [X_538: $int] :
( ? [X_539: $int] : mem3(X_539,X_538,X_530)
=> mem0(X_538,g_s37_36) ) ) ).
tff('Define:seext:8',axiom,
! [X_540: $int] :
( mem0(X_540,g_s314_311)
=> ( $greatereq(X_540,1)
& $lesseq(X_540,g_s126_121) ) ) ).
tff('Define:seext:9',axiom,
! [X_541: $int] :
( mem0(X_541,g_s315_312)
=> ( $greatereq(X_541,1)
& $lesseq(X_541,g_s126_121) ) ) ).
%Global hypotheses
tff(gh_0_def,hypothesis,
( g_s327_347
<=> g_s327_1_348 ) ).
tff(gh_1_def,hypothesis,
( g_s330_349
<=> g_s330_1_350 ) ).
tff(gh_2_def,hypothesis,
! [X_5517: $int,X_5518: $int,X_5519: $int] :
( mem4(X_5519,X_5518,X_5517,g_s328_319)
<=> mem4(X_5519,X_5518,X_5517,g_s328_1_336) ) ).
tff(gh_3_def,hypothesis,
! [X_5520: $int,X_5521: $int,X_5522: $int] :
( mem4(X_5522,X_5521,X_5520,g_s329_320)
<=> mem4(X_5522,X_5521,X_5520,g_s329_1_337) ) ).
tff(gh_4_def,hypothesis,
! [X_5523: $int,X_5524: $int,X_5525: $int] :
( mem4(X_5525,X_5524,X_5523,g_s331_321)
<=> mem4(X_5525,X_5524,X_5523,g_s331_1_338) ) ).
tff(gh_5_def,hypothesis,
! [X_5526: $int,X_5527: $int,X_5528: $int] :
( mem4(X_5528,X_5527,X_5526,g_s332_322)
<=> mem4(X_5528,X_5527,X_5526,g_s332_1_339) ) ).
tff(gh_6_def,hypothesis,
! [X_5529: $int] :
( mem0(X_5529,g_s339_323)
<=> mem0(X_5529,g_s339_1_340) ) ).
tff(gh_7_def,hypothesis,
! [X_5530: $int] :
( mem0(X_5530,g_s340_324)
<=> mem0(X_5530,g_s340_1_341) ) ).
tff(gh_8_def,hypothesis,
g_s326_325 = g_s326_1_342 ).
tff(gh_9_def,hypothesis,
( g_s333_351
<=> g_s333_1_352 ) ).
tff(gh_10_def,hypothesis,
( g_s334_353
<=> g_s334_1_354 ) ).
tff(gh_11_def,hypothesis,
! [X_5531: $int,X_5532: $int] :
( mem3(X_5532,X_5531,g_s335_326)
<=> mem3(X_5532,X_5531,g_s335_1_343) ) ).
tff(gh_12_def,hypothesis,
! [X_5533: $int,X_5534: $int] :
( mem3(X_5534,X_5533,g_s336_327)
<=> mem3(X_5534,X_5533,g_s336_1_344) ) ).
tff(gh_13_def,hypothesis,
! [X_5535: $int,X_5536: $int] :
( mem3(X_5536,X_5535,g_s337_328)
<=> mem3(X_5536,X_5535,g_s337_1_345) ) ).
tff(gh_14_def,hypothesis,
! [X_5537: $int,X_5538: $int] :
( mem3(X_5538,X_5537,g_s338_329)
<=> mem3(X_5538,X_5537,g_s338_1_346) ) ).
%----Local hypotheses
tff('Local_Hyp:0',hypothesis,
mem0(g_s358_335,g_s37_36) ).
tff('Local_Hyp:1',hypothesis,
( $greatereq(g_s358_335,0)
& $lesseq(g_s358_335,g_s127_122) ) ).
tff('Local_Hyp:2',hypothesis,
mem0(g_s369_361,g_s37_36) ).
tff('Local_Hyp:3',hypothesis,
mem0(g_s369_1_362,g_s37_36) ).
tff('Local_Hyp:4',hypothesis,
mem0(g_s375_364,g_s35_34) ).
tff('Local_Hyp:5',hypothesis,
! [X_5539: $o] :
( ( (X_5539)
<=> ! [X_5540: $int] :
( ( X_5540 = $sum(g_s358_335,1) )
=> mem0(X_5540,g_s306_303) ) )
=> mem2((X_5539),g_s38_38,g_s41_41) ) ).
tff('Local_Hyp:6',hypothesis,
! [X_5542: $int] :
( ( X_5542 = $sum(g_s358_335,1) )
=> mem0(X_5542,g_s306_303) ) ).
tff('Local_Hyp:7',hypothesis,
! [X_5546: $int] :
( ! [X_5547: $o] :
( ( (X_5547)
<=> ! [X_5548: $int] :
( ( X_5548 = $sum(g_s358_335,1) )
=> mem0(X_5548,g_s306_303) ) )
=> mem2((X_5547),X_5546,g_s41_41) )
=> mem0(X_5546,g_s37_36) ) ).
tff('Local_Hyp:12',hypothesis,
~ ! [X_5570: $o] :
( ( (X_5570)
<=> ? [X_5571: $int] :
! [X_5572: $int] :
( ( X_5572 = $sum(g_s358_335,1) )
=> mem3(X_5572,X_5571,g_s319_316) ) )
=> mem2((X_5570),g_s38_38,g_s41_41) ) ).
%----Goal
tff('Goal',conjecture,
! [X_5584: $int] :
( ! [X_5585: $o] :
( ( (X_5585)
<=> ? [X_5586: $int] :
! [X_5587: $int] :
( ( X_5587 = $sum(g_s358_335,1) )
=> mem3(X_5587,X_5586,g_s319_316) ) )
=> mem2((X_5585),X_5584,g_s41_41) )
=> mem0(X_5584,g_s40_40) ) ).
%------------------------------------------------------------------------------