TPTP Problem File: SWC536_1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWC536_1 : TPTP v9.0.0. Released v9.0.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 24 1 Group s312 Tag s283
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0015-00172-24-1.tptp [Deh24]
% Status : Theorem
% Rating : 0.62 v9.0.0
% Syntax : Number of formulae : 692 ( 146 unt; 338 typ; 0 def)
% Number of atoms : 1679 ( 271 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 1421 ( 96 ~; 53 |; 673 &)
% ( 211 <=>; 388 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 1484 ( 170 atm; 20 fun; 121 num;1173 var)
% Number of types : 13 ( 10 usr; 2 ari)
% Number of type conns : 52 ( 25 >; 27 *; 0 +; 0 <<)
% Number of predicates : 17 ( 10 usr; 2 prp; 0-4 aty)
% Number of functors : 329 ( 318 usr; 309 con; 0-2 aty)
% Number of variables : 1386 (1085 !; 301 ?;1386 :)
% SPC : TF0_THM_EQU_ARI
% Comments : Autogenerated by PPTRANS-TPTP - github.com/CLEARSY/pptranspog
%------------------------------------------------------------------------------
tff(set_0_type,type,
set_0: $tType ).
tff(mem0_type,type,
mem0: ( $int * set_0 ) > $o ).
tff(set_1_type,type,
set_1: $tType ).
tff(mem1_type,type,
mem1: ( $real * set_1 ) > $o ).
tff(b_division_type,type,
divB: ( $int * $int ) > $int ).
tff(b_division_def_1,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(0,Y) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_2,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(0,Y) )
=> ( divB(X,Y) = $uminus($quotient_f($uminus(X),Y)) ) ) ).
tff(b_division_def_3,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_4,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f($uminus(X),$uminus(Y)) ) ) ).
tff(exp_type,type,
exp: ( $int * $int ) > $int ).
tff(exp_def_1,axiom,
! [X: $int] : ( exp(X,0) = 1 ) ).
tff(exp_def_2,axiom,
! [X: $int,Y: $int] :
( $greatereq(Y,1)
=> ( exp(X,Y) = $sum(X,exp(X,$difference(Y,1))) ) ) ).
tff(rexp_type,type,
rexp: ( $real * $int ) > $real ).
tff(rexp_def_1,axiom,
! [X: $real] :
( ( X != 0.0 )
=> ( rexp(X,0) = 1.0 ) ) ).
tff(rexp_def_2,axiom,
! [X: $real,Y: $int] :
( $greatereq(Y,1)
=> ( rexp(X,Y) = $sum(X,rexp(X,$difference(Y,1))) ) ) ).
tff(isum_type,type,
isum: set_0 > $int ).
tff(isum_def_1,axiom,
! [S: set_0] :
( ! [X: $int] : ~ mem0(X,S)
=> ( isum(S) = 0 ) ) ).
tff(isum_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( isum(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( mem0(X,S1)
=> mem0(X,S2) ) )
=> ( isum(S2) = $sum(N,E) ) ) ).
tff(rsum_type,type,
rsum: set_1 > $real ).
tff(rsum_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rsum(S) = 0.0 ) ) ).
tff(rsum_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rsum(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( mem1(X,S1)
=> mem1(X,S2) ) )
=> ( rsum(S2) = $sum(N,E) ) ) ).
tff(iprod_type,type,
iprod: set_0 > $int ).
tff(iprod_def_1,axiom,
! [S: set_0,X: $int] :
( ~ mem0(X,S)
=> ( iprod(S) = 1 ) ) ).
tff(iprod_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( iprod(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( ( ( X = E )
| mem0(X,S1) )
=> mem0(X,S2) ) )
=> ( isum(S2) = $product(N,E) ) ) ).
tff(rprod_type,type,
rprod: set_1 > $real ).
tff(rprod_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rprod(S) = 1.0 ) ) ).
tff(rprod_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rprod(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( ( ( X = E )
| mem1(X,S1) )
=> mem1(X,S2) ) )
=> ( rprod(S2) = $sum(N,E) ) ) ).
tff(min_int_type,type,
min_int: $int ).
tff(max_int_type,type,
max_int: $int ).
tff(min_int_axiom,axiom,
min_int = $uminus(2147483648) ).
tff(max_int_axiom,axiom,
max_int = 2147483647 ).
%--------------------------------------------------------------------------
%----Global declarations
tff(g_s0_0_type,type,
g_s0_0: set_0 ).
tff(g_s100_100_type,type,
g_s100_100: set_0 ).
tff(g_s101_101_type,type,
g_s101_101: set_0 ).
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: set_2 ).
tff(g_s105_105_type,type,
g_s105_105: $int ).
tff(g_s106_106_type,type,
g_s106_106: set_0 ).
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: set_2 ).
tff(g_s10_10_type,type,
g_s10_10: $int ).
tff(g_s110_110_type,type,
g_s110_110: $int ).
tff(g_s111_111_type,type,
g_s111_111: set_3 ).
tff(g_s112_112_type,type,
g_s112_112: set_0 ).
tff(g_s113_113_type,type,
g_s113_113: set_3 ).
tff(g_s114_114_type,type,
g_s114_114: set_3 ).
tff(g_s115_115_type,type,
g_s115_115: set_3 ).
tff(g_s116_116_type,type,
g_s116_116: set_4 ).
tff(g_s117_117_type,type,
g_s117_117: set_4 ).
tff(g_s118_118_type,type,
g_s118_118: set_4 ).
tff(g_s119_119_type,type,
g_s119_119: set_4 ).
tff(g_s11_11_type,type,
g_s11_11: set_0 ).
tff(g_s120_120_type,type,
g_s120_120: set_4 ).
tff(g_s121_121_type,type,
g_s121_121: set_2 ).
tff(g_s122_122_type,type,
g_s122_122: set_2 ).
tff(g_s123_123_type,type,
g_s123_123: set_3 ).
tff(g_s124_124_type,type,
g_s124_124: set_3 ).
tff(g_s125_125_type,type,
g_s125_125: set_3 ).
tff(g_s126_126_type,type,
g_s126_126: set_3 ).
tff(g_s127_127_type,type,
g_s127_127: set_2 ).
tff(g_s128_128_type,type,
g_s128_128: set_2 ).
tff(g_s129_129_type,type,
g_s129_129: set_3 ).
tff(g_s12_12_type,type,
g_s12_12: $int ).
tff(g_s130_130_type,type,
g_s130_130: set_3 ).
tff(g_s131_131_type,type,
g_s131_131: set_3 ).
tff(g_s132_132_type,type,
g_s132_132: set_3 ).
tff(g_s133_133_type,type,
g_s133_133: set_3 ).
tff(g_s134_134_type,type,
g_s134_134: set_3 ).
tff(g_s137_135_type,type,
g_s137_135: set_0 ).
tff(g_s138_136_type,type,
g_s138_136: $int ).
tff(g_s139_137_type,type,
g_s139_137: set_2 ).
tff(g_s13_13_type,type,
g_s13_13: $int ).
tff(g_s140_138_type,type,
g_s140_138: set_0 ).
tff(g_s141_139_type,type,
g_s141_139: $int ).
tff(g_s142_140_type,type,
g_s142_140: set_2 ).
tff(g_s143_141_type,type,
g_s143_141: set_0 ).
tff(g_s144_142_type,type,
g_s144_142: $int ).
tff(g_s145_143_type,type,
g_s145_143: set_2 ).
tff(g_s146_144_type,type,
g_s146_144: set_0 ).
tff(g_s147_145_type,type,
g_s147_145: $int ).
tff(g_s148_146_type,type,
g_s148_146: set_2 ).
tff(g_s149_147_type,type,
g_s149_147: $int ).
tff(g_s14_14_type,type,
g_s14_14: $int ).
tff(g_s150_148_type,type,
g_s150_148: set_0 ).
tff(g_s151_149_type,type,
g_s151_149: $int ).
tff(g_s152_150_type,type,
g_s152_150: set_0 ).
tff(g_s153_151_type,type,
g_s153_151: $int ).
tff(g_s154_152_type,type,
g_s154_152: set_0 ).
tff(g_s155_153_type,type,
g_s155_153: set_0 ).
tff(g_s156_154_type,type,
g_s156_154: $int ).
tff(g_s157_155_type,type,
g_s157_155: set_0 ).
tff(g_s158_156_type,type,
g_s158_156: set_0 ).
tff(g_s159_157_type,type,
g_s159_157: $int ).
tff(g_s15_15_type,type,
g_s15_15: $int ).
tff(g_s160_158_type,type,
g_s160_158: set_0 ).
tff(g_s161_159_type,type,
g_s161_159: $int ).
tff(g_s162_160_type,type,
g_s162_160: set_2 ).
tff(g_s163_161_type,type,
g_s163_161: set_0 ).
tff(g_s164_162_type,type,
g_s164_162: $int ).
tff(g_s165_163_type,type,
g_s165_163: set_2 ).
tff(g_s166_164_type,type,
g_s166_164: set_0 ).
tff(g_s167_165_type,type,
g_s167_165: $int ).
tff(g_s168_166_type,type,
g_s168_166: set_2 ).
tff(g_s169_167_type,type,
g_s169_167: set_0 ).
tff(g_s16_16_type,type,
g_s16_16: set_0 ).
tff(g_s170_168_type,type,
g_s170_168: $int ).
tff(g_s171_169_type,type,
g_s171_169: set_2 ).
tff(g_s172_170_type,type,
g_s172_170: set_0 ).
tff(g_s173_171_type,type,
g_s173_171: $int ).
tff(g_s174_172_type,type,
g_s174_172: set_2 ).
tff(g_s175_173_type,type,
g_s175_173: set_2 ).
tff(g_s176_174_type,type,
g_s176_174: set_2 ).
tff(g_s177_175_type,type,
g_s177_175: $int ).
tff(g_s178_176_type,type,
g_s178_176: $int ).
tff(g_s179_177_type,type,
g_s179_177: set_2 ).
tff(g_s17_17_type,type,
g_s17_17: $int ).
tff(g_s180_178_type,type,
g_s180_178: $int ).
tff(g_s181_179_type,type,
g_s181_179: $int ).
tff(g_s182_180_type,type,
g_s182_180: $int ).
tff(g_s183_181_type,type,
g_s183_181: $int ).
tff(g_s184_182_type,type,
g_s184_182: $int ).
tff(g_s185_183_type,type,
g_s185_183: $int ).
tff(g_s186_184_type,type,
g_s186_184: $int ).
tff(g_s187_185_type,type,
g_s187_185: $int ).
tff(g_s188_186_type,type,
g_s188_186: $int ).
tff(g_s189_187_type,type,
g_s189_187: $int ).
tff(g_s18_18_type,type,
g_s18_18: $int ).
tff(g_s190_188_type,type,
g_s190_188: $int ).
tff(g_s191_189_type,type,
g_s191_189: $int ).
tff(g_s192_190_type,type,
g_s192_190: $int ).
tff(g_s193_191_type,type,
g_s193_191: $int ).
tff(g_s194_192_type,type,
g_s194_192: $int ).
tff(g_s195_193_type,type,
g_s195_193: $int ).
tff(g_s196_194_type,type,
g_s196_194: $int ).
tff(g_s197_195_type,type,
g_s197_195: $int ).
tff(g_s198_196_type,type,
g_s198_196: $int ).
tff(g_s199_197_type,type,
g_s199_197: $int ).
tff(g_s19_19_type,type,
g_s19_19: $int ).
tff(g_s1_1_type,type,
g_s1_1: set_0 ).
tff(g_s200_198_type,type,
g_s200_198: $int ).
tff(g_s201_199_type,type,
g_s201_199: $int ).
tff(g_s202_200_type,type,
g_s202_200: $int ).
tff(g_s203_201_type,type,
g_s203_201: $int ).
tff(g_s204_202_type,type,
g_s204_202: $int ).
tff(g_s205_203_type,type,
g_s205_203: $int ).
tff(g_s206_204_type,type,
g_s206_204: $int ).
tff(g_s207_205_type,type,
g_s207_205: $int ).
tff(g_s208_206_type,type,
g_s208_206: $int ).
tff(g_s209_207_type,type,
g_s209_207: $int ).
tff(g_s20_20_type,type,
g_s20_20: set_0 ).
tff(g_s210_208_type,type,
g_s210_208: $int ).
tff(g_s211_209_type,type,
g_s211_209: $int ).
tff(g_s212_210_type,type,
g_s212_210: $int ).
tff(g_s213_211_type,type,
g_s213_211: $int ).
tff(g_s214_212_type,type,
g_s214_212: $int ).
tff(g_s215_213_type,type,
g_s215_213: $int ).
tff(g_s216_214_type,type,
g_s216_214: $int ).
tff(g_s217_215_type,type,
g_s217_215: $int ).
tff(g_s218_216_type,type,
g_s218_216: $int ).
tff(g_s219_217_type,type,
g_s219_217: $int ).
tff(g_s21_21_type,type,
g_s21_21: $int ).
tff(g_s220_218_type,type,
g_s220_218: $int ).
tff(g_s221_219_type,type,
g_s221_219: set_0 ).
tff(g_s222_221_type,type,
g_s222_221: $int ).
tff(g_s223_220_type,type,
g_s223_220: set_0 ).
tff(g_s224_222_type,type,
g_s224_222: $int ).
tff(g_s225_224_type,type,
g_s225_224: $int ).
tff(g_s226_223_type,type,
g_s226_223: set_0 ).
tff(g_s227_225_type,type,
g_s227_225: $int ).
tff(g_s228_226_type,type,
g_s228_226: set_0 ).
tff(g_s229_227_type,type,
g_s229_227: set_0 ).
tff(g_s22_22_type,type,
g_s22_22: $int ).
tff(g_s230_228_type,type,
g_s230_228: set_2 ).
tff(g_s231_229_type,type,
g_s231_229: set_2 ).
tff(g_s232_230_type,type,
g_s232_230: set_2 ).
tff(g_s233_231_type,type,
g_s233_231: set_0 ).
tff(g_s234_232_type,type,
g_s234_232: set_2 ).
tff(g_s235_233_type,type,
g_s235_233: set_0 ).
tff(g_s236_234_type,type,
g_s236_234: set_0 ).
tff(g_s237_235_type,type,
g_s237_235: set_2 ).
tff(g_s238_236_type,type,
g_s238_236: set_0 ).
tff(g_s239_237_type,type,
g_s239_237: set_0 ).
tff(g_s23_23_type,type,
g_s23_23: $int ).
tff(g_s240_238_type,type,
g_s240_238: set_2 ).
tff(g_s241_239_type,type,
g_s241_239: set_0 ).
tff(g_s242_240_type,type,
g_s242_240: set_2 ).
tff(g_s243_241_type,type,
g_s243_241: set_0 ).
tff(g_s244_242_type,type,
g_s244_242: set_0 ).
tff(g_s245_243_type,type,
g_s245_243: set_2 ).
tff(g_s246_244_type,type,
g_s246_244: set_0 ).
tff(g_s247_245_type,type,
g_s247_245: set_0 ).
tff(g_s249_246_type,type,
g_s249_246: set_5 ).
tff(g_s24_24_type,type,
g_s24_24: set_0 ).
tff(g_s250_247_type,type,
g_s250_247: set_5 ).
tff(g_s252_248_type,type,
g_s252_248: set_5 ).
tff(g_s253_249_type,type,
g_s253_249: set_2 ).
tff(g_s255_250_type,type,
g_s255_250: set_2 ).
tff(g_s256_251_type,type,
g_s256_251: set_2 ).
tff(g_s257_252_type,type,
g_s257_252: set_5 ).
tff(g_s258_253_type,type,
g_s258_253: set_5 ).
tff(g_s259_254_type,type,
g_s259_254: set_5 ).
tff(g_s25_25_type,type,
g_s25_25: $int ).
tff(g_s260_255_type,type,
g_s260_255: set_5 ).
tff(g_s261_256_type,type,
g_s261_256: set_2 ).
tff(g_s262_257_type,type,
g_s262_257: set_2 ).
tff(g_s263_258_type,type,
g_s263_258: set_0 ).
tff(g_s264_259_type,type,
g_s264_259: set_0 ).
tff(g_s265_260_type,type,
g_s265_260: set_2 ).
tff(g_s266_261_type,type,
g_s266_261: set_2 ).
tff(g_s267_262_type,type,
g_s267_262: set_2 ).
tff(g_s268_263_type,type,
g_s268_263: set_0 ).
tff(g_s269_264_type,type,
g_s269_264: set_0 ).
tff(g_s26_26_type,type,
g_s26_26: $int ).
tff(g_s270_265_type,type,
g_s270_265: $int ).
tff(g_s271_1_278_type,type,
g_s271_1_278: set_2 ).
tff(g_s271_267_type,type,
g_s271_267: set_2 ).
tff(g_s272_1_279_type,type,
g_s272_1_279: set_2 ).
tff(g_s272_268_type,type,
g_s272_268: set_2 ).
tff(g_s273_1_284_type,type,
g_s273_1_284: set_5 ).
tff(g_s273_269_type,type,
g_s273_269: set_5 ).
tff(g_s274_1_283_type,type,
g_s274_1_283: set_5 ).
tff(g_s274_270_type,type,
g_s274_270: set_5 ).
tff(g_s275_1_285_type,type,
g_s275_1_285: set_5 ).
tff(g_s275_271_type,type,
g_s275_271: set_5 ).
tff(g_s276_1_286_type,type,
g_s276_1_286: set_5 ).
tff(g_s276_272_type,type,
g_s276_272: set_5 ).
tff(g_s277_1_280_type,type,
g_s277_1_280: set_0 ).
tff(g_s277_273_type,type,
g_s277_273: set_0 ).
tff(g_s278_1_281_type,type,
g_s278_1_281: set_0 ).
tff(g_s278_274_type,type,
g_s278_274: set_0 ).
tff(g_s279_1_282_type,type,
g_s279_1_282: set_2 ).
tff(g_s279_275_type,type,
g_s279_275: set_2 ).
tff(g_s27_27_type,type,
g_s27_27: $int ).
tff(g_s280_1_287_type,type,
g_s280_1_287: set_2 ).
tff(g_s280_276_type,type,
g_s280_276: set_2 ).
tff(g_s281_1_288_type,type,
g_s281_1_288: set_0 ).
tff(g_s281_277_type,type,
g_s281_277: set_0 ).
tff(g_s285_289_type,type,
g_s285_289: $int ).
tff(g_s289_293_type,type,
g_s289_293: $int ).
tff(g_s28_28_type,type,
g_s28_28: set_0 ).
tff(g_s295_1_295_type,type,
g_s295_1_295: $int ).
tff(g_s295_294_type,type,
g_s295_294: $int ).
tff(g_s295_2_296_type,type,
g_s295_2_296: $int ).
tff(g_s29_29_type,type,
g_s29_29: $int ).
tff(g_s2_2_type,type,
g_s2_2: set_0 ).
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: set_0 ).
tff(g_s34_34_type,type,
g_s34_34: $int ).
tff(g_s35_35_type,type,
g_s35_35: $int ).
tff(g_s36_36_type,type,
g_s36_36: $int ).
tff(g_s37_37_type,type,
g_s37_37: $int ).
tff(g_s38_38_type,type,
g_s38_38: $int ).
tff(g_s39_39_type,type,
g_s39_39: $int ).
tff(g_s3_3_type,type,
g_s3_3: $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: set_0 ).
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: set_0 ).
tff(g_s48_48_type,type,
g_s48_48: $int ).
tff(g_s49_49_type,type,
g_s49_49: $int ).
tff(g_s4_4_type,type,
g_s4_4: $int ).
tff(g_s50_50_type,type,
g_s50_50: $int ).
tff(g_s51_51_type,type,
g_s51_51: $int ).
tff(g_s52_52_type,type,
g_s52_52: $int ).
tff(g_s53_53_type,type,
g_s53_53: $int ).
tff(g_s54_54_type,type,
g_s54_54: $int ).
tff(g_s55_55_type,type,
g_s55_55: $int ).
tff(g_s56_56_type,type,
g_s56_56: set_0 ).
tff(g_s57_57_type,type,
g_s57_57: $int ).
tff(g_s58_58_type,type,
g_s58_58: $int ).
tff(g_s59_59_type,type,
g_s59_59: $int ).
tff(g_s5_5_type,type,
g_s5_5: set_0 ).
tff(g_s60_60_type,type,
g_s60_60: set_0 ).
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: set_0 ).
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: set_0 ).
tff(g_s69_69_type,type,
g_s69_69: $int ).
tff(g_s6_6_type,type,
g_s6_6: $int ).
tff(g_s70_70_type,type,
g_s70_70: $int ).
tff(g_s71_71_type,type,
g_s71_71: set_0 ).
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: set_0 ).
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: set_0 ).
tff(g_s79_79_type,type,
g_s79_79: $int ).
tff(g_s7_7_type,type,
g_s7_7: $int ).
tff(g_s80_80_type,type,
g_s80_80: $int ).
tff(g_s81_81_type,type,
g_s81_81: set_0 ).
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: set_0 ).
tff(g_s86_86_type,type,
g_s86_86: set_0 ).
tff(g_s87_87_type,type,
g_s87_87: set_0 ).
tff(g_s88_88_type,type,
g_s88_88: set_0 ).
tff(g_s89_89_type,type,
g_s89_89: set_0 ).
tff(g_s8_8_type,type,
g_s8_8: $int ).
tff(g_s90_90_type,type,
g_s90_90: set_0 ).
tff(g_s91_91_type,type,
g_s91_91: set_0 ).
tff(g_s92_92_type,type,
g_s92_92: set_0 ).
tff(g_s93_93_type,type,
g_s93_93: set_0 ).
tff(g_s94_94_type,type,
g_s94_94: set_0 ).
tff(g_s95_95_type,type,
g_s95_95: set_0 ).
tff(g_s96_96_type,type,
g_s96_96: set_0 ).
tff(g_s97_97_type,type,
g_s97_97: set_0 ).
tff(g_s98_98_type,type,
g_s98_98: $int ).
tff(g_s99_99_type,type,
g_s99_99: $int ).
tff(g_s9_9_type,type,
g_s9_9: $int ).
tff(mem2_type,type,
mem2: ( $int * $int * set_2 ) > $o ).
tff(mem3_type,type,
mem3: ( $int * $int * $int * set_3 ) > $o ).
tff(mem4_type,type,
mem4: ( $int * $int * set_0 * set_4 ) > $o ).
tff(mem5_type,type,
mem5: ( $int * set_2 * set_5 ) > $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: ( $int * $int ) > prod_0 ).
tff(prod_0_in,type,
prod_0_in: ( $int * $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: ( prod_0 * $int ) > prod_1 ).
tff(prod_1_in,type,
prod_1_in: ( prod_0 * $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_0 * set_0 ) > prod_2 ).
tff(prod_2_in,type,
prod_2_in: ( prod_0 * set_0 * prod_2 ) > $o ).
tff(prod_3_type,type,
prod_3: $tType ).
tff(prod_3_empty,type,
prod_3_empty: prod_3 ).
tff(prod_3_insert,type,
prod_3: ( $int * set_2 ) > prod_3 ).
tff(prod_3_in,type,
prod_3_in: ( $int * set_2 * prod_3 ) > $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 ).
tff(set_5_type,type,
set_5: $tType ).
tff(set_5_empty,type,
set_5_empty: set_5 ).
tff(set_5_insert,type,
set_5: prod_3 > set_5 ).
%----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,
! [L_s254: $int] :
( ( mem0(L_s254,g_s163_161)
& mem2(L_s254,g_s4_4,g_s271_267) )
=> ( ? [X_1183: $int] : mem2(L_s254,X_1183,g_s272_268)
& ! [X_1184: $int] :
( ? [X_1185: $int] :
! [X_1186: set_2] :
( mem5(L_s254,X_1186,g_s273_269)
=> mem2(X_1184,X_1185,X_1186) )
<=> ? [X_1187: $int] :
! [X_1188: set_2] :
( mem5(L_s254,X_1188,g_s274_270)
=> mem2(X_1184,X_1187,X_1188) ) )
& ! [X_1189: $int] :
( ? [X_1190: $int] :
! [X_1191: set_2] :
( mem5(L_s254,X_1191,g_s275_271)
=> mem2(X_1189,X_1190,X_1191) )
<=> ? [X_1192: $int] :
! [X_1193: set_2] :
( mem5(L_s254,X_1193,g_s274_270)
=> mem2(X_1189,X_1192,X_1193) ) )
& ! [X_1194: $int] :
( ? [X_1195: $int] :
! [X_1196: set_2] :
( mem5(L_s254,X_1196,g_s276_272)
=> mem2(X_1194,X_1195,X_1196) )
<=> ? [X_1197: $int] :
! [X_1198: set_2] :
( mem5(L_s254,X_1198,g_s274_270)
=> mem2(X_1194,X_1197,X_1198) ) ) ) ) ).
tff('Define:abs:1',axiom,
! [L_s254: $int] :
( ? [X_1199: $int] : mem2(L_s254,X_1199,g_s272_268)
=> mem2(L_s254,g_s4_4,g_s271_267) ) ).
tff('Define:abs:10',axiom,
? [X_1270: set_5] :
( ! [X_1271: set_2,X_1272: $int] :
( mem5(X_1272,X_1271,X_1270)
<=> mem5(X_1272,X_1271,g_s276_272) )
& ! [X_1273: $int,X_1274: set_2,X_1275: set_2] :
( ( mem5(X_1273,X_1274,X_1270)
& mem5(X_1273,X_1275,X_1270) )
=> ! [X_1276: $int,X_1277: $int] :
( mem2(X_1277,X_1276,X_1274)
<=> mem2(X_1277,X_1276,X_1275) ) )
& ! [X_1278: $int] :
( mem0(X_1278,g_s163_161)
<=> ? [X_1279: set_2] : mem5(X_1278,X_1279,X_1270) )
& ! [X_1280: set_2] :
( ? [X_1281: $int] : mem5(X_1281,X_1280,X_1270)
=> ( ! [X_1282: $int,X_1283: $int] :
( mem2(X_1283,X_1282,X_1280)
=> ( mem0(X_1283,g_s137_135)
& mem0(X_1282,g_s158_156) ) )
& ! [X_1284: $int,X_1285: $int,X_1286: $int] :
( ( mem2(X_1284,X_1285,X_1280)
& mem2(X_1284,X_1286,X_1280) )
=> ( X_1285 = X_1286 ) ) ) ) ) ).
tff('Define:abs:11',axiom,
( ! [X_1287: $int,X_1288: $int] :
( mem2(X_1288,X_1287,g_s280_276)
=> ( mem0(X_1288,g_s163_161)
& mem0(X_1287,g_s96_96) ) )
& ! [X_1289: $int,X_1290: $int,X_1291: $int] :
( ( mem2(X_1289,X_1290,g_s280_276)
& mem2(X_1289,X_1291,g_s280_276) )
=> ( X_1290 = X_1291 ) ) ) ).
tff('Define:abs:12',axiom,
! [X_1292: $int] :
( mem0(X_1292,g_s281_277)
=> mem0(X_1292,g_s163_161) ) ).
tff('Define:abs:2',axiom,
? [X_1200: set_2] :
( ! [X_1201: $int,X_1202: $int] :
( mem2(X_1202,X_1201,X_1200)
<=> mem2(X_1202,X_1201,g_s271_267) )
& ! [X_1203: $int,X_1204: $int,X_1205: $int] :
( ( mem2(X_1203,X_1204,X_1200)
& mem2(X_1203,X_1205,X_1200) )
=> ( X_1204 = X_1205 ) )
& ! [X_1206: $int] :
( mem0(X_1206,g_s163_161)
<=> ? [X_1207: $int] : mem2(X_1206,X_1207,X_1200) )
& ! [X_1208: $int] :
( ? [X_1209: $int] : mem2(X_1209,X_1208,X_1200)
=> mem0(X_1208,g_s2_2) ) ) ).
tff('Define:abs:3',axiom,
( ! [X_1210: $int,X_1211: $int] :
( mem2(X_1211,X_1210,g_s272_268)
=> ( mem0(X_1211,g_s163_161)
& mem0(X_1210,g_s152_150) ) )
& ! [X_1212: $int,X_1213: $int,X_1214: $int] :
( ( mem2(X_1212,X_1213,g_s272_268)
& mem2(X_1212,X_1214,g_s272_268) )
=> ( X_1213 = X_1214 ) ) ) ).
tff('Define:abs:4',axiom,
! [X_1215: $int] :
( mem0(X_1215,g_s277_273)
=> mem0(X_1215,g_s163_161) ) ).
tff('Define:abs:5',axiom,
! [X_1216: $int] :
( mem0(X_1216,g_s278_274)
=> mem0(X_1216,g_s163_161) ) ).
tff('Define:abs:6',axiom,
! [X_1217: $int,X_1218: $int] :
( mem2(X_1218,X_1217,g_s279_275)
=> ( mem0(X_1218,g_s163_161)
& mem0(X_1217,g_s137_135) ) ) ).
tff('Define:abs:7',axiom,
? [X_1219: set_5] :
( ! [X_1220: set_2,X_1221: $int] :
( mem5(X_1221,X_1220,X_1219)
<=> mem5(X_1221,X_1220,g_s274_270) )
& ! [X_1222: $int,X_1223: set_2,X_1224: set_2] :
( ( mem5(X_1222,X_1223,X_1219)
& mem5(X_1222,X_1224,X_1219) )
=> ! [X_1225: $int,X_1226: $int] :
( mem2(X_1226,X_1225,X_1223)
<=> mem2(X_1226,X_1225,X_1224) ) )
& ! [X_1227: $int] :
( mem0(X_1227,g_s163_161)
<=> ? [X_1228: set_2] : mem5(X_1227,X_1228,X_1219) )
& ! [X_1229: set_2] :
( ? [X_1230: $int] : mem5(X_1230,X_1229,X_1219)
=> ( ! [X_1231: $int,X_1232: $int] :
( mem2(X_1232,X_1231,X_1229)
=> ( mem0(X_1232,g_s137_135)
& mem0(X_1231,g_s155_153) ) )
& ! [X_1233: $int,X_1234: $int,X_1235: $int] :
( ( mem2(X_1233,X_1234,X_1229)
& mem2(X_1233,X_1235,X_1229) )
=> ( X_1234 = X_1235 ) ) ) ) ) ).
tff('Define:abs:8',axiom,
? [X_1236: set_5] :
( ! [X_1237: set_2,X_1238: $int] :
( mem5(X_1238,X_1237,X_1236)
<=> mem5(X_1238,X_1237,g_s273_269) )
& ! [X_1239: $int,X_1240: set_2,X_1241: set_2] :
( ( mem5(X_1239,X_1240,X_1236)
& mem5(X_1239,X_1241,X_1236) )
=> ! [X_1242: $int,X_1243: $int] :
( mem2(X_1243,X_1242,X_1240)
<=> mem2(X_1243,X_1242,X_1241) ) )
& ! [X_1244: $int] :
( mem0(X_1244,g_s163_161)
<=> ? [X_1245: set_2] : mem5(X_1244,X_1245,X_1236) )
& ! [X_1246: set_2] :
( ? [X_1247: $int] : mem5(X_1247,X_1246,X_1236)
=> ( ! [X_1248: $int,X_1249: $int] :
( mem2(X_1249,X_1248,X_1246)
=> ( mem0(X_1249,g_s137_135)
& mem0(X_1248,g_s143_141) ) )
& ! [X_1250: $int,X_1251: $int,X_1252: $int] :
( ( mem2(X_1250,X_1251,X_1246)
& mem2(X_1250,X_1252,X_1246) )
=> ( X_1251 = X_1252 ) ) ) ) ) ).
tff('Define:abs:9',axiom,
? [X_1253: set_5] :
( ! [X_1254: set_2,X_1255: $int] :
( mem5(X_1255,X_1254,X_1253)
<=> mem5(X_1255,X_1254,g_s275_271) )
& ! [X_1256: $int,X_1257: set_2,X_1258: set_2] :
( ( mem5(X_1256,X_1257,X_1253)
& mem5(X_1256,X_1258,X_1253) )
=> ! [X_1259: $int,X_1260: $int] :
( mem2(X_1260,X_1259,X_1257)
<=> mem2(X_1260,X_1259,X_1258) ) )
& ! [X_1261: $int] :
( mem0(X_1261,g_s163_161)
<=> ? [X_1262: set_2] : mem5(X_1261,X_1262,X_1253) )
& ! [X_1263: set_2] :
( ? [X_1264: $int] : mem5(X_1264,X_1263,X_1253)
=> ( ! [X_1265: $int,X_1266: $int] :
( mem2(X_1266,X_1265,X_1263)
=> ( mem0(X_1266,g_s137_135)
& mem0(X_1265,g_s158_156) ) )
& ! [X_1267: $int,X_1268: $int,X_1269: $int] :
( ( mem2(X_1267,X_1268,X_1263)
& mem2(X_1267,X_1269,X_1263) )
=> ( X_1268 = X_1269 ) ) ) ) ) ).
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,
( ! [X_51: $int] :
( mem0(X_51,g_s42_42)
<=> ( ( X_51 = g_s43_43 )
| ( X_51 = g_s44_44 )
| ( X_51 = g_s45_45 )
| ( X_51 = g_s46_46 ) ) )
& ( g_s43_43 != g_s44_44 )
& ( g_s44_44 != g_s45_45 )
& ( g_s45_45 != g_s46_46 ) ) ).
tff('Define:ctx:100',axiom,
mem0(g_s147_145,g_s88_88) ).
tff('Define:ctx:101',axiom,
~ mem0(g_s147_145,g_s146_144) ).
tff('Define:ctx:102',axiom,
( ! [X_623: $int,X_624: $int] :
( mem2(X_624,X_623,g_s148_146)
=> ( $greatereq(X_624,0)
& $lesseq(X_624,max_int)
& mem0(X_623,g_s88_88) ) )
& ! [X_625: $int,X_626: $int,X_627: $int] :
( ( mem2(X_625,X_626,g_s148_146)
& mem2(X_625,X_627,g_s148_146) )
=> ( X_626 = X_627 ) ) ) ).
tff('Define:ctx:103',axiom,
? [X_628: $int] :
( ? [X_629: set_2] :
( ! [X_630: $int,X_631: $int] :
( mem2(X_631,X_630,X_629)
<=> mem2(X_631,X_630,g_s148_146) )
& ! [X_632: $int,X_633: $int,X_634: $int] :
( ( mem2(X_632,X_633,X_629)
& mem2(X_632,X_634,X_629) )
=> ( X_633 = X_634 ) )
& ! [X_635: $int] :
( ( $greatereq(X_635,1)
& $lesseq(X_635,X_628) )
<=> ? [X_636: $int] : mem2(X_635,X_636,X_629) )
& ! [X_637: $int] :
( ? [X_638: $int] : mem2(X_638,X_637,X_629)
=> mem0(X_637,g_s146_144) ) )
& ! [X_639: $int] :
( mem0(X_639,g_s146_144)
=> ? [X_640: $int] : mem2(X_640,X_639,g_s148_146) )
& ! [X_641: $int,X_642: $int,X_643: $int] :
( ( mem2(X_642,X_641,g_s148_146)
& mem2(X_643,X_641,g_s148_146) )
=> ( X_642 = X_643 ) ) ) ).
tff('Define:ctx:104',axiom,
mem0(g_s149_147,g_s89_89) ).
tff('Define:ctx:105',axiom,
! [X_644: $int] :
( mem0(X_644,g_s150_148)
=> ( $greatereq(X_644,min_int)
& $lesseq(X_644,max_int) ) ) ).
tff('Define:ctx:106',axiom,
! [X_645: $int] :
( mem0(X_645,g_s150_148)
<=> ( $greatereq(X_645,0)
& $lesseq(X_645,g_s151_149) ) ) ).
tff('Define:ctx:107',axiom,
! [X_646: $int] :
( mem0(X_646,g_s152_150)
=> mem0(X_646,g_s150_148) ) ).
tff('Define:ctx:108',axiom,
! [X_647: $int] :
( mem0(X_647,g_s152_150)
=> ( $greatereq(X_647,0)
& $lesseq(X_647,max_int) ) ) ).
tff('Define:ctx:109',axiom,
mem0(g_s153_151,g_s150_148) ).
tff('Define:ctx:11',axiom,
( ! [X_52: $int] :
( mem0(X_52,g_s47_47)
<=> ( ( X_52 = g_s48_48 )
| ( X_52 = g_s49_49 )
| ( X_52 = g_s50_50 )
| ( X_52 = g_s51_51 )
| ( X_52 = g_s52_52 )
| ( X_52 = g_s53_53 )
| ( X_52 = g_s54_54 )
| ( X_52 = g_s55_55 ) ) )
& ( g_s48_48 != g_s49_49 )
& ( g_s49_49 != g_s50_50 )
& ( g_s50_50 != g_s51_51 )
& ( g_s51_51 != g_s52_52 )
& ( g_s52_52 != g_s53_53 )
& ( g_s53_53 != g_s54_54 )
& ( g_s54_54 != g_s55_55 ) ) ).
tff('Define:ctx:110',axiom,
~ mem0(g_s153_151,g_s152_150) ).
tff('Define:ctx:111',axiom,
! [X_648: $int] :
( mem0(X_648,g_s154_152)
<=> ( $greatereq(X_648,min_int)
& $lesseq(X_648,max_int) ) ) ).
tff('Define:ctx:112',axiom,
! [X_649: $int] :
( mem0(X_649,g_s155_153)
=> ( $greatereq(X_649,0)
& $lesseq(X_649,max_int) ) ) ).
tff('Define:ctx:113',axiom,
! [X_650: $int] :
( mem0(X_650,g_s155_153)
=> mem0(X_650,g_s154_152) ) ).
tff('Define:ctx:114',axiom,
mem0(g_s156_154,g_s154_152) ).
tff('Define:ctx:115',axiom,
~ mem0(g_s156_154,g_s155_153) ).
tff('Define:ctx:116',axiom,
! [X_651: $int] :
( mem0(X_651,g_s157_155)
<=> ( $greatereq(X_651,min_int)
& $lesseq(X_651,max_int) ) ) ).
tff('Define:ctx:117',axiom,
! [X_652: $int] :
( mem0(X_652,g_s158_156)
=> ( $greatereq(X_652,min_int)
& $lesseq(X_652,max_int) ) ) ).
tff('Define:ctx:118',axiom,
! [X_653: $int] :
( mem0(X_653,g_s158_156)
=> mem0(X_653,g_s157_155) ) ).
tff('Define:ctx:119',axiom,
mem0(g_s159_157,g_s157_155) ).
tff('Define:ctx:12',axiom,
( ! [X_53: $int] :
( mem0(X_53,g_s56_56)
<=> ( ( X_53 = g_s57_57 )
| ( X_53 = g_s58_58 )
| ( X_53 = g_s59_59 ) ) )
& ( g_s57_57 != g_s58_58 )
& ( g_s58_58 != g_s59_59 ) ) ).
tff('Define:ctx:120',axiom,
~ mem0(g_s159_157,g_s158_156) ).
tff('Define:ctx:121',axiom,
! [X_654: $int] :
( mem0(X_654,g_s160_158)
=> mem0(X_654,g_s90_90) ) ).
tff('Define:ctx:122',axiom,
mem0(g_s161_159,g_s90_90) ).
tff('Define:ctx:123',axiom,
~ mem0(g_s161_159,g_s160_158) ).
tff('Define:ctx:124',axiom,
( ! [X_655: $int,X_656: $int] :
( mem2(X_656,X_655,g_s162_160)
=> ( $greatereq(X_656,0)
& $lesseq(X_656,max_int)
& mem0(X_655,g_s90_90) ) )
& ! [X_657: $int,X_658: $int,X_659: $int] :
( ( mem2(X_657,X_658,g_s162_160)
& mem2(X_657,X_659,g_s162_160) )
=> ( X_658 = X_659 ) ) ) ).
tff('Define:ctx:125',axiom,
? [X_660: $int] :
( ? [X_661: set_2] :
( ! [X_662: $int,X_663: $int] :
( mem2(X_663,X_662,X_661)
<=> mem2(X_663,X_662,g_s162_160) )
& ! [X_664: $int,X_665: $int,X_666: $int] :
( ( mem2(X_664,X_665,X_661)
& mem2(X_664,X_666,X_661) )
=> ( X_665 = X_666 ) )
& ! [X_667: $int] :
( ( $greatereq(X_667,1)
& $lesseq(X_667,X_660) )
<=> ? [X_668: $int] : mem2(X_667,X_668,X_661) )
& ! [X_669: $int] :
( ? [X_670: $int] : mem2(X_670,X_669,X_661)
=> mem0(X_669,g_s160_158) ) )
& ! [X_671: $int] :
( mem0(X_671,g_s160_158)
=> ? [X_672: $int] : mem2(X_672,X_671,g_s162_160) )
& ! [X_673: $int,X_674: $int,X_675: $int] :
( ( mem2(X_674,X_673,g_s162_160)
& mem2(X_675,X_673,g_s162_160) )
=> ( X_674 = X_675 ) ) ) ).
tff('Define:ctx:126',axiom,
! [X_676: $int] :
( mem0(X_676,g_s163_161)
=> mem0(X_676,g_s91_91) ) ).
tff('Define:ctx:127',axiom,
mem0(g_s164_162,g_s91_91) ).
tff('Define:ctx:128',axiom,
~ mem0(g_s164_162,g_s163_161) ).
tff('Define:ctx:129',axiom,
( ! [X_677: $int,X_678: $int] :
( mem2(X_678,X_677,g_s165_163)
=> ( $greatereq(X_678,0)
& $lesseq(X_678,max_int)
& mem0(X_677,g_s91_91) ) )
& ! [X_679: $int,X_680: $int,X_681: $int] :
( ( mem2(X_679,X_680,g_s165_163)
& mem2(X_679,X_681,g_s165_163) )
=> ( X_680 = X_681 ) ) ) ).
tff('Define:ctx:13',axiom,
( ! [X_54: $int] :
( mem0(X_54,g_s60_60)
<=> ( ( X_54 = g_s61_61 )
| ( X_54 = g_s62_62 )
| ( X_54 = g_s63_63 ) ) )
& ( g_s61_61 != g_s62_62 )
& ( g_s62_62 != g_s63_63 ) ) ).
tff('Define:ctx:130',axiom,
? [X_682: $int] :
( ? [X_683: set_2] :
( ! [X_684: $int,X_685: $int] :
( mem2(X_685,X_684,X_683)
<=> mem2(X_685,X_684,g_s165_163) )
& ! [X_686: $int,X_687: $int,X_688: $int] :
( ( mem2(X_686,X_687,X_683)
& mem2(X_686,X_688,X_683) )
=> ( X_687 = X_688 ) )
& ! [X_689: $int] :
( ( $greatereq(X_689,1)
& $lesseq(X_689,X_682) )
<=> ? [X_690: $int] : mem2(X_689,X_690,X_683) )
& ! [X_691: $int] :
( ? [X_692: $int] : mem2(X_692,X_691,X_683)
=> mem0(X_691,g_s163_161) ) )
& ! [X_693: $int] :
( mem0(X_693,g_s163_161)
=> ? [X_694: $int] : mem2(X_694,X_693,g_s165_163) )
& ! [X_695: $int,X_696: $int,X_697: $int] :
( ( mem2(X_696,X_695,g_s165_163)
& mem2(X_697,X_695,g_s165_163) )
=> ( X_696 = X_697 ) ) ) ).
tff('Define:ctx:131',axiom,
! [X_698: $int] :
( mem0(X_698,g_s166_164)
=> mem0(X_698,g_s92_92) ) ).
tff('Define:ctx:132',axiom,
mem0(g_s167_165,g_s92_92) ).
tff('Define:ctx:133',axiom,
~ mem0(g_s167_165,g_s166_164) ).
tff('Define:ctx:134',axiom,
( ! [X_699: $int,X_700: $int] :
( mem2(X_700,X_699,g_s168_166)
=> ( $greatereq(X_700,0)
& $lesseq(X_700,max_int)
& mem0(X_699,g_s92_92) ) )
& ! [X_701: $int,X_702: $int,X_703: $int] :
( ( mem2(X_701,X_702,g_s168_166)
& mem2(X_701,X_703,g_s168_166) )
=> ( X_702 = X_703 ) ) ) ).
tff('Define:ctx:135',axiom,
? [X_704: $int] :
( ? [X_705: set_2] :
( ! [X_706: $int,X_707: $int] :
( mem2(X_707,X_706,X_705)
<=> mem2(X_707,X_706,g_s168_166) )
& ! [X_708: $int,X_709: $int,X_710: $int] :
( ( mem2(X_708,X_709,X_705)
& mem2(X_708,X_710,X_705) )
=> ( X_709 = X_710 ) )
& ! [X_711: $int] :
( ( $greatereq(X_711,1)
& $lesseq(X_711,X_704) )
<=> ? [X_712: $int] : mem2(X_711,X_712,X_705) )
& ! [X_713: $int] :
( ? [X_714: $int] : mem2(X_714,X_713,X_705)
=> mem0(X_713,g_s166_164) ) )
& ! [X_715: $int] :
( mem0(X_715,g_s166_164)
=> ? [X_716: $int] : mem2(X_716,X_715,g_s168_166) )
& ! [X_717: $int,X_718: $int,X_719: $int] :
( ( mem2(X_718,X_717,g_s168_166)
& mem2(X_719,X_717,g_s168_166) )
=> ( X_718 = X_719 ) ) ) ).
tff('Define:ctx:136',axiom,
! [X_720: $int] :
( mem0(X_720,g_s169_167)
=> mem0(X_720,g_s93_93) ) ).
tff('Define:ctx:137',axiom,
mem0(g_s170_168,g_s93_93) ).
tff('Define:ctx:138',axiom,
~ mem0(g_s170_168,g_s169_167) ).
tff('Define:ctx:139',axiom,
( ! [X_721: $int,X_722: $int] :
( mem2(X_722,X_721,g_s171_169)
=> ( $greatereq(X_722,0)
& $lesseq(X_722,max_int)
& mem0(X_721,g_s93_93) ) )
& ! [X_723: $int,X_724: $int,X_725: $int] :
( ( mem2(X_723,X_724,g_s171_169)
& mem2(X_723,X_725,g_s171_169) )
=> ( X_724 = X_725 ) ) ) ).
tff('Define:ctx:14',axiom,
( ! [X_55: $int] :
( mem0(X_55,g_s64_64)
<=> ( ( X_55 = g_s65_65 )
| ( X_55 = g_s66_66 )
| ( X_55 = g_s67_67 ) ) )
& ( g_s65_65 != g_s66_66 )
& ( g_s66_66 != g_s67_67 ) ) ).
tff('Define:ctx:140',axiom,
? [X_726: $int] :
( ? [X_727: set_2] :
( ! [X_728: $int,X_729: $int] :
( mem2(X_729,X_728,X_727)
<=> mem2(X_729,X_728,g_s171_169) )
& ! [X_730: $int,X_731: $int,X_732: $int] :
( ( mem2(X_730,X_731,X_727)
& mem2(X_730,X_732,X_727) )
=> ( X_731 = X_732 ) )
& ! [X_733: $int] :
( ( $greatereq(X_733,1)
& $lesseq(X_733,X_726) )
<=> ? [X_734: $int] : mem2(X_733,X_734,X_727) )
& ! [X_735: $int] :
( ? [X_736: $int] : mem2(X_736,X_735,X_727)
=> mem0(X_735,g_s169_167) ) )
& ! [X_737: $int] :
( mem0(X_737,g_s169_167)
=> ? [X_738: $int] : mem2(X_738,X_737,g_s171_169) )
& ! [X_739: $int,X_740: $int,X_741: $int] :
( ( mem2(X_740,X_739,g_s171_169)
& mem2(X_741,X_739,g_s171_169) )
=> ( X_740 = X_741 ) ) ) ).
tff('Define:ctx:141',axiom,
! [X_742: $int] :
( mem0(X_742,g_s172_170)
=> mem0(X_742,g_s94_94) ) ).
tff('Define:ctx:142',axiom,
mem0(g_s173_171,g_s94_94) ).
tff('Define:ctx:143',axiom,
~ mem0(g_s173_171,g_s172_170) ).
tff('Define:ctx:144',axiom,
( ! [X_743: $int,X_744: $int] :
( mem2(X_744,X_743,g_s174_172)
=> ( $greatereq(X_744,0)
& $lesseq(X_744,max_int)
& mem0(X_743,g_s94_94) ) )
& ! [X_745: $int,X_746: $int,X_747: $int] :
( ( mem2(X_745,X_746,g_s174_172)
& mem2(X_745,X_747,g_s174_172) )
=> ( X_746 = X_747 ) ) ) ).
tff('Define:ctx:145',axiom,
? [X_748: $int] :
( ? [X_749: set_2] :
( ! [X_750: $int,X_751: $int] :
( mem2(X_751,X_750,X_749)
<=> mem2(X_751,X_750,g_s174_172) )
& ! [X_752: $int,X_753: $int,X_754: $int] :
( ( mem2(X_752,X_753,X_749)
& mem2(X_752,X_754,X_749) )
=> ( X_753 = X_754 ) )
& ! [X_755: $int] :
( ( $greatereq(X_755,1)
& $lesseq(X_755,X_748) )
<=> ? [X_756: $int] : mem2(X_755,X_756,X_749) )
& ! [X_757: $int] :
( ? [X_758: $int] : mem2(X_758,X_757,X_749)
=> mem0(X_757,g_s172_170) ) )
& ! [X_759: $int] :
( mem0(X_759,g_s172_170)
=> ? [X_760: $int] : mem2(X_760,X_759,g_s174_172) )
& ! [X_761: $int,X_762: $int,X_763: $int] :
( ( mem2(X_762,X_761,g_s174_172)
& mem2(X_763,X_761,g_s174_172) )
=> ( X_762 = X_763 ) ) ) ).
tff('Define:ctx:146',axiom,
( ? [X_764: set_2] :
( ! [X_765: $int,X_766: $int] :
( mem2(X_766,X_765,X_764)
<=> mem2(X_766,X_765,g_s175_173) )
& ! [X_767: $int,X_768: $int,X_769: $int] :
( ( mem2(X_767,X_768,X_764)
& mem2(X_767,X_769,X_764) )
=> ( X_768 = X_769 ) )
& ! [X_770: $int] :
( mem0(X_770,g_s160_158)
<=> ? [X_771: $int] : mem2(X_770,X_771,X_764) )
& ! [X_772: $int] :
( ? [X_773: $int] : mem2(X_773,X_772,X_764)
=> mem0(X_772,g_s106_106) ) )
& ! [X_774: $int,X_775: $int,X_776: $int] :
( ( mem2(X_775,X_774,g_s175_173)
& mem2(X_776,X_774,g_s175_173) )
=> ( X_775 = X_776 ) ) ) ).
tff('Define:ctx:147',axiom,
( ? [X_777: set_2] :
( ! [X_778: $int,X_779: $int] :
( mem2(X_779,X_778,X_777)
<=> mem2(X_779,X_778,g_s176_174) )
& ! [X_780: $int,X_781: $int,X_782: $int] :
( ( mem2(X_780,X_781,X_777)
& mem2(X_780,X_782,X_777) )
=> ( X_781 = X_782 ) )
& ! [X_783: $int] :
( mem0(X_783,g_s163_161)
<=> ? [X_784: $int] : mem2(X_783,X_784,X_777) )
& ! [X_785: $int] :
( ? [X_786: $int] : mem2(X_786,X_785,X_777)
=> mem0(X_785,g_s106_106) ) )
& ! [X_787: $int,X_788: $int,X_789: $int] :
( ( mem2(X_788,X_787,g_s176_174)
& mem2(X_789,X_787,g_s176_174) )
=> ( X_788 = X_789 ) ) ) ).
tff('Define:ctx:148',axiom,
mem0(g_s177_175,g_s1_1) ).
tff('Define:ctx:149',axiom,
( ( g_s178_176 != 0 )
=> mem0(g_s177_175,g_s106_106) ) ).
tff('Define:ctx:15',axiom,
( ! [X_56: $int] :
( mem0(X_56,g_s68_68)
<=> ( ( X_56 = g_s69_69 )
| ( X_56 = g_s70_70 ) ) )
& ( g_s69_69 != g_s70_70 ) ) ).
tff('Define:ctx:150',axiom,
( ? [X_790: set_2] :
( ! [X_791: $int,X_792: $int] :
( mem2(X_792,X_791,X_790)
<=> mem2(X_792,X_791,g_s179_177) )
& ! [X_793: $int,X_794: $int,X_795: $int] :
( ( mem2(X_793,X_794,X_790)
& mem2(X_793,X_795,X_790) )
=> ( X_794 = X_795 ) )
& ! [X_796: $int] :
( mem0(X_796,g_s169_167)
<=> ? [X_797: $int] : mem2(X_796,X_797,X_790) )
& ! [X_798: $int] :
( ? [X_799: $int] : mem2(X_799,X_798,X_790)
=> mem0(X_798,g_s106_106) ) )
& ! [X_800: $int,X_801: $int,X_802: $int] :
( ( mem2(X_801,X_800,g_s179_177)
& mem2(X_802,X_800,g_s179_177) )
=> ( X_801 = X_802 ) ) ) ).
tff('Define:ctx:151',axiom,
! [X_803: $int] :
( ( ? [X_804: $int] : mem2(X_804,X_803,g_s175_173)
& ? [X_805: $int] : mem2(X_805,X_803,g_s176_174) )
<=> $false ) ).
tff('Define:ctx:152',axiom,
! [X_806: $int] :
( ( ? [X_807: $int] : mem2(X_807,X_806,g_s175_173)
& ? [X_808: $int] : mem2(X_808,X_806,g_s179_177) )
<=> $false ) ).
tff('Define:ctx:153',axiom,
! [X_809: $int] :
( ( ? [X_810: $int] : mem2(X_810,X_809,g_s179_177)
& ? [X_811: $int] : mem2(X_811,X_809,g_s176_174) )
<=> $false ) ).
tff('Define:ctx:154',axiom,
( ( g_s178_176 != 0 )
=> ~ ? [X_812: $int] : mem2(X_812,g_s177_175,g_s175_173) ) ).
tff('Define:ctx:155',axiom,
( ( g_s178_176 != 0 )
=> ~ ? [X_813: $int] : mem2(X_813,g_s177_175,g_s176_174) ) ).
tff('Define:ctx:156',axiom,
( ( g_s178_176 != 0 )
=> ~ ? [X_814: $int] : mem2(X_814,g_s177_175,g_s179_177) ) ).
tff('Define:ctx:157',axiom,
$greater(g_s180_178,0) ).
tff('Define:ctx:158',axiom,
$greater(g_s181_179,0) ).
tff('Define:ctx:159',axiom,
$greater(g_s182_180,0) ).
tff('Define:ctx:16',axiom,
( ! [X_57: $int] :
( mem0(X_57,g_s71_71)
<=> ( ( X_57 = g_s72_72 )
| ( X_57 = g_s73_73 ) ) )
& ( g_s72_72 != g_s73_73 ) ) ).
tff('Define:ctx:160',axiom,
$greater(g_s183_181,0) ).
tff('Define:ctx:161',axiom,
$greater(g_s184_182,0) ).
tff('Define:ctx:162',axiom,
$greater(g_s185_183,0) ).
tff('Define:ctx:163',axiom,
$greater(g_s186_184,0) ).
tff('Define:ctx:164',axiom,
$greater(g_s187_185,0) ).
tff('Define:ctx:165',axiom,
$greater(g_s188_186,0) ).
tff('Define:ctx:166',axiom,
$greater(g_s189_187,0) ).
tff('Define:ctx:167',axiom,
$greater(g_s190_188,0) ).
tff('Define:ctx:168',axiom,
$greater(g_s191_189,0) ).
tff('Define:ctx:169',axiom,
$greater(g_s192_190,0) ).
tff('Define:ctx:17',axiom,
( ! [X_58: $int] :
( mem0(X_58,g_s74_74)
<=> ( ( X_58 = g_s75_75 )
| ( X_58 = g_s76_76 )
| ( X_58 = g_s77_77 ) ) )
& ( g_s75_75 != g_s76_76 )
& ( g_s76_76 != g_s77_77 ) ) ).
tff('Define:ctx:170',axiom,
$greater(g_s193_191,0) ).
tff('Define:ctx:171',axiom,
$greater(g_s194_192,0) ).
tff('Define:ctx:172',axiom,
$greater(g_s195_193,0) ).
tff('Define:ctx:173',axiom,
$greater(g_s196_194,0) ).
tff('Define:ctx:174',axiom,
$greater(g_s197_195,0) ).
tff('Define:ctx:175',axiom,
$greater(g_s198_196,0) ).
tff('Define:ctx:176',axiom,
$greater(g_s199_197,0) ).
tff('Define:ctx:177',axiom,
$greater(g_s200_198,0) ).
tff('Define:ctx:178',axiom,
$greater(g_s201_199,0) ).
tff('Define:ctx:179',axiom,
$greater(g_s202_200,0) ).
tff('Define:ctx:18',axiom,
( ! [X_59: $int] :
( mem0(X_59,g_s78_78)
<=> ( ( X_59 = g_s79_79 )
| ( X_59 = g_s80_80 ) ) )
& ( g_s79_79 != g_s80_80 ) ) ).
tff('Define:ctx:180',axiom,
$greater(g_s203_201,0) ).
tff('Define:ctx:181',axiom,
$greater(g_s204_202,0) ).
tff('Define:ctx:182',axiom,
$greater(g_s205_203,0) ).
tff('Define:ctx:183',axiom,
$greater(g_s206_204,0) ).
tff('Define:ctx:184',axiom,
$greater(g_s207_205,0) ).
tff('Define:ctx:185',axiom,
$greater(g_s208_206,0) ).
tff('Define:ctx:186',axiom,
$greater(g_s209_207,0) ).
tff('Define:ctx:187',axiom,
$greater(g_s210_208,0) ).
tff('Define:ctx:188',axiom,
$greater(g_s211_209,0) ).
tff('Define:ctx:189',axiom,
$greater(g_s212_210,0) ).
tff('Define:ctx:19',axiom,
( ! [X_60: $int] :
( mem0(X_60,g_s81_81)
<=> ( ( X_60 = g_s82_82 )
| ( X_60 = g_s83_83 )
| ( X_60 = g_s84_84 ) ) )
& ( g_s82_82 != g_s83_83 )
& ( g_s83_83 != g_s84_84 ) ) ).
tff('Define:ctx:190',axiom,
$greater(g_s213_211,0) ).
tff('Define:ctx:191',axiom,
$greater(g_s214_212,0) ).
tff('Define:ctx:192',axiom,
$greater(g_s215_213,0) ).
tff('Define:ctx:193',axiom,
$greater(g_s216_214,0) ).
tff('Define:ctx:194',axiom,
$greater(g_s217_215,0) ).
tff('Define:ctx:195',axiom,
$greatereq(g_s218_216,0) ).
tff('Define:ctx:196',axiom,
$greater(g_s219_217,0) ).
tff('Define:ctx:197',axiom,
$greatereq(g_s220_218,0) ).
tff('Define:ctx:198',axiom,
! [X_815: $int] :
( ( X_815 = $sum(g_s217_215,g_s218_216) )
=> mem0(X_815,g_s100_100) ) ).
tff('Define:ctx:199',axiom,
! [X_816: $int] :
( ( X_816 = $sum(g_s187_185,g_s210_208) )
=> mem0(X_816,g_s221_219) ) ).
tff('Define:ctx:2',axiom,
( ! [X_43: $int] :
( mem0(X_43,g_s2_2)
<=> ( ( X_43 = g_s3_3 )
| ( X_43 = g_s4_4 ) ) )
& ( g_s3_3 != g_s4_4 ) ) ).
tff('Define:ctx:20',axiom,
( ~ ! [X_61: $int] :
( mem0(X_61,g_s85_85)
<=> $false )
& ! [X_64: $int] :
( mem0(X_64,g_s85_85)
=> $true )
& ? [X_62: $int,X_63: set_2] :
( ? [X_65: set_2] :
( ! [X_66: $int,X_67: $int] :
( mem2(X_67,X_66,X_65)
<=> mem2(X_67,X_66,X_63) )
& ! [X_68: $int,X_69: $int,X_70: $int] :
( ( mem2(X_68,X_69,X_65)
& mem2(X_68,X_70,X_65) )
=> ( X_69 = X_70 ) )
& ! [X_71: $int] :
( ( $greatereq(X_71,1)
& $lesseq(X_71,X_62) )
<=> ? [X_72: $int] : mem2(X_71,X_72,X_65) )
& ! [X_73: $int] :
( ? [X_74: $int] : mem2(X_74,X_73,X_65)
=> mem0(X_73,g_s85_85) ) )
& ! [X_75: $int] :
( mem0(X_75,g_s85_85)
=> ? [X_76: $int] : mem2(X_76,X_75,X_63) )
& ! [X_77: $int,X_78: $int,X_79: $int] :
( ( mem2(X_78,X_77,X_63)
& mem2(X_79,X_77,X_63) )
=> ( X_78 = X_79 ) ) ) ) ).
tff('Define:ctx:200',axiom,
! [X_817: $int] :
( ( X_817 = $sum(g_s184_182,g_s210_208) )
=> mem0(X_817,g_s221_219) ) ).
tff('Define:ctx:201',axiom,
mem0(g_s180_178,g_s100_100) ).
tff('Define:ctx:202',axiom,
mem0(g_s181_179,g_s100_100) ).
tff('Define:ctx:203',axiom,
mem0(g_s182_180,g_s221_219) ).
tff('Define:ctx:204',axiom,
mem0(g_s183_181,g_s221_219) ).
tff('Define:ctx:205',axiom,
mem0(g_s184_182,g_s221_219) ).
tff('Define:ctx:206',axiom,
mem0(g_s185_183,g_s221_219) ).
tff('Define:ctx:207',axiom,
mem0(g_s186_184,g_s221_219) ).
tff('Define:ctx:208',axiom,
mem0(g_s187_185,g_s221_219) ).
tff('Define:ctx:209',axiom,
mem0(g_s188_186,g_s221_219) ).
tff('Define:ctx:21',axiom,
( ~ ! [X_80: $int] :
( mem0(X_80,g_s86_86)
<=> $false )
& ! [X_83: $int] :
( mem0(X_83,g_s86_86)
=> $true )
& ? [X_81: $int,X_82: set_2] :
( ? [X_84: set_2] :
( ! [X_85: $int,X_86: $int] :
( mem2(X_86,X_85,X_84)
<=> mem2(X_86,X_85,X_82) )
& ! [X_87: $int,X_88: $int,X_89: $int] :
( ( mem2(X_87,X_88,X_84)
& mem2(X_87,X_89,X_84) )
=> ( X_88 = X_89 ) )
& ! [X_90: $int] :
( ( $greatereq(X_90,1)
& $lesseq(X_90,X_81) )
<=> ? [X_91: $int] : mem2(X_90,X_91,X_84) )
& ! [X_92: $int] :
( ? [X_93: $int] : mem2(X_93,X_92,X_84)
=> mem0(X_92,g_s86_86) ) )
& ! [X_94: $int] :
( mem0(X_94,g_s86_86)
=> ? [X_95: $int] : mem2(X_95,X_94,X_82) )
& ! [X_96: $int,X_97: $int,X_98: $int] :
( ( mem2(X_97,X_96,X_82)
& mem2(X_98,X_96,X_82) )
=> ( X_97 = X_98 ) ) ) ) ).
tff('Define:ctx:210',axiom,
mem0(g_s189_187,g_s100_100) ).
tff('Define:ctx:211',axiom,
mem0(g_s190_188,g_s221_219) ).
tff('Define:ctx:212',axiom,
mem0(g_s191_189,g_s221_219) ).
tff('Define:ctx:213',axiom,
mem0(g_s192_190,g_s221_219) ).
tff('Define:ctx:214',axiom,
mem0(g_s193_191,g_s221_219) ).
tff('Define:ctx:215',axiom,
mem0(g_s194_192,g_s221_219) ).
tff('Define:ctx:216',axiom,
mem0(g_s195_193,g_s100_100) ).
tff('Define:ctx:217',axiom,
mem0(g_s196_194,g_s100_100) ).
tff('Define:ctx:218',axiom,
mem0(g_s197_195,g_s100_100) ).
tff('Define:ctx:219',axiom,
mem0(g_s198_196,g_s100_100) ).
tff('Define:ctx:22',axiom,
( ~ ! [X_99: $int] :
( mem0(X_99,g_s87_87)
<=> $false )
& ! [X_102: $int] :
( mem0(X_102,g_s87_87)
=> $true )
& ? [X_100: $int,X_101: set_2] :
( ? [X_103: set_2] :
( ! [X_104: $int,X_105: $int] :
( mem2(X_105,X_104,X_103)
<=> mem2(X_105,X_104,X_101) )
& ! [X_106: $int,X_107: $int,X_108: $int] :
( ( mem2(X_106,X_107,X_103)
& mem2(X_106,X_108,X_103) )
=> ( X_107 = X_108 ) )
& ! [X_109: $int] :
( ( $greatereq(X_109,1)
& $lesseq(X_109,X_100) )
<=> ? [X_110: $int] : mem2(X_109,X_110,X_103) )
& ! [X_111: $int] :
( ? [X_112: $int] : mem2(X_112,X_111,X_103)
=> mem0(X_111,g_s87_87) ) )
& ! [X_113: $int] :
( mem0(X_113,g_s87_87)
=> ? [X_114: $int] : mem2(X_114,X_113,X_101) )
& ! [X_115: $int,X_116: $int,X_117: $int] :
( ( mem2(X_116,X_115,X_101)
& mem2(X_117,X_115,X_101) )
=> ( X_116 = X_117 ) ) ) ) ).
tff('Define:ctx:220',axiom,
mem0(g_s199_197,g_s100_100) ).
tff('Define:ctx:221',axiom,
mem0(g_s200_198,g_s100_100) ).
tff('Define:ctx:222',axiom,
mem0(g_s201_199,g_s100_100) ).
tff('Define:ctx:223',axiom,
mem0(g_s202_200,g_s100_100) ).
tff('Define:ctx:224',axiom,
mem0(g_s203_201,g_s100_100) ).
tff('Define:ctx:225',axiom,
mem0(g_s204_202,g_s100_100) ).
tff('Define:ctx:226',axiom,
mem0(g_s205_203,g_s100_100) ).
tff('Define:ctx:227',axiom,
mem0(g_s206_204,g_s221_219) ).
tff('Define:ctx:228',axiom,
mem0(g_s207_205,g_s100_100) ).
tff('Define:ctx:229',axiom,
mem0(g_s208_206,g_s100_100) ).
tff('Define:ctx:23',axiom,
( ~ ! [X_118: $int] :
( mem0(X_118,g_s88_88)
<=> $false )
& ! [X_121: $int] :
( mem0(X_121,g_s88_88)
=> $true )
& ? [X_119: $int,X_120: set_2] :
( ? [X_122: set_2] :
( ! [X_123: $int,X_124: $int] :
( mem2(X_124,X_123,X_122)
<=> mem2(X_124,X_123,X_120) )
& ! [X_125: $int,X_126: $int,X_127: $int] :
( ( mem2(X_125,X_126,X_122)
& mem2(X_125,X_127,X_122) )
=> ( X_126 = X_127 ) )
& ! [X_128: $int] :
( ( $greatereq(X_128,1)
& $lesseq(X_128,X_119) )
<=> ? [X_129: $int] : mem2(X_128,X_129,X_122) )
& ! [X_130: $int] :
( ? [X_131: $int] : mem2(X_131,X_130,X_122)
=> mem0(X_130,g_s88_88) ) )
& ! [X_132: $int] :
( mem0(X_132,g_s88_88)
=> ? [X_133: $int] : mem2(X_133,X_132,X_120) )
& ! [X_134: $int,X_135: $int,X_136: $int] :
( ( mem2(X_135,X_134,X_120)
& mem2(X_136,X_134,X_120) )
=> ( X_135 = X_136 ) ) ) ) ).
tff('Define:ctx:230',axiom,
mem0(g_s209_207,g_s100_100) ).
tff('Define:ctx:231',axiom,
mem0(g_s210_208,g_s100_100) ).
tff('Define:ctx:232',axiom,
mem0(g_s211_209,g_s221_219) ).
tff('Define:ctx:233',axiom,
mem0(g_s212_210,g_s100_100) ).
tff('Define:ctx:234',axiom,
mem0(g_s213_211,g_s100_100) ).
tff('Define:ctx:235',axiom,
mem0(g_s214_212,g_s221_219) ).
tff('Define:ctx:236',axiom,
mem0(g_s215_213,g_s221_219) ).
tff('Define:ctx:237',axiom,
mem0(g_s216_214,g_s221_219) ).
tff('Define:ctx:238',axiom,
mem0(g_s217_215,g_s100_100) ).
tff('Define:ctx:239',axiom,
mem0(g_s218_216,g_s100_100) ).
tff('Define:ctx:24',axiom,
( ~ ! [X_137: $int] :
( mem0(X_137,g_s89_89)
<=> $false )
& ! [X_140: $int] :
( mem0(X_140,g_s89_89)
=> $true )
& ? [X_138: $int,X_139: set_2] :
( ? [X_141: set_2] :
( ! [X_142: $int,X_143: $int] :
( mem2(X_143,X_142,X_141)
<=> mem2(X_143,X_142,X_139) )
& ! [X_144: $int,X_145: $int,X_146: $int] :
( ( mem2(X_144,X_145,X_141)
& mem2(X_144,X_146,X_141) )
=> ( X_145 = X_146 ) )
& ! [X_147: $int] :
( ( $greatereq(X_147,1)
& $lesseq(X_147,X_138) )
<=> ? [X_148: $int] : mem2(X_147,X_148,X_141) )
& ! [X_149: $int] :
( ? [X_150: $int] : mem2(X_150,X_149,X_141)
=> mem0(X_149,g_s89_89) ) )
& ! [X_151: $int] :
( mem0(X_151,g_s89_89)
=> ? [X_152: $int] : mem2(X_152,X_151,X_139) )
& ! [X_153: $int,X_154: $int,X_155: $int] :
( ( mem2(X_154,X_153,X_139)
& mem2(X_155,X_153,X_139) )
=> ( X_154 = X_155 ) ) ) ) ).
tff('Define:ctx:240',axiom,
mem0(g_s219_217,g_s221_219) ).
tff('Define:ctx:241',axiom,
mem0(g_s220_218,g_s100_100) ).
tff('Define:ctx:242',axiom,
mem0(g_s222_221,g_s223_220) ).
tff('Define:ctx:243',axiom,
mem0(g_s224_222,g_s223_220) ).
tff('Define:ctx:244',axiom,
mem0(g_s225_224,g_s226_223) ).
tff('Define:ctx:245',axiom,
mem0(g_s227_225,g_s226_223) ).
tff('Define:ctx:246',axiom,
( ( g_s224_222 != g_s222_221 )
=> ( g_s178_176 != 0 ) ) ).
tff('Define:ctx:247',axiom,
mem0(g_s222_221,g_s228_226) ).
tff('Define:ctx:248',axiom,
mem0(g_s224_222,g_s228_226) ).
tff('Define:ctx:249',axiom,
mem0(g_s225_224,g_s229_227) ).
tff('Define:ctx:25',axiom,
( ~ ! [X_156: $int] :
( mem0(X_156,g_s90_90)
<=> $false )
& ! [X_159: $int] :
( mem0(X_159,g_s90_90)
=> $true )
& ? [X_157: $int,X_158: set_2] :
( ? [X_160: set_2] :
( ! [X_161: $int,X_162: $int] :
( mem2(X_162,X_161,X_160)
<=> mem2(X_162,X_161,X_158) )
& ! [X_163: $int,X_164: $int,X_165: $int] :
( ( mem2(X_163,X_164,X_160)
& mem2(X_163,X_165,X_160) )
=> ( X_164 = X_165 ) )
& ! [X_166: $int] :
( ( $greatereq(X_166,1)
& $lesseq(X_166,X_157) )
<=> ? [X_167: $int] : mem2(X_166,X_167,X_160) )
& ! [X_168: $int] :
( ? [X_169: $int] : mem2(X_169,X_168,X_160)
=> mem0(X_168,g_s90_90) ) )
& ! [X_170: $int] :
( mem0(X_170,g_s90_90)
=> ? [X_171: $int] : mem2(X_171,X_170,X_158) )
& ! [X_172: $int,X_173: $int,X_174: $int] :
( ( mem2(X_173,X_172,X_158)
& mem2(X_174,X_172,X_158) )
=> ( X_173 = X_174 ) ) ) ) ).
tff('Define:ctx:250',axiom,
mem0(g_s227_225,g_s229_227) ).
tff('Define:ctx:251',axiom,
( ? [X_818: set_2] :
( ! [X_819: $int,X_820: $int] :
( mem2(X_820,X_819,X_818)
<=> mem2(X_820,X_819,g_s230_228) )
& ! [X_821: $int,X_822: $int,X_823: $int] :
( ( mem2(X_821,X_822,X_818)
& mem2(X_821,X_823,X_818) )
=> ( X_822 = X_823 ) )
& ! [X_824: $int] :
( mem0(X_824,g_s160_158)
<=> ? [X_825: $int] : mem2(X_824,X_825,X_818) )
& ! [X_826: $int] :
( ? [X_827: $int] : mem2(X_827,X_826,X_818)
=> mem0(X_826,g_s223_220) ) )
& ! [X_828: $int,X_829: $int,X_830: $int] :
( ( mem2(X_829,X_828,g_s230_228)
& mem2(X_830,X_828,g_s230_228) )
=> ( X_829 = X_830 ) ) ) ).
tff('Define:ctx:252',axiom,
( ? [X_831: set_2] :
( ! [X_832: $int,X_833: $int] :
( mem2(X_833,X_832,X_831)
<=> mem2(X_833,X_832,g_s231_229) )
& ! [X_834: $int,X_835: $int,X_836: $int] :
( ( mem2(X_834,X_835,X_831)
& mem2(X_834,X_836,X_831) )
=> ( X_835 = X_836 ) )
& ! [X_837: $int] :
( mem0(X_837,g_s163_161)
<=> ? [X_838: $int] : mem2(X_837,X_838,X_831) )
& ! [X_839: $int] :
( ? [X_840: $int] : mem2(X_840,X_839,X_831)
=> mem0(X_839,g_s223_220) ) )
& ! [X_841: $int,X_842: $int,X_843: $int] :
( ( mem2(X_842,X_841,g_s231_229)
& mem2(X_843,X_841,g_s231_229) )
=> ( X_842 = X_843 ) ) ) ).
tff('Define:ctx:253',axiom,
( ? [X_844: set_2] :
( ! [X_845: $int,X_846: $int] :
( mem2(X_846,X_845,X_844)
<=> mem2(X_846,X_845,g_s232_230) )
& ! [X_847: $int,X_848: $int,X_849: $int] :
( ( mem2(X_847,X_848,X_844)
& mem2(X_847,X_849,X_844) )
=> ( X_848 = X_849 ) )
& ! [X_850: $int] :
( mem0(X_850,g_s169_167)
<=> ? [X_851: $int] : mem2(X_850,X_851,X_844) )
& ! [X_852: $int] :
( ? [X_853: $int] : mem2(X_853,X_852,X_844)
=> mem0(X_852,g_s233_231) ) )
& ! [X_854: $int,X_855: $int,X_856: $int] :
( ( mem2(X_855,X_854,g_s232_230)
& mem2(X_856,X_854,g_s232_230) )
=> ( X_855 = X_856 ) ) ) ).
tff('Define:ctx:254',axiom,
( ? [X_857: set_2] :
( ! [X_858: $int,X_859: $int] :
( mem2(X_859,X_858,X_857)
<=> mem2(X_859,X_858,g_s234_232) )
& ! [X_860: $int,X_861: $int,X_862: $int] :
( ( mem2(X_860,X_861,X_857)
& mem2(X_860,X_862,X_857) )
=> ( X_861 = X_862 ) )
& ! [X_863: $int] :
( mem0(X_863,g_s235_233)
<=> ? [X_864: $int] : mem2(X_863,X_864,X_857) )
& ! [X_865: $int] :
( ? [X_866: $int] : mem2(X_866,X_865,X_857)
=> mem0(X_865,g_s236_234) ) )
& ! [X_867: $int,X_868: $int,X_869: $int] :
( ( mem2(X_868,X_867,g_s234_232)
& mem2(X_869,X_867,g_s234_232) )
=> ( X_868 = X_869 ) ) ) ).
tff('Define:ctx:255',axiom,
( ? [X_870: set_2] :
( ! [X_871: $int,X_872: $int] :
( mem2(X_872,X_871,X_870)
<=> mem2(X_872,X_871,g_s237_235) )
& ! [X_873: $int,X_874: $int,X_875: $int] :
( ( mem2(X_873,X_874,X_870)
& mem2(X_873,X_875,X_870) )
=> ( X_874 = X_875 ) )
& ! [X_876: $int] :
( mem0(X_876,g_s238_236)
<=> ? [X_877: $int] : mem2(X_876,X_877,X_870) )
& ! [X_878: $int] :
( ? [X_879: $int] : mem2(X_879,X_878,X_870)
=> mem0(X_878,g_s239_237) ) )
& ! [X_880: $int,X_881: $int,X_882: $int] :
( ( mem2(X_881,X_880,g_s237_235)
& mem2(X_882,X_880,g_s237_235) )
=> ( X_881 = X_882 ) ) ) ).
tff('Define:ctx:256',axiom,
( ? [X_883: set_2] :
( ! [X_884: $int,X_885: $int] :
( mem2(X_885,X_884,X_883)
<=> mem2(X_885,X_884,g_s240_238) )
& ! [X_886: $int,X_887: $int,X_888: $int] :
( ( mem2(X_886,X_887,X_883)
& mem2(X_886,X_888,X_883) )
=> ( X_887 = X_888 ) )
& ! [X_889: $int] :
( mem0(X_889,g_s238_236)
<=> ? [X_890: $int] : mem2(X_889,X_890,X_883) )
& ! [X_891: $int] :
( ? [X_892: $int] : mem2(X_892,X_891,X_883)
=> mem0(X_891,g_s241_239) ) )
& ! [X_893: $int,X_894: $int,X_895: $int] :
( ( mem2(X_894,X_893,g_s240_238)
& mem2(X_895,X_893,g_s240_238) )
=> ( X_894 = X_895 ) ) ) ).
tff('Define:ctx:257',axiom,
( ? [X_896: set_2] :
( ! [X_897: $int,X_898: $int] :
( mem2(X_898,X_897,X_896)
<=> mem2(X_898,X_897,g_s242_240) )
& ! [X_899: $int,X_900: $int,X_901: $int] :
( ( mem2(X_899,X_900,X_896)
& mem2(X_899,X_901,X_896) )
=> ( X_900 = X_901 ) )
& ! [X_902: $int] :
( mem0(X_902,g_s243_241)
<=> ? [X_903: $int] : mem2(X_902,X_903,X_896) )
& ! [X_904: $int] :
( ? [X_905: $int] : mem2(X_905,X_904,X_896)
=> mem0(X_904,g_s244_242) ) )
& ! [X_906: $int,X_907: $int,X_908: $int] :
( ( mem2(X_907,X_906,g_s242_240)
& mem2(X_908,X_906,g_s242_240) )
=> ( X_907 = X_908 ) ) ) ).
tff('Define:ctx:258',axiom,
( ? [X_909: set_2] :
( ! [X_910: $int,X_911: $int] :
( mem2(X_911,X_910,X_909)
<=> mem2(X_911,X_910,g_s245_243) )
& ! [X_912: $int,X_913: $int,X_914: $int] :
( ( mem2(X_912,X_913,X_909)
& mem2(X_912,X_914,X_909) )
=> ( X_913 = X_914 ) )
& ! [X_915: $int] :
( mem0(X_915,g_s246_244)
<=> ? [X_916: $int] : mem2(X_915,X_916,X_909) )
& ! [X_917: $int] :
( ? [X_918: $int] : mem2(X_918,X_917,X_909)
=> mem0(X_917,g_s247_245) ) )
& ! [X_919: $int,X_920: $int,X_921: $int] :
( ( mem2(X_920,X_919,g_s245_243)
& mem2(X_921,X_919,g_s245_243) )
=> ( X_920 = X_921 ) ) ) ).
tff('Define:ctx:259',axiom,
~ ? [X_922: $int] : mem2(X_922,g_s222_221,g_s230_228) ).
tff('Define:ctx:26',axiom,
( ~ ! [X_175: $int] :
( mem0(X_175,g_s91_91)
<=> $false )
& ! [X_178: $int] :
( mem0(X_178,g_s91_91)
=> $true )
& ? [X_176: $int,X_177: set_2] :
( ? [X_179: set_2] :
( ! [X_180: $int,X_181: $int] :
( mem2(X_181,X_180,X_179)
<=> mem2(X_181,X_180,X_177) )
& ! [X_182: $int,X_183: $int,X_184: $int] :
( ( mem2(X_182,X_183,X_179)
& mem2(X_182,X_184,X_179) )
=> ( X_183 = X_184 ) )
& ! [X_185: $int] :
( ( $greatereq(X_185,1)
& $lesseq(X_185,X_176) )
<=> ? [X_186: $int] : mem2(X_185,X_186,X_179) )
& ! [X_187: $int] :
( ? [X_188: $int] : mem2(X_188,X_187,X_179)
=> mem0(X_187,g_s91_91) ) )
& ! [X_189: $int] :
( mem0(X_189,g_s91_91)
=> ? [X_190: $int] : mem2(X_190,X_189,X_177) )
& ! [X_191: $int,X_192: $int,X_193: $int] :
( ( mem2(X_192,X_191,X_177)
& mem2(X_193,X_191,X_177) )
=> ( X_192 = X_193 ) ) ) ) ).
tff('Define:ctx:260',axiom,
~ ? [X_923: $int] : mem2(X_923,g_s222_221,g_s231_229) ).
tff('Define:ctx:27',axiom,
( ~ ! [X_194: $int] :
( mem0(X_194,g_s92_92)
<=> $false )
& ! [X_197: $int] :
( mem0(X_197,g_s92_92)
=> $true )
& ? [X_195: $int,X_196: set_2] :
( ? [X_198: set_2] :
( ! [X_199: $int,X_200: $int] :
( mem2(X_200,X_199,X_198)
<=> mem2(X_200,X_199,X_196) )
& ! [X_201: $int,X_202: $int,X_203: $int] :
( ( mem2(X_201,X_202,X_198)
& mem2(X_201,X_203,X_198) )
=> ( X_202 = X_203 ) )
& ! [X_204: $int] :
( ( $greatereq(X_204,1)
& $lesseq(X_204,X_195) )
<=> ? [X_205: $int] : mem2(X_204,X_205,X_198) )
& ! [X_206: $int] :
( ? [X_207: $int] : mem2(X_207,X_206,X_198)
=> mem0(X_206,g_s92_92) ) )
& ! [X_208: $int] :
( mem0(X_208,g_s92_92)
=> ? [X_209: $int] : mem2(X_209,X_208,X_196) )
& ! [X_210: $int,X_211: $int,X_212: $int] :
( ( mem2(X_211,X_210,X_196)
& mem2(X_212,X_210,X_196) )
=> ( X_211 = X_212 ) ) ) ) ).
tff('Define:ctx:28',axiom,
( ~ ! [X_213: $int] :
( mem0(X_213,g_s93_93)
<=> $false )
& ! [X_216: $int] :
( mem0(X_216,g_s93_93)
=> $true )
& ? [X_214: $int,X_215: set_2] :
( ? [X_217: set_2] :
( ! [X_218: $int,X_219: $int] :
( mem2(X_219,X_218,X_217)
<=> mem2(X_219,X_218,X_215) )
& ! [X_220: $int,X_221: $int,X_222: $int] :
( ( mem2(X_220,X_221,X_217)
& mem2(X_220,X_222,X_217) )
=> ( X_221 = X_222 ) )
& ! [X_223: $int] :
( ( $greatereq(X_223,1)
& $lesseq(X_223,X_214) )
<=> ? [X_224: $int] : mem2(X_223,X_224,X_217) )
& ! [X_225: $int] :
( ? [X_226: $int] : mem2(X_226,X_225,X_217)
=> mem0(X_225,g_s93_93) ) )
& ! [X_227: $int] :
( mem0(X_227,g_s93_93)
=> ? [X_228: $int] : mem2(X_228,X_227,X_215) )
& ! [X_229: $int,X_230: $int,X_231: $int] :
( ( mem2(X_230,X_229,X_215)
& mem2(X_231,X_229,X_215) )
=> ( X_230 = X_231 ) ) ) ) ).
tff('Define:ctx:29',axiom,
( ~ ! [X_232: $int] :
( mem0(X_232,g_s94_94)
<=> $false )
& ! [X_235: $int] :
( mem0(X_235,g_s94_94)
=> $true )
& ? [X_233: $int,X_234: set_2] :
( ? [X_236: set_2] :
( ! [X_237: $int,X_238: $int] :
( mem2(X_238,X_237,X_236)
<=> mem2(X_238,X_237,X_234) )
& ! [X_239: $int,X_240: $int,X_241: $int] :
( ( mem2(X_239,X_240,X_236)
& mem2(X_239,X_241,X_236) )
=> ( X_240 = X_241 ) )
& ! [X_242: $int] :
( ( $greatereq(X_242,1)
& $lesseq(X_242,X_233) )
<=> ? [X_243: $int] : mem2(X_242,X_243,X_236) )
& ! [X_244: $int] :
( ? [X_245: $int] : mem2(X_245,X_244,X_236)
=> mem0(X_244,g_s94_94) ) )
& ! [X_246: $int] :
( mem0(X_246,g_s94_94)
=> ? [X_247: $int] : mem2(X_247,X_246,X_234) )
& ! [X_248: $int,X_249: $int,X_250: $int] :
( ( mem2(X_249,X_248,X_234)
& mem2(X_250,X_248,X_234) )
=> ( X_249 = X_250 ) ) ) ) ).
tff('Define:ctx:3',axiom,
( ! [X_44: $int] :
( mem0(X_44,g_s5_5)
<=> ( ( X_44 = g_s6_6 )
| ( X_44 = g_s7_7 )
| ( X_44 = g_s8_8 )
| ( X_44 = g_s9_9 )
| ( X_44 = g_s10_10 ) ) )
& ( g_s6_6 != g_s7_7 )
& ( g_s7_7 != g_s8_8 )
& ( g_s8_8 != g_s9_9 )
& ( g_s9_9 != g_s10_10 ) ) ).
tff('Define:ctx:30',axiom,
! [X_251: $int] :
( mem0(X_251,g_s95_95)
<=> ( $greatereq(X_251,min_int)
& $lesseq(X_251,max_int) ) ) ).
tff('Define:ctx:31',axiom,
! [X_252: $int] :
( mem0(X_252,g_s96_96)
<=> ( $greatereq(X_252,0)
& $lesseq(X_252,max_int) ) ) ).
tff('Define:ctx:32',axiom,
! [X_253: $int] :
( mem0(X_253,g_s97_97)
<=> ( $greater(X_253,0)
& $lesseq(X_253,max_int) ) ) ).
tff('Define:ctx:33',axiom,
! [X_254: $int] :
( mem0(X_254,g_s97_97)
=> mem0(X_254,g_s96_96) ) ).
tff('Define:ctx:34',axiom,
! [X_255: $int] :
( mem0(X_255,g_s96_96)
=> mem0(X_255,g_s95_95) ) ).
tff('Define:ctx:35',axiom,
mem0(g_s98_98,g_s95_95) ).
tff('Define:ctx:36',axiom,
mem0(g_s98_98,g_s96_96) ).
tff('Define:ctx:37',axiom,
~ mem0(g_s98_98,g_s97_97) ).
tff('Define:ctx:38',axiom,
mem0(g_s99_99,g_s95_95) ).
tff('Define:ctx:39',axiom,
~ mem0(g_s99_99,g_s96_96) ).
tff('Define:ctx:4',axiom,
( ! [X_45: $int] :
( mem0(X_45,g_s11_11)
<=> ( ( X_45 = g_s12_12 )
| ( X_45 = g_s13_13 )
| ( X_45 = g_s14_14 )
| ( X_45 = g_s15_15 ) ) )
& ( g_s12_12 != g_s13_13 )
& ( g_s13_13 != g_s14_14 )
& ( g_s14_14 != g_s15_15 ) ) ).
tff('Define:ctx:40',axiom,
! [X_256: $int] :
( mem0(X_256,g_s100_100)
<=> ( $greatereq(X_256,min_int)
& $lesseq(X_256,max_int) ) ) ).
tff('Define:ctx:41',axiom,
! [X_257: $int] :
( mem0(X_257,g_s101_101)
=> mem0(X_257,g_s0_0) ) ).
tff('Define:ctx:42',axiom,
mem0(g_s102_102,g_s0_0) ).
tff('Define:ctx:43',axiom,
mem0(g_s102_102,g_s101_101) ).
tff('Define:ctx:44',axiom,
mem0(g_s103_103,g_s0_0) ).
tff('Define:ctx:45',axiom,
~ mem0(g_s103_103,g_s101_101) ).
tff('Define:ctx:46',axiom,
( ! [X_258: $int,X_259: $int] :
( mem2(X_259,X_258,g_s104_104)
=> ( $greatereq(X_259,0)
& $lesseq(X_259,max_int)
& mem0(X_258,g_s0_0) ) )
& ! [X_260: $int,X_261: $int,X_262: $int] :
( ( mem2(X_260,X_261,g_s104_104)
& mem2(X_260,X_262,g_s104_104) )
=> ( X_261 = X_262 ) ) ) ).
tff('Define:ctx:47',axiom,
? [X_263: $int] :
( ? [X_264: set_2] :
( ! [X_265: $int,X_266: $int] :
( mem2(X_266,X_265,X_264)
<=> mem2(X_266,X_265,g_s104_104) )
& ! [X_267: $int,X_268: $int,X_269: $int] :
( ( mem2(X_267,X_268,X_264)
& mem2(X_267,X_269,X_264) )
=> ( X_268 = X_269 ) )
& ! [X_270: $int] :
( ( $greatereq(X_270,1)
& $lesseq(X_270,X_263) )
<=> ? [X_271: $int] : mem2(X_270,X_271,X_264) )
& ! [X_272: $int] :
( ? [X_273: $int] : mem2(X_273,X_272,X_264)
=> mem0(X_272,g_s101_101) ) )
& ! [X_274: $int] :
( mem0(X_274,g_s101_101)
=> ? [X_275: $int] : mem2(X_275,X_274,g_s104_104) )
& ! [X_276: $int,X_277: $int,X_278: $int] :
( ( mem2(X_277,X_276,g_s104_104)
& mem2(X_278,X_276,g_s104_104) )
=> ( X_277 = X_278 ) ) ) ).
tff('Define:ctx:48',axiom,
? [X_279: set_2] :
( ? [X_280: set_2] :
( ! [X_281: $int,X_282: $int] :
( mem2(X_282,X_281,X_280)
<=> mem2(X_282,X_281,X_279) )
& ! [X_283: $int,X_284: $int,X_285: $int] :
( ( mem2(X_283,X_284,X_280)
& mem2(X_283,X_285,X_280) )
=> ( X_284 = X_285 ) )
& ! [X_286: $int] :
( mem0(X_286,g_s101_101)
<=> ? [X_287: $int] : mem2(X_286,X_287,X_280) )
& ! [X_288: $int] :
( ? [X_289: $int] : mem2(X_289,X_288,X_280)
=> ( $greatereq(X_288,1)
& $lesseq(X_288,g_s105_105) ) ) )
& ! [X_290: $int] :
( ( $greatereq(X_290,1)
& $lesseq(X_290,g_s105_105) )
=> ? [X_291: $int] : mem2(X_291,X_290,X_279) )
& ! [X_292: $int,X_293: $int,X_294: $int] :
( ( mem2(X_293,X_292,X_279)
& mem2(X_294,X_292,X_279) )
=> ( X_293 = X_294 ) ) ) ).
tff('Define:ctx:49',axiom,
! [X_295: $int] :
( mem0(X_295,g_s106_106)
=> mem0(X_295,g_s1_1) ) ).
tff('Define:ctx:5',axiom,
( ! [X_46: $int] :
( mem0(X_46,g_s16_16)
<=> ( ( X_46 = g_s17_17 )
| ( X_46 = g_s18_18 )
| ( X_46 = g_s19_19 ) ) )
& ( g_s17_17 != g_s18_18 )
& ( g_s18_18 != g_s19_19 ) ) ).
tff('Define:ctx:50',axiom,
mem0(g_s107_107,g_s1_1) ).
tff('Define:ctx:51',axiom,
mem0(g_s107_107,g_s106_106) ).
tff('Define:ctx:52',axiom,
mem0(g_s108_108,g_s1_1) ).
tff('Define:ctx:53',axiom,
~ mem0(g_s108_108,g_s106_106) ).
tff('Define:ctx:54',axiom,
( ! [X_296: $int,X_297: $int] :
( mem2(X_297,X_296,g_s109_109)
=> ( $greatereq(X_297,0)
& $lesseq(X_297,max_int)
& mem0(X_296,g_s1_1) ) )
& ! [X_298: $int,X_299: $int,X_300: $int] :
( ( mem2(X_298,X_299,g_s109_109)
& mem2(X_298,X_300,g_s109_109) )
=> ( X_299 = X_300 ) ) ) ).
tff('Define:ctx:55',axiom,
? [X_301: $int] :
( ? [X_302: set_2] :
( ! [X_303: $int,X_304: $int] :
( mem2(X_304,X_303,X_302)
<=> mem2(X_304,X_303,g_s109_109) )
& ! [X_305: $int,X_306: $int,X_307: $int] :
( ( mem2(X_305,X_306,X_302)
& mem2(X_305,X_307,X_302) )
=> ( X_306 = X_307 ) )
& ! [X_308: $int] :
( ( $greatereq(X_308,1)
& $lesseq(X_308,X_301) )
<=> ? [X_309: $int] : mem2(X_308,X_309,X_302) )
& ! [X_310: $int] :
( ? [X_311: $int] : mem2(X_311,X_310,X_302)
=> mem0(X_310,g_s106_106) ) )
& ! [X_312: $int] :
( mem0(X_312,g_s106_106)
=> ? [X_313: $int] : mem2(X_313,X_312,g_s109_109) )
& ! [X_314: $int,X_315: $int,X_316: $int] :
( ( mem2(X_315,X_314,g_s109_109)
& mem2(X_316,X_314,g_s109_109) )
=> ( X_315 = X_316 ) ) ) ).
tff('Define:ctx:56',axiom,
? [X_317: set_2] :
( ? [X_318: set_2] :
( ! [X_319: $int,X_320: $int] :
( mem2(X_320,X_319,X_318)
<=> mem2(X_320,X_319,X_317) )
& ! [X_321: $int,X_322: $int,X_323: $int] :
( ( mem2(X_321,X_322,X_318)
& mem2(X_321,X_323,X_318) )
=> ( X_322 = X_323 ) )
& ! [X_324: $int] :
( mem0(X_324,g_s106_106)
<=> ? [X_325: $int] : mem2(X_324,X_325,X_318) )
& ! [X_326: $int] :
( ? [X_327: $int] : mem2(X_327,X_326,X_318)
=> ( $greatereq(X_326,1)
& $lesseq(X_326,g_s110_110) ) ) )
& ! [X_328: $int] :
( ( $greatereq(X_328,1)
& $lesseq(X_328,g_s110_110) )
=> ? [X_329: $int] : mem2(X_329,X_328,X_317) )
& ! [X_330: $int,X_331: $int,X_332: $int] :
( ( mem2(X_331,X_330,X_317)
& mem2(X_332,X_330,X_317) )
=> ( X_331 = X_332 ) ) ) ).
tff('Define:ctx:57',axiom,
( ! [X_333: $int,X_334: $int,X_335: $int] :
( mem3(X_335,X_334,X_333,g_s111_111)
=> ( mem0(X_335,g_s100_100)
& mem0(X_334,g_s100_100)
& mem0(X_333,g_s100_100) ) )
& ! [X_336: $int,X_337: $int,X_338: $int,X_339: $int] :
( ( mem3(X_337,X_336,X_338,g_s111_111)
& mem3(X_337,X_336,X_339,g_s111_111) )
=> ( X_338 = X_339 ) ) ) ).
tff('Define:ctx:58',axiom,
! [X_340: $int] :
( mem0(X_340,g_s112_112)
=> mem0(X_340,g_s100_100) ) ).
tff('Define:ctx:59',axiom,
? [X_341: set_3] :
( ! [X_342: $int,X_343: $int,X_344: $int] :
( mem3(X_344,X_343,X_342,X_341)
<=> mem3(X_344,X_343,X_342,g_s113_113) )
& ! [X_345: $int,X_346: $int,X_347: $int,X_348: $int] :
( ( mem3(X_346,X_345,X_347,X_341)
& mem3(X_346,X_345,X_348,X_341) )
=> ( X_347 = X_348 ) )
& ! [X_349: $int,X_350: $int] :
( ( mem0(X_350,g_s96_96)
& mem0(X_349,g_s96_96) )
<=> ? [X_351: $int] : mem3(X_350,X_349,X_351,X_341) )
& ! [X_352: $int] :
( ? [X_353: $int,X_354: $int] : mem3(X_354,X_353,X_352,X_341)
=> mem0(X_352,g_s100_100) ) ) ).
tff('Define:ctx:6',axiom,
( ! [X_47: $int] :
( mem0(X_47,g_s20_20)
<=> ( ( X_47 = g_s21_21 )
| ( X_47 = g_s22_22 )
| ( X_47 = g_s23_23 ) ) )
& ( g_s21_21 != g_s22_22 )
& ( g_s22_22 != g_s23_23 ) ) ).
tff('Define:ctx:60',axiom,
( ! [X_355: $int,X_356: $int,X_357: $int] :
( mem3(X_357,X_356,X_355,g_s114_114)
=> ( mem0(X_357,g_s96_96)
& mem0(X_356,g_s100_100)
& mem0(X_355,g_s96_96) ) )
& ! [X_358: $int,X_359: $int,X_360: $int,X_361: $int] :
( ( mem3(X_359,X_358,X_360,g_s114_114)
& mem3(X_359,X_358,X_361,g_s114_114) )
=> ( X_360 = X_361 ) ) ) ).
tff('Define:ctx:61',axiom,
? [X_362: set_3] :
( ! [X_363: $int,X_364: $int,X_365: $int] :
( mem3(X_365,X_364,X_363,X_362)
<=> mem3(X_365,X_364,X_363,g_s115_115) )
& ! [X_366: $int,X_367: $int,X_368: $int,X_369: $int] :
( ( mem3(X_367,X_366,X_368,X_362)
& mem3(X_367,X_366,X_369,X_362) )
=> ( X_368 = X_369 ) )
& ! [X_370: $int,X_371: $int] :
( ( mem0(X_371,g_s96_96)
& mem0(X_370,g_s100_100) )
<=> ? [X_372: $int] : mem3(X_371,X_370,X_372,X_362) )
& ! [X_373: $int] :
( ? [X_374: $int,X_375: $int] : mem3(X_375,X_374,X_373,X_362)
=> mem0(X_373,g_s96_96) ) ) ).
tff('Define:ctx:62',axiom,
? [X_376: set_4] :
( ! [X_377: set_0,X_378: $int,X_379: $int] :
( mem4(X_379,X_378,X_377,X_376)
<=> mem4(X_379,X_378,X_377,g_s116_116) )
& ! [X_380: $int,X_381: $int,X_382: set_0,X_383: set_0] :
( ( mem4(X_381,X_380,X_382,X_376)
& mem4(X_381,X_380,X_383,X_376) )
=> ! [X_384: $int] :
( mem0(X_384,X_382)
<=> mem0(X_384,X_383) ) )
& ! [X_385: $int,X_386: $int] :
( ( mem0(X_386,g_s96_96)
& mem0(X_385,g_s100_100) )
<=> ? [X_387: set_0] : mem4(X_386,X_385,X_387,X_376) )
& ! [X_388: set_0] :
( ? [X_389: $int,X_390: $int] : mem4(X_390,X_389,X_388,X_376)
=> ! [X_391: $int] :
( mem0(X_391,X_388)
=> mem0(X_391,g_s96_96) ) ) ) ).
tff('Define:ctx:63',axiom,
? [X_392: set_4] :
( ! [X_393: set_0,X_394: $int,X_395: $int] :
( mem4(X_395,X_394,X_393,X_392)
<=> mem4(X_395,X_394,X_393,g_s117_117) )
& ! [X_396: $int,X_397: $int,X_398: set_0,X_399: set_0] :
( ( mem4(X_397,X_396,X_398,X_392)
& mem4(X_397,X_396,X_399,X_392) )
=> ! [X_400: $int] :
( mem0(X_400,X_398)
<=> mem0(X_400,X_399) ) )
& ! [X_401: $int,X_402: $int] :
( ( mem0(X_402,g_s96_96)
& mem0(X_401,g_s96_96) )
<=> ? [X_403: set_0] : mem4(X_402,X_401,X_403,X_392) )
& ! [X_404: set_0] :
( ? [X_405: $int,X_406: $int] : mem4(X_406,X_405,X_404,X_392)
=> ! [X_407: $int] :
( mem0(X_407,X_404)
=> mem0(X_407,g_s96_96) ) ) ) ).
tff('Define:ctx:64',axiom,
? [X_408: set_4] :
( ! [X_409: set_0,X_410: $int,X_411: $int] :
( mem4(X_411,X_410,X_409,X_408)
<=> mem4(X_411,X_410,X_409,g_s118_118) )
& ! [X_412: $int,X_413: $int,X_414: set_0,X_415: set_0] :
( ( mem4(X_413,X_412,X_414,X_408)
& mem4(X_413,X_412,X_415,X_408) )
=> ! [X_416: $int] :
( mem0(X_416,X_414)
<=> mem0(X_416,X_415) ) )
& ! [X_417: $int,X_418: $int] :
( ( mem0(X_418,g_s96_96)
& mem0(X_417,g_s96_96) )
<=> ? [X_419: set_0] : mem4(X_418,X_417,X_419,X_408) )
& ! [X_420: set_0] :
( ? [X_421: $int,X_422: $int] : mem4(X_422,X_421,X_420,X_408)
=> ! [X_423: $int] :
( mem0(X_423,X_420)
=> mem0(X_423,g_s96_96) ) ) ) ).
tff('Define:ctx:65',axiom,
? [X_424: set_4] :
( ! [X_425: set_0,X_426: $int,X_427: $int] :
( mem4(X_427,X_426,X_425,X_424)
<=> mem4(X_427,X_426,X_425,g_s119_119) )
& ! [X_428: $int,X_429: $int,X_430: set_0,X_431: set_0] :
( ( mem4(X_429,X_428,X_430,X_424)
& mem4(X_429,X_428,X_431,X_424) )
=> ! [X_432: $int] :
( mem0(X_432,X_430)
<=> mem0(X_432,X_431) ) )
& ! [X_433: $int,X_434: $int] :
( ( mem0(X_434,g_s96_96)
& mem0(X_433,g_s96_96) )
<=> ? [X_435: set_0] : mem4(X_434,X_433,X_435,X_424) )
& ! [X_436: set_0] :
( ? [X_437: $int,X_438: $int] : mem4(X_438,X_437,X_436,X_424)
=> ! [X_439: $int] :
( mem0(X_439,X_436)
=> mem0(X_439,g_s96_96) ) ) ) ).
tff('Define:ctx:66',axiom,
? [X_440: set_4] :
( ! [X_441: set_0,X_442: $int,X_443: $int] :
( mem4(X_443,X_442,X_441,X_440)
<=> mem4(X_443,X_442,X_441,g_s120_120) )
& ! [X_444: $int,X_445: $int,X_446: set_0,X_447: set_0] :
( ( mem4(X_445,X_444,X_446,X_440)
& mem4(X_445,X_444,X_447,X_440) )
=> ! [X_448: $int] :
( mem0(X_448,X_446)
<=> mem0(X_448,X_447) ) )
& ! [X_449: $int,X_450: $int] :
( ( mem0(X_450,g_s96_96)
& mem0(X_449,g_s96_96) )
<=> ? [X_451: set_0] : mem4(X_450,X_449,X_451,X_440) )
& ! [X_452: set_0] :
( ? [X_453: $int,X_454: $int] : mem4(X_454,X_453,X_452,X_440)
=> ! [X_455: $int] :
( mem0(X_455,X_452)
=> mem0(X_455,g_s96_96) ) ) ) ).
tff('Define:ctx:67',axiom,
! [X_456: $int,X_457: $int] :
( mem2(X_457,X_456,g_s121_121)
=> ( mem0(X_457,g_s96_96)
& mem0(X_456,g_s96_96) ) ) ).
tff('Define:ctx:68',axiom,
! [X_458: $int,X_459: $int] :
( mem2(X_459,X_458,g_s122_122)
=> ( mem0(X_459,g_s96_96)
& mem0(X_458,g_s96_96) ) ) ).
tff('Define:ctx:69',axiom,
! [X_460: $int,X_461: $int,X_462: $int] :
( mem3(X_462,X_461,X_460,g_s123_123)
=> ( mem0(X_462,g_s96_96)
& mem0(X_461,g_s100_100)
& mem0(X_460,g_s96_96) ) ) ).
tff('Define:ctx:7',axiom,
( ! [X_48: $int] :
( mem0(X_48,g_s24_24)
<=> ( ( X_48 = g_s25_25 )
| ( X_48 = g_s26_26 )
| ( X_48 = g_s27_27 ) ) )
& ( g_s25_25 != g_s26_26 )
& ( g_s26_26 != g_s27_27 ) ) ).
tff('Define:ctx:70',axiom,
! [X_463: $int,X_464: $int,X_465: $int] :
( mem3(X_465,X_464,X_463,g_s124_124)
=> ( mem0(X_465,g_s96_96)
& mem0(X_464,g_s100_100)
& mem0(X_463,g_s96_96) ) ) ).
tff('Define:ctx:71',axiom,
! [X_466: $int,X_467: $int,X_468: $int] :
( mem3(X_468,X_467,X_466,g_s125_125)
=> ( mem0(X_468,g_s96_96)
& mem0(X_467,g_s100_100)
& mem0(X_466,g_s96_96) ) ) ).
tff('Define:ctx:72',axiom,
! [X_469: $int,X_470: $int,X_471: $int] :
( mem3(X_471,X_470,X_469,g_s126_126)
=> ( mem0(X_471,g_s96_96)
& mem0(X_470,g_s100_100)
& mem0(X_469,g_s96_96) ) ) ).
tff('Define:ctx:73',axiom,
! [X_472: $int,X_473: $int] :
( mem2(X_473,X_472,g_s127_127)
=> ( mem0(X_473,g_s96_96)
& mem0(X_472,g_s96_96) ) ) ).
tff('Define:ctx:74',axiom,
! [X_474: $int,X_475: $int] :
( mem2(X_475,X_474,g_s128_128)
=> ( mem0(X_475,g_s96_96)
& mem0(X_474,g_s96_96) ) ) ).
tff('Define:ctx:75',axiom,
! [X_476: $int,X_477: $int,X_478: $int] :
( mem3(X_478,X_477,X_476,g_s129_129)
=> ( mem0(X_478,g_s96_96)
& mem0(X_477,g_s100_100)
& mem0(X_476,g_s96_96) ) ) ).
tff('Define:ctx:76',axiom,
! [X_479: $int,X_480: $int,X_481: $int] :
( mem3(X_481,X_480,X_479,g_s130_130)
=> ( mem0(X_481,g_s96_96)
& mem0(X_480,g_s100_100)
& mem0(X_479,g_s96_96) ) ) ).
tff('Define:ctx:77',axiom,
! [X_482: $int,X_483: $int,X_484: $int] :
( mem3(X_484,X_483,X_482,g_s131_131)
=> ( mem0(X_484,g_s96_96)
& mem0(X_483,g_s100_100)
& mem0(X_482,g_s96_96) ) ) ).
tff('Define:ctx:78',axiom,
! [X_485: $int,X_486: $int,X_487: $int] :
( mem3(X_487,X_486,X_485,g_s132_132)
=> ( mem0(X_487,g_s96_96)
& mem0(X_486,g_s100_100)
& mem0(X_485,g_s96_96) ) ) ).
tff('Define:ctx:79',axiom,
? [X_488: set_3] :
( ! [X_489: $int,X_490: $int,X_491: $int] :
( mem3(X_491,X_490,X_489,X_488)
<=> mem3(X_491,X_490,X_489,g_s133_133) )
& ! [X_492: $int,X_493: $int,X_494: $int,X_495: $int] :
( ( mem3(X_493,X_492,X_494,X_488)
& mem3(X_493,X_492,X_495,X_488) )
=> ( X_494 = X_495 ) )
& ! [X_496: $int,X_497: $int] :
( ( mem0(X_497,g_s96_96)
& mem0(X_496,g_s96_96) )
<=> ? [X_498: $int] : mem3(X_497,X_496,X_498,X_488) )
& ! [X_499: $int] :
( ? [X_500: $int,X_501: $int] : mem3(X_501,X_500,X_499,X_488)
=> mem0(X_499,g_s96_96) ) ) ).
tff('Define:ctx:8',axiom,
( ! [X_49: $int] :
( mem0(X_49,g_s28_28)
<=> ( ( X_49 = g_s29_29 )
| ( X_49 = g_s30_30 )
| ( X_49 = g_s31_31 )
| ( X_49 = g_s32_32 ) ) )
& ( g_s29_29 != g_s30_30 )
& ( g_s30_30 != g_s31_31 )
& ( g_s31_31 != g_s32_32 ) ) ).
tff('Define:ctx:80',axiom,
? [X_502: set_3] :
( ! [X_503: $int,X_504: $int,X_505: $int] :
( mem3(X_505,X_504,X_503,X_502)
<=> mem3(X_505,X_504,X_503,g_s134_134) )
& ! [X_506: $int,X_507: $int,X_508: $int,X_509: $int] :
( ( mem3(X_507,X_506,X_508,X_502)
& mem3(X_507,X_506,X_509,X_502) )
=> ( X_508 = X_509 ) )
& ! [X_510: $int,X_511: $int] :
( ( mem0(X_511,g_s96_96)
& mem0(X_510,g_s96_96) )
<=> ? [X_512: $int] : mem3(X_511,X_510,X_512,X_502) )
& ! [X_513: $int] :
( ? [X_514: $int,X_515: $int] : mem3(X_515,X_514,X_513,X_502)
=> mem0(X_513,g_s96_96) ) ) ).
tff('Define:ctx:81',axiom,
! [X_516: $int,X_517: $int] :
( ? [X_518: $int] : mem3(X_517,X_516,X_518,g_s114_114)
<=> ( mem0(X_517,g_s96_96)
& $greatereq(X_516,0)
& $lesseq(X_516,max_int) ) ) ).
tff('Define:ctx:82',axiom,
! [X_519: $int,X_520: $int] :
( ? [X_521: $int] : mem3(X_520,X_519,X_521,g_s111_111)
<=> ( mem0(X_520,g_s100_100)
& mem0(X_519,g_s100_100)
& $greatereq(X_519,0) ) ) ).
tff('Define:ctx:83',axiom,
! [X_522: $int] :
( mem0(X_522,g_s137_135)
=> mem0(X_522,g_s85_85) ) ).
tff('Define:ctx:84',axiom,
mem0(g_s138_136,g_s85_85) ).
tff('Define:ctx:85',axiom,
~ mem0(g_s138_136,g_s137_135) ).
tff('Define:ctx:86',axiom,
( ! [X_523: $int,X_524: $int] :
( mem2(X_524,X_523,g_s139_137)
=> ( $greatereq(X_524,0)
& $lesseq(X_524,max_int)
& mem0(X_523,g_s85_85) ) )
& ! [X_525: $int,X_526: $int,X_527: $int] :
( ( mem2(X_525,X_526,g_s139_137)
& mem2(X_525,X_527,g_s139_137) )
=> ( X_526 = X_527 ) ) ) ).
tff('Define:ctx:87',axiom,
? [X_528: $int] :
( ? [X_529: set_2] :
( ! [X_530: $int,X_531: $int] :
( mem2(X_531,X_530,X_529)
<=> mem2(X_531,X_530,g_s139_137) )
& ! [X_532: $int,X_533: $int,X_534: $int] :
( ( mem2(X_532,X_533,X_529)
& mem2(X_532,X_534,X_529) )
=> ( X_533 = X_534 ) )
& ! [X_535: $int] :
( ( $greatereq(X_535,1)
& $lesseq(X_535,X_528) )
<=> ? [X_536: $int] : mem2(X_535,X_536,X_529) )
& ! [X_537: $int] :
( ? [X_538: $int] : mem2(X_538,X_537,X_529)
=> mem0(X_537,g_s137_135) ) )
& ! [X_539: $int] :
( mem0(X_539,g_s137_135)
=> ? [X_540: $int] : mem2(X_540,X_539,g_s139_137) )
& ! [X_541: $int,X_542: $int,X_543: $int] :
( ( mem2(X_542,X_541,g_s139_137)
& mem2(X_543,X_541,g_s139_137) )
=> ( X_542 = X_543 ) ) ) ).
tff('Define:ctx:88',axiom,
! [X_544: $int,X_545: $int] :
( ( ? [X_546: set_2] :
( ? [X_547: set_2] :
( ! [X_548: $int,X_549: $int] :
( mem2(X_549,X_548,X_547)
<=> mem2(X_549,X_548,X_546) )
& ! [X_550: $int,X_551: $int,X_552: $int] :
( ( mem2(X_550,X_551,X_547)
& mem2(X_550,X_552,X_547) )
=> ( X_551 = X_552 ) )
& ! [X_553: $int] :
( mem0(X_553,g_s137_135)
<=> ? [X_554: $int] : mem2(X_553,X_554,X_547) )
& ! [X_555: $int] :
( ? [X_556: $int] : mem2(X_556,X_555,X_547)
=> ( $greatereq(X_555,1)
& $lesseq(X_555,X_544) ) ) )
& ! [X_557: $int] :
( ( $greatereq(X_557,1)
& $lesseq(X_557,X_544) )
=> ? [X_558: $int] : mem2(X_558,X_557,X_546) )
& ! [X_559: $int,X_560: $int,X_561: $int] :
( ( mem2(X_560,X_559,X_546)
& mem2(X_561,X_559,X_546) )
=> ( X_560 = X_561 ) ) )
& ? [X_562: set_2] :
( ? [X_563: set_2] :
( ! [X_564: $int,X_565: $int] :
( mem2(X_565,X_564,X_563)
<=> mem2(X_565,X_564,X_562) )
& ! [X_566: $int,X_567: $int,X_568: $int] :
( ( mem2(X_566,X_567,X_563)
& mem2(X_566,X_568,X_563) )
=> ( X_567 = X_568 ) )
& ! [X_569: $int] :
( mem0(X_569,g_s137_135)
<=> ? [X_570: $int] : mem2(X_569,X_570,X_563) )
& ! [X_571: $int] :
( ? [X_572: $int] : mem2(X_572,X_571,X_563)
=> ( $greatereq(X_571,1)
& $lesseq(X_571,X_545) ) ) )
& ! [X_573: $int] :
( ( $greatereq(X_573,1)
& $lesseq(X_573,X_545) )
=> ? [X_574: $int] : mem2(X_574,X_573,X_562) )
& ! [X_575: $int,X_576: $int,X_577: $int] :
( ( mem2(X_576,X_575,X_562)
& mem2(X_577,X_575,X_562) )
=> ( X_576 = X_577 ) ) ) )
=> ( $greatereq(X_544,0)
& $lesseq(X_545,max_int) ) ) ).
tff('Define:ctx:89',axiom,
! [X_578: $int] :
( mem0(X_578,g_s140_138)
=> mem0(X_578,g_s86_86) ) ).
tff('Define:ctx:9',axiom,
( ! [X_50: $int] :
( mem0(X_50,g_s33_33)
<=> ( ( X_50 = g_s34_34 )
| ( X_50 = g_s35_35 )
| ( X_50 = g_s36_36 )
| ( X_50 = g_s37_37 )
| ( X_50 = g_s38_38 )
| ( X_50 = g_s39_39 )
| ( X_50 = g_s40_40 )
| ( X_50 = g_s41_41 ) ) )
& ( g_s34_34 != g_s35_35 )
& ( g_s35_35 != g_s36_36 )
& ( g_s36_36 != g_s37_37 )
& ( g_s37_37 != g_s38_38 )
& ( g_s38_38 != g_s39_39 )
& ( g_s39_39 != g_s40_40 )
& ( g_s40_40 != g_s41_41 ) ) ).
tff('Define:ctx:90',axiom,
mem0(g_s141_139,g_s86_86) ).
tff('Define:ctx:91',axiom,
~ mem0(g_s141_139,g_s140_138) ).
tff('Define:ctx:92',axiom,
( ! [X_579: $int,X_580: $int] :
( mem2(X_580,X_579,g_s142_140)
=> ( $greatereq(X_580,0)
& $lesseq(X_580,max_int)
& mem0(X_579,g_s86_86) ) )
& ! [X_581: $int,X_582: $int,X_583: $int] :
( ( mem2(X_581,X_582,g_s142_140)
& mem2(X_581,X_583,g_s142_140) )
=> ( X_582 = X_583 ) ) ) ).
tff('Define:ctx:93',axiom,
? [X_584: $int] :
( ? [X_585: set_2] :
( ! [X_586: $int,X_587: $int] :
( mem2(X_587,X_586,X_585)
<=> mem2(X_587,X_586,g_s142_140) )
& ! [X_588: $int,X_589: $int,X_590: $int] :
( ( mem2(X_588,X_589,X_585)
& mem2(X_588,X_590,X_585) )
=> ( X_589 = X_590 ) )
& ! [X_591: $int] :
( ( $greatereq(X_591,1)
& $lesseq(X_591,X_584) )
<=> ? [X_592: $int] : mem2(X_591,X_592,X_585) )
& ! [X_593: $int] :
( ? [X_594: $int] : mem2(X_594,X_593,X_585)
=> mem0(X_593,g_s140_138) ) )
& ! [X_595: $int] :
( mem0(X_595,g_s140_138)
=> ? [X_596: $int] : mem2(X_596,X_595,g_s142_140) )
& ! [X_597: $int,X_598: $int,X_599: $int] :
( ( mem2(X_598,X_597,g_s142_140)
& mem2(X_599,X_597,g_s142_140) )
=> ( X_598 = X_599 ) ) ) ).
tff('Define:ctx:94',axiom,
! [X_600: $int] :
( mem0(X_600,g_s143_141)
=> mem0(X_600,g_s87_87) ) ).
tff('Define:ctx:95',axiom,
mem0(g_s144_142,g_s87_87) ).
tff('Define:ctx:96',axiom,
~ mem0(g_s144_142,g_s143_141) ).
tff('Define:ctx:97',axiom,
( ! [X_601: $int,X_602: $int] :
( mem2(X_602,X_601,g_s145_143)
=> ( $greatereq(X_602,0)
& $lesseq(X_602,max_int)
& mem0(X_601,g_s87_87) ) )
& ! [X_603: $int,X_604: $int,X_605: $int] :
( ( mem2(X_603,X_604,g_s145_143)
& mem2(X_603,X_605,g_s145_143) )
=> ( X_604 = X_605 ) ) ) ).
tff('Define:ctx:98',axiom,
? [X_606: $int] :
( ? [X_607: set_2] :
( ! [X_608: $int,X_609: $int] :
( mem2(X_609,X_608,X_607)
<=> mem2(X_609,X_608,g_s145_143) )
& ! [X_610: $int,X_611: $int,X_612: $int] :
( ( mem2(X_610,X_611,X_607)
& mem2(X_610,X_612,X_607) )
=> ( X_611 = X_612 ) )
& ! [X_613: $int] :
( ( $greatereq(X_613,1)
& $lesseq(X_613,X_606) )
<=> ? [X_614: $int] : mem2(X_613,X_614,X_607) )
& ! [X_615: $int] :
( ? [X_616: $int] : mem2(X_616,X_615,X_607)
=> mem0(X_615,g_s143_141) ) )
& ! [X_617: $int] :
( mem0(X_617,g_s143_141)
=> ? [X_618: $int] : mem2(X_618,X_617,g_s145_143) )
& ! [X_619: $int,X_620: $int,X_621: $int] :
( ( mem2(X_620,X_619,g_s145_143)
& mem2(X_621,X_619,g_s145_143) )
=> ( X_620 = X_621 ) ) ) ).
tff('Define:ctx:99',axiom,
! [X_622: $int] :
( mem0(X_622,g_s146_144)
=> mem0(X_622,g_s88_88) ) ).
tff('Define:inv:0',axiom,
! [X_1293: $int,X_1294: $int] :
( mem2(X_1294,X_1293,g_s271_267)
<=> mem2(X_1294,X_1293,g_s271_1_278) ) ).
tff('Define:inv:1',axiom,
! [X_1295: $int,X_1296: $int] :
( mem2(X_1296,X_1295,g_s272_268)
<=> mem2(X_1296,X_1295,g_s272_1_279) ) ).
tff('Define:inv:10',axiom,
! [X_1311: $int] :
( mem0(X_1311,g_s281_277)
<=> mem0(X_1311,g_s281_1_288) ) ).
tff('Define:inv:11',axiom,
? [X_1312: set_2] :
( ! [X_1313: $int,X_1314: $int] :
( mem2(X_1314,X_1313,X_1312)
<=> mem2(X_1314,X_1313,g_s271_1_278) )
& ! [X_1315: $int,X_1316: $int,X_1317: $int] :
( ( mem2(X_1315,X_1316,X_1312)
& mem2(X_1315,X_1317,X_1312) )
=> ( X_1316 = X_1317 ) )
& ! [X_1318: $int] :
( mem0(X_1318,g_s163_161)
<=> ? [X_1319: $int] : mem2(X_1318,X_1319,X_1312) )
& ! [X_1320: $int] :
( ? [X_1321: $int] : mem2(X_1321,X_1320,X_1312)
=> mem0(X_1320,g_s2_2) ) ) ).
tff('Define:inv:12',axiom,
( ! [X_1322: $int,X_1323: $int] :
( mem2(X_1323,X_1322,g_s272_1_279)
=> ( mem0(X_1323,g_s163_161)
& mem0(X_1322,g_s152_150) ) )
& ! [X_1324: $int,X_1325: $int,X_1326: $int] :
( ( mem2(X_1324,X_1325,g_s272_1_279)
& mem2(X_1324,X_1326,g_s272_1_279) )
=> ( X_1325 = X_1326 ) ) ) ).
tff('Define:inv:13',axiom,
! [X_1327: $int] :
( mem0(X_1327,g_s277_1_280)
=> mem0(X_1327,g_s163_161) ) ).
tff('Define:inv:14',axiom,
! [X_1328: $int] :
( mem0(X_1328,g_s278_1_281)
=> mem0(X_1328,g_s163_161) ) ).
tff('Define:inv:15',axiom,
! [X_1329: $int,X_1330: $int] :
( mem2(X_1330,X_1329,g_s279_1_282)
=> ( mem0(X_1330,g_s163_161)
& mem0(X_1329,g_s137_135) ) ) ).
tff('Define:inv:16',axiom,
? [X_1331: set_5] :
( ! [X_1332: set_2,X_1333: $int] :
( mem5(X_1333,X_1332,X_1331)
<=> mem5(X_1333,X_1332,g_s274_1_283) )
& ! [X_1334: $int,X_1335: set_2,X_1336: set_2] :
( ( mem5(X_1334,X_1335,X_1331)
& mem5(X_1334,X_1336,X_1331) )
=> ! [X_1337: $int,X_1338: $int] :
( mem2(X_1338,X_1337,X_1335)
<=> mem2(X_1338,X_1337,X_1336) ) )
& ! [X_1339: $int] :
( mem0(X_1339,g_s163_161)
<=> ? [X_1340: set_2] : mem5(X_1339,X_1340,X_1331) )
& ! [X_1341: set_2] :
( ? [X_1342: $int] : mem5(X_1342,X_1341,X_1331)
=> ( ! [X_1343: $int,X_1344: $int] :
( mem2(X_1344,X_1343,X_1341)
=> ( mem0(X_1344,g_s137_135)
& mem0(X_1343,g_s155_153) ) )
& ! [X_1345: $int,X_1346: $int,X_1347: $int] :
( ( mem2(X_1345,X_1346,X_1341)
& mem2(X_1345,X_1347,X_1341) )
=> ( X_1346 = X_1347 ) ) ) ) ) ).
tff('Define:inv:17',axiom,
? [X_1348: set_5] :
( ! [X_1349: set_2,X_1350: $int] :
( mem5(X_1350,X_1349,X_1348)
<=> mem5(X_1350,X_1349,g_s273_1_284) )
& ! [X_1351: $int,X_1352: set_2,X_1353: set_2] :
( ( mem5(X_1351,X_1352,X_1348)
& mem5(X_1351,X_1353,X_1348) )
=> ! [X_1354: $int,X_1355: $int] :
( mem2(X_1355,X_1354,X_1352)
<=> mem2(X_1355,X_1354,X_1353) ) )
& ! [X_1356: $int] :
( mem0(X_1356,g_s163_161)
<=> ? [X_1357: set_2] : mem5(X_1356,X_1357,X_1348) )
& ! [X_1358: set_2] :
( ? [X_1359: $int] : mem5(X_1359,X_1358,X_1348)
=> ( ! [X_1360: $int,X_1361: $int] :
( mem2(X_1361,X_1360,X_1358)
=> ( mem0(X_1361,g_s137_135)
& mem0(X_1360,g_s143_141) ) )
& ! [X_1362: $int,X_1363: $int,X_1364: $int] :
( ( mem2(X_1362,X_1363,X_1358)
& mem2(X_1362,X_1364,X_1358) )
=> ( X_1363 = X_1364 ) ) ) ) ) ).
tff('Define:inv:18',axiom,
? [X_1365: set_5] :
( ! [X_1366: set_2,X_1367: $int] :
( mem5(X_1367,X_1366,X_1365)
<=> mem5(X_1367,X_1366,g_s275_1_285) )
& ! [X_1368: $int,X_1369: set_2,X_1370: set_2] :
( ( mem5(X_1368,X_1369,X_1365)
& mem5(X_1368,X_1370,X_1365) )
=> ! [X_1371: $int,X_1372: $int] :
( mem2(X_1372,X_1371,X_1369)
<=> mem2(X_1372,X_1371,X_1370) ) )
& ! [X_1373: $int] :
( mem0(X_1373,g_s163_161)
<=> ? [X_1374: set_2] : mem5(X_1373,X_1374,X_1365) )
& ! [X_1375: set_2] :
( ? [X_1376: $int] : mem5(X_1376,X_1375,X_1365)
=> ( ! [X_1377: $int,X_1378: $int] :
( mem2(X_1378,X_1377,X_1375)
=> ( mem0(X_1378,g_s137_135)
& mem0(X_1377,g_s158_156) ) )
& ! [X_1379: $int,X_1380: $int,X_1381: $int] :
( ( mem2(X_1379,X_1380,X_1375)
& mem2(X_1379,X_1381,X_1375) )
=> ( X_1380 = X_1381 ) ) ) ) ) ).
tff('Define:inv:19',axiom,
? [X_1382: set_5] :
( ! [X_1383: set_2,X_1384: $int] :
( mem5(X_1384,X_1383,X_1382)
<=> mem5(X_1384,X_1383,g_s276_1_286) )
& ! [X_1385: $int,X_1386: set_2,X_1387: set_2] :
( ( mem5(X_1385,X_1386,X_1382)
& mem5(X_1385,X_1387,X_1382) )
=> ! [X_1388: $int,X_1389: $int] :
( mem2(X_1389,X_1388,X_1386)
<=> mem2(X_1389,X_1388,X_1387) ) )
& ! [X_1390: $int] :
( mem0(X_1390,g_s163_161)
<=> ? [X_1391: set_2] : mem5(X_1390,X_1391,X_1382) )
& ! [X_1392: set_2] :
( ? [X_1393: $int] : mem5(X_1393,X_1392,X_1382)
=> ( ! [X_1394: $int,X_1395: $int] :
( mem2(X_1395,X_1394,X_1392)
=> ( mem0(X_1395,g_s137_135)
& mem0(X_1394,g_s158_156) ) )
& ! [X_1396: $int,X_1397: $int,X_1398: $int] :
( ( mem2(X_1396,X_1397,X_1392)
& mem2(X_1396,X_1398,X_1392) )
=> ( X_1397 = X_1398 ) ) ) ) ) ).
tff('Define:inv:2',axiom,
! [X_1297: $int] :
( mem0(X_1297,g_s277_273)
<=> mem0(X_1297,g_s277_1_280) ) ).
tff('Define:inv:20',axiom,
( ! [X_1399: $int,X_1400: $int] :
( mem2(X_1400,X_1399,g_s280_1_287)
=> ( mem0(X_1400,g_s163_161)
& mem0(X_1399,g_s96_96) ) )
& ! [X_1401: $int,X_1402: $int,X_1403: $int] :
( ( mem2(X_1401,X_1402,g_s280_1_287)
& mem2(X_1401,X_1403,g_s280_1_287) )
=> ( X_1402 = X_1403 ) ) ) ).
tff('Define:inv:21',axiom,
! [X_1404: $int] :
( mem0(X_1404,g_s281_1_288)
=> mem0(X_1404,g_s163_161) ) ).
tff('Define:inv:3',axiom,
! [X_1298: $int] :
( mem0(X_1298,g_s278_274)
<=> mem0(X_1298,g_s278_1_281) ) ).
tff('Define:inv:4',axiom,
! [X_1299: $int,X_1300: $int] :
( mem2(X_1300,X_1299,g_s279_275)
<=> mem2(X_1300,X_1299,g_s279_1_282) ) ).
tff('Define:inv:5',axiom,
! [X_1301: set_2,X_1302: $int] :
( mem5(X_1302,X_1301,g_s274_270)
<=> mem5(X_1302,X_1301,g_s274_1_283) ) ).
tff('Define:inv:6',axiom,
! [X_1303: set_2,X_1304: $int] :
( mem5(X_1304,X_1303,g_s273_269)
<=> mem5(X_1304,X_1303,g_s273_1_284) ) ).
tff('Define:inv:7',axiom,
! [X_1305: set_2,X_1306: $int] :
( mem5(X_1306,X_1305,g_s275_271)
<=> mem5(X_1306,X_1305,g_s275_1_285) ) ).
tff('Define:inv:8',axiom,
! [X_1307: set_2,X_1308: $int] :
( mem5(X_1308,X_1307,g_s276_272)
<=> mem5(X_1308,X_1307,g_s276_1_286) ) ).
tff('Define:inv:9',axiom,
! [X_1309: $int,X_1310: $int] :
( mem2(X_1310,X_1309,g_s280_276)
<=> mem2(X_1310,X_1309,g_s280_1_287) ) ).
tff('Define:seext:0',axiom,
! [L_s248: $int] :
( ( mem0(L_s248,g_s106_106)
& ~ ! [X_924: set_2] :
( ! [X_925: $int,X_926: $int] :
( mem2(X_926,X_925,X_924)
<=> $false )
=> mem5(L_s248,X_924,g_s249_246) ) )
=> ? [X_927: set_2] : mem5(L_s248,X_927,g_s250_247) ) ).
tff('Define:seext:1',axiom,
$true ).
tff('Define:seext:10',axiom,
? [X_1003: set_2] :
( ! [X_1004: $int,X_1005: $int] :
( mem2(X_1005,X_1004,X_1003)
<=> mem2(X_1005,X_1004,g_s255_250) )
& ! [X_1006: $int,X_1007: $int,X_1008: $int] :
( ( mem2(X_1006,X_1007,X_1003)
& mem2(X_1006,X_1008,X_1003) )
=> ( X_1007 = X_1008 ) )
& ! [X_1009: $int] :
( mem0(X_1009,g_s163_161)
<=> ? [X_1010: $int] : mem2(X_1009,X_1010,X_1003) )
& ! [X_1011: $int] :
( ? [X_1012: $int] : mem2(X_1012,X_1011,X_1003)
=> mem0(X_1011,g_s2_2) ) ) ).
tff('Define:seext:11',axiom,
( ! [X_1013: $int,X_1014: $int] :
( mem2(X_1014,X_1013,g_s256_251)
=> ( mem0(X_1014,g_s163_161)
& mem0(X_1013,g_s152_150) ) )
& ! [X_1015: $int,X_1016: $int,X_1017: $int] :
( ( mem2(X_1015,X_1016,g_s256_251)
& mem2(X_1015,X_1017,g_s256_251) )
=> ( X_1016 = X_1017 ) ) ) ).
tff('Define:seext:12',axiom,
! [X_1018: $int] :
( mem0(X_1018,g_s263_258)
=> mem0(X_1018,g_s163_161) ) ).
tff('Define:seext:13',axiom,
! [X_1019: $int] :
( mem0(X_1019,g_s264_259)
=> mem0(X_1019,g_s163_161) ) ).
tff('Define:seext:14',axiom,
! [X_1020: $int,X_1021: $int] :
( mem2(X_1021,X_1020,g_s265_260)
=> ( mem0(X_1021,g_s163_161)
& mem0(X_1020,g_s137_135) ) ) ).
tff('Define:seext:15',axiom,
? [X_1022: set_5] :
( ! [X_1023: set_2,X_1024: $int] :
( mem5(X_1024,X_1023,X_1022)
<=> mem5(X_1024,X_1023,g_s258_253) )
& ! [X_1025: $int,X_1026: set_2,X_1027: set_2] :
( ( mem5(X_1025,X_1026,X_1022)
& mem5(X_1025,X_1027,X_1022) )
=> ! [X_1028: $int,X_1029: $int] :
( mem2(X_1029,X_1028,X_1026)
<=> mem2(X_1029,X_1028,X_1027) ) )
& ! [X_1030: $int] :
( mem0(X_1030,g_s163_161)
<=> ? [X_1031: set_2] : mem5(X_1030,X_1031,X_1022) )
& ! [X_1032: set_2] :
( ? [X_1033: $int] : mem5(X_1033,X_1032,X_1022)
=> ( ! [X_1034: $int,X_1035: $int] :
( mem2(X_1035,X_1034,X_1032)
=> ( mem0(X_1035,g_s137_135)
& mem0(X_1034,g_s155_153) ) )
& ! [X_1036: $int,X_1037: $int,X_1038: $int] :
( ( mem2(X_1036,X_1037,X_1032)
& mem2(X_1036,X_1038,X_1032) )
=> ( X_1037 = X_1038 ) ) ) ) ) ).
tff('Define:seext:16',axiom,
? [X_1039: set_5] :
( ! [X_1040: set_2,X_1041: $int] :
( mem5(X_1041,X_1040,X_1039)
<=> mem5(X_1041,X_1040,g_s257_252) )
& ! [X_1042: $int,X_1043: set_2,X_1044: set_2] :
( ( mem5(X_1042,X_1043,X_1039)
& mem5(X_1042,X_1044,X_1039) )
=> ! [X_1045: $int,X_1046: $int] :
( mem2(X_1046,X_1045,X_1043)
<=> mem2(X_1046,X_1045,X_1044) ) )
& ! [X_1047: $int] :
( mem0(X_1047,g_s163_161)
<=> ? [X_1048: set_2] : mem5(X_1047,X_1048,X_1039) )
& ! [X_1049: set_2] :
( ? [X_1050: $int] : mem5(X_1050,X_1049,X_1039)
=> ( ! [X_1051: $int,X_1052: $int] :
( mem2(X_1052,X_1051,X_1049)
=> ( mem0(X_1052,g_s137_135)
& mem0(X_1051,g_s143_141) ) )
& ! [X_1053: $int,X_1054: $int,X_1055: $int] :
( ( mem2(X_1053,X_1054,X_1049)
& mem2(X_1053,X_1055,X_1049) )
=> ( X_1054 = X_1055 ) ) ) ) ) ).
tff('Define:seext:17',axiom,
? [X_1056: set_5] :
( ! [X_1057: set_2,X_1058: $int] :
( mem5(X_1058,X_1057,X_1056)
<=> mem5(X_1058,X_1057,g_s259_254) )
& ! [X_1059: $int,X_1060: set_2,X_1061: set_2] :
( ( mem5(X_1059,X_1060,X_1056)
& mem5(X_1059,X_1061,X_1056) )
=> ! [X_1062: $int,X_1063: $int] :
( mem2(X_1063,X_1062,X_1060)
<=> mem2(X_1063,X_1062,X_1061) ) )
& ! [X_1064: $int] :
( mem0(X_1064,g_s163_161)
<=> ? [X_1065: set_2] : mem5(X_1064,X_1065,X_1056) )
& ! [X_1066: set_2] :
( ? [X_1067: $int] : mem5(X_1067,X_1066,X_1056)
=> ( ! [X_1068: $int,X_1069: $int] :
( mem2(X_1069,X_1068,X_1066)
=> ( mem0(X_1069,g_s137_135)
& mem0(X_1068,g_s158_156) ) )
& ! [X_1070: $int,X_1071: $int,X_1072: $int] :
( ( mem2(X_1070,X_1071,X_1066)
& mem2(X_1070,X_1072,X_1066) )
=> ( X_1071 = X_1072 ) ) ) ) ) ).
tff('Define:seext:18',axiom,
? [X_1073: set_5] :
( ! [X_1074: set_2,X_1075: $int] :
( mem5(X_1075,X_1074,X_1073)
<=> mem5(X_1075,X_1074,g_s260_255) )
& ! [X_1076: $int,X_1077: set_2,X_1078: set_2] :
( ( mem5(X_1076,X_1077,X_1073)
& mem5(X_1076,X_1078,X_1073) )
=> ! [X_1079: $int,X_1080: $int] :
( mem2(X_1080,X_1079,X_1077)
<=> mem2(X_1080,X_1079,X_1078) ) )
& ! [X_1081: $int] :
( mem0(X_1081,g_s163_161)
<=> ? [X_1082: set_2] : mem5(X_1081,X_1082,X_1073) )
& ! [X_1083: set_2] :
( ? [X_1084: $int] : mem5(X_1084,X_1083,X_1073)
=> ( ! [X_1085: $int,X_1086: $int] :
( mem2(X_1086,X_1085,X_1083)
=> ( mem0(X_1086,g_s137_135)
& mem0(X_1085,g_s158_156) ) )
& ! [X_1087: $int,X_1088: $int,X_1089: $int] :
( ( mem2(X_1087,X_1088,X_1083)
& mem2(X_1087,X_1089,X_1083) )
=> ( X_1088 = X_1089 ) ) ) ) ) ).
tff('Define:seext:19',axiom,
( ! [X_1090: $int,X_1091: $int] :
( mem2(X_1091,X_1090,g_s266_261)
=> ( mem0(X_1091,g_s163_161)
& mem0(X_1090,g_s96_96) ) )
& ! [X_1092: $int,X_1093: $int,X_1094: $int] :
( ( mem2(X_1092,X_1093,g_s266_261)
& mem2(X_1092,X_1094,g_s266_261) )
=> ( X_1093 = X_1094 ) ) ) ).
tff('Define:seext:2',axiom,
( ! [X_928: set_2,X_929: $int] :
( mem5(X_929,X_928,g_s252_248)
=> ( mem0(X_929,g_s106_106)
& ! [X_930: $int,X_931: $int] :
( mem2(X_931,X_930,X_928)
=> ( mem0(X_931,g_s96_96)
& mem0(X_930,g_s96_96) ) )
& ! [X_932: $int,X_933: $int,X_934: $int] :
( ( mem2(X_932,X_933,X_928)
& mem2(X_932,X_934,X_928) )
=> ( X_933 = X_934 ) ) ) )
& ! [X_935: $int,X_936: set_2,X_937: set_2] :
( ( mem5(X_935,X_936,g_s252_248)
& mem5(X_935,X_937,g_s252_248) )
=> ! [X_938: $int,X_939: $int] :
( mem2(X_939,X_938,X_936)
<=> mem2(X_939,X_938,X_937) ) ) ) ).
tff('Define:seext:20',axiom,
( ! [X_1095: $int,X_1096: $int] :
( mem2(X_1096,X_1095,g_s267_262)
=> ( mem0(X_1096,g_s163_161)
& mem0(X_1095,g_s96_96) ) )
& ! [X_1097: $int,X_1098: $int,X_1099: $int] :
( ( mem2(X_1097,X_1098,g_s267_262)
& mem2(X_1097,X_1099,g_s267_262) )
=> ( X_1098 = X_1099 ) ) ) ).
tff('Define:seext:21',axiom,
! [X_1100: $int] :
( mem0(X_1100,g_s268_263)
=> mem0(X_1100,g_s163_161) ) ).
tff('Define:seext:22',axiom,
! [X_1101: $int] :
( mem0(X_1101,g_s269_264)
=> mem0(X_1101,g_s163_161) ) ).
tff('Define:seext:23',axiom,
mem0(g_s270_265,g_s96_96) ).
tff('Define:seext:3',axiom,
( ! [X_940: $int,X_941: $int] :
( mem2(X_941,X_940,g_s253_249)
=> ( mem0(X_941,g_s106_106)
& mem0(X_940,g_s96_96) ) )
& ! [X_942: $int,X_943: $int,X_944: $int] :
( ( mem2(X_942,X_943,g_s253_249)
& mem2(X_942,X_944,g_s253_249) )
=> ( X_943 = X_944 ) ) ) ).
tff('Define:seext:4',axiom,
( ! [X_945: set_2,X_946: $int] :
( mem5(X_946,X_945,g_s250_247)
=> ( mem0(X_946,g_s106_106)
& ? [X_947: set_2] :
( ! [X_948: $int,X_949: $int] :
( mem2(X_949,X_948,X_947)
<=> mem2(X_949,X_948,X_945) )
& ! [X_950: $int,X_951: $int,X_952: $int] :
( ( mem2(X_950,X_951,X_947)
& mem2(X_950,X_952,X_947) )
=> ( X_951 = X_952 ) )
& ! [X_953: $int] :
( mem0(X_953,g_s96_96)
<=> ? [X_954: $int] : mem2(X_953,X_954,X_947) )
& ! [X_955: $int] :
( ? [X_956: $int] : mem2(X_956,X_955,X_947)
=> mem0(X_955,g_s96_96) ) ) ) )
& ! [X_957: $int,X_958: set_2,X_959: set_2] :
( ( mem5(X_957,X_958,g_s250_247)
& mem5(X_957,X_959,g_s250_247) )
=> ! [X_960: $int,X_961: $int] :
( mem2(X_961,X_960,X_958)
<=> mem2(X_961,X_960,X_959) ) ) ) ).
tff('Define:seext:5',axiom,
? [X_962: set_5] :
( ! [X_963: set_2,X_964: $int] :
( mem5(X_964,X_963,X_962)
<=> mem5(X_964,X_963,g_s249_246) )
& ! [X_965: $int,X_966: set_2,X_967: set_2] :
( ( mem5(X_965,X_966,X_962)
& mem5(X_965,X_967,X_962) )
=> ! [X_968: $int,X_969: $int] :
( mem2(X_969,X_968,X_966)
<=> mem2(X_969,X_968,X_967) ) )
& ! [X_970: $int] :
( mem0(X_970,g_s106_106)
<=> ? [X_971: set_2] : mem5(X_970,X_971,X_962) )
& ! [X_972: set_2] :
( ? [X_973: $int] : mem5(X_973,X_972,X_962)
=> ! [X_974: $int,X_975: $int] :
( mem2(X_975,X_974,X_972)
=> ( mem0(X_975,g_s96_96)
& mem0(X_974,g_s100_100) ) ) ) ) ).
tff('Define:seext:6',axiom,
! [L_s254: $int] :
( ( mem0(L_s254,g_s163_161)
& mem2(L_s254,g_s4_4,g_s255_250) )
=> ( ? [X_976: $int] : mem2(L_s254,X_976,g_s256_251)
& ! [X_977: $int] :
( ? [X_978: $int] :
! [X_979: set_2] :
( mem5(L_s254,X_979,g_s257_252)
=> mem2(X_977,X_978,X_979) )
<=> ? [X_980: $int] :
! [X_981: set_2] :
( mem5(L_s254,X_981,g_s258_253)
=> mem2(X_977,X_980,X_981) ) )
& ! [X_982: $int] :
( ? [X_983: $int] :
! [X_984: set_2] :
( mem5(L_s254,X_984,g_s259_254)
=> mem2(X_982,X_983,X_984) )
<=> ? [X_985: $int] :
! [X_986: set_2] :
( mem5(L_s254,X_986,g_s258_253)
=> mem2(X_982,X_985,X_986) ) )
& ! [X_987: $int] :
( ? [X_988: $int] :
! [X_989: set_2] :
( mem5(L_s254,X_989,g_s260_255)
=> mem2(X_987,X_988,X_989) )
<=> ? [X_990: $int] :
! [X_991: set_2] :
( mem5(L_s254,X_991,g_s258_253)
=> mem2(X_987,X_990,X_991) ) ) ) ) ).
tff('Define:seext:7',axiom,
! [L_s254: $int] :
( ? [X_992: $int] : mem2(L_s254,X_992,g_s256_251)
=> mem2(L_s254,g_s4_4,g_s255_250) ) ).
tff('Define:seext:8',axiom,
( ! [X_993: $int,X_994: $int] :
( mem2(X_994,X_993,g_s261_256)
=> ( mem0(X_994,g_s163_161)
& mem0(X_993,g_s223_220) ) )
& ! [X_995: $int,X_996: $int,X_997: $int] :
( ( mem2(X_995,X_996,g_s261_256)
& mem2(X_995,X_997,g_s261_256) )
=> ( X_996 = X_997 ) ) ) ).
tff('Define:seext:9',axiom,
( ! [X_998: $int,X_999: $int] :
( mem2(X_999,X_998,g_s262_257)
=> ( mem0(X_999,g_s163_161)
& mem0(X_998,g_s223_220) ) )
& ! [X_1000: $int,X_1001: $int,X_1002: $int] :
( ( mem2(X_1000,X_1001,g_s262_257)
& mem2(X_1000,X_1002,g_s262_257) )
=> ( X_1001 = X_1002 ) ) ) ).
%Global hypotheses
tff(gh_0_def,hypothesis,
mem0(g_s285_289,g_s91_91) ).
tff(gh_1_def,hypothesis,
mem0(g_s285_289,g_s163_161) ).
tff(gh_2_def,hypothesis,
mem0(g_s289_293,g_s85_85) ).
tff(gh_3_def,hypothesis,
mem0(g_s289_293,g_s137_135) ).
tff(gh_4_def,hypothesis,
? [X_2315: $int] :
! [X_2316: set_2] :
( mem5(g_s285_289,X_2316,g_s274_270)
=> mem2(g_s289_293,X_2315,X_2316) ) ).
tff(gh_5_def,hypothesis,
g_s295_294 = g_s295_1_295 ).
tff(gh_6_def,hypothesis,
mem0(g_s285_289,g_s91_91) ).
tff(gh_7_def,hypothesis,
mem0(g_s285_289,g_s163_161) ).
tff(gh_8_def,hypothesis,
mem0(g_s289_293,g_s85_85) ).
tff(gh_9_def,hypothesis,
mem0(g_s289_293,g_s137_135) ).
tff(gh_10_def,hypothesis,
? [X_2317: $int] :
! [X_2318: set_2] :
( mem5(g_s285_289,X_2318,g_s274_1_283)
=> mem2(g_s289_293,X_2317,X_2318) ) ).
%----Local hypotheses
tff('Local_Hyp:0',hypothesis,
mem0(g_s295_2_296,g_s154_152) ).
tff('Local_Hyp:1',hypothesis,
! [X_2319: set_2] :
( mem5(g_s285_289,X_2319,g_s274_1_283)
=> mem2(g_s289_293,g_s295_2_296,X_2319) ) ).
%----Goal
tff('Goal',conjecture,
( ! [X_2321: set_2,X_2322: $int] :
( mem5(X_2322,X_2321,g_s274_270)
=> ( ? [X_2323: set_2] : mem5(X_2322,X_2323,g_s274_270)
& ? [X_2324: $int] : mem5(X_2324,X_2321,g_s274_270) ) )
& ! [X_2325: $int,X_2326: set_2,X_2327: set_2] :
( ( mem5(X_2325,X_2326,g_s274_270)
& mem5(X_2325,X_2327,g_s274_270) )
=> ! [X_2328: $int,X_2329: $int] :
( mem2(X_2329,X_2328,X_2326)
<=> mem2(X_2329,X_2328,X_2327) ) ) ) ).
%------------------------------------------------------------------------------