TPTP Problem File: SWC529_1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWC529_1 : TPTP v9.0.0. Released v9.0.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 1 832 Group s155 Tag s154
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0012-00103-1-832.tptp [Deh24]
% Status : Theorem
% Rating : 0.00 v9.0.0
% Syntax : Number of formulae : 441 ( 144 unt; 203 typ; 0 def)
% Number of atoms : 618 ( 101 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 399 ( 17 ~; 9 |; 203 &)
% ( 79 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 12 ( 0 fml; 12 var)
% Number arithmetic : 686 ( 96 atm; 108 fun; 97 num; 385 var)
% Number of types : 15 ( 12 usr; 2 ari)
% Number of type conns : 63 ( 29 >; 34 *; 0 +; 0 <<)
% Number of predicates : 25 ( 18 usr; 8 prp; 0-5 aty)
% Number of functors : 189 ( 173 usr; 166 con; 0-2 aty)
% Number of variables : 432 ( 342 !; 90 ?; 432 :)
% SPC : TX0_THM_EQU_ARI
% Comments : Autogenerated by PPTRANS-TPTP - github.com/CLEARSY/pptranspog
%------------------------------------------------------------------------------
tff(set_0_type,type,
set_0: $tType ).
tff(mem0_type,type,
mem0: ( $int * set_0 ) > $o ).
tff(set_1_type,type,
set_1: $tType ).
tff(mem1_type,type,
mem1: ( $real * set_1 ) > $o ).
tff(b_division_type,type,
divB: ( $int * $int ) > $int ).
tff(b_division_def_1,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(0,Y) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_2,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(0,Y) )
=> ( divB(X,Y) = $uminus($quotient_f($uminus(X),Y)) ) ) ).
tff(b_division_def_3,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_4,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f($uminus(X),$uminus(Y)) ) ) ).
tff(exp_type,type,
exp: ( $int * $int ) > $int ).
tff(exp_def_1,axiom,
! [X: $int] : ( exp(X,0) = 1 ) ).
tff(exp_def_2,axiom,
! [X: $int,Y: $int] :
( $greatereq(Y,1)
=> ( exp(X,Y) = $sum(X,exp(X,$difference(Y,1))) ) ) ).
tff(rexp_type,type,
rexp: ( $real * $int ) > $real ).
tff(rexp_def_1,axiom,
! [X: $real] :
( ( X != 0.0 )
=> ( rexp(X,0) = 1.0 ) ) ).
tff(rexp_def_2,axiom,
! [X: $real,Y: $int] :
( $greatereq(Y,1)
=> ( rexp(X,Y) = $sum(X,rexp(X,$difference(Y,1))) ) ) ).
tff(isum_type,type,
isum: set_0 > $int ).
tff(isum_def_1,axiom,
! [S: set_0] :
( ! [X: $int] : ~ mem0(X,S)
=> ( isum(S) = 0 ) ) ).
tff(isum_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( isum(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( mem0(X,S1)
=> mem0(X,S2) ) )
=> ( isum(S2) = $sum(N,E) ) ) ).
tff(rsum_type,type,
rsum: set_1 > $real ).
tff(rsum_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rsum(S) = 0.0 ) ) ).
tff(rsum_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rsum(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( mem1(X,S1)
=> mem1(X,S2) ) )
=> ( rsum(S2) = $sum(N,E) ) ) ).
tff(iprod_type,type,
iprod: set_0 > $int ).
tff(iprod_def_1,axiom,
! [S: set_0,X: $int] :
( ~ mem0(X,S)
=> ( iprod(S) = 1 ) ) ).
tff(iprod_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( iprod(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( ( ( X = E )
| mem0(X,S1) )
=> mem0(X,S2) ) )
=> ( isum(S2) = $product(N,E) ) ) ).
tff(rprod_type,type,
rprod: set_1 > $real ).
tff(rprod_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rprod(S) = 1.0 ) ) ).
tff(rprod_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rprod(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( ( ( X = E )
| mem1(X,S1) )
=> mem1(X,S2) ) )
=> ( rprod(S2) = $sum(N,E) ) ) ).
tff(min_int_type,type,
min_int: $int ).
tff(max_int_type,type,
max_int: $int ).
tff(min_int_axiom,axiom,
min_int = $uminus(2147483648) ).
tff(max_int_axiom,axiom,
max_int = 2147483647 ).
%--------------------------------------------------------------------------
%----Global declarations
tff(g_s0_0_type,type,
g_s0_0: set_0 ).
tff(g_s100_99_type,type,
g_s100_99: set_3 ).
tff(g_s105_100_type,type,
g_s105_100: set_5 ).
tff(g_s106_101_type,type,
g_s106_101: set_4 ).
tff(g_s107_102_type,type,
g_s107_102: $int ).
tff(g_s108_103_type,type,
g_s108_103: $int ).
tff(g_s109_104_type,type,
g_s109_104: $int ).
tff(g_s10_10_type,type,
g_s10_10: $int ).
tff(g_s110_105_type,type,
g_s110_105: $int ).
tff(g_s111_106_type,type,
g_s111_106: $int ).
tff(g_s112_107_type,type,
g_s112_107: $int ).
tff(g_s113_108_type,type,
g_s113_108: $int ).
tff(g_s114_109_type,type,
g_s114_109: $int ).
tff(g_s115_110_type,type,
g_s115_110: $int ).
tff(g_s116_111_type,type,
g_s116_111: $int ).
tff(g_s117_112_type,type,
g_s117_112: $int ).
tff(g_s118_113_type,type,
g_s118_113: $int ).
tff(g_s119_114_type,type,
g_s119_114: set_4 ).
tff(g_s11_11_type,type,
g_s11_11: set_0 ).
tff(g_s120_115_type,type,
g_s120_115: $int ).
tff(g_s121_116_type,type,
g_s121_116: $int ).
tff(g_s122_117_type,type,
g_s122_117: $int ).
tff(g_s123_118_type,type,
g_s123_118: $int ).
tff(g_s124_119_type,type,
g_s124_119: $int ).
tff(g_s125_120_type,type,
g_s125_120: $int ).
tff(g_s126_121_type,type,
g_s126_121: $int ).
tff(g_s127_122_type,type,
g_s127_122: set_4 ).
tff(g_s128_123_type,type,
g_s128_123: $int ).
tff(g_s129_124_type,type,
g_s129_124: $int ).
tff(g_s12_12_type,type,
g_s12_12: set_2 ).
tff(g_s130_125_type,type,
g_s130_125: $int ).
tff(g_s131_126_type,type,
g_s131_126: $int ).
tff(g_s132_127_type,type,
g_s132_127: $int ).
tff(g_s133_128_type,type,
g_s133_128: $int ).
tff(g_s134_129_type,type,
g_s134_129: $int ).
tff(g_s135_130_type,type,
g_s135_130: $int ).
tff(g_s136_131_type,type,
g_s136_131: $int ).
tff(g_s137_132_type,type,
g_s137_132: $int ).
tff(g_s138_133_type,type,
g_s138_133: $int ).
tff(g_s139_134_type,type,
g_s139_134: $int ).
tff(g_s13_13_type,type,
g_s13_13: $int ).
tff(g_s140_135_type,type,
g_s140_135: $int ).
tff(g_s141_136_type,type,
g_s141_136: $int ).
tff(g_s145_137_type,type,
g_s145_137: $int ).
tff(g_s145_1_139_type,type,
g_s145_1_139: $int ).
tff(g_s146_138_type,type,
g_s146_138: set_0 ).
tff(g_s146_1_140_type,type,
g_s146_1_140: set_0 ).
tff(g_s147_141_type,type,
g_s147_141: $o ).
tff(g_s147_1_142_type,type,
g_s147_1_142: $o ).
tff(g_s148_143_type,type,
g_s148_143: $o ).
tff(g_s148_1_144_type,type,
g_s148_1_144: $o ).
tff(g_s149_145_type,type,
g_s149_145: $o ).
tff(g_s149_1_146_type,type,
g_s149_1_146: $o ).
tff(g_s14_14_type,type,
g_s14_14: $int ).
tff(g_s150_1_147_type,type,
g_s150_1_147: $int ).
tff(g_s151_1_148_type,type,
g_s151_1_148: $int ).
tff(g_s152_1_149_type,type,
g_s152_1_149: $int ).
tff(g_s15_15_type,type,
g_s15_15: $int ).
tff(g_s16_16_type,type,
g_s16_16: $int ).
tff(g_s17_17_type,type,
g_s17_17: $int ).
tff(g_s18_18_type,type,
g_s18_18: $int ).
tff(g_s19_19_type,type,
g_s19_19: $int ).
tff(g_s1_1_type,type,
g_s1_1: $int ).
tff(g_s20_20_type,type,
g_s20_20: $int ).
tff(g_s21_21_type,type,
g_s21_21: $int ).
tff(g_s22_22_type,type,
g_s22_22: $int ).
tff(g_s23_23_type,type,
g_s23_23: $int ).
tff(g_s24_24_type,type,
g_s24_24: $int ).
tff(g_s25_25_type,type,
g_s25_25: $int ).
tff(g_s26_26_type,type,
g_s26_26: $int ).
tff(g_s27_27_type,type,
g_s27_27: $int ).
tff(g_s28_28_type,type,
g_s28_28: $int ).
tff(g_s29_29_type,type,
g_s29_29: $int ).
tff(g_s2_2_type,type,
g_s2_2: $int ).
tff(g_s30_30_type,type,
g_s30_30: $int ).
tff(g_s31_31_type,type,
g_s31_31: $int ).
tff(g_s32_32_type,type,
g_s32_32: $int ).
tff(g_s33_33_type,type,
g_s33_33: $int ).
tff(g_s34_34_type,type,
g_s34_34: $int ).
tff(g_s35_35_type,type,
g_s35_35: $int ).
tff(g_s36_36_type,type,
g_s36_36: $int ).
tff(g_s37_37_type,type,
g_s37_37: $int ).
tff(g_s39_38_type,type,
g_s39_38: set_3 ).
tff(g_s3_4_type,type,
g_s3_4: $int ).
tff(g_s40_39_type,type,
g_s40_39: $int ).
tff(g_s41_40_type,type,
g_s41_40: $int ).
tff(g_s42_41_type,type,
g_s42_41: $int ).
tff(g_s43_42_type,type,
g_s43_42: $int ).
tff(g_s44_43_type,type,
g_s44_43: $int ).
tff(g_s45_44_type,type,
g_s45_44: $int ).
tff(g_s46_45_type,type,
g_s46_45: $int ).
tff(g_s47_46_type,type,
g_s47_46: $int ).
tff(g_s48_47_type,type,
g_s48_47: $int ).
tff(g_s49_48_type,type,
g_s49_48: $int ).
tff(g_s4_3_type,type,
g_s4_3: set_0 ).
tff(g_s50_49_type,type,
g_s50_49: $int ).
tff(g_s51_50_type,type,
g_s51_50: $int ).
tff(g_s52_51_type,type,
g_s52_51: $int ).
tff(g_s53_52_type,type,
g_s53_52: $int ).
tff(g_s54_53_type,type,
g_s54_53: $int ).
tff(g_s55_54_type,type,
g_s55_54: $int ).
tff(g_s56_55_type,type,
g_s56_55: $int ).
tff(g_s57_56_type,type,
g_s57_56: $int ).
tff(g_s58_57_type,type,
g_s58_57: $int ).
tff(g_s59_58_type,type,
g_s59_58: $int ).
tff(g_s5_6_type,type,
g_s5_6: $int ).
tff(g_s60_59_type,type,
g_s60_59: $int ).
tff(g_s61_60_type,type,
g_s61_60: $int ).
tff(g_s62_61_type,type,
g_s62_61: $int ).
tff(g_s63_62_type,type,
g_s63_62: $int ).
tff(g_s64_63_type,type,
g_s64_63: $int ).
tff(g_s65_64_type,type,
g_s65_64: $int ).
tff(g_s66_65_type,type,
g_s66_65: $int ).
tff(g_s67_66_type,type,
g_s67_66: $int ).
tff(g_s68_67_type,type,
g_s68_67: $int ).
tff(g_s69_68_type,type,
g_s69_68: $int ).
tff(g_s6_5_type,type,
g_s6_5: set_0 ).
tff(g_s70_69_type,type,
g_s70_69: $int ).
tff(g_s71_70_type,type,
g_s71_70: $int ).
tff(g_s72_71_type,type,
g_s72_71: $int ).
tff(g_s73_72_type,type,
g_s73_72: $int ).
tff(g_s74_73_type,type,
g_s74_73: $int ).
tff(g_s75_74_type,type,
g_s75_74: $int ).
tff(g_s76_75_type,type,
g_s76_75: $int ).
tff(g_s77_76_type,type,
g_s77_76: $int ).
tff(g_s78_77_type,type,
g_s78_77: $int ).
tff(g_s79_78_type,type,
g_s79_78: $int ).
tff(g_s7_8_type,type,
g_s7_8: $int ).
tff(g_s80_79_type,type,
g_s80_79: $int ).
tff(g_s81_80_type,type,
g_s81_80: $int ).
tff(g_s82_81_type,type,
g_s82_81: $int ).
tff(g_s83_82_type,type,
g_s83_82: set_4 ).
tff(g_s84_83_type,type,
g_s84_83: set_3 ).
tff(g_s85_84_type,type,
g_s85_84: set_4 ).
tff(g_s86_85_type,type,
g_s86_85: set_3 ).
tff(g_s87_86_type,type,
g_s87_86: set_3 ).
tff(g_s88_87_type,type,
g_s88_87: set_4 ).
tff(g_s89_88_type,type,
g_s89_88: set_3 ).
tff(g_s8_7_type,type,
g_s8_7: set_0 ).
tff(g_s90_89_type,type,
g_s90_89: set_3 ).
tff(g_s91_90_type,type,
g_s91_90: set_3 ).
tff(g_s92_91_type,type,
g_s92_91: set_3 ).
tff(g_s93_92_type,type,
g_s93_92: set_3 ).
tff(g_s94_93_type,type,
g_s94_93: set_3 ).
tff(g_s95_94_type,type,
g_s95_94: set_3 ).
tff(g_s96_95_type,type,
g_s96_95: set_3 ).
tff(g_s97_96_type,type,
g_s97_96: set_3 ).
tff(g_s98_97_type,type,
g_s98_97: set_3 ).
tff(g_s99_98_type,type,
g_s99_98: set_3 ).
tff(g_s9_9_type,type,
g_s9_9: $int ).
tff(mem2_type,type,
mem2: ( $o * $int * set_2 ) > $o ).
tff(mem3_type,type,
mem3: ( $int * $int * $int * set_3 ) > $o ).
tff(mem4_type,type,
mem4: ( $int * $int * set_4 ) > $o ).
tff(mem5_type,type,
mem5: ( $int * set_4 * $int * $int * 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: ( $o * $int ) > prod_0 ).
tff(prod_0_in,type,
prod_0_in: ( $o * $int * prod_0 ) > $o ).
tff(prod_1_type,type,
prod_1: $tType ).
tff(prod_1_empty,type,
prod_1_empty: prod_1 ).
tff(prod_1_insert,type,
prod_1: ( prod_2 * $int ) > prod_1 ).
tff(prod_1_in,type,
prod_1_in: ( prod_2 * $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: ( $int * $int ) > prod_2 ).
tff(prod_2_in,type,
prod_2_in: ( $int * $int * 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: ( prod_4 * $int ) > prod_3 ).
tff(prod_3_in,type,
prod_3_in: ( prod_4 * $int * prod_3 ) > $o ).
tff(prod_4_type,type,
prod_4: $tType ).
tff(prod_4_empty,type,
prod_4_empty: prod_4 ).
tff(prod_4_insert,type,
prod_4: ( prod_5 * $int ) > prod_4 ).
tff(prod_4_in,type,
prod_4_in: ( prod_5 * $int * prod_4 ) > $o ).
tff(prod_5_type,type,
prod_5: $tType ).
tff(prod_5_empty,type,
prod_5_empty: prod_5 ).
tff(prod_5_insert,type,
prod_5: ( $int * set_4 ) > prod_5 ).
tff(prod_5_in,type,
prod_5_in: ( $int * set_4 * prod_5 ) > $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,
$greatereq(g_s145_137,0) ).
tff('Define:abs:1',axiom,
! [X_374: $int] :
( mem0(X_374,g_s146_138)
=> ( $greatereq(X_374,0)
& $lesseq(X_374,g_s145_137) ) ) ).
tff('Define:abs:10',axiom,
$true ).
tff('Define:abs:2',axiom,
$true ).
tff('Define:abs:3',axiom,
$true ).
tff('Define:abs:4',axiom,
$true ).
tff('Define:abs:5',axiom,
! [X_375: $int] :
( mem0(X_375,g_s146_138)
<=> mem0(X_375,g_s146_138) ) ).
tff('Define:abs:6',axiom,
$greatereq(g_s145_137,0) ).
tff('Define:abs:7',axiom,
! [X_376: $int] :
( mem0(X_376,g_s146_138)
=> ( $greatereq(X_376,0)
& $lesseq(X_376,g_s145_137) ) ) ).
tff('Define:abs:8',axiom,
$true ).
tff('Define:abs:9',axiom,
$true ).
tff('Define:ctx:0',axiom,
( ! [X_5: $int] :
( mem0(X_5,g_s0_0)
<=> ( ( X_5 = g_s1_1 )
| ( X_5 = g_s2_2 ) ) )
& ( g_s1_1 != g_s2_2 ) ) ).
tff('Define:ctx:1',axiom,
mem0(g_s3_4,g_s4_3) ).
tff('Define:ctx:10',axiom,
( $greatereq(g_s10_10,0)
& $lesseq(g_s10_10,g_s7_8) ) ).
tff('Define:ctx:100',axiom,
mem0(g_s78_77,g_s4_3) ).
tff('Define:ctx:101',axiom,
mem0(g_s79_78,g_s4_3) ).
tff('Define:ctx:102',axiom,
mem0(g_s80_79,g_s4_3) ).
tff('Define:ctx:103',axiom,
mem0(g_s81_80,g_s4_3) ).
tff('Define:ctx:104',axiom,
mem0(g_s82_81,g_s4_3) ).
tff('Define:ctx:105',axiom,
! [X_10: $int] :
( mem0(X_10,g_s4_3)
<=> ( $greatereq(X_10,0)
& $lesseq(X_10,4294967295) ) ) ).
tff('Define:ctx:106',axiom,
! [X_11: $int] :
( mem0(X_11,g_s6_5)
<=> ( $greatereq(X_11,0)
& $lesseq(X_11,65535) ) ) ).
tff('Define:ctx:107',axiom,
! [X_12: $int] :
( mem0(X_12,g_s8_7)
<=> ( $greatereq(X_12,0)
& $lesseq(X_12,255) ) ) ).
tff('Define:ctx:108',axiom,
? [X_13: set_4] :
( ! [X_14: $int,X_15: $int] :
( mem4(X_15,X_14,X_13)
<=> mem4(X_15,X_14,g_s83_82) )
& ! [X_16: $int,X_17: $int,X_18: $int] :
( ( mem4(X_16,X_17,X_13)
& mem4(X_16,X_18,X_13) )
=> ( X_17 = X_18 ) )
& ! [X_19: $int] :
( mem0(X_19,g_s4_3)
<=> ? [X_20: $int] : mem4(X_19,X_20,X_13) )
& ! [X_21: $int] :
( ? [X_22: $int] : mem4(X_22,X_21,X_13)
=> mem0(X_21,g_s4_3) ) ) ).
tff('Define:ctx:109',axiom,
? [X_23: set_3] :
( ! [X_24: $int,X_25: $int,X_26: $int] :
( mem3(X_26,X_25,X_24,X_23)
<=> mem3(X_26,X_25,X_24,g_s39_38) )
& ! [X_27: $int,X_28: $int,X_29: $int,X_30: $int] :
( ( mem3(X_28,X_27,X_29,X_23)
& mem3(X_28,X_27,X_30,X_23) )
=> ( X_29 = X_30 ) )
& ! [X_31: $int,X_32: $int] :
( ( mem0(X_32,g_s4_3)
& mem0(X_31,g_s4_3) )
<=> ? [X_33: $int] : mem3(X_32,X_31,X_33,X_23) )
& ! [X_34: $int] :
( ? [X_35: $int,X_36: $int] : mem3(X_36,X_35,X_34,X_23)
=> mem0(X_34,g_s4_3) ) ) ).
tff('Define:ctx:11',axiom,
g_s9_9 != g_s10_10 ).
tff('Define:ctx:110',axiom,
? [X_37: set_3] :
( ! [X_38: $int,X_39: $int,X_40: $int] :
( mem3(X_40,X_39,X_38,X_37)
<=> mem3(X_40,X_39,X_38,g_s84_83) )
& ! [X_41: $int,X_42: $int,X_43: $int,X_44: $int] :
( ( mem3(X_42,X_41,X_43,X_37)
& mem3(X_42,X_41,X_44,X_37) )
=> ( X_43 = X_44 ) )
& ! [X_45: $int,X_46: $int] :
( ( mem0(X_46,g_s4_3)
& mem0(X_45,g_s4_3) )
<=> ? [X_47: $int] : mem3(X_46,X_45,X_47,X_37) )
& ! [X_48: $int] :
( ? [X_49: $int,X_50: $int] : mem3(X_50,X_49,X_48,X_37)
=> mem0(X_48,g_s4_3) ) ) ).
tff('Define:ctx:111',axiom,
? [X_51: set_4] :
( ! [X_52: $int,X_53: $int] :
( mem4(X_53,X_52,X_51)
<=> mem4(X_53,X_52,g_s85_84) )
& ! [X_54: $int,X_55: $int,X_56: $int] :
( ( mem4(X_54,X_55,X_51)
& mem4(X_54,X_56,X_51) )
=> ( X_55 = X_56 ) )
& ! [X_57: $int] :
( mem0(X_57,g_s6_5)
<=> ? [X_58: $int] : mem4(X_57,X_58,X_51) )
& ! [X_59: $int] :
( ? [X_60: $int] : mem4(X_60,X_59,X_51)
=> mem0(X_59,g_s6_5) ) ) ).
tff('Define:ctx:112',axiom,
? [X_61: set_3] :
( ! [X_62: $int,X_63: $int,X_64: $int] :
( mem3(X_64,X_63,X_62,X_61)
<=> mem3(X_64,X_63,X_62,g_s86_85) )
& ! [X_65: $int,X_66: $int,X_67: $int,X_68: $int] :
( ( mem3(X_66,X_65,X_67,X_61)
& mem3(X_66,X_65,X_68,X_61) )
=> ( X_67 = X_68 ) )
& ! [X_69: $int,X_70: $int] :
( ( mem0(X_70,g_s6_5)
& mem0(X_69,g_s6_5) )
<=> ? [X_71: $int] : mem3(X_70,X_69,X_71,X_61) )
& ! [X_72: $int] :
( ? [X_73: $int,X_74: $int] : mem3(X_74,X_73,X_72,X_61)
=> mem0(X_72,g_s6_5) ) ) ).
tff('Define:ctx:113',axiom,
? [X_75: set_3] :
( ! [X_76: $int,X_77: $int,X_78: $int] :
( mem3(X_78,X_77,X_76,X_75)
<=> mem3(X_78,X_77,X_76,g_s87_86) )
& ! [X_79: $int,X_80: $int,X_81: $int,X_82: $int] :
( ( mem3(X_80,X_79,X_81,X_75)
& mem3(X_80,X_79,X_82,X_75) )
=> ( X_81 = X_82 ) )
& ! [X_83: $int,X_84: $int] :
( ( mem0(X_84,g_s6_5)
& mem0(X_83,g_s6_5) )
<=> ? [X_85: $int] : mem3(X_84,X_83,X_85,X_75) )
& ! [X_86: $int] :
( ? [X_87: $int,X_88: $int] : mem3(X_88,X_87,X_86,X_75)
=> mem0(X_86,g_s6_5) ) ) ).
tff('Define:ctx:114',axiom,
? [X_89: set_4] :
( ! [X_90: $int,X_91: $int] :
( mem4(X_91,X_90,X_89)
<=> mem4(X_91,X_90,g_s88_87) )
& ! [X_92: $int,X_93: $int,X_94: $int] :
( ( mem4(X_92,X_93,X_89)
& mem4(X_92,X_94,X_89) )
=> ( X_93 = X_94 ) )
& ! [X_95: $int] :
( mem0(X_95,g_s8_7)
<=> ? [X_96: $int] : mem4(X_95,X_96,X_89) )
& ! [X_97: $int] :
( ? [X_98: $int] : mem4(X_98,X_97,X_89)
=> mem0(X_97,g_s8_7) ) ) ).
tff('Define:ctx:115',axiom,
? [X_99: set_3] :
( ! [X_100: $int,X_101: $int,X_102: $int] :
( mem3(X_102,X_101,X_100,X_99)
<=> mem3(X_102,X_101,X_100,g_s89_88) )
& ! [X_103: $int,X_104: $int,X_105: $int,X_106: $int] :
( ( mem3(X_104,X_103,X_105,X_99)
& mem3(X_104,X_103,X_106,X_99) )
=> ( X_105 = X_106 ) )
& ! [X_107: $int,X_108: $int] :
( ( mem0(X_108,g_s8_7)
& mem0(X_107,g_s8_7) )
<=> ? [X_109: $int] : mem3(X_108,X_107,X_109,X_99) )
& ! [X_110: $int] :
( ? [X_111: $int,X_112: $int] : mem3(X_112,X_111,X_110,X_99)
=> mem0(X_110,g_s8_7) ) ) ).
tff('Define:ctx:116',axiom,
? [X_113: set_3] :
( ! [X_114: $int,X_115: $int,X_116: $int] :
( mem3(X_116,X_115,X_114,X_113)
<=> mem3(X_116,X_115,X_114,g_s90_89) )
& ! [X_117: $int,X_118: $int,X_119: $int,X_120: $int] :
( ( mem3(X_118,X_117,X_119,X_113)
& mem3(X_118,X_117,X_120,X_113) )
=> ( X_119 = X_120 ) )
& ! [X_121: $int,X_122: $int] :
( ( mem0(X_122,g_s8_7)
& mem0(X_121,g_s8_7) )
<=> ? [X_123: $int] : mem3(X_122,X_121,X_123,X_113) )
& ! [X_124: $int] :
( ? [X_125: $int,X_126: $int] : mem3(X_126,X_125,X_124,X_113)
=> mem0(X_124,g_s8_7) ) ) ).
tff('Define:ctx:117',axiom,
? [X_127: set_3] :
( ! [X_128: $int,X_129: $int,X_130: $int] :
( mem3(X_130,X_129,X_128,X_127)
<=> mem3(X_130,X_129,X_128,g_s91_90) )
& ! [X_131: $int,X_132: $int,X_133: $int,X_134: $int] :
( ( mem3(X_132,X_131,X_133,X_127)
& mem3(X_132,X_131,X_134,X_127) )
=> ( X_133 = X_134 ) )
& ! [X_135: $int,X_136: $int] :
( ( mem0(X_136,g_s8_7)
& mem0(X_135,g_s8_7) )
<=> ? [X_137: $int] : mem3(X_136,X_135,X_137,X_127) )
& ! [X_138: $int] :
( ? [X_139: $int,X_140: $int] : mem3(X_140,X_139,X_138,X_127)
=> mem0(X_138,g_s8_7) ) ) ).
tff('Define:ctx:118',axiom,
? [X_141: set_3] :
( ! [X_142: $int,X_143: $int,X_144: $int] :
( mem3(X_144,X_143,X_142,X_141)
<=> mem3(X_144,X_143,X_142,g_s92_91) )
& ! [X_145: $int,X_146: $int,X_147: $int,X_148: $int] :
( ( mem3(X_146,X_145,X_147,X_141)
& mem3(X_146,X_145,X_148,X_141) )
=> ( X_147 = X_148 ) )
& ! [X_149: $int,X_150: $int] :
( ( mem0(X_150,g_s4_3)
& mem0(X_149,g_s4_3) )
<=> ? [X_151: $int] : mem3(X_150,X_149,X_151,X_141) )
& ! [X_152: $int] :
( ? [X_153: $int,X_154: $int] : mem3(X_154,X_153,X_152,X_141)
=> mem0(X_152,g_s4_3) ) ) ).
tff('Define:ctx:119',axiom,
? [X_155: set_3] :
( ! [X_156: $int,X_157: $int,X_158: $int] :
( mem3(X_158,X_157,X_156,X_155)
<=> mem3(X_158,X_157,X_156,g_s93_92) )
& ! [X_159: $int,X_160: $int,X_161: $int,X_162: $int] :
( ( mem3(X_160,X_159,X_161,X_155)
& mem3(X_160,X_159,X_162,X_155) )
=> ( X_161 = X_162 ) )
& ! [X_163: $int,X_164: $int] :
( ( mem0(X_164,g_s4_3)
& mem0(X_163,g_s4_3) )
<=> ? [X_165: $int] : mem3(X_164,X_163,X_165,X_155) )
& ! [X_166: $int] :
( ? [X_167: $int,X_168: $int] : mem3(X_168,X_167,X_166,X_155)
=> mem0(X_166,g_s4_3) ) ) ).
tff('Define:ctx:12',axiom,
! [X_6: $int] :
( mem0(X_6,g_s11_11)
<=> ( ( X_6 = g_s9_9 )
| ( X_6 = g_s10_10 ) ) ) ).
tff('Define:ctx:120',axiom,
? [X_169: set_3] :
( ! [X_170: $int,X_171: $int,X_172: $int] :
( mem3(X_172,X_171,X_170,X_169)
<=> mem3(X_172,X_171,X_170,g_s94_93) )
& ! [X_173: $int,X_174: $int,X_175: $int,X_176: $int] :
( ( mem3(X_174,X_173,X_175,X_169)
& mem3(X_174,X_173,X_176,X_169) )
=> ( X_175 = X_176 ) )
& ! [X_177: $int,X_178: $int] :
( ( mem0(X_178,g_s4_3)
& mem0(X_177,g_s4_3) )
<=> ? [X_179: $int] : mem3(X_178,X_177,X_179,X_169) )
& ! [X_180: $int] :
( ? [X_181: $int,X_182: $int] : mem3(X_182,X_181,X_180,X_169)
=> mem0(X_180,g_s4_3) ) ) ).
tff('Define:ctx:121',axiom,
? [X_183: set_3] :
( ! [X_184: $int,X_185: $int,X_186: $int] :
( mem3(X_186,X_185,X_184,X_183)
<=> mem3(X_186,X_185,X_184,g_s95_94) )
& ! [X_187: $int,X_188: $int,X_189: $int,X_190: $int] :
( ( mem3(X_188,X_187,X_189,X_183)
& mem3(X_188,X_187,X_190,X_183) )
=> ( X_189 = X_190 ) )
& ! [X_191: $int,X_192: $int] :
( ( mem0(X_192,g_s6_5)
& mem0(X_191,g_s6_5) )
<=> ? [X_193: $int] : mem3(X_192,X_191,X_193,X_183) )
& ! [X_194: $int] :
( ? [X_195: $int,X_196: $int] : mem3(X_196,X_195,X_194,X_183)
=> mem0(X_194,g_s6_5) ) ) ).
tff('Define:ctx:122',axiom,
? [X_197: set_3] :
( ! [X_198: $int,X_199: $int,X_200: $int] :
( mem3(X_200,X_199,X_198,X_197)
<=> mem3(X_200,X_199,X_198,g_s96_95) )
& ! [X_201: $int,X_202: $int,X_203: $int,X_204: $int] :
( ( mem3(X_202,X_201,X_203,X_197)
& mem3(X_202,X_201,X_204,X_197) )
=> ( X_203 = X_204 ) )
& ! [X_205: $int,X_206: $int] :
( ( mem0(X_206,g_s6_5)
& mem0(X_205,g_s6_5) )
<=> ? [X_207: $int] : mem3(X_206,X_205,X_207,X_197) )
& ! [X_208: $int] :
( ? [X_209: $int,X_210: $int] : mem3(X_210,X_209,X_208,X_197)
=> mem0(X_208,g_s6_5) ) ) ).
tff('Define:ctx:123',axiom,
? [X_211: set_3] :
( ! [X_212: $int,X_213: $int,X_214: $int] :
( mem3(X_214,X_213,X_212,X_211)
<=> mem3(X_214,X_213,X_212,g_s97_96) )
& ! [X_215: $int,X_216: $int,X_217: $int,X_218: $int] :
( ( mem3(X_216,X_215,X_217,X_211)
& mem3(X_216,X_215,X_218,X_211) )
=> ( X_217 = X_218 ) )
& ! [X_219: $int,X_220: $int] :
( ( mem0(X_220,g_s6_5)
& mem0(X_219,g_s6_5) )
<=> ? [X_221: $int] : mem3(X_220,X_219,X_221,X_211) )
& ! [X_222: $int] :
( ? [X_223: $int,X_224: $int] : mem3(X_224,X_223,X_222,X_211)
=> mem0(X_222,g_s6_5) ) ) ).
tff('Define:ctx:124',axiom,
? [X_225: set_3] :
( ! [X_226: $int,X_227: $int,X_228: $int] :
( mem3(X_228,X_227,X_226,X_225)
<=> mem3(X_228,X_227,X_226,g_s98_97) )
& ! [X_229: $int,X_230: $int,X_231: $int,X_232: $int] :
( ( mem3(X_230,X_229,X_231,X_225)
& mem3(X_230,X_229,X_232,X_225) )
=> ( X_231 = X_232 ) )
& ! [X_233: $int,X_234: $int] :
( ( mem0(X_234,g_s8_7)
& mem0(X_233,g_s8_7) )
<=> ? [X_235: $int] : mem3(X_234,X_233,X_235,X_225) )
& ! [X_236: $int] :
( ? [X_237: $int,X_238: $int] : mem3(X_238,X_237,X_236,X_225)
=> mem0(X_236,g_s8_7) ) ) ).
tff('Define:ctx:125',axiom,
? [X_239: set_3] :
( ! [X_240: $int,X_241: $int,X_242: $int] :
( mem3(X_242,X_241,X_240,X_239)
<=> mem3(X_242,X_241,X_240,g_s99_98) )
& ! [X_243: $int,X_244: $int,X_245: $int,X_246: $int] :
( ( mem3(X_244,X_243,X_245,X_239)
& mem3(X_244,X_243,X_246,X_239) )
=> ( X_245 = X_246 ) )
& ! [X_247: $int,X_248: $int] :
( ( mem0(X_248,g_s8_7)
& mem0(X_247,g_s8_7) )
<=> ? [X_249: $int] : mem3(X_248,X_247,X_249,X_239) )
& ! [X_250: $int] :
( ? [X_251: $int,X_252: $int] : mem3(X_252,X_251,X_250,X_239)
=> mem0(X_250,g_s8_7) ) ) ).
tff('Define:ctx:126',axiom,
? [X_253: set_3] :
( ! [X_254: $int,X_255: $int,X_256: $int] :
( mem3(X_256,X_255,X_254,X_253)
<=> mem3(X_256,X_255,X_254,g_s100_99) )
& ! [X_257: $int,X_258: $int,X_259: $int,X_260: $int] :
( ( mem3(X_258,X_257,X_259,X_253)
& mem3(X_258,X_257,X_260,X_253) )
=> ( X_259 = X_260 ) )
& ! [X_261: $int,X_262: $int] :
( ( mem0(X_262,g_s8_7)
& mem0(X_261,g_s8_7) )
<=> ? [X_263: $int] : mem3(X_262,X_261,X_263,X_253) )
& ! [X_264: $int] :
( ? [X_265: $int,X_266: $int] : mem3(X_266,X_265,X_264,X_253)
=> mem0(X_264,g_s8_7) ) ) ).
tff('Define:ctx:127',axiom,
! [X_267: $int,X_268: $int,X_269: $int] :
( mem3(X_269,X_268,X_267,g_s92_91)
<=> ( mem0(X_269,g_s4_3)
& mem0(X_268,g_s4_3)
& ( X_267 = $remainder_f($sum(X_269,X_268),$sum(g_s3_4,1)) ) ) ) ).
tff('Define:ctx:128',axiom,
! [X_270: $int,X_271: $int,X_272: $int] :
( mem3(X_272,X_271,X_270,g_s93_92)
<=> ( mem0(X_272,g_s4_3)
& mem0(X_271,g_s4_3)
& ( X_270 = $remainder_f($sum($sum($difference(X_272,X_271),g_s3_4),1),$sum(g_s3_4,1)) ) ) ) ).
tff('Define:ctx:129',axiom,
! [X_273: $int,X_274: $int,X_275: $int] :
( mem3(X_275,X_274,X_273,g_s94_93)
<=> ( mem0(X_275,g_s4_3)
& mem0(X_274,g_s4_3)
& ( X_273 = $remainder_f($product(X_275,X_274),$sum(g_s3_4,1)) ) ) ) ).
tff('Define:ctx:13',axiom,
! [X_7: $int,X_8: $o] :
( mem2((X_8),X_7,g_s12_12)
<=> ( ( ( (X_8)
<=> $true )
& ( X_7 = g_s9_9 ) )
| ( ( (X_8)
<=> $false )
& ( X_7 = g_s10_10 ) ) ) ) ).
tff('Define:ctx:130',axiom,
! [X_276: $int,X_277: $int,X_278: $int] :
( mem3(X_278,X_277,X_276,g_s95_94)
<=> ( mem0(X_278,g_s6_5)
& mem0(X_277,g_s6_5)
& ( X_276 = $remainder_f($sum(X_278,X_277),$sum(g_s5_6,1)) ) ) ) ).
tff('Define:ctx:131',axiom,
! [X_279: $int,X_280: $int,X_281: $int] :
( mem3(X_281,X_280,X_279,g_s96_95)
<=> ( mem0(X_281,g_s6_5)
& mem0(X_280,g_s6_5)
& ( X_279 = $remainder_f($sum($sum($difference(X_281,X_280),g_s5_6),1),$sum(g_s5_6,1)) ) ) ) ).
tff('Define:ctx:132',axiom,
! [X_282: $int,X_283: $int,X_284: $int] :
( mem3(X_284,X_283,X_282,g_s97_96)
<=> ( mem0(X_284,g_s6_5)
& mem0(X_283,g_s6_5)
& ( X_282 = $remainder_f($product(X_284,X_283),$sum(g_s5_6,1)) ) ) ) ).
tff('Define:ctx:133',axiom,
! [X_285: $int,X_286: $int,X_287: $int] :
( mem3(X_287,X_286,X_285,g_s98_97)
<=> ( mem0(X_287,g_s8_7)
& mem0(X_286,g_s8_7)
& ( X_285 = $remainder_f($sum(X_287,X_286),$sum(g_s7_8,1)) ) ) ) ).
tff('Define:ctx:134',axiom,
! [X_288: $int,X_289: $int,X_290: $int] :
( mem3(X_290,X_289,X_288,g_s99_98)
<=> ( mem0(X_290,g_s8_7)
& mem0(X_289,g_s8_7)
& ( X_288 = $remainder_f($sum($sum($difference(X_290,X_289),g_s7_8),1),$sum(g_s7_8,1)) ) ) ) ).
tff('Define:ctx:135',axiom,
! [X_291: $int,X_292: $int,X_293: $int] :
( mem3(X_293,X_292,X_291,g_s100_99)
<=> ( mem0(X_293,g_s8_7)
& mem0(X_292,g_s8_7)
& ( X_291 = $remainder_f($product(X_293,X_292),$sum(g_s7_8,1)) ) ) ) ).
tff('Define:ctx:136',axiom,
! [L_s38: $int] :
( mem0(L_s38,g_s4_3)
=> ! [X_294: $int] :
( ! [X_295: $int] :
( ( X_295 = 1023 )
=> mem3(L_s38,X_295,X_294,g_s39_38) )
=> $lesseq(X_294,1023) ) ) ).
tff('Define:ctx:137',axiom,
? [X_296: set_5] :
( ! [X_297: $int,X_298: $int,X_299: set_4,X_300: $int] :
( mem5(X_300,X_299,X_298,X_297,X_296)
<=> mem5(X_300,X_299,X_298,X_297,g_s105_100) )
& ! [X_301: $int,X_302: set_4,X_303: $int,X_304: $int,X_305: $int] :
( ( mem5(X_303,X_302,X_301,X_304,X_296)
& mem5(X_303,X_302,X_301,X_305,X_296) )
=> ( X_304 = X_305 ) )
& ! [X_306: $int,X_307: set_4,X_308: $int] :
( ( mem0(X_308,g_s4_3)
& ? [X_309: set_4] :
( ! [X_310: $int,X_311: $int] :
( mem4(X_311,X_310,X_309)
<=> mem4(X_311,X_310,X_307) )
& ! [X_312: $int,X_313: $int,X_314: $int] :
( ( mem4(X_312,X_313,X_309)
& mem4(X_312,X_314,X_309) )
=> ( X_313 = X_314 ) )
& ! [X_315: $int] :
( ( $greatereq(X_315,0)
& $lesseq(X_315,g_s15_15) )
<=> ? [X_316: $int] : mem4(X_315,X_316,X_309) )
& ! [X_317: $int] :
( ? [X_318: $int] : mem4(X_318,X_317,X_309)
=> mem0(X_317,g_s4_3) ) )
& mem0(X_306,g_s4_3) )
<=> ? [X_319: $int] : mem5(X_308,X_307,X_306,X_319,X_296) )
& ! [X_320: $int] :
( ? [X_321: $int,X_322: set_4,X_323: $int] : mem5(X_323,X_322,X_321,X_320,X_296)
=> mem0(X_320,g_s6_5) ) ) ).
tff('Define:ctx:14',axiom,
mem0(g_s13_13,g_s4_3) ).
tff('Define:ctx:15',axiom,
$less(g_s13_13,g_s3_4) ).
tff('Define:ctx:16',axiom,
mem0(g_s14_14,g_s4_3) ).
tff('Define:ctx:17',axiom,
$less(g_s14_14,g_s3_4) ).
tff('Define:ctx:18',axiom,
mem0(g_s15_15,g_s4_3) ).
tff('Define:ctx:19',axiom,
g_s15_15 = $difference(g_s14_14,1) ).
tff('Define:ctx:2',axiom,
mem0(g_s5_6,g_s6_5) ).
tff('Define:ctx:20',axiom,
mem0(g_s16_16,g_s4_3) ).
tff('Define:ctx:21',axiom,
mem0(g_s17_17,g_s4_3) ).
tff('Define:ctx:22',axiom,
mem0(g_s18_18,g_s4_3) ).
tff('Define:ctx:23',axiom,
( $greater(g_s19_19,0)
& $lesseq(g_s19_19,max_int) ) ).
tff('Define:ctx:24',axiom,
( $greater(g_s20_20,0)
& $lesseq(g_s20_20,max_int) ) ).
tff('Define:ctx:25',axiom,
( $greater(g_s21_21,0)
& $lesseq(g_s21_21,max_int) ) ).
tff('Define:ctx:26',axiom,
$lesseq(g_s21_21,g_s20_20) ).
tff('Define:ctx:27',axiom,
mem0(g_s22_22,g_s8_7) ).
tff('Define:ctx:28',axiom,
mem0(g_s23_23,g_s8_7) ).
tff('Define:ctx:29',axiom,
mem0(g_s24_24,g_s4_3) ).
tff('Define:ctx:3',axiom,
mem0(g_s7_8,g_s8_7) ).
tff('Define:ctx:30',axiom,
mem0(g_s25_25,g_s4_3) ).
tff('Define:ctx:31',axiom,
g_s23_23 = $sum(g_s22_22,g_s19_19) ).
tff('Define:ctx:32',axiom,
g_s24_24 = $sum(g_s22_22,g_s20_20) ).
tff('Define:ctx:33',axiom,
g_s25_25 = $difference($sum(g_s22_22,g_s20_20),g_s21_21) ).
tff('Define:ctx:34',axiom,
mem0(g_s26_26,g_s4_3) ).
tff('Define:ctx:35',axiom,
mem0(g_s27_27,g_s4_3) ).
tff('Define:ctx:36',axiom,
( $greater(g_s28_28,0)
& $lesseq(g_s28_28,max_int) ) ).
tff('Define:ctx:37',axiom,
( $greater(g_s29_29,0)
& $lesseq(g_s29_29,max_int) ) ).
tff('Define:ctx:38',axiom,
( $greater(g_s30_30,0)
& $lesseq(g_s30_30,max_int) ) ).
tff('Define:ctx:39',axiom,
mem0(g_s31_31,g_s8_7) ).
tff('Define:ctx:4',axiom,
mem0(g_s9_9,g_s8_7) ).
tff('Define:ctx:40',axiom,
mem0(g_s32_32,g_s8_7) ).
tff('Define:ctx:41',axiom,
mem0(g_s33_33,g_s6_5) ).
tff('Define:ctx:42',axiom,
mem0(g_s34_34,g_s8_7) ).
tff('Define:ctx:43',axiom,
g_s32_32 = $sum(g_s31_31,g_s28_28) ).
tff('Define:ctx:44',axiom,
g_s33_33 = $sum(g_s31_31,g_s29_29) ).
tff('Define:ctx:45',axiom,
g_s34_34 = $sum(g_s31_31,g_s30_30) ).
tff('Define:ctx:46',axiom,
mem0(g_s35_35,g_s6_5) ).
tff('Define:ctx:47',axiom,
mem0(g_s36_36,g_s6_5) ).
tff('Define:ctx:48',axiom,
mem0(g_s37_37,g_s6_5) ).
tff('Define:ctx:49',axiom,
! [L_s38: $int] :
( mem0(L_s38,g_s4_3)
=> ! [X_9: $int] :
( mem3(L_s38,g_s37_37,X_9,g_s39_38)
=> $lesseq(X_9,1023) ) ) ).
tff('Define:ctx:5',axiom,
mem0(g_s10_10,g_s8_7) ).
tff('Define:ctx:50',axiom,
mem0(g_s40_39,g_s6_5) ).
tff('Define:ctx:51',axiom,
( $greater(g_s41_40,0)
& $lesseq(g_s41_40,max_int) ) ).
tff('Define:ctx:52',axiom,
mem0(g_s42_41,g_s6_5) ).
tff('Define:ctx:53',axiom,
mem0(g_s43_42,g_s6_5) ).
tff('Define:ctx:54',axiom,
g_s43_42 = $sum(g_s42_41,g_s41_40) ).
tff('Define:ctx:55',axiom,
( $greater(g_s44_43,0)
& $lesseq(g_s44_43,max_int) ) ).
tff('Define:ctx:56',axiom,
mem0(g_s45_44,g_s6_5) ).
tff('Define:ctx:57',axiom,
mem0(g_s46_45,g_s6_5) ).
tff('Define:ctx:58',axiom,
g_s46_45 = $sum(g_s45_44,g_s44_43) ).
tff('Define:ctx:59',axiom,
mem0(g_s47_46,g_s4_3) ).
tff('Define:ctx:6',axiom,
g_s3_4 = 4294967295 ).
tff('Define:ctx:60',axiom,
mem0(g_s48_47,g_s4_3) ).
tff('Define:ctx:61',axiom,
mem0(g_s49_48,g_s4_3) ).
tff('Define:ctx:62',axiom,
mem0(g_s50_49,g_s4_3) ).
tff('Define:ctx:63',axiom,
$lesseq(1,g_s50_49) ).
tff('Define:ctx:64',axiom,
mem0(g_s51_50,g_s4_3) ).
tff('Define:ctx:65',axiom,
mem0(g_s52_51,g_s4_3) ).
tff('Define:ctx:66',axiom,
mem0(g_s53_52,g_s4_3) ).
tff('Define:ctx:67',axiom,
( $greater(g_s54_53,0)
& $lesseq(g_s54_53,max_int) ) ).
tff('Define:ctx:68',axiom,
g_s52_51 = $sum(g_s51_50,g_s54_53) ).
tff('Define:ctx:69',axiom,
( $greater(g_s55_54,0)
& $lesseq(g_s55_54,max_int) ) ).
tff('Define:ctx:7',axiom,
g_s5_6 = 65535 ).
tff('Define:ctx:70',axiom,
g_s53_52 = $sum(g_s51_50,g_s55_54) ).
tff('Define:ctx:71',axiom,
mem0(g_s56_55,g_s4_3) ).
tff('Define:ctx:72',axiom,
mem0(g_s57_56,g_s6_5) ).
tff('Define:ctx:73',axiom,
mem0(g_s58_57,g_s6_5) ).
tff('Define:ctx:74',axiom,
( $greater(g_s59_58,0)
& $lesseq(g_s59_58,max_int) ) ).
tff('Define:ctx:75',axiom,
g_s58_57 = $sum(g_s57_56,g_s59_58) ).
tff('Define:ctx:76',axiom,
mem0(g_s60_59,g_s8_7) ).
tff('Define:ctx:77',axiom,
$less(g_s60_59,g_s3_4) ).
tff('Define:ctx:78',axiom,
( $greater(g_s61_60,0)
& $lesseq(g_s61_60,max_int) ) ).
tff('Define:ctx:79',axiom,
g_s60_59 = $sum(g_s57_56,g_s61_60) ).
tff('Define:ctx:8',axiom,
g_s7_8 = 255 ).
tff('Define:ctx:80',axiom,
mem0(g_s62_61,g_s6_5) ).
tff('Define:ctx:81',axiom,
mem0(g_s63_62,g_s4_3) ).
tff('Define:ctx:82',axiom,
mem0(g_s64_63,g_s8_7) ).
tff('Define:ctx:83',axiom,
mem0(g_s65_64,g_s8_7) ).
tff('Define:ctx:84',axiom,
g_s65_64 = $difference(g_s64_63,1) ).
tff('Define:ctx:85',axiom,
mem0(g_s66_65,g_s6_5) ).
tff('Define:ctx:86',axiom,
mem0(g_s67_66,g_s6_5) ).
tff('Define:ctx:87',axiom,
g_s67_66 = $product(g_s66_65,g_s64_63) ).
tff('Define:ctx:88',axiom,
mem0(g_s68_67,g_s6_5) ).
tff('Define:ctx:89',axiom,
mem0(g_s69_68,g_s8_7) ).
tff('Define:ctx:9',axiom,
( $greatereq(g_s9_9,0)
& $lesseq(g_s9_9,g_s7_8) ) ).
tff('Define:ctx:90',axiom,
$lesseq(g_s66_65,g_s68_67) ).
tff('Define:ctx:91',axiom,
$less(g_s67_66,g_s68_67) ).
tff('Define:ctx:92',axiom,
g_s70_69 = $difference(g_s66_65,g_s69_68) ).
tff('Define:ctx:93',axiom,
g_s71_70 = $difference(g_s68_67,$product(g_s69_68,g_s64_63)) ).
tff('Define:ctx:94',axiom,
mem0(g_s72_71,g_s4_3) ).
tff('Define:ctx:95',axiom,
mem0(g_s73_72,g_s4_3) ).
tff('Define:ctx:96',axiom,
mem0(g_s74_73,g_s4_3) ).
tff('Define:ctx:97',axiom,
mem0(g_s75_74,g_s4_3) ).
tff('Define:ctx:98',axiom,
mem0(g_s76_75,g_s4_3) ).
tff('Define:ctx:99',axiom,
mem0(g_s77_76,g_s4_3) ).
tff('Define:inv:0',axiom,
g_s145_137 = g_s145_1_139 ).
tff('Define:inv:1',axiom,
! [X_377: $int] :
( mem0(X_377,g_s146_138)
<=> mem0(X_377,g_s146_1_140) ) ).
tff('Define:inv:10',axiom,
$lesseq(g_s152_1_149,g_s30_30) ).
tff('Define:inv:11',axiom,
! [X_378: $int] :
( ( $greatereq(X_378,$sum($sum($difference(g_s145_1_139,g_s28_28),g_s150_1_147),1))
& $lesseq(X_378,g_s145_1_139)
& mem0(X_378,g_s146_1_140) )
<=> $false ) ).
tff('Define:inv:12',axiom,
! [X_379: $int] :
( ( X_379 = $sum($difference(g_s145_1_139,g_s28_28),g_s150_1_147) )
=> mem0(X_379,g_s146_1_140) ) ).
tff('Define:inv:13',axiom,
! [X_380: $int] :
( ( $greatereq(X_380,$sum($sum($difference(g_s145_1_139,g_s29_29),g_s151_1_148),1))
& $lesseq(X_380,g_s145_1_139)
& mem0(X_380,g_s146_1_140) )
<=> $false ) ).
tff('Define:inv:14',axiom,
! [X_381: $int] :
( ( X_381 = $sum($difference(g_s145_1_139,g_s29_29),g_s151_1_148) )
=> mem0(X_381,g_s146_1_140) ) ).
tff('Define:inv:15',axiom,
! [X_382: $int] :
( ( $greatereq(X_382,$sum($sum($difference(g_s145_1_139,g_s30_30),g_s152_1_149),1))
& $lesseq(X_382,g_s145_1_139)
& mem0(X_382,g_s146_1_140) )
<=> $false ) ).
tff('Define:inv:16',axiom,
! [X_383: $int] :
( ( X_383 = $sum($difference(g_s145_1_139,g_s30_30),g_s152_1_149) )
=> mem0(X_383,g_s146_1_140) ) ).
tff('Define:inv:2',axiom,
( g_s147_141
<=> g_s147_1_142 ) ).
tff('Define:inv:3',axiom,
( g_s148_143
<=> g_s148_1_144 ) ).
tff('Define:inv:4',axiom,
( g_s149_145
<=> g_s149_1_146 ) ).
tff('Define:inv:5',axiom,
$true ).
tff('Define:inv:6',axiom,
$true ).
tff('Define:inv:7',axiom,
$true ).
tff('Define:inv:8',axiom,
$lesseq(g_s150_1_147,g_s28_28) ).
tff('Define:inv:9',axiom,
$lesseq(g_s151_1_148,g_s29_29) ).
tff('Define:seext:0',axiom,
? [X_324: set_4] :
( ! [X_325: $int,X_326: $int] :
( mem4(X_326,X_325,X_324)
<=> mem4(X_326,X_325,g_s106_101) )
& ! [X_327: $int,X_328: $int,X_329: $int] :
( ( mem4(X_327,X_328,X_324)
& mem4(X_327,X_329,X_324) )
=> ( X_328 = X_329 ) )
& ! [X_330: $int] :
( ( $greatereq(X_330,0)
& $lesseq(X_330,g_s13_13) )
<=> ? [X_331: $int] : mem4(X_330,X_331,X_324) )
& ! [X_332: $int] :
( ? [X_333: $int] : mem4(X_333,X_332,X_324)
=> mem0(X_332,g_s8_7) ) ) ).
tff('Define:seext:1',axiom,
mem0(g_s107_102,g_s4_3) ).
tff('Define:seext:10',axiom,
mem0(g_s115_110,g_s4_3) ).
tff('Define:seext:11',axiom,
mem0(g_s116_111,g_s4_3) ).
tff('Define:seext:12',axiom,
mem0(g_s117_112,g_s8_7) ).
tff('Define:seext:13',axiom,
mem0(g_s118_113,g_s6_5) ).
tff('Define:seext:14',axiom,
? [X_335: set_4] :
( ! [X_336: $int,X_337: $int] :
( mem4(X_337,X_336,X_335)
<=> mem4(X_337,X_336,g_s119_114) )
& ! [X_338: $int,X_339: $int,X_340: $int] :
( ( mem4(X_338,X_339,X_335)
& mem4(X_338,X_340,X_335) )
=> ( X_339 = X_340 ) )
& ! [X_341: $int] :
( ( $greatereq(X_341,0)
& $lesseq(X_341,g_s15_15) )
<=> ? [X_342: $int] : mem4(X_341,X_342,X_335) )
& ! [X_343: $int] :
( ? [X_344: $int] : mem4(X_344,X_343,X_335)
=> mem0(X_343,g_s8_7) ) ) ).
tff('Define:seext:15',axiom,
mem0(g_s120_115,g_s8_7) ).
tff('Define:seext:16',axiom,
mem0(g_s121_116,g_s4_3) ).
tff('Define:seext:17',axiom,
mem0(g_s122_117,g_s4_3) ).
tff('Define:seext:18',axiom,
mem0(g_s123_118,g_s4_3) ).
tff('Define:seext:19',axiom,
mem0(g_s124_119,g_s4_3) ).
tff('Define:seext:2',axiom,
mem0(g_s108_103,g_s4_3) ).
tff('Define:seext:20',axiom,
mem0(g_s125_120,g_s4_3) ).
tff('Define:seext:21',axiom,
mem0(g_s126_121,g_s6_5) ).
tff('Define:seext:22',axiom,
? [X_345: set_4] :
( ! [X_346: $int,X_347: $int] :
( mem4(X_347,X_346,X_345)
<=> mem4(X_347,X_346,g_s127_122) )
& ! [X_348: $int,X_349: $int,X_350: $int] :
( ( mem4(X_348,X_349,X_345)
& mem4(X_348,X_350,X_345) )
=> ( X_349 = X_350 ) )
& ! [X_351: $int] :
( ( $greatereq(X_351,0)
& $lesseq(X_351,g_s15_15) )
<=> ? [X_352: $int] : mem4(X_351,X_352,X_345) )
& ! [X_353: $int] :
( ? [X_354: $int] : mem4(X_354,X_353,X_345)
=> mem0(X_353,g_s8_7) ) ) ).
tff('Define:seext:23',axiom,
mem0(g_s128_123,g_s4_3) ).
tff('Define:seext:24',axiom,
mem0(g_s129_124,g_s4_3) ).
tff('Define:seext:25',axiom,
mem0(g_s130_125,g_s4_3) ).
tff('Define:seext:26',axiom,
mem0(g_s131_126,g_s4_3) ).
tff('Define:seext:27',axiom,
mem0(g_s132_127,g_s4_3) ).
tff('Define:seext:28',axiom,
mem0(g_s133_128,g_s4_3) ).
tff('Define:seext:29',axiom,
mem0(g_s134_129,g_s4_3) ).
tff('Define:seext:3',axiom,
mem0(g_s109_104,g_s4_3) ).
tff('Define:seext:30',axiom,
mem0(g_s135_130,g_s4_3) ).
tff('Define:seext:31',axiom,
mem0(g_s136_131,g_s4_3) ).
tff('Define:seext:32',axiom,
mem0(g_s137_132,g_s4_3) ).
tff('Define:seext:33',axiom,
mem0(g_s138_133,g_s8_7) ).
tff('Define:seext:34',axiom,
mem0(g_s139_134,g_s4_3) ).
tff('Define:seext:35',axiom,
mem0(g_s140_135,g_s4_3) ).
tff('Define:seext:36',axiom,
$greatereq(g_s141_136,0) ).
tff('Define:seext:37',axiom,
$true ).
tff('Define:seext:38',axiom,
$true ).
tff('Define:seext:39',axiom,
$true ).
tff('Define:seext:4',axiom,
mem0(g_s110_105,g_s6_5) ).
tff('Define:seext:40',axiom,
( ! [X_355: $int,X_356: $o] :
( mem2((X_356),X_355,g_s12_12)
=> ( $true
& mem0(X_355,g_s8_7) ) )
& ! [X_357: $o,X_358: $int,X_359: $int] :
( ( mem2((X_357),X_358,g_s12_12)
& mem2((X_357),X_359,g_s12_12) )
=> ( X_358 = X_359 ) ) ) ).
tff('Define:seext:41',axiom,
( ! [X_360: $int,X_361: $o] :
( mem2((X_361),X_360,g_s12_12)
=> ( $true
& mem0(X_360,g_s6_5) ) )
& ! [X_362: $o,X_363: $int,X_364: $int] :
( ( mem2((X_362),X_363,g_s12_12)
& mem2((X_362),X_364,g_s12_12) )
=> ( X_363 = X_364 ) ) ) ).
tff('Define:seext:42',axiom,
( ! [X_365: $int,X_366: $o] :
( mem2((X_366),X_365,g_s12_12)
=> ( $true
& mem0(X_365,g_s4_3) ) )
& ! [X_367: $o,X_368: $int,X_369: $int] :
( ( mem2((X_367),X_368,g_s12_12)
& mem2((X_367),X_369,g_s12_12) )
=> ( X_368 = X_369 ) ) ) ).
tff('Define:seext:43',axiom,
! [X_370: $int] :
( ( X_370 = $sum(g_s110_105,g_s69_68) )
=> mem0(X_370,g_s6_5) ) ).
tff('Define:seext:5',axiom,
! [X_334: $int] :
( ( X_334 = $sum($sum(g_s110_105,g_s69_68),g_s68_67) )
=> mem0(X_334,g_s6_5) ) ).
tff('Define:seext:6',axiom,
mem0(g_s111_106,g_s4_3) ).
tff('Define:seext:7',axiom,
mem0(g_s112_107,g_s4_3) ).
tff('Define:seext:8',axiom,
mem0(g_s113_108,g_s4_3) ).
tff('Define:seext:9',axiom,
mem0(g_s114_109,g_s4_3) ).
%Global hypotheses
%----Local hypotheses
tff('Local_Hyp:3',hypothesis,
~ ( ( g_s117_112 = g_s9_9 )
& ! [X_393: $int] :
( mem5(g_s26_26,g_s119_114,g_s14_14,X_393,g_s105_100)
=> mem3(g_s118_113,g_s35_35,X_393,g_s84_83) )
& ! [X_394: $int] :
( mem5(g_s26_26,g_s127_122,g_s14_14,X_394,g_s105_100)
=> mem3(g_s126_121,g_s36_36,X_394,g_s84_83) ) ) ).
tff('Local_Hyp:15',hypothesis,
~ $lesseq($difference(g_s152_1_149,1),0) ).
tff('Local_Hyp:14',hypothesis,
~ $lesseq($difference(g_s150_1_147,1),0) ).
tff('Local_Hyp:13',hypothesis,
~ $lesseq($difference(g_s151_1_148,1),0) ).
tff('Local_Hyp:9',hypothesis,
~ ! [X_416: $int] :
( ( $greatereq(X_416,$difference($sum($sum(g_s145_137,1),1),g_s30_30))
& $lesseq(X_416,$sum(g_s145_137,1))
& mem0(X_416,g_s146_138) )
<=> $false ) ).
tff('Local_Hyp:5',hypothesis,
! [X_396: $int] :
( ( $greatereq(X_396,$difference($sum($sum(g_s145_137,1),1),g_s28_28))
& $lesseq(X_396,$sum(g_s145_137,1))
& mem0(X_396,g_s146_138) )
<=> $false ) ).
tff('Local_Hyp:8',hypothesis,
~ ! [X_408: $int] :
( ( $greatereq(X_408,$difference($sum($sum(g_s145_137,1),1),g_s29_29))
& $lesseq(X_408,$sum(g_s145_137,1))
& mem0(X_408,g_s146_138) )
<=> $false ) ).
%----Goal
tff('Goal',conjecture,
! [X_827: $int] :
( ( $greatereq(X_827,$sum($sum($difference($sum(g_s145_1_139,1),g_s28_28),$difference(g_s150_1_147,1)),1))
& $lesseq(X_827,$sum(g_s145_1_139,1))
& mem0(X_827,g_s146_1_140) )
<=> $false ) ).
%------------------------------------------------------------------------------