TPTP Problem File: SWC537_1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWC537_1 : TPTP v9.1.0. Bugfixed v9.1.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 5 0 Group s158 Tag s151
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0015-00173-5-0.tptp [Deh24]
% Status : Theorem
% Rating : 0.25 v9.1.0
% Syntax : Number of formulae : 343 ( 55 unt; 166 typ; 0 def)
% Number of atoms : 998 ( 114 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 852 ( 31 ~; 5 |; 443 &)
% ( 122 <=>; 251 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 921 ( 68 atm; 5 fun; 38 num; 810 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 20 ( 9 >; 11 *; 0 +; 0 <<)
% Number of predicates : 11 ( 5 usr; 2 prp; 0-4 aty)
% Number of functors : 162 ( 156 usr; 156 con; 0-2 aty)
% Number of variables : 918 ( 709 !; 209 ?; 918 :)
% SPC : TF0_THM_EQU_ARI
% Comments : Autogenerated by PPTRANS-TPTP - github.com/CLEARSY/pptranspog
% Bugfixes : v9.1.0 - Added missing types, and maybe more.
%------------------------------------------------------------------------------
tff(set_0_type,type,
set_0: $tType ).
tff(mem0_type,type,
mem0: ( $int * set_0 ) > $o ).
tff(min_int_type,type,
min_int: $int ).
tff(max_int_type,type,
max_int: $int ).
tff(min_int_axiom,axiom,
min_int = $uminus(2147483648) ).
tff(max_int_axiom,axiom,
max_int = 2147483647 ).
%----Global declarations
tff(g_s0_0_type,type,
g_s0_0: set_0 ).
tff(set_2_type,type,
set_2: $tType ).
tff(set_2_empty,type,
set_2_empty: set_2 ).
tff(set_2_insert,type,
set_2_insert: set_2 > set_2 ).
tff(mem2_type,type,
mem2: ( $int * $int * set_2 ) > $o ).
tff(g_s1_1_type,type,
g_s1_1: set_0 ).
tff(g_s2_2_type,type,
g_s2_2: set_0 ).
tff(g_s3_3_type,type,
g_s3_3: set_0 ).
tff(g_s4_4_type,type,
g_s4_4: set_0 ).
tff(g_s5_5_type,type,
g_s5_5: set_0 ).
tff(g_s6_6_type,type,
g_s6_6: set_0 ).
tff(g_s7_7_type,type,
g_s7_7: set_2 ).
tff(g_s9_8_type,type,
g_s9_8: set_2 ).
tff(g_s11_9_type,type,
g_s11_9: set_0 ).
tff(g_s12_10_type,type,
g_s12_10: set_0 ).
tff(g_s13_11_type,type,
g_s13_11: set_0 ).
tff(g_s14_12_type,type,
g_s14_12: $int ).
tff(g_s15_13_type,type,
g_s15_13: $int ).
tff(g_s16_14_type,type,
g_s16_14: set_0 ).
tff(g_s17_15_type,type,
g_s17_15: set_0 ).
tff(g_s18_16_type,type,
g_s18_16: $int ).
tff(g_s19_17_type,type,
g_s19_17: $int ).
tff(g_s20_18_type,type,
g_s20_18: set_2 ).
tff(g_s21_19_type,type,
g_s21_19: $int ).
tff(g_s22_20_type,type,
g_s22_20: set_0 ).
tff(g_s23_21_type,type,
g_s23_21: $int ).
tff(g_s24_22_type,type,
g_s24_22: $int ).
tff(g_s25_23_type,type,
g_s25_23: set_2 ).
tff(g_s26_24_type,type,
g_s26_24: $int ).
tff(set_3_type,type,
set_3: $tType ).
tff(set_3_empty,type,
set_3_empty: set_3 ).
tff(set_3_insert,type,
set_3_insert: set_3 > set_3 ).
tff(g_s27_25_type,type,
g_s27_25: set_3 ).
tff(mem3_type,type,
mem3: ( $int * $int * $int * set_3 ) > $o ).
tff(g_s28_26_type,type,
g_s28_26: set_0 ).
tff(g_s29_27_type,type,
g_s29_27: set_3 ).
tff(g_s30_28_type,type,
g_s30_28: set_3 ).
tff(g_s31_29_type,type,
g_s31_29: set_3 ).
tff(set_4_type,type,
set_4: $tType ).
tff(set_4_empty,type,
set_4_empty: set_4 ).
tff(set_4_insert,type,
set_4_insert: set_4 > set_4 ).
tff(mem4_type,type,
mem4: ( $int * $int * set_0 * set_4 ) > $o ).
tff(g_s32_30_type,type,
g_s32_30: set_4 ).
tff(g_s33_31_type,type,
g_s33_31: set_4 ).
tff(g_s34_32_type,type,
g_s34_32: set_4 ).
tff(g_s35_33_type,type,
g_s35_33: set_4 ).
tff(g_s36_34_type,type,
g_s36_34: set_4 ).
tff(g_s37_35_type,type,
g_s37_35: set_2 ).
tff(g_s38_36_type,type,
g_s38_36: set_2 ).
tff(g_s39_37_type,type,
g_s39_37: set_3 ).
tff(g_s40_38_type,type,
g_s40_38: set_3 ).
tff(g_s41_39_type,type,
g_s41_39: set_3 ).
tff(g_s42_40_type,type,
g_s42_40: set_3 ).
tff(g_s43_41_type,type,
g_s43_41: set_2 ).
tff(g_s44_42_type,type,
g_s44_42: set_2 ).
tff(g_s45_43_type,type,
g_s45_43: set_3 ).
tff(g_s46_44_type,type,
g_s46_44: set_3 ).
tff(g_s47_45_type,type,
g_s47_45: set_3 ).
tff(g_s48_46_type,type,
g_s48_46: set_3 ).
tff(g_s49_47_type,type,
g_s49_47: set_3 ).
tff(g_s50_48_type,type,
g_s50_48: set_3 ).
tff(g_s53_49_type,type,
g_s53_49: set_0 ).
tff(g_s54_50_type,type,
g_s54_50: $int ).
tff(g_s55_51_type,type,
g_s55_51: set_2 ).
tff(g_s56_52_type,type,
g_s56_52: set_0 ).
tff(g_s57_53_type,type,
g_s57_53: $int ).
tff(g_s58_54_type,type,
g_s58_54: set_2 ).
tff(g_s59_55_type,type,
g_s59_55: set_0 ).
tff(g_s60_56_type,type,
g_s60_56: $int ).
tff(g_s61_57_type,type,
g_s61_57: set_2 ).
tff(g_s62_58_type,type,
g_s62_58: set_0 ).
tff(g_s63_59_type,type,
g_s63_59: $int ).
tff(g_s64_60_type,type,
g_s64_60: set_2 ).
tff(g_s65_61_type,type,
g_s65_61: set_0 ).
tff(g_s66_62_type,type,
g_s66_62: $int ).
tff(g_s67_63_type,type,
g_s67_63: set_2 ).
tff(g_s68_64_type,type,
g_s68_64: set_2 ).
tff(g_s69_65_type,type,
g_s69_65: set_2 ).
tff(g_s70_66_type,type,
g_s70_66: $int ).
tff(g_s71_67_type,type,
g_s71_67: $int ).
tff(g_s72_68_type,type,
g_s72_68: set_2 ).
tff(g_s73_69_type,type,
g_s73_69: set_2 ).
tff(g_s74_70_type,type,
g_s74_70: set_0 ).
tff(g_s75_71_type,type,
g_s75_71: set_2 ).
tff(g_s76_72_type,type,
g_s76_72: set_2 ).
tff(g_s77_73_type,type,
g_s77_73: set_0 ).
tff(g_s78_74_type,type,
g_s78_74: set_2 ).
tff(g_s79_75_type,type,
g_s79_75: set_0 ).
tff(g_s80_76_type,type,
g_s80_76: set_0 ).
tff(g_s81_77_type,type,
g_s81_77: set_2 ).
tff(g_s82_78_type,type,
g_s82_78: set_0 ).
tff(g_s83_79_type,type,
g_s83_79: set_0 ).
tff(g_s84_80_type,type,
g_s84_80: set_2 ).
tff(g_s85_81_type,type,
g_s85_81: set_0 ).
tff(g_s86_82_type,type,
g_s86_82: set_2 ).
tff(g_s87_83_type,type,
g_s87_83: set_0 ).
tff(g_s88_84_type,type,
g_s88_84: set_0 ).
tff(g_s89_85_type,type,
g_s89_85: set_2 ).
tff(g_s90_86_type,type,
g_s90_86: set_0 ).
tff(g_s91_87_type,type,
g_s91_87: set_0 ).
tff(g_s92_88_type,type,
g_s92_88: $int ).
tff(g_s93_89_type,type,
g_s93_89: $int ).
tff(g_s95_90_type,type,
g_s95_90: set_0 ).
tff(g_s94_91_type,type,
g_s94_91: $int ).
tff(g_s96_92_type,type,
g_s96_92: $int ).
tff(g_s97_93_type,type,
g_s97_93: set_0 ).
tff(g_s98_94_type,type,
g_s98_94: set_0 ).
tff(g_s99_95_type,type,
g_s99_95: set_2 ).
tff(g_s100_96_type,type,
g_s100_96: set_2 ).
tff(g_s101_97_type,type,
g_s101_97: set_2 ).
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_insert: set_5 > set_5 ).
tff(mem5_type,type,
mem5: ( $int * set_2 * set_5 ) > $o ).
tff(g_s102_98_type,type,
g_s102_98: set_5 ).
tff(g_s103_99_type,type,
g_s103_99: set_0 ).
tff(g_s104_100_type,type,
g_s104_100: set_0 ).
tff(g_s105_101_type,type,
g_s105_101: set_2 ).
tff(g_s106_102_type,type,
g_s106_102: set_2 ).
tff(g_s107_103_type,type,
g_s107_103: set_0 ).
tff(g_s108_104_type,type,
g_s108_104: set_0 ).
tff(g_s109_105_type,type,
g_s109_105: $int ).
tff(g_s110_106_type,type,
g_s110_106: $int ).
tff(g_s111_107_type,type,
g_s111_107: set_2 ).
tff(g_s112_108_type,type,
g_s112_108: set_2 ).
tff(g_s113_109_type,type,
g_s113_109: set_2 ).
tff(g_s114_110_type,type,
g_s114_110: set_2 ).
tff(g_s115_111_type,type,
g_s115_111: $int ).
tff(g_s116_112_type,type,
g_s116_112: $int ).
tff(g_s117_113_type,type,
g_s117_113: set_0 ).
tff(g_s119_114_type,type,
g_s119_114: set_0 ).
tff(g_s118_115_type,type,
g_s118_115: $int ).
tff(g_s121_116_type,type,
g_s121_116: set_0 ).
tff(g_s122_117_type,type,
g_s122_117: set_0 ).
tff(g_s123_118_type,type,
g_s123_118: set_0 ).
tff(g_s124_119_type,type,
g_s124_119: set_0 ).
tff(g_s125_120_type,type,
g_s125_120: set_0 ).
tff(g_s126_121_type,type,
g_s126_121: $int ).
tff(g_s127_122_type,type,
g_s127_122: $int ).
tff(g_s131_123_type,type,
g_s131_123: set_2 ).
tff(g_s132_124_type,type,
g_s132_124: set_2 ).
tff(g_s133_125_type,type,
g_s133_125: set_5 ).
tff(g_s134_126_type,type,
g_s134_126: set_5 ).
tff(g_s135_127_type,type,
g_s135_127: set_5 ).
tff(g_s136_128_type,type,
g_s136_128: set_5 ).
tff(g_s137_129_type,type,
g_s137_129: set_2 ).
tff(g_s138_130_type,type,
g_s138_130: set_2 ).
tff(g_s139_131_type,type,
g_s139_131: set_0 ).
tff(g_s140_132_type,type,
g_s140_132: set_0 ).
tff(g_s141_133_type,type,
g_s141_133: set_0 ).
tff(g_s142_134_type,type,
g_s142_134: set_2 ).
tff(g_s143_135_type,type,
g_s143_135: set_2 ).
tff(g_s144_136_type,type,
g_s144_136: set_2 ).
tff(g_s145_137_type,type,
g_s145_137: set_0 ).
tff(g_s146_138_type,type,
g_s146_138: set_0 ).
tff(g_s147_139_type,type,
g_s147_139: set_2 ).
tff(g_s148_140_type,type,
g_s148_140: $int ).
tff(g_s149_141_type,type,
g_s149_141: set_2 ).
tff(g_s147_1_142_type,type,
g_s147_1_142: set_2 ).
tff(g_s148_1_143_type,type,
g_s148_1_143: $int ).
tff(g_s149_1_144_type,type,
g_s149_1_144: set_2 ).
tff(g_s157_148_type,type,
g_s157_148: $int ).
%----Defines
tff('Define:abs:0',axiom,
( ! [X_897: $int,X_898: $int] :
( mem2(X_898,X_897,g_s147_139)
=> ( mem0(X_898,g_s53_49)
& mem0(X_897,g_s12_10) ) )
& ! [X_899: $int,X_900: $int,X_901: $int] :
( ( mem2(X_899,X_900,g_s147_139)
& mem2(X_899,X_901,g_s147_139) )
=> ( X_900 = X_901 ) ) ) ).
tff('Define:abs:1',axiom,
mem0(g_s148_140,g_s11_9) ).
tff('Define:abs:2',axiom,
( ! [X_902: $int,X_903: $int] :
( mem2(X_903,X_902,g_s149_141)
=> ( mem0(X_903,g_s56_52)
& mem0(X_902,g_s12_10) ) )
& ! [X_904: $int,X_905: $int,X_906: $int] :
( ( mem2(X_904,X_905,g_s149_141)
& mem2(X_904,X_906,g_s149_141) )
=> ( X_905 = X_906 ) ) ) ).
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_145: $int] :
( mem0(X_145,g_s12_10)
<=> ( $greatereq(X_145,0)
& $lesseq(X_145,max_int) ) ) ).
tff('Define:ctx:100',axiom,
( ? [X_602: set_2] :
( ! [X_603: $int,X_604: $int] :
( mem2(X_604,X_603,X_602)
<=> mem2(X_604,X_603,g_s76_72) )
& ! [X_605: $int,X_606: $int,X_607: $int] :
( ( mem2(X_605,X_606,X_602)
& mem2(X_605,X_607,X_602) )
=> ( X_606 = X_607 ) )
& ! [X_608: $int] :
( mem0(X_608,g_s62_58)
<=> ? [X_609: $int] : mem2(X_608,X_609,X_602) )
& ! [X_610: $int] :
( ? [X_611: $int] : mem2(X_611,X_610,X_602)
=> mem0(X_610,g_s77_73) ) )
& ! [X_612: $int,X_613: $int,X_614: $int] :
( ( mem2(X_613,X_612,g_s76_72)
& mem2(X_614,X_612,g_s76_72) )
=> ( X_613 = X_614 ) ) ) ).
tff('Define:ctx:101',axiom,
( ? [X_615: set_2] :
( ! [X_616: $int,X_617: $int] :
( mem2(X_617,X_616,X_615)
<=> mem2(X_617,X_616,g_s78_74) )
& ! [X_618: $int,X_619: $int,X_620: $int] :
( ( mem2(X_618,X_619,X_615)
& mem2(X_618,X_620,X_615) )
=> ( X_619 = X_620 ) )
& ! [X_621: $int] :
( mem0(X_621,g_s79_75)
<=> ? [X_622: $int] : mem2(X_621,X_622,X_615) )
& ! [X_623: $int] :
( ? [X_624: $int] : mem2(X_624,X_623,X_615)
=> mem0(X_623,g_s80_76) ) )
& ! [X_625: $int,X_626: $int,X_627: $int] :
( ( mem2(X_626,X_625,g_s78_74)
& mem2(X_627,X_625,g_s78_74) )
=> ( X_626 = X_627 ) ) ) ).
tff('Define:ctx:102',axiom,
( ? [X_628: set_2] :
( ! [X_629: $int,X_630: $int] :
( mem2(X_630,X_629,X_628)
<=> mem2(X_630,X_629,g_s81_77) )
& ! [X_631: $int,X_632: $int,X_633: $int] :
( ( mem2(X_631,X_632,X_628)
& mem2(X_631,X_633,X_628) )
=> ( X_632 = X_633 ) )
& ! [X_634: $int] :
( mem0(X_634,g_s82_78)
<=> ? [X_635: $int] : mem2(X_634,X_635,X_628) )
& ! [X_636: $int] :
( ? [X_637: $int] : mem2(X_637,X_636,X_628)
=> mem0(X_636,g_s83_79) ) )
& ! [X_638: $int,X_639: $int,X_640: $int] :
( ( mem2(X_639,X_638,g_s81_77)
& mem2(X_640,X_638,g_s81_77) )
=> ( X_639 = X_640 ) ) ) ).
tff('Define:ctx:103',axiom,
( ? [X_641: set_2] :
( ! [X_642: $int,X_643: $int] :
( mem2(X_643,X_642,X_641)
<=> mem2(X_643,X_642,g_s84_80) )
& ! [X_644: $int,X_645: $int,X_646: $int] :
( ( mem2(X_644,X_645,X_641)
& mem2(X_644,X_646,X_641) )
=> ( X_645 = X_646 ) )
& ! [X_647: $int] :
( mem0(X_647,g_s82_78)
<=> ? [X_648: $int] : mem2(X_647,X_648,X_641) )
& ! [X_649: $int] :
( ? [X_650: $int] : mem2(X_650,X_649,X_641)
=> mem0(X_649,g_s85_81) ) )
& ! [X_651: $int,X_652: $int,X_653: $int] :
( ( mem2(X_652,X_651,g_s84_80)
& mem2(X_653,X_651,g_s84_80) )
=> ( X_652 = X_653 ) ) ) ).
tff('Define:ctx:104',axiom,
( ? [X_654: set_2] :
( ! [X_655: $int,X_656: $int] :
( mem2(X_656,X_655,X_654)
<=> mem2(X_656,X_655,g_s86_82) )
& ! [X_657: $int,X_658: $int,X_659: $int] :
( ( mem2(X_657,X_658,X_654)
& mem2(X_657,X_659,X_654) )
=> ( X_658 = X_659 ) )
& ! [X_660: $int] :
( mem0(X_660,g_s87_83)
<=> ? [X_661: $int] : mem2(X_660,X_661,X_654) )
& ! [X_662: $int] :
( ? [X_663: $int] : mem2(X_663,X_662,X_654)
=> mem0(X_662,g_s88_84) ) )
& ! [X_664: $int,X_665: $int,X_666: $int] :
( ( mem2(X_665,X_664,g_s86_82)
& mem2(X_666,X_664,g_s86_82) )
=> ( X_665 = X_666 ) ) ) ).
tff('Define:ctx:105',axiom,
( ? [X_667: set_2] :
( ! [X_668: $int,X_669: $int] :
( mem2(X_669,X_668,X_667)
<=> mem2(X_669,X_668,g_s89_85) )
& ! [X_670: $int,X_671: $int,X_672: $int] :
( ( mem2(X_670,X_671,X_667)
& mem2(X_670,X_672,X_667) )
=> ( X_671 = X_672 ) )
& ! [X_673: $int] :
( mem0(X_673,g_s90_86)
<=> ? [X_674: $int] : mem2(X_673,X_674,X_667) )
& ! [X_675: $int] :
( ? [X_676: $int] : mem2(X_676,X_675,X_667)
=> mem0(X_675,g_s91_87) ) )
& ! [X_677: $int,X_678: $int,X_679: $int] :
( ( mem2(X_678,X_677,g_s89_85)
& mem2(X_679,X_677,g_s89_85) )
=> ( X_678 = X_679 ) ) ) ).
tff('Define:ctx:106',axiom,
~ ? [X_680: $int] : mem2(X_680,g_s92_88,g_s73_69) ).
tff('Define:ctx:107',axiom,
~ ? [X_681: $int] : mem2(X_681,g_s92_88,g_s75_71) ).
tff('Define:ctx:108',axiom,
mem0(g_s92_88,g_s74_70) ).
tff('Define:ctx:109',axiom,
mem0(g_s93_89,g_s74_70) ).
tff('Define:ctx:11',axiom,
! [X_146: $int] :
( mem0(X_146,g_s13_11)
<=> ( $greater(X_146,0)
& $lesseq(X_146,max_int) ) ) ).
tff('Define:ctx:110',axiom,
mem0(g_s94_91,g_s95_90) ).
tff('Define:ctx:111',axiom,
mem0(g_s96_92,g_s95_90) ).
tff('Define:ctx:112',axiom,
( ( g_s93_89 != g_s92_88 )
=> ( g_s71_67 != 0 ) ) ).
tff('Define:ctx:113',axiom,
mem0(g_s92_88,g_s97_93) ).
tff('Define:ctx:114',axiom,
mem0(g_s93_89,g_s97_93) ).
tff('Define:ctx:115',axiom,
mem0(g_s94_91,g_s98_94) ).
tff('Define:ctx:116',axiom,
mem0(g_s96_92,g_s98_94) ).
tff('Define:ctx:12',axiom,
! [X_147: $int] :
( mem0(X_147,g_s13_11)
=> mem0(X_147,g_s12_10) ) ).
tff('Define:ctx:13',axiom,
! [X_148: $int] :
( mem0(X_148,g_s12_10)
=> mem0(X_148,g_s11_9) ) ).
tff('Define:ctx:14',axiom,
mem0(g_s14_12,g_s11_9) ).
tff('Define:ctx:15',axiom,
mem0(g_s14_12,g_s12_10) ).
tff('Define:ctx:16',axiom,
~ mem0(g_s14_12,g_s13_11) ).
tff('Define:ctx:17',axiom,
mem0(g_s15_13,g_s11_9) ).
tff('Define:ctx:18',axiom,
~ mem0(g_s15_13,g_s12_10) ).
tff('Define:ctx:19',axiom,
! [X_149: $int] :
( mem0(X_149,g_s16_14)
<=> ( $greatereq(X_149,min_int)
& $lesseq(X_149,max_int) ) ) ).
tff('Define:ctx:2',axiom,
( ~ ! [X_43: $int] :
( mem0(X_43,g_s2_2)
<=> $false )
& ! [X_46: $int] :
( mem0(X_46,g_s2_2)
=> $true )
& ? [X_44: $int,X_45: set_2] :
( ? [X_47: set_2] :
( ! [X_48: $int,X_49: $int] :
( mem2(X_49,X_48,X_47)
<=> mem2(X_49,X_48,X_45) )
& ! [X_50: $int,X_51: $int,X_52: $int] :
( ( mem2(X_50,X_51,X_47)
& mem2(X_50,X_52,X_47) )
=> ( X_51 = X_52 ) )
& ! [X_53: $int] :
( ( $greatereq(X_53,1)
& $lesseq(X_53,X_44) )
<=> ? [X_54: $int] : mem2(X_53,X_54,X_47) )
& ! [X_55: $int] :
( ? [X_56: $int] : mem2(X_56,X_55,X_47)
=> mem0(X_55,g_s2_2) ) )
& ! [X_57: $int] :
( mem0(X_57,g_s2_2)
=> ? [X_58: $int] : mem2(X_58,X_57,X_45) )
& ! [X_59: $int,X_60: $int,X_61: $int] :
( ( mem2(X_60,X_59,X_45)
& mem2(X_61,X_59,X_45) )
=> ( X_60 = X_61 ) ) ) ) ).
tff('Define:ctx:20',axiom,
! [X_150: $int] :
( mem0(X_150,g_s17_15)
=> mem0(X_150,g_s0_0) ) ).
tff('Define:ctx:21',axiom,
mem0(g_s18_16,g_s0_0) ).
tff('Define:ctx:22',axiom,
mem0(g_s18_16,g_s17_15) ).
tff('Define:ctx:23',axiom,
mem0(g_s19_17,g_s0_0) ).
tff('Define:ctx:24',axiom,
~ mem0(g_s19_17,g_s17_15) ).
tff('Define:ctx:25',axiom,
( ! [X_151: $int,X_152: $int] :
( mem2(X_152,X_151,g_s20_18)
=> ( $greatereq(X_152,0)
& $lesseq(X_152,max_int)
& mem0(X_151,g_s0_0) ) )
& ! [X_153: $int,X_154: $int,X_155: $int] :
( ( mem2(X_153,X_154,g_s20_18)
& mem2(X_153,X_155,g_s20_18) )
=> ( X_154 = X_155 ) ) ) ).
tff('Define:ctx:26',axiom,
? [X_156: $int] :
( ? [X_157: set_2] :
( ! [X_158: $int,X_159: $int] :
( mem2(X_159,X_158,X_157)
<=> mem2(X_159,X_158,g_s20_18) )
& ! [X_160: $int,X_161: $int,X_162: $int] :
( ( mem2(X_160,X_161,X_157)
& mem2(X_160,X_162,X_157) )
=> ( X_161 = X_162 ) )
& ! [X_163: $int] :
( ( $greatereq(X_163,1)
& $lesseq(X_163,X_156) )
<=> ? [X_164: $int] : mem2(X_163,X_164,X_157) )
& ! [X_165: $int] :
( ? [X_166: $int] : mem2(X_166,X_165,X_157)
=> mem0(X_165,g_s17_15) ) )
& ! [X_167: $int] :
( mem0(X_167,g_s17_15)
=> ? [X_168: $int] : mem2(X_168,X_167,g_s20_18) )
& ! [X_169: $int,X_170: $int,X_171: $int] :
( ( mem2(X_170,X_169,g_s20_18)
& mem2(X_171,X_169,g_s20_18) )
=> ( X_170 = X_171 ) ) ) ).
tff('Define:ctx:27',axiom,
? [X_172: set_2] :
( ? [X_173: set_2] :
( ! [X_174: $int,X_175: $int] :
( mem2(X_175,X_174,X_173)
<=> mem2(X_175,X_174,X_172) )
& ! [X_176: $int,X_177: $int,X_178: $int] :
( ( mem2(X_176,X_177,X_173)
& mem2(X_176,X_178,X_173) )
=> ( X_177 = X_178 ) )
& ! [X_179: $int] :
( mem0(X_179,g_s17_15)
<=> ? [X_180: $int] : mem2(X_179,X_180,X_173) )
& ! [X_181: $int] :
( ? [X_182: $int] : mem2(X_182,X_181,X_173)
=> ( $greatereq(X_181,1)
& $lesseq(X_181,g_s21_19) ) ) )
& ! [X_183: $int] :
( ( $greatereq(X_183,1)
& $lesseq(X_183,g_s21_19) )
=> ? [X_184: $int] : mem2(X_184,X_183,X_172) )
& ! [X_185: $int,X_186: $int,X_187: $int] :
( ( mem2(X_186,X_185,X_172)
& mem2(X_187,X_185,X_172) )
=> ( X_186 = X_187 ) ) ) ).
tff('Define:ctx:28',axiom,
! [X_188: $int] :
( mem0(X_188,g_s22_20)
=> mem0(X_188,g_s1_1) ) ).
tff('Define:ctx:29',axiom,
mem0(g_s23_21,g_s1_1) ).
tff('Define:ctx:3',axiom,
( ~ ! [X_62: $int] :
( mem0(X_62,g_s3_3)
<=> $false )
& ! [X_65: $int] :
( mem0(X_65,g_s3_3)
=> $true )
& ? [X_63: $int,X_64: set_2] :
( ? [X_66: set_2] :
( ! [X_67: $int,X_68: $int] :
( mem2(X_68,X_67,X_66)
<=> mem2(X_68,X_67,X_64) )
& ! [X_69: $int,X_70: $int,X_71: $int] :
( ( mem2(X_69,X_70,X_66)
& mem2(X_69,X_71,X_66) )
=> ( X_70 = X_71 ) )
& ! [X_72: $int] :
( ( $greatereq(X_72,1)
& $lesseq(X_72,X_63) )
<=> ? [X_73: $int] : mem2(X_72,X_73,X_66) )
& ! [X_74: $int] :
( ? [X_75: $int] : mem2(X_75,X_74,X_66)
=> mem0(X_74,g_s3_3) ) )
& ! [X_76: $int] :
( mem0(X_76,g_s3_3)
=> ? [X_77: $int] : mem2(X_77,X_76,X_64) )
& ! [X_78: $int,X_79: $int,X_80: $int] :
( ( mem2(X_79,X_78,X_64)
& mem2(X_80,X_78,X_64) )
=> ( X_79 = X_80 ) ) ) ) ).
tff('Define:ctx:30',axiom,
mem0(g_s23_21,g_s22_20) ).
tff('Define:ctx:31',axiom,
mem0(g_s24_22,g_s1_1) ).
tff('Define:ctx:32',axiom,
~ mem0(g_s24_22,g_s22_20) ).
tff('Define:ctx:33',axiom,
( ! [X_189: $int,X_190: $int] :
( mem2(X_190,X_189,g_s25_23)
=> ( $greatereq(X_190,0)
& $lesseq(X_190,max_int)
& mem0(X_189,g_s1_1) ) )
& ! [X_191: $int,X_192: $int,X_193: $int] :
( ( mem2(X_191,X_192,g_s25_23)
& mem2(X_191,X_193,g_s25_23) )
=> ( X_192 = X_193 ) ) ) ).
tff('Define:ctx:34',axiom,
? [X_194: $int] :
( ? [X_195: set_2] :
( ! [X_196: $int,X_197: $int] :
( mem2(X_197,X_196,X_195)
<=> mem2(X_197,X_196,g_s25_23) )
& ! [X_198: $int,X_199: $int,X_200: $int] :
( ( mem2(X_198,X_199,X_195)
& mem2(X_198,X_200,X_195) )
=> ( X_199 = X_200 ) )
& ! [X_201: $int] :
( ( $greatereq(X_201,1)
& $lesseq(X_201,X_194) )
<=> ? [X_202: $int] : mem2(X_201,X_202,X_195) )
& ! [X_203: $int] :
( ? [X_204: $int] : mem2(X_204,X_203,X_195)
=> mem0(X_203,g_s22_20) ) )
& ! [X_205: $int] :
( mem0(X_205,g_s22_20)
=> ? [X_206: $int] : mem2(X_206,X_205,g_s25_23) )
& ! [X_207: $int,X_208: $int,X_209: $int] :
( ( mem2(X_208,X_207,g_s25_23)
& mem2(X_209,X_207,g_s25_23) )
=> ( X_208 = X_209 ) ) ) ).
tff('Define:ctx:35',axiom,
? [X_210: set_2] :
( ? [X_211: set_2] :
( ! [X_212: $int,X_213: $int] :
( mem2(X_213,X_212,X_211)
<=> mem2(X_213,X_212,X_210) )
& ! [X_214: $int,X_215: $int,X_216: $int] :
( ( mem2(X_214,X_215,X_211)
& mem2(X_214,X_216,X_211) )
=> ( X_215 = X_216 ) )
& ! [X_217: $int] :
( mem0(X_217,g_s22_20)
<=> ? [X_218: $int] : mem2(X_217,X_218,X_211) )
& ! [X_219: $int] :
( ? [X_220: $int] : mem2(X_220,X_219,X_211)
=> ( $greatereq(X_219,1)
& $lesseq(X_219,g_s26_24) ) ) )
& ! [X_221: $int] :
( ( $greatereq(X_221,1)
& $lesseq(X_221,g_s26_24) )
=> ? [X_222: $int] : mem2(X_222,X_221,X_210) )
& ! [X_223: $int,X_224: $int,X_225: $int] :
( ( mem2(X_224,X_223,X_210)
& mem2(X_225,X_223,X_210) )
=> ( X_224 = X_225 ) ) ) ).
tff('Define:ctx:36',axiom,
( ! [X_226: $int,X_227: $int,X_228: $int] :
( mem3(X_228,X_227,X_226,g_s27_25)
=> ( mem0(X_228,g_s16_14)
& mem0(X_227,g_s16_14)
& mem0(X_226,g_s16_14) ) )
& ! [X_229: $int,X_230: $int,X_231: $int,X_232: $int] :
( ( mem3(X_230,X_229,X_231,g_s27_25)
& mem3(X_230,X_229,X_232,g_s27_25) )
=> ( X_231 = X_232 ) ) ) ).
tff('Define:ctx:37',axiom,
! [X_233: $int] :
( mem0(X_233,g_s28_26)
=> mem0(X_233,g_s16_14) ) ).
tff('Define:ctx:38',axiom,
? [X_234: set_3] :
( ! [X_235: $int,X_236: $int,X_237: $int] :
( mem3(X_237,X_236,X_235,X_234)
<=> mem3(X_237,X_236,X_235,g_s29_27) )
& ! [X_238: $int,X_239: $int,X_240: $int,X_241: $int] :
( ( mem3(X_239,X_238,X_240,X_234)
& mem3(X_239,X_238,X_241,X_234) )
=> ( X_240 = X_241 ) )
& ! [X_242: $int,X_243: $int] :
( ( mem0(X_243,g_s12_10)
& mem0(X_242,g_s12_10) )
<=> ? [X_244: $int] : mem3(X_243,X_242,X_244,X_234) )
& ! [X_245: $int] :
( ? [X_246: $int,X_247: $int] : mem3(X_247,X_246,X_245,X_234)
=> mem0(X_245,g_s16_14) ) ) ).
tff('Define:ctx:39',axiom,
( ! [X_248: $int,X_249: $int,X_250: $int] :
( mem3(X_250,X_249,X_248,g_s30_28)
=> ( mem0(X_250,g_s12_10)
& mem0(X_249,g_s16_14)
& mem0(X_248,g_s12_10) ) )
& ! [X_251: $int,X_252: $int,X_253: $int,X_254: $int] :
( ( mem3(X_252,X_251,X_253,g_s30_28)
& mem3(X_252,X_251,X_254,g_s30_28) )
=> ( X_253 = X_254 ) ) ) ).
tff('Define:ctx:4',axiom,
( ~ ! [X_81: $int] :
( mem0(X_81,g_s4_4)
<=> $false )
& ! [X_84: $int] :
( mem0(X_84,g_s4_4)
=> $true )
& ? [X_82: $int,X_83: set_2] :
( ? [X_85: set_2] :
( ! [X_86: $int,X_87: $int] :
( mem2(X_87,X_86,X_85)
<=> mem2(X_87,X_86,X_83) )
& ! [X_88: $int,X_89: $int,X_90: $int] :
( ( mem2(X_88,X_89,X_85)
& mem2(X_88,X_90,X_85) )
=> ( X_89 = X_90 ) )
& ! [X_91: $int] :
( ( $greatereq(X_91,1)
& $lesseq(X_91,X_82) )
<=> ? [X_92: $int] : mem2(X_91,X_92,X_85) )
& ! [X_93: $int] :
( ? [X_94: $int] : mem2(X_94,X_93,X_85)
=> mem0(X_93,g_s4_4) ) )
& ! [X_95: $int] :
( mem0(X_95,g_s4_4)
=> ? [X_96: $int] : mem2(X_96,X_95,X_83) )
& ! [X_97: $int,X_98: $int,X_99: $int] :
( ( mem2(X_98,X_97,X_83)
& mem2(X_99,X_97,X_83) )
=> ( X_98 = X_99 ) ) ) ) ).
tff('Define:ctx:40',axiom,
? [X_255: set_3] :
( ! [X_256: $int,X_257: $int,X_258: $int] :
( mem3(X_258,X_257,X_256,X_255)
<=> mem3(X_258,X_257,X_256,g_s31_29) )
& ! [X_259: $int,X_260: $int,X_261: $int,X_262: $int] :
( ( mem3(X_260,X_259,X_261,X_255)
& mem3(X_260,X_259,X_262,X_255) )
=> ( X_261 = X_262 ) )
& ! [X_263: $int,X_264: $int] :
( ( mem0(X_264,g_s12_10)
& mem0(X_263,g_s16_14) )
<=> ? [X_265: $int] : mem3(X_264,X_263,X_265,X_255) )
& ! [X_266: $int] :
( ? [X_267: $int,X_268: $int] : mem3(X_268,X_267,X_266,X_255)
=> mem0(X_266,g_s12_10) ) ) ).
tff('Define:ctx:41',axiom,
? [X_269: set_4] :
( ! [X_270: set_0,X_271: $int,X_272: $int] :
( mem4(X_272,X_271,X_270,X_269)
<=> mem4(X_272,X_271,X_270,g_s32_30) )
& ! [X_273: $int,X_274: $int,X_275: set_0,X_276: set_0] :
( ( mem4(X_274,X_273,X_275,X_269)
& mem4(X_274,X_273,X_276,X_269) )
=> ! [X_277: $int] :
( mem0(X_277,X_275)
<=> mem0(X_277,X_276) ) )
& ! [X_278: $int,X_279: $int] :
( ( mem0(X_279,g_s12_10)
& mem0(X_278,g_s16_14) )
<=> ? [X_280: set_0] : mem4(X_279,X_278,X_280,X_269) )
& ! [X_281: set_0] :
( ? [X_282: $int,X_283: $int] : mem4(X_283,X_282,X_281,X_269)
=> ! [X_284: $int] :
( mem0(X_284,X_281)
=> mem0(X_284,g_s12_10) ) ) ) ).
tff('Define:ctx:42',axiom,
? [X_285: set_4] :
( ! [X_286: set_0,X_287: $int,X_288: $int] :
( mem4(X_288,X_287,X_286,X_285)
<=> mem4(X_288,X_287,X_286,g_s33_31) )
& ! [X_289: $int,X_290: $int,X_291: set_0,X_292: set_0] :
( ( mem4(X_290,X_289,X_291,X_285)
& mem4(X_290,X_289,X_292,X_285) )
=> ! [X_293: $int] :
( mem0(X_293,X_291)
<=> mem0(X_293,X_292) ) )
& ! [X_294: $int,X_295: $int] :
( ( mem0(X_295,g_s12_10)
& mem0(X_294,g_s12_10) )
<=> ? [X_296: set_0] : mem4(X_295,X_294,X_296,X_285) )
& ! [X_297: set_0] :
( ? [X_298: $int,X_299: $int] : mem4(X_299,X_298,X_297,X_285)
=> ! [X_300: $int] :
( mem0(X_300,X_297)
=> mem0(X_300,g_s12_10) ) ) ) ).
tff('Define:ctx:43',axiom,
? [X_301: set_4] :
( ! [X_302: set_0,X_303: $int,X_304: $int] :
( mem4(X_304,X_303,X_302,X_301)
<=> mem4(X_304,X_303,X_302,g_s34_32) )
& ! [X_305: $int,X_306: $int,X_307: set_0,X_308: set_0] :
( ( mem4(X_306,X_305,X_307,X_301)
& mem4(X_306,X_305,X_308,X_301) )
=> ! [X_309: $int] :
( mem0(X_309,X_307)
<=> mem0(X_309,X_308) ) )
& ! [X_310: $int,X_311: $int] :
( ( mem0(X_311,g_s12_10)
& mem0(X_310,g_s12_10) )
<=> ? [X_312: set_0] : mem4(X_311,X_310,X_312,X_301) )
& ! [X_313: set_0] :
( ? [X_314: $int,X_315: $int] : mem4(X_315,X_314,X_313,X_301)
=> ! [X_316: $int] :
( mem0(X_316,X_313)
=> mem0(X_316,g_s12_10) ) ) ) ).
tff('Define:ctx:44',axiom,
? [X_317: set_4] :
( ! [X_318: set_0,X_319: $int,X_320: $int] :
( mem4(X_320,X_319,X_318,X_317)
<=> mem4(X_320,X_319,X_318,g_s35_33) )
& ! [X_321: $int,X_322: $int,X_323: set_0,X_324: set_0] :
( ( mem4(X_322,X_321,X_323,X_317)
& mem4(X_322,X_321,X_324,X_317) )
=> ! [X_325: $int] :
( mem0(X_325,X_323)
<=> mem0(X_325,X_324) ) )
& ! [X_326: $int,X_327: $int] :
( ( mem0(X_327,g_s12_10)
& mem0(X_326,g_s12_10) )
<=> ? [X_328: set_0] : mem4(X_327,X_326,X_328,X_317) )
& ! [X_329: set_0] :
( ? [X_330: $int,X_331: $int] : mem4(X_331,X_330,X_329,X_317)
=> ! [X_332: $int] :
( mem0(X_332,X_329)
=> mem0(X_332,g_s12_10) ) ) ) ).
tff('Define:ctx:45',axiom,
? [X_333: set_4] :
( ! [X_334: set_0,X_335: $int,X_336: $int] :
( mem4(X_336,X_335,X_334,X_333)
<=> mem4(X_336,X_335,X_334,g_s36_34) )
& ! [X_337: $int,X_338: $int,X_339: set_0,X_340: set_0] :
( ( mem4(X_338,X_337,X_339,X_333)
& mem4(X_338,X_337,X_340,X_333) )
=> ! [X_341: $int] :
( mem0(X_341,X_339)
<=> mem0(X_341,X_340) ) )
& ! [X_342: $int,X_343: $int] :
( ( mem0(X_343,g_s12_10)
& mem0(X_342,g_s12_10) )
<=> ? [X_344: set_0] : mem4(X_343,X_342,X_344,X_333) )
& ! [X_345: set_0] :
( ? [X_346: $int,X_347: $int] : mem4(X_347,X_346,X_345,X_333)
=> ! [X_348: $int] :
( mem0(X_348,X_345)
=> mem0(X_348,g_s12_10) ) ) ) ).
tff('Define:ctx:46',axiom,
! [X_349: $int,X_350: $int] :
( mem2(X_350,X_349,g_s37_35)
=> ( mem0(X_350,g_s12_10)
& mem0(X_349,g_s12_10) ) ) ).
tff('Define:ctx:47',axiom,
! [X_351: $int,X_352: $int] :
( mem2(X_352,X_351,g_s38_36)
=> ( mem0(X_352,g_s12_10)
& mem0(X_351,g_s12_10) ) ) ).
tff('Define:ctx:48',axiom,
! [X_353: $int,X_354: $int,X_355: $int] :
( mem3(X_355,X_354,X_353,g_s39_37)
=> ( mem0(X_355,g_s12_10)
& mem0(X_354,g_s16_14)
& mem0(X_353,g_s12_10) ) ) ).
tff('Define:ctx:49',axiom,
! [X_356: $int,X_357: $int,X_358: $int] :
( mem3(X_358,X_357,X_356,g_s40_38)
=> ( mem0(X_358,g_s12_10)
& mem0(X_357,g_s16_14)
& mem0(X_356,g_s12_10) ) ) ).
tff('Define:ctx:5',axiom,
( ~ ! [X_100: $int] :
( mem0(X_100,g_s5_5)
<=> $false )
& ! [X_103: $int] :
( mem0(X_103,g_s5_5)
=> $true )
& ? [X_101: $int,X_102: set_2] :
( ? [X_104: set_2] :
( ! [X_105: $int,X_106: $int] :
( mem2(X_106,X_105,X_104)
<=> mem2(X_106,X_105,X_102) )
& ! [X_107: $int,X_108: $int,X_109: $int] :
( ( mem2(X_107,X_108,X_104)
& mem2(X_107,X_109,X_104) )
=> ( X_108 = X_109 ) )
& ! [X_110: $int] :
( ( $greatereq(X_110,1)
& $lesseq(X_110,X_101) )
<=> ? [X_111: $int] : mem2(X_110,X_111,X_104) )
& ! [X_112: $int] :
( ? [X_113: $int] : mem2(X_113,X_112,X_104)
=> mem0(X_112,g_s5_5) ) )
& ! [X_114: $int] :
( mem0(X_114,g_s5_5)
=> ? [X_115: $int] : mem2(X_115,X_114,X_102) )
& ! [X_116: $int,X_117: $int,X_118: $int] :
( ( mem2(X_117,X_116,X_102)
& mem2(X_118,X_116,X_102) )
=> ( X_117 = X_118 ) ) ) ) ).
tff('Define:ctx:50',axiom,
! [X_359: $int,X_360: $int,X_361: $int] :
( mem3(X_361,X_360,X_359,g_s41_39)
=> ( mem0(X_361,g_s12_10)
& mem0(X_360,g_s16_14)
& mem0(X_359,g_s12_10) ) ) ).
tff('Define:ctx:51',axiom,
! [X_362: $int,X_363: $int,X_364: $int] :
( mem3(X_364,X_363,X_362,g_s42_40)
=> ( mem0(X_364,g_s12_10)
& mem0(X_363,g_s16_14)
& mem0(X_362,g_s12_10) ) ) ).
tff('Define:ctx:52',axiom,
! [X_365: $int,X_366: $int] :
( mem2(X_366,X_365,g_s43_41)
=> ( mem0(X_366,g_s12_10)
& mem0(X_365,g_s12_10) ) ) ).
tff('Define:ctx:53',axiom,
! [X_367: $int,X_368: $int] :
( mem2(X_368,X_367,g_s44_42)
=> ( mem0(X_368,g_s12_10)
& mem0(X_367,g_s12_10) ) ) ).
tff('Define:ctx:54',axiom,
! [X_369: $int,X_370: $int,X_371: $int] :
( mem3(X_371,X_370,X_369,g_s45_43)
=> ( mem0(X_371,g_s12_10)
& mem0(X_370,g_s16_14)
& mem0(X_369,g_s12_10) ) ) ).
tff('Define:ctx:55',axiom,
! [X_372: $int,X_373: $int,X_374: $int] :
( mem3(X_374,X_373,X_372,g_s46_44)
=> ( mem0(X_374,g_s12_10)
& mem0(X_373,g_s16_14)
& mem0(X_372,g_s12_10) ) ) ).
tff('Define:ctx:56',axiom,
! [X_375: $int,X_376: $int,X_377: $int] :
( mem3(X_377,X_376,X_375,g_s47_45)
=> ( mem0(X_377,g_s12_10)
& mem0(X_376,g_s16_14)
& mem0(X_375,g_s12_10) ) ) ).
tff('Define:ctx:57',axiom,
! [X_378: $int,X_379: $int,X_380: $int] :
( mem3(X_380,X_379,X_378,g_s48_46)
=> ( mem0(X_380,g_s12_10)
& mem0(X_379,g_s16_14)
& mem0(X_378,g_s12_10) ) ) ).
tff('Define:ctx:58',axiom,
? [X_381: set_3] :
( ! [X_382: $int,X_383: $int,X_384: $int] :
( mem3(X_384,X_383,X_382,X_381)
<=> mem3(X_384,X_383,X_382,g_s49_47) )
& ! [X_385: $int,X_386: $int,X_387: $int,X_388: $int] :
( ( mem3(X_386,X_385,X_387,X_381)
& mem3(X_386,X_385,X_388,X_381) )
=> ( X_387 = X_388 ) )
& ! [X_389: $int,X_390: $int] :
( ( mem0(X_390,g_s12_10)
& mem0(X_389,g_s12_10) )
<=> ? [X_391: $int] : mem3(X_390,X_389,X_391,X_381) )
& ! [X_392: $int] :
( ? [X_393: $int,X_394: $int] : mem3(X_394,X_393,X_392,X_381)
=> mem0(X_392,g_s12_10) ) ) ).
tff('Define:ctx:59',axiom,
? [X_395: set_3] :
( ! [X_396: $int,X_397: $int,X_398: $int] :
( mem3(X_398,X_397,X_396,X_395)
<=> mem3(X_398,X_397,X_396,g_s50_48) )
& ! [X_399: $int,X_400: $int,X_401: $int,X_402: $int] :
( ( mem3(X_400,X_399,X_401,X_395)
& mem3(X_400,X_399,X_402,X_395) )
=> ( X_401 = X_402 ) )
& ! [X_403: $int,X_404: $int] :
( ( mem0(X_404,g_s12_10)
& mem0(X_403,g_s12_10) )
<=> ? [X_405: $int] : mem3(X_404,X_403,X_405,X_395) )
& ! [X_406: $int] :
( ? [X_407: $int,X_408: $int] : mem3(X_408,X_407,X_406,X_395)
=> mem0(X_406,g_s12_10) ) ) ).
tff('Define:ctx:6',axiom,
( ~ ! [X_119: $int] :
( mem0(X_119,g_s6_6)
<=> $false )
& ! [X_122: $int] :
( mem0(X_122,g_s6_6)
=> $true )
& ? [X_120: $int,X_121: set_2] :
( ? [X_123: set_2] :
( ! [X_124: $int,X_125: $int] :
( mem2(X_125,X_124,X_123)
<=> mem2(X_125,X_124,X_121) )
& ! [X_126: $int,X_127: $int,X_128: $int] :
( ( mem2(X_126,X_127,X_123)
& mem2(X_126,X_128,X_123) )
=> ( X_127 = X_128 ) )
& ! [X_129: $int] :
( ( $greatereq(X_129,1)
& $lesseq(X_129,X_120) )
<=> ? [X_130: $int] : mem2(X_129,X_130,X_123) )
& ! [X_131: $int] :
( ? [X_132: $int] : mem2(X_132,X_131,X_123)
=> mem0(X_131,g_s6_6) ) )
& ! [X_133: $int] :
( mem0(X_133,g_s6_6)
=> ? [X_134: $int] : mem2(X_134,X_133,X_121) )
& ! [X_135: $int,X_136: $int,X_137: $int] :
( ( mem2(X_136,X_135,X_121)
& mem2(X_137,X_135,X_121) )
=> ( X_136 = X_137 ) ) ) ) ).
tff('Define:ctx:60',axiom,
! [X_409: $int,X_410: $int] :
( ? [X_411: $int] : mem3(X_410,X_409,X_411,g_s30_28)
<=> ( mem0(X_410,g_s12_10)
& $greatereq(X_409,0)
& $lesseq(X_409,max_int) ) ) ).
tff('Define:ctx:61',axiom,
! [X_412: $int,X_413: $int] :
( ? [X_414: $int] : mem3(X_413,X_412,X_414,g_s27_25)
<=> ( mem0(X_413,g_s16_14)
& mem0(X_412,g_s16_14)
& $greatereq(X_412,0) ) ) ).
tff('Define:ctx:62',axiom,
! [X_415: $int] :
( mem0(X_415,g_s53_49)
=> mem0(X_415,g_s2_2) ) ).
tff('Define:ctx:63',axiom,
mem0(g_s54_50,g_s2_2) ).
tff('Define:ctx:64',axiom,
~ mem0(g_s54_50,g_s53_49) ).
tff('Define:ctx:65',axiom,
( ! [X_416: $int,X_417: $int] :
( mem2(X_417,X_416,g_s55_51)
=> ( $greatereq(X_417,0)
& $lesseq(X_417,max_int)
& mem0(X_416,g_s2_2) ) )
& ! [X_418: $int,X_419: $int,X_420: $int] :
( ( mem2(X_418,X_419,g_s55_51)
& mem2(X_418,X_420,g_s55_51) )
=> ( X_419 = X_420 ) ) ) ).
tff('Define:ctx:66',axiom,
? [X_421: $int] :
( ? [X_422: set_2] :
( ! [X_423: $int,X_424: $int] :
( mem2(X_424,X_423,X_422)
<=> mem2(X_424,X_423,g_s55_51) )
& ! [X_425: $int,X_426: $int,X_427: $int] :
( ( mem2(X_425,X_426,X_422)
& mem2(X_425,X_427,X_422) )
=> ( X_426 = X_427 ) )
& ! [X_428: $int] :
( ( $greatereq(X_428,1)
& $lesseq(X_428,X_421) )
<=> ? [X_429: $int] : mem2(X_428,X_429,X_422) )
& ! [X_430: $int] :
( ? [X_431: $int] : mem2(X_431,X_430,X_422)
=> mem0(X_430,g_s53_49) ) )
& ! [X_432: $int] :
( mem0(X_432,g_s53_49)
=> ? [X_433: $int] : mem2(X_433,X_432,g_s55_51) )
& ! [X_434: $int,X_435: $int,X_436: $int] :
( ( mem2(X_435,X_434,g_s55_51)
& mem2(X_436,X_434,g_s55_51) )
=> ( X_435 = X_436 ) ) ) ).
tff('Define:ctx:67',axiom,
! [X_437: $int] :
( mem0(X_437,g_s56_52)
=> mem0(X_437,g_s3_3) ) ).
tff('Define:ctx:68',axiom,
mem0(g_s57_53,g_s3_3) ).
tff('Define:ctx:69',axiom,
~ mem0(g_s57_53,g_s56_52) ).
tff('Define:ctx:7',axiom,
! [X_138: $int,X_139: $int] :
( mem2(X_139,X_138,g_s7_7)
<=> ( $true
& ( ( X_138 = X_139 )
| ( X_138 = $uminus(X_139) ) )
& ! [X_140: $int] :
( ( ( X_140 = X_139 )
| ( X_140 = $uminus(X_139) ) )
=> $greatereq(X_138,X_140) ) ) ) ).
tff('Define:ctx:70',axiom,
( ! [X_438: $int,X_439: $int] :
( mem2(X_439,X_438,g_s58_54)
=> ( $greatereq(X_439,0)
& $lesseq(X_439,max_int)
& mem0(X_438,g_s3_3) ) )
& ! [X_440: $int,X_441: $int,X_442: $int] :
( ( mem2(X_440,X_441,g_s58_54)
& mem2(X_440,X_442,g_s58_54) )
=> ( X_441 = X_442 ) ) ) ).
tff('Define:ctx:71',axiom,
? [X_443: $int] :
( ? [X_444: set_2] :
( ! [X_445: $int,X_446: $int] :
( mem2(X_446,X_445,X_444)
<=> mem2(X_446,X_445,g_s58_54) )
& ! [X_447: $int,X_448: $int,X_449: $int] :
( ( mem2(X_447,X_448,X_444)
& mem2(X_447,X_449,X_444) )
=> ( X_448 = X_449 ) )
& ! [X_450: $int] :
( ( $greatereq(X_450,1)
& $lesseq(X_450,X_443) )
<=> ? [X_451: $int] : mem2(X_450,X_451,X_444) )
& ! [X_452: $int] :
( ? [X_453: $int] : mem2(X_453,X_452,X_444)
=> mem0(X_452,g_s56_52) ) )
& ! [X_454: $int] :
( mem0(X_454,g_s56_52)
=> ? [X_455: $int] : mem2(X_455,X_454,g_s58_54) )
& ! [X_456: $int,X_457: $int,X_458: $int] :
( ( mem2(X_457,X_456,g_s58_54)
& mem2(X_458,X_456,g_s58_54) )
=> ( X_457 = X_458 ) ) ) ).
tff('Define:ctx:72',axiom,
! [X_459: $int] :
( mem0(X_459,g_s59_55)
=> mem0(X_459,g_s4_4) ) ).
tff('Define:ctx:73',axiom,
mem0(g_s60_56,g_s4_4) ).
tff('Define:ctx:74',axiom,
~ mem0(g_s60_56,g_s59_55) ).
tff('Define:ctx:75',axiom,
( ! [X_460: $int,X_461: $int] :
( mem2(X_461,X_460,g_s61_57)
=> ( $greatereq(X_461,0)
& $lesseq(X_461,max_int)
& mem0(X_460,g_s4_4) ) )
& ! [X_462: $int,X_463: $int,X_464: $int] :
( ( mem2(X_462,X_463,g_s61_57)
& mem2(X_462,X_464,g_s61_57) )
=> ( X_463 = X_464 ) ) ) ).
tff('Define:ctx:76',axiom,
? [X_465: $int] :
( ? [X_466: set_2] :
( ! [X_467: $int,X_468: $int] :
( mem2(X_468,X_467,X_466)
<=> mem2(X_468,X_467,g_s61_57) )
& ! [X_469: $int,X_470: $int,X_471: $int] :
( ( mem2(X_469,X_470,X_466)
& mem2(X_469,X_471,X_466) )
=> ( X_470 = X_471 ) )
& ! [X_472: $int] :
( ( $greatereq(X_472,1)
& $lesseq(X_472,X_465) )
<=> ? [X_473: $int] : mem2(X_472,X_473,X_466) )
& ! [X_474: $int] :
( ? [X_475: $int] : mem2(X_475,X_474,X_466)
=> mem0(X_474,g_s59_55) ) )
& ! [X_476: $int] :
( mem0(X_476,g_s59_55)
=> ? [X_477: $int] : mem2(X_477,X_476,g_s61_57) )
& ! [X_478: $int,X_479: $int,X_480: $int] :
( ( mem2(X_479,X_478,g_s61_57)
& mem2(X_480,X_478,g_s61_57) )
=> ( X_479 = X_480 ) ) ) ).
tff('Define:ctx:77',axiom,
! [X_481: $int] :
( mem0(X_481,g_s62_58)
=> mem0(X_481,g_s5_5) ) ).
tff('Define:ctx:78',axiom,
mem0(g_s63_59,g_s5_5) ).
tff('Define:ctx:79',axiom,
~ mem0(g_s63_59,g_s62_58) ).
tff('Define:ctx:8',axiom,
! [X_141: $int,X_142: $int] :
( mem2(X_142,X_141,g_s9_8)
<=> ( $greatereq(X_142,0)
& $true
& $lesseq($product(X_141,X_141),X_142)
& ! [X_143: $int] :
( ( $true
& $lesseq($product(X_143,X_143),X_142) )
=> $greatereq(X_141,X_143) ) ) ) ).
tff('Define:ctx:80',axiom,
( ! [X_482: $int,X_483: $int] :
( mem2(X_483,X_482,g_s64_60)
=> ( $greatereq(X_483,0)
& $lesseq(X_483,max_int)
& mem0(X_482,g_s5_5) ) )
& ! [X_484: $int,X_485: $int,X_486: $int] :
( ( mem2(X_484,X_485,g_s64_60)
& mem2(X_484,X_486,g_s64_60) )
=> ( X_485 = X_486 ) ) ) ).
tff('Define:ctx:81',axiom,
? [X_487: $int] :
( ? [X_488: set_2] :
( ! [X_489: $int,X_490: $int] :
( mem2(X_490,X_489,X_488)
<=> mem2(X_490,X_489,g_s64_60) )
& ! [X_491: $int,X_492: $int,X_493: $int] :
( ( mem2(X_491,X_492,X_488)
& mem2(X_491,X_493,X_488) )
=> ( X_492 = X_493 ) )
& ! [X_494: $int] :
( ( $greatereq(X_494,1)
& $lesseq(X_494,X_487) )
<=> ? [X_495: $int] : mem2(X_494,X_495,X_488) )
& ! [X_496: $int] :
( ? [X_497: $int] : mem2(X_497,X_496,X_488)
=> mem0(X_496,g_s62_58) ) )
& ! [X_498: $int] :
( mem0(X_498,g_s62_58)
=> ? [X_499: $int] : mem2(X_499,X_498,g_s64_60) )
& ! [X_500: $int,X_501: $int,X_502: $int] :
( ( mem2(X_501,X_500,g_s64_60)
& mem2(X_502,X_500,g_s64_60) )
=> ( X_501 = X_502 ) ) ) ).
tff('Define:ctx:82',axiom,
! [X_503: $int] :
( mem0(X_503,g_s65_61)
=> mem0(X_503,g_s6_6) ) ).
tff('Define:ctx:83',axiom,
mem0(g_s66_62,g_s6_6) ).
tff('Define:ctx:84',axiom,
~ mem0(g_s66_62,g_s65_61) ).
tff('Define:ctx:85',axiom,
( ! [X_504: $int,X_505: $int] :
( mem2(X_505,X_504,g_s67_63)
=> ( $greatereq(X_505,0)
& $lesseq(X_505,max_int)
& mem0(X_504,g_s6_6) ) )
& ! [X_506: $int,X_507: $int,X_508: $int] :
( ( mem2(X_506,X_507,g_s67_63)
& mem2(X_506,X_508,g_s67_63) )
=> ( X_507 = X_508 ) ) ) ).
tff('Define:ctx:86',axiom,
? [X_509: $int] :
( ? [X_510: set_2] :
( ! [X_511: $int,X_512: $int] :
( mem2(X_512,X_511,X_510)
<=> mem2(X_512,X_511,g_s67_63) )
& ! [X_513: $int,X_514: $int,X_515: $int] :
( ( mem2(X_513,X_514,X_510)
& mem2(X_513,X_515,X_510) )
=> ( X_514 = X_515 ) )
& ! [X_516: $int] :
( ( $greatereq(X_516,1)
& $lesseq(X_516,X_509) )
<=> ? [X_517: $int] : mem2(X_516,X_517,X_510) )
& ! [X_518: $int] :
( ? [X_519: $int] : mem2(X_519,X_518,X_510)
=> mem0(X_518,g_s65_61) ) )
& ! [X_520: $int] :
( mem0(X_520,g_s65_61)
=> ? [X_521: $int] : mem2(X_521,X_520,g_s67_63) )
& ! [X_522: $int,X_523: $int,X_524: $int] :
( ( mem2(X_523,X_522,g_s67_63)
& mem2(X_524,X_522,g_s67_63) )
=> ( X_523 = X_524 ) ) ) ).
tff('Define:ctx:87',axiom,
( ? [X_525: set_2] :
( ! [X_526: $int,X_527: $int] :
( mem2(X_527,X_526,X_525)
<=> mem2(X_527,X_526,g_s68_64) )
& ! [X_528: $int,X_529: $int,X_530: $int] :
( ( mem2(X_528,X_529,X_525)
& mem2(X_528,X_530,X_525) )
=> ( X_529 = X_530 ) )
& ! [X_531: $int] :
( mem0(X_531,g_s53_49)
<=> ? [X_532: $int] : mem2(X_531,X_532,X_525) )
& ! [X_533: $int] :
( ? [X_534: $int] : mem2(X_534,X_533,X_525)
=> mem0(X_533,g_s22_20) ) )
& ! [X_535: $int,X_536: $int,X_537: $int] :
( ( mem2(X_536,X_535,g_s68_64)
& mem2(X_537,X_535,g_s68_64) )
=> ( X_536 = X_537 ) ) ) ).
tff('Define:ctx:88',axiom,
( ? [X_538: set_2] :
( ! [X_539: $int,X_540: $int] :
( mem2(X_540,X_539,X_538)
<=> mem2(X_540,X_539,g_s69_65) )
& ! [X_541: $int,X_542: $int,X_543: $int] :
( ( mem2(X_541,X_542,X_538)
& mem2(X_541,X_543,X_538) )
=> ( X_542 = X_543 ) )
& ! [X_544: $int] :
( mem0(X_544,g_s56_52)
<=> ? [X_545: $int] : mem2(X_544,X_545,X_538) )
& ! [X_546: $int] :
( ? [X_547: $int] : mem2(X_547,X_546,X_538)
=> mem0(X_546,g_s22_20) ) )
& ! [X_548: $int,X_549: $int,X_550: $int] :
( ( mem2(X_549,X_548,g_s69_65)
& mem2(X_550,X_548,g_s69_65) )
=> ( X_549 = X_550 ) ) ) ).
tff('Define:ctx:89',axiom,
mem0(g_s70_66,g_s1_1) ).
tff('Define:ctx:9',axiom,
! [X_144: $int] :
( mem0(X_144,g_s11_9)
<=> ( $greatereq(X_144,min_int)
& $lesseq(X_144,max_int) ) ) ).
tff('Define:ctx:90',axiom,
( ( g_s71_67 != 0 )
=> mem0(g_s70_66,g_s22_20) ) ).
tff('Define:ctx:91',axiom,
( ? [X_551: set_2] :
( ! [X_552: $int,X_553: $int] :
( mem2(X_553,X_552,X_551)
<=> mem2(X_553,X_552,g_s72_68) )
& ! [X_554: $int,X_555: $int,X_556: $int] :
( ( mem2(X_554,X_555,X_551)
& mem2(X_554,X_556,X_551) )
=> ( X_555 = X_556 ) )
& ! [X_557: $int] :
( mem0(X_557,g_s62_58)
<=> ? [X_558: $int] : mem2(X_557,X_558,X_551) )
& ! [X_559: $int] :
( ? [X_560: $int] : mem2(X_560,X_559,X_551)
=> mem0(X_559,g_s22_20) ) )
& ! [X_561: $int,X_562: $int,X_563: $int] :
( ( mem2(X_562,X_561,g_s72_68)
& mem2(X_563,X_561,g_s72_68) )
=> ( X_562 = X_563 ) ) ) ).
tff('Define:ctx:92',axiom,
! [X_564: $int] :
( ( ? [X_565: $int] : mem2(X_565,X_564,g_s68_64)
& ? [X_566: $int] : mem2(X_566,X_564,g_s69_65) )
<=> $false ) ).
tff('Define:ctx:93',axiom,
! [X_567: $int] :
( ( ? [X_568: $int] : mem2(X_568,X_567,g_s68_64)
& ? [X_569: $int] : mem2(X_569,X_567,g_s72_68) )
<=> $false ) ).
tff('Define:ctx:94',axiom,
! [X_570: $int] :
( ( ? [X_571: $int] : mem2(X_571,X_570,g_s72_68)
& ? [X_572: $int] : mem2(X_572,X_570,g_s69_65) )
<=> $false ) ).
tff('Define:ctx:95',axiom,
( ( g_s71_67 != 0 )
=> ~ ? [X_573: $int] : mem2(X_573,g_s70_66,g_s68_64) ) ).
tff('Define:ctx:96',axiom,
( ( g_s71_67 != 0 )
=> ~ ? [X_574: $int] : mem2(X_574,g_s70_66,g_s69_65) ) ).
tff('Define:ctx:97',axiom,
( ( g_s71_67 != 0 )
=> ~ ? [X_575: $int] : mem2(X_575,g_s70_66,g_s72_68) ) ).
tff('Define:ctx:98',axiom,
( ? [X_576: set_2] :
( ! [X_577: $int,X_578: $int] :
( mem2(X_578,X_577,X_576)
<=> mem2(X_578,X_577,g_s73_69) )
& ! [X_579: $int,X_580: $int,X_581: $int] :
( ( mem2(X_579,X_580,X_576)
& mem2(X_579,X_581,X_576) )
=> ( X_580 = X_581 ) )
& ! [X_582: $int] :
( mem0(X_582,g_s53_49)
<=> ? [X_583: $int] : mem2(X_582,X_583,X_576) )
& ! [X_584: $int] :
( ? [X_585: $int] : mem2(X_585,X_584,X_576)
=> mem0(X_584,g_s74_70) ) )
& ! [X_586: $int,X_587: $int,X_588: $int] :
( ( mem2(X_587,X_586,g_s73_69)
& mem2(X_588,X_586,g_s73_69) )
=> ( X_587 = X_588 ) ) ) ).
tff('Define:ctx:99',axiom,
( ? [X_589: set_2] :
( ! [X_590: $int,X_591: $int] :
( mem2(X_591,X_590,X_589)
<=> mem2(X_591,X_590,g_s75_71) )
& ! [X_592: $int,X_593: $int,X_594: $int] :
( ( mem2(X_592,X_593,X_589)
& mem2(X_592,X_594,X_589) )
=> ( X_593 = X_594 ) )
& ! [X_595: $int] :
( mem0(X_595,g_s56_52)
<=> ? [X_596: $int] : mem2(X_595,X_596,X_589) )
& ! [X_597: $int] :
( ? [X_598: $int] : mem2(X_598,X_597,X_589)
=> mem0(X_597,g_s74_70) ) )
& ! [X_599: $int,X_600: $int,X_601: $int] :
( ( mem2(X_600,X_599,g_s75_71)
& mem2(X_601,X_599,g_s75_71) )
=> ( X_600 = X_601 ) ) ) ).
tff('Define:inv:0',axiom,
! [X_907: $int,X_908: $int] :
( mem2(X_908,X_907,g_s147_139)
<=> mem2(X_908,X_907,g_s147_1_142) ) ).
tff('Define:inv:1',axiom,
g_s148_140 = g_s148_1_143 ).
tff('Define:inv:2',axiom,
! [X_909: $int,X_910: $int] :
( mem2(X_910,X_909,g_s149_141)
<=> mem2(X_910,X_909,g_s149_1_144) ) ).
tff('Define:inv:3',axiom,
( ! [X_911: $int,X_912: $int] :
( mem2(X_912,X_911,g_s147_1_142)
=> ( mem0(X_912,g_s53_49)
& mem0(X_911,g_s12_10) ) )
& ! [X_913: $int,X_914: $int,X_915: $int] :
( ( mem2(X_913,X_914,g_s147_1_142)
& mem2(X_913,X_915,g_s147_1_142) )
=> ( X_914 = X_915 ) ) ) ).
tff('Define:inv:4',axiom,
mem0(g_s148_1_143,g_s11_9) ).
tff('Define:inv:5',axiom,
( ! [X_916: $int,X_917: $int] :
( mem2(X_917,X_916,g_s149_1_144)
=> ( mem0(X_917,g_s56_52)
& mem0(X_916,g_s12_10) ) )
& ! [X_918: $int,X_919: $int,X_920: $int] :
( ( mem2(X_918,X_919,g_s149_1_144)
& mem2(X_918,X_920,g_s149_1_144) )
=> ( X_919 = X_920 ) ) ) ).
tff('Define:seext:0',axiom,
( ! [X_682: $int,X_683: $int] :
( mem2(X_683,X_682,g_s99_95)
=> ( mem0(X_683,g_s53_49)
& mem0(X_682,g_s74_70) ) )
& ! [X_684: $int,X_685: $int,X_686: $int] :
( ( mem2(X_684,X_685,g_s99_95)
& mem2(X_684,X_686,g_s99_95) )
=> ( X_685 = X_686 ) ) ) ).
tff('Define:seext:1',axiom,
( ! [X_687: $int,X_688: $int] :
( mem2(X_688,X_687,g_s100_96)
=> ( mem0(X_688,g_s53_49)
& mem0(X_687,g_s74_70) ) )
& ! [X_689: $int,X_690: $int,X_691: $int] :
( ( mem2(X_689,X_690,g_s100_96)
& mem2(X_689,X_691,g_s100_96) )
=> ( X_690 = X_691 ) ) ) ).
tff('Define:seext:10',axiom,
mem0(g_s116_112,g_s97_93) ).
tff('Define:seext:11',axiom,
mem0(g_s109_105,g_s117_113) ).
tff('Define:seext:12',axiom,
mem0(g_s118_115,g_s119_114) ).
tff('Define:seext:13',axiom,
$true ).
tff('Define:seext:14',axiom,
! [X_740: $int] :
( mem0(X_740,g_s121_116)
=> mem0(X_740,g_s122_117) ) ).
tff('Define:seext:15',axiom,
( ! [X_741: $int,X_742: $int] :
( mem2(X_742,X_741,g_s112_108)
=> ( mem0(X_742,g_s122_117)
& mem0(X_741,g_s123_118) ) )
& ! [X_743: $int,X_744: $int,X_745: $int] :
( ( mem2(X_743,X_744,g_s112_108)
& mem2(X_743,X_745,g_s112_108) )
=> ( X_744 = X_745 ) ) ) ).
tff('Define:seext:16',axiom,
( ! [X_746: $int,X_747: $int] :
( mem2(X_747,X_746,g_s111_107)
=> ( mem0(X_747,g_s122_117)
& mem0(X_746,g_s124_119) ) )
& ! [X_748: $int,X_749: $int,X_750: $int] :
( ( mem2(X_748,X_749,g_s111_107)
& mem2(X_748,X_750,g_s111_107) )
=> ( X_749 = X_750 ) ) ) ).
tff('Define:seext:17',axiom,
( ! [X_751: $int,X_752: $int] :
( mem2(X_752,X_751,g_s113_109)
=> ( mem0(X_752,g_s122_117)
& mem0(X_751,g_s125_120) ) )
& ! [X_753: $int,X_754: $int,X_755: $int] :
( ( mem2(X_753,X_754,g_s113_109)
& mem2(X_753,X_755,g_s113_109) )
=> ( X_754 = X_755 ) ) ) ).
tff('Define:seext:18',axiom,
( ! [X_756: $int,X_757: $int] :
( mem2(X_757,X_756,g_s114_110)
=> ( mem0(X_757,g_s122_117)
& mem0(X_756,g_s125_120) ) )
& ! [X_758: $int,X_759: $int,X_760: $int] :
( ( mem2(X_758,X_759,g_s114_110)
& mem2(X_758,X_760,g_s114_110) )
=> ( X_759 = X_760 ) ) ) ).
tff('Define:seext:19',axiom,
mem0(g_s126_121,g_s11_9) ).
tff('Define:seext:2',axiom,
? [X_692: set_2] :
( ! [X_693: $int,X_694: $int] :
( mem2(X_694,X_693,X_692)
<=> mem2(X_694,X_693,g_s101_97) )
& ! [X_695: $int,X_696: $int,X_697: $int] :
( ( mem2(X_695,X_696,X_692)
& mem2(X_695,X_697,X_692) )
=> ( X_696 = X_697 ) )
& ! [X_698: $int] :
( mem0(X_698,g_s53_49)
<=> ? [X_699: $int] : mem2(X_698,X_699,X_692) )
& ! [X_700: $int] :
( ? [X_701: $int] : mem2(X_701,X_700,X_692)
=> ( $greatereq(X_700,0)
& $lesseq(X_700,max_int) ) ) ) ).
tff('Define:seext:20',axiom,
mem0(g_s127_122,g_s11_9) ).
tff('Define:seext:21',axiom,
$true ).
tff('Define:seext:22',axiom,
$true ).
tff('Define:seext:23',axiom,
! [L_s130: $int] :
( ( mem0(L_s130,g_s56_52)
& mem2(L_s130,g_s110_106,g_s131_123) )
=> ( ? [X_761: $int] : mem2(L_s130,X_761,g_s132_124)
& ! [X_762: $int] :
( ? [X_763: $int] :
! [X_764: set_2] :
( mem5(L_s130,X_764,g_s133_125)
=> mem2(X_762,X_763,X_764) )
<=> ? [X_765: $int] :
! [X_766: set_2] :
( mem5(L_s130,X_766,g_s134_126)
=> mem2(X_762,X_765,X_766) ) )
& ! [X_767: $int] :
( ? [X_768: $int] :
! [X_769: set_2] :
( mem5(L_s130,X_769,g_s135_127)
=> mem2(X_767,X_768,X_769) )
<=> ? [X_770: $int] :
! [X_771: set_2] :
( mem5(L_s130,X_771,g_s134_126)
=> mem2(X_767,X_770,X_771) ) )
& ! [X_772: $int] :
( ? [X_773: $int] :
! [X_774: set_2] :
( mem5(L_s130,X_774,g_s136_128)
=> mem2(X_772,X_773,X_774) )
<=> ? [X_775: $int] :
! [X_776: set_2] :
( mem5(L_s130,X_776,g_s134_126)
=> mem2(X_772,X_775,X_776) ) ) ) ) ).
tff('Define:seext:24',axiom,
! [L_s130: $int] :
( ? [X_777: $int] : mem2(L_s130,X_777,g_s132_124)
=> mem2(L_s130,g_s110_106,g_s131_123) ) ).
tff('Define:seext:25',axiom,
( ! [X_778: $int,X_779: $int] :
( mem2(X_779,X_778,g_s137_129)
=> ( mem0(X_779,g_s56_52)
& mem0(X_778,g_s74_70) ) )
& ! [X_780: $int,X_781: $int,X_782: $int] :
( ( mem2(X_780,X_781,g_s137_129)
& mem2(X_780,X_782,g_s137_129) )
=> ( X_781 = X_782 ) ) ) ).
tff('Define:seext:26',axiom,
( ! [X_783: $int,X_784: $int] :
( mem2(X_784,X_783,g_s138_130)
=> ( mem0(X_784,g_s56_52)
& mem0(X_783,g_s74_70) ) )
& ! [X_785: $int,X_786: $int,X_787: $int] :
( ( mem2(X_785,X_786,g_s138_130)
& mem2(X_785,X_787,g_s138_130) )
=> ( X_786 = X_787 ) ) ) ).
tff('Define:seext:27',axiom,
? [X_788: set_2] :
( ! [X_789: $int,X_790: $int] :
( mem2(X_790,X_789,X_788)
<=> mem2(X_790,X_789,g_s131_123) )
& ! [X_791: $int,X_792: $int,X_793: $int] :
( ( mem2(X_791,X_792,X_788)
& mem2(X_791,X_793,X_788) )
=> ( X_792 = X_793 ) )
& ! [X_794: $int] :
( mem0(X_794,g_s56_52)
<=> ? [X_795: $int] : mem2(X_794,X_795,X_788) )
& ! [X_796: $int] :
( ? [X_797: $int] : mem2(X_797,X_796,X_788)
=> mem0(X_796,g_s117_113) ) ) ).
tff('Define:seext:28',axiom,
( ! [X_798: $int,X_799: $int] :
( mem2(X_799,X_798,g_s132_124)
=> ( mem0(X_799,g_s56_52)
& mem0(X_798,g_s139_131) ) )
& ! [X_800: $int,X_801: $int,X_802: $int] :
( ( mem2(X_800,X_801,g_s132_124)
& mem2(X_800,X_802,g_s132_124) )
=> ( X_801 = X_802 ) ) ) ).
tff('Define:seext:29',axiom,
! [X_803: $int] :
( mem0(X_803,g_s140_132)
=> mem0(X_803,g_s56_52) ) ).
tff('Define:seext:3',axiom,
? [X_702: set_5] :
( ! [X_703: set_2,X_704: $int] :
( mem5(X_704,X_703,X_702)
<=> mem5(X_704,X_703,g_s102_98) )
& ! [X_705: $int,X_706: set_2,X_707: set_2] :
( ( mem5(X_705,X_706,X_702)
& mem5(X_705,X_707,X_702) )
=> ! [X_708: $int,X_709: $int] :
( mem2(X_709,X_708,X_706)
<=> mem2(X_709,X_708,X_707) ) )
& ! [X_710: $int] :
( mem0(X_710,g_s53_49)
<=> ? [X_711: set_2] : mem5(X_710,X_711,X_702) )
& ! [X_712: set_2] :
( ? [X_713: $int] : mem5(X_713,X_712,X_702)
=> ( ! [X_714: $int,X_715: $int] :
( mem2(X_715,X_714,X_712)
=> ( mem0(X_715,g_s103_99)
& mem0(X_714,g_s104_100) ) )
& ! [X_716: $int,X_717: $int,X_718: $int] :
( ( mem2(X_716,X_717,X_712)
& mem2(X_716,X_718,X_712) )
=> ( X_717 = X_718 ) ) ) ) ) ).
tff('Define:seext:30',axiom,
! [X_804: $int] :
( mem0(X_804,g_s141_133)
=> mem0(X_804,g_s56_52) ) ).
tff('Define:seext:31',axiom,
! [X_805: $int,X_806: $int] :
( mem2(X_806,X_805,g_s142_134)
=> ( mem0(X_806,g_s56_52)
& mem0(X_805,g_s122_117) ) ) ).
tff('Define:seext:32',axiom,
? [X_807: set_5] :
( ! [X_808: set_2,X_809: $int] :
( mem5(X_809,X_808,X_807)
<=> mem5(X_809,X_808,g_s134_126) )
& ! [X_810: $int,X_811: set_2,X_812: set_2] :
( ( mem5(X_810,X_811,X_807)
& mem5(X_810,X_812,X_807) )
=> ! [X_813: $int,X_814: $int] :
( mem2(X_814,X_813,X_811)
<=> mem2(X_814,X_813,X_812) ) )
& ! [X_815: $int] :
( mem0(X_815,g_s56_52)
<=> ? [X_816: set_2] : mem5(X_815,X_816,X_807) )
& ! [X_817: set_2] :
( ? [X_818: $int] : mem5(X_818,X_817,X_807)
=> ( ! [X_819: $int,X_820: $int] :
( mem2(X_820,X_819,X_817)
=> ( mem0(X_820,g_s122_117)
& mem0(X_819,g_s123_118) ) )
& ! [X_821: $int,X_822: $int,X_823: $int] :
( ( mem2(X_821,X_822,X_817)
& mem2(X_821,X_823,X_817) )
=> ( X_822 = X_823 ) ) ) ) ) ).
tff('Define:seext:33',axiom,
? [X_824: set_5] :
( ! [X_825: set_2,X_826: $int] :
( mem5(X_826,X_825,X_824)
<=> mem5(X_826,X_825,g_s133_125) )
& ! [X_827: $int,X_828: set_2,X_829: set_2] :
( ( mem5(X_827,X_828,X_824)
& mem5(X_827,X_829,X_824) )
=> ! [X_830: $int,X_831: $int] :
( mem2(X_831,X_830,X_828)
<=> mem2(X_831,X_830,X_829) ) )
& ! [X_832: $int] :
( mem0(X_832,g_s56_52)
<=> ? [X_833: set_2] : mem5(X_832,X_833,X_824) )
& ! [X_834: set_2] :
( ? [X_835: $int] : mem5(X_835,X_834,X_824)
=> ( ! [X_836: $int,X_837: $int] :
( mem2(X_837,X_836,X_834)
=> ( mem0(X_837,g_s122_117)
& mem0(X_836,g_s124_119) ) )
& ! [X_838: $int,X_839: $int,X_840: $int] :
( ( mem2(X_838,X_839,X_834)
& mem2(X_838,X_840,X_834) )
=> ( X_839 = X_840 ) ) ) ) ) ).
tff('Define:seext:34',axiom,
? [X_841: set_5] :
( ! [X_842: set_2,X_843: $int] :
( mem5(X_843,X_842,X_841)
<=> mem5(X_843,X_842,g_s135_127) )
& ! [X_844: $int,X_845: set_2,X_846: set_2] :
( ( mem5(X_844,X_845,X_841)
& mem5(X_844,X_846,X_841) )
=> ! [X_847: $int,X_848: $int] :
( mem2(X_848,X_847,X_845)
<=> mem2(X_848,X_847,X_846) ) )
& ! [X_849: $int] :
( mem0(X_849,g_s56_52)
<=> ? [X_850: set_2] : mem5(X_849,X_850,X_841) )
& ! [X_851: set_2] :
( ? [X_852: $int] : mem5(X_852,X_851,X_841)
=> ( ! [X_853: $int,X_854: $int] :
( mem2(X_854,X_853,X_851)
=> ( mem0(X_854,g_s122_117)
& mem0(X_853,g_s125_120) ) )
& ! [X_855: $int,X_856: $int,X_857: $int] :
( ( mem2(X_855,X_856,X_851)
& mem2(X_855,X_857,X_851) )
=> ( X_856 = X_857 ) ) ) ) ) ).
tff('Define:seext:35',axiom,
? [X_858: set_5] :
( ! [X_859: set_2,X_860: $int] :
( mem5(X_860,X_859,X_858)
<=> mem5(X_860,X_859,g_s136_128) )
& ! [X_861: $int,X_862: set_2,X_863: set_2] :
( ( mem5(X_861,X_862,X_858)
& mem5(X_861,X_863,X_858) )
=> ! [X_864: $int,X_865: $int] :
( mem2(X_865,X_864,X_862)
<=> mem2(X_865,X_864,X_863) ) )
& ! [X_866: $int] :
( mem0(X_866,g_s56_52)
<=> ? [X_867: set_2] : mem5(X_866,X_867,X_858) )
& ! [X_868: set_2] :
( ? [X_869: $int] : mem5(X_869,X_868,X_858)
=> ( ! [X_870: $int,X_871: $int] :
( mem2(X_871,X_870,X_868)
=> ( mem0(X_871,g_s122_117)
& mem0(X_870,g_s125_120) ) )
& ! [X_872: $int,X_873: $int,X_874: $int] :
( ( mem2(X_872,X_873,X_868)
& mem2(X_872,X_874,X_868) )
=> ( X_873 = X_874 ) ) ) ) ) ).
tff('Define:seext:36',axiom,
( ! [X_875: $int,X_876: $int] :
( mem2(X_876,X_875,g_s143_135)
=> ( mem0(X_876,g_s56_52)
& mem0(X_875,g_s12_10) ) )
& ! [X_877: $int,X_878: $int,X_879: $int] :
( ( mem2(X_877,X_878,g_s143_135)
& mem2(X_877,X_879,g_s143_135) )
=> ( X_878 = X_879 ) ) ) ).
tff('Define:seext:37',axiom,
( ! [X_880: $int,X_881: $int] :
( mem2(X_881,X_880,g_s144_136)
=> ( mem0(X_881,g_s56_52)
& mem0(X_880,g_s12_10) ) )
& ! [X_882: $int,X_883: $int,X_884: $int] :
( ( mem2(X_882,X_883,g_s144_136)
& mem2(X_882,X_884,g_s144_136) )
=> ( X_883 = X_884 ) ) ) ).
tff('Define:seext:38',axiom,
! [X_885: $int] :
( mem0(X_885,g_s145_137)
=> mem0(X_885,g_s56_52) ) ).
tff('Define:seext:39',axiom,
! [X_886: $int] :
( mem0(X_886,g_s146_138)
=> mem0(X_886,g_s56_52) ) ).
tff('Define:seext:4',axiom,
( ! [X_719: $int,X_720: $int] :
( mem2(X_720,X_719,g_s105_101)
=> ( mem0(X_720,g_s53_49)
& mem0(X_719,g_s12_10) ) )
& ! [X_721: $int,X_722: $int,X_723: $int] :
( ( mem2(X_721,X_722,g_s105_101)
& mem2(X_721,X_723,g_s105_101) )
=> ( X_722 = X_723 ) ) ) ).
tff('Define:seext:5',axiom,
( ! [X_724: $int,X_725: $int] :
( mem2(X_725,X_724,g_s106_102)
=> ( mem0(X_725,g_s53_49)
& mem0(X_724,g_s12_10) ) )
& ! [X_726: $int,X_727: $int,X_728: $int] :
( ( mem2(X_726,X_727,g_s106_102)
& mem2(X_726,X_728,g_s106_102) )
=> ( X_727 = X_728 ) ) ) ).
tff('Define:seext:6',axiom,
! [X_729: $int] :
( mem0(X_729,g_s107_103)
=> mem0(X_729,g_s53_49) ) ).
tff('Define:seext:7',axiom,
! [X_730: $int] :
( mem0(X_730,g_s108_104)
=> mem0(X_730,g_s53_49) ) ).
tff('Define:seext:8',axiom,
( ( g_s109_105 = g_s110_106 )
=> ( ! [X_731: $int] :
( ? [X_732: $int] : mem2(X_731,X_732,g_s111_107)
<=> ? [X_733: $int] : mem2(X_731,X_733,g_s112_108) )
& ! [X_734: $int] :
( ? [X_735: $int] : mem2(X_734,X_735,g_s113_109)
<=> ? [X_736: $int] : mem2(X_734,X_736,g_s112_108) )
& ! [X_737: $int] :
( ? [X_738: $int] : mem2(X_737,X_738,g_s114_110)
<=> ? [X_739: $int] : mem2(X_737,X_739,g_s112_108) ) ) ) ).
tff('Define:seext:9',axiom,
mem0(g_s115_111,g_s97_93) ).
%Global hypotheses
tff(gh_0_def,hypothesis,
mem0(g_s157_148,g_s3_3) ).
tff(gh_1_def,hypothesis,
mem0(g_s157_148,g_s56_52) ).
tff(gh_2_def,hypothesis,
g_s92_88 = g_s93_89 ).
tff(gh_3_def,hypothesis,
mem0(g_s157_148,g_s3_3) ).
tff(gh_4_def,hypothesis,
mem0(g_s157_148,g_s56_52) ).
tff(gh_5_def,hypothesis,
g_s92_88 = g_s93_89 ).
%----Local hypotheses
tff('Local_Hyp:0',hypothesis,
( mem0(g_s157_148,g_s146_138)
& ? [X_1010: $int] : mem2(g_s157_148,X_1010,g_s143_135) ) ).
tff('Local_Hyp:1',hypothesis,
~ ? [X_1011: $int] : mem2(g_s157_148,X_1011,g_s149_1_144) ).
%----Goal
tff('Goal',conjecture,
( ! [X_1012: $int,X_1013: $int] :
( ( ( ( X_1013 = g_s157_148 )
& mem2(g_s157_148,X_1012,g_s143_135) )
| ( mem2(X_1013,X_1012,g_s149_1_144)
& ~ ? [X_1014: $int] :
( ( X_1013 = g_s157_148 )
& mem2(g_s157_148,X_1014,g_s143_135) ) ) )
=> ( mem0(X_1013,g_s56_52)
& mem0(X_1012,g_s12_10) ) )
& ! [X_1015: $int,X_1016: $int,X_1017: $int] :
( ( ( ( ( X_1015 = g_s157_148 )
& mem2(g_s157_148,X_1016,g_s143_135) )
| ( mem2(X_1015,X_1016,g_s149_1_144)
& ~ ? [X_1018: $int] :
( ( X_1015 = g_s157_148 )
& mem2(g_s157_148,X_1018,g_s143_135) ) ) )
& ( ( ( X_1015 = g_s157_148 )
& mem2(g_s157_148,X_1017,g_s143_135) )
| ( mem2(X_1015,X_1017,g_s149_1_144)
& ~ ? [X_1019: $int] :
( ( X_1015 = g_s157_148 )
& mem2(g_s157_148,X_1019,g_s143_135) ) ) ) )
=> ( X_1016 = X_1017 ) ) ) ).
%------------------------------------------------------------------------------