TPTP Problem File: SWC539_1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWC539_1 : TPTP v9.0.0. Released v9.0.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 0 11 Group s109 Tag s110
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0015-00214-0-11.tptp [Deh24]
% Status : Theorem
% Rating : 0.38 v9.0.0
% Syntax : Number of formulae : 272 ( 38 unt; 114 typ; 0 def)
% Number of atoms : 1038 ( 142 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 930 ( 50 ~; 8 |; 476 &)
% ( 126 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 1069 ( 116 atm; 17 fun; 78 num; 858 var)
% Number of types : 7 ( 4 usr; 2 ari)
% Number of type conns : 23 ( 13 >; 10 *; 0 +; 0 <<)
% Number of predicates : 10 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 117 ( 106 usr; 103 con; 0-2 aty)
% Number of variables : 936 ( 692 !; 244 ?; 936 :)
% SPC : TF0_THM_EQU_ARI
% Comments : Autogenerated by PPTRANS-TPTP - github.com/CLEARSY/pptranspog
%------------------------------------------------------------------------------
tff(set_0_type,type,
set_0: $tType ).
tff(mem0_type,type,
mem0: ( $int * set_0 ) > $o ).
tff(set_1_type,type,
set_1: $tType ).
tff(mem1_type,type,
mem1: ( $real * set_1 ) > $o ).
tff(b_division_type,type,
divB: ( $int * $int ) > $int ).
tff(b_division_def_1,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(0,Y) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_2,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(0,Y) )
=> ( divB(X,Y) = $uminus($quotient_f($uminus(X),Y)) ) ) ).
tff(b_division_def_3,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f(X,Y) ) ) ).
tff(b_division_def_4,axiom,
! [X: $int,Y: $int] :
( ( $lesseq(X,0)
& $less(Y,0) )
=> ( divB(X,Y) = $quotient_f($uminus(X),$uminus(Y)) ) ) ).
tff(exp_type,type,
exp: ( $int * $int ) > $int ).
tff(exp_def_1,axiom,
! [X: $int] : ( exp(X,0) = 1 ) ).
tff(exp_def_2,axiom,
! [X: $int,Y: $int] :
( $greatereq(Y,1)
=> ( exp(X,Y) = $sum(X,exp(X,$difference(Y,1))) ) ) ).
tff(rexp_type,type,
rexp: ( $real * $int ) > $real ).
tff(rexp_def_1,axiom,
! [X: $real] :
( ( X != 0.0 )
=> ( rexp(X,0) = 1.0 ) ) ).
tff(rexp_def_2,axiom,
! [X: $real,Y: $int] :
( $greatereq(Y,1)
=> ( rexp(X,Y) = $sum(X,rexp(X,$difference(Y,1))) ) ) ).
tff(isum_type,type,
isum: set_0 > $int ).
tff(isum_def_1,axiom,
! [S: set_0] :
( ! [X: $int] : ~ mem0(X,S)
=> ( isum(S) = 0 ) ) ).
tff(isum_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( isum(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( mem0(X,S1)
=> mem0(X,S2) ) )
=> ( isum(S2) = $sum(N,E) ) ) ).
tff(rsum_type,type,
rsum: set_1 > $real ).
tff(rsum_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rsum(S) = 0.0 ) ) ).
tff(rsum_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rsum(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( mem1(X,S1)
=> mem1(X,S2) ) )
=> ( rsum(S2) = $sum(N,E) ) ) ).
tff(iprod_type,type,
iprod: set_0 > $int ).
tff(iprod_def_1,axiom,
! [S: set_0,X: $int] :
( ~ mem0(X,S)
=> ( iprod(S) = 1 ) ) ).
tff(iprod_def_2,axiom,
! [S1: set_0,S2: set_0,E: $int,N: $int] :
( ( ( iprod(S1) = N )
& ~ mem0(E,S1)
& ! [X: $int] :
( mem0(X,S2)
=> ( ( X = E )
| mem0(X,S1) ) )
& ! [X: $int] :
( ( ( X = E )
| mem0(X,S1) )
=> mem0(X,S2) ) )
=> ( isum(S2) = $product(N,E) ) ) ).
tff(rprod_type,type,
rprod: set_1 > $real ).
tff(rprod_def_1,axiom,
! [S: set_1,X: $real] :
( ~ mem1(X,S)
=> ( rprod(S) = 1.0 ) ) ).
tff(rprod_def_2,axiom,
! [S1: set_1,S2: set_1,E: $real,N: $real] :
( ( ( rprod(S1) = N )
& ~ mem1(E,S1)
& ! [X: $real] :
( mem1(X,S2)
=> ( ( X = E )
| mem1(X,S1) ) )
& ! [X: $real] :
( ( ( X = E )
| mem1(X,S1) )
=> mem1(X,S2) ) )
=> ( rprod(S2) = $sum(N,E) ) ) ).
tff(min_int_type,type,
min_int: $int ).
tff(max_int_type,type,
max_int: $int ).
tff(min_int_axiom,axiom,
min_int = $uminus(2147483648) ).
tff(max_int_axiom,axiom,
max_int = 2147483647 ).
%--------------------------------------------------------------------------
%----Global declarations
tff(g_s0_0_type,type,
g_s0_0: set_0 ).
tff(g_s100_85_type,type,
g_s100_85: set_2 ).
tff(g_s101_86_type,type,
g_s101_86: set_2 ).
tff(g_s102_87_type,type,
g_s102_87: set_2 ).
tff(g_s103_88_type,type,
g_s103_88: set_2 ).
tff(g_s104_89_type,type,
g_s104_89: set_2 ).
tff(g_s105_90_type,type,
g_s105_90: set_2 ).
tff(g_s106_91_type,type,
g_s106_91: set_2 ).
tff(g_s107_92_type,type,
g_s107_92: set_2 ).
tff(g_s108_79_type,type,
g_s108_79: set_2 ).
tff(g_s10_10_type,type,
g_s10_10: set_0 ).
tff(g_s11_11_type,type,
g_s11_11: set_0 ).
tff(g_s12_12_type,type,
g_s12_12: set_0 ).
tff(g_s13_13_type,type,
g_s13_13: set_0 ).
tff(g_s14_14_type,type,
g_s14_14: set_0 ).
tff(g_s15_15_type,type,
g_s15_15: set_0 ).
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: set_0 ).
tff(g_s1_1_type,type,
g_s1_1: set_0 ).
tff(g_s20_20_type,type,
g_s20_20: $int ).
tff(g_s21_21_type,type,
g_s21_21: set_2 ).
tff(g_s22_22_type,type,
g_s22_22: set_0 ).
tff(g_s23_23_type,type,
g_s23_23: $int ).
tff(g_s24_24_type,type,
g_s24_24: set_2 ).
tff(g_s25_25_type,type,
g_s25_25: set_0 ).
tff(g_s26_26_type,type,
g_s26_26: $int ).
tff(g_s27_27_type,type,
g_s27_27: set_2 ).
tff(g_s28_28_type,type,
g_s28_28: set_0 ).
tff(g_s29_29_type,type,
g_s29_29: $int ).
tff(g_s2_2_type,type,
g_s2_2: set_0 ).
tff(g_s30_30_type,type,
g_s30_30: set_2 ).
tff(g_s31_31_type,type,
g_s31_31: set_0 ).
tff(g_s32_32_type,type,
g_s32_32: $int ).
tff(g_s33_33_type,type,
g_s33_33: set_2 ).
tff(g_s34_34_type,type,
g_s34_34: set_0 ).
tff(g_s35_35_type,type,
g_s35_35: $int ).
tff(g_s36_36_type,type,
g_s36_36: set_2 ).
tff(g_s37_37_type,type,
g_s37_37: set_0 ).
tff(g_s38_38_type,type,
g_s38_38: $int ).
tff(g_s39_39_type,type,
g_s39_39: set_2 ).
tff(g_s3_3_type,type,
g_s3_3: set_0 ).
tff(g_s40_40_type,type,
g_s40_40: set_0 ).
tff(g_s41_41_type,type,
g_s41_41: $int ).
tff(g_s42_42_type,type,
g_s42_42: set_2 ).
tff(g_s43_43_type,type,
g_s43_43: set_2 ).
tff(g_s44_44_type,type,
g_s44_44: set_0 ).
tff(g_s45_45_type,type,
g_s45_45: set_2 ).
tff(g_s46_47_type,type,
g_s46_47: $int ).
tff(g_s47_46_type,type,
g_s47_46: set_0 ).
tff(g_s48_48_type,type,
g_s48_48: $int ).
tff(g_s49_49_type,type,
g_s49_49: set_2 ).
tff(g_s4_4_type,type,
g_s4_4: set_0 ).
tff(g_s50_50_type,type,
g_s50_50: set_0 ).
tff(g_s51_51_type,type,
g_s51_51: $int ).
tff(g_s52_52_type,type,
g_s52_52: set_2 ).
tff(g_s53_53_type,type,
g_s53_53: set_0 ).
tff(g_s54_54_type,type,
g_s54_54: set_0 ).
tff(g_s55_55_type,type,
g_s55_55: set_2 ).
tff(g_s56_56_type,type,
g_s56_56: set_0 ).
tff(g_s57_57_type,type,
g_s57_57: $int ).
tff(g_s58_58_type,type,
g_s58_58: set_2 ).
tff(g_s59_59_type,type,
g_s59_59: set_0 ).
tff(g_s5_5_type,type,
g_s5_5: set_0 ).
tff(g_s60_60_type,type,
g_s60_60: $int ).
tff(g_s61_61_type,type,
g_s61_61: set_2 ).
tff(g_s62_62_type,type,
g_s62_62: set_0 ).
tff(g_s63_63_type,type,
g_s63_63: $int ).
tff(g_s64_64_type,type,
g_s64_64: set_2 ).
tff(g_s65_65_type,type,
g_s65_65: set_0 ).
tff(g_s66_66_type,type,
g_s66_66: set_0 ).
tff(g_s67_67_type,type,
g_s67_67: set_2 ).
tff(g_s68_68_type,type,
g_s68_68: set_0 ).
tff(g_s69_69_type,type,
g_s69_69: $int ).
tff(g_s6_6_type,type,
g_s6_6: set_0 ).
tff(g_s70_70_type,type,
g_s70_70: set_2 ).
tff(g_s71_71_type,type,
g_s71_71: set_0 ).
tff(g_s72_72_type,type,
g_s72_72: $int ).
tff(g_s73_73_type,type,
g_s73_73: set_2 ).
tff(g_s74_74_type,type,
g_s74_74: set_0 ).
tff(g_s75_75_type,type,
g_s75_75: $int ).
tff(g_s76_76_type,type,
g_s76_76: set_2 ).
tff(g_s7_7_type,type,
g_s7_7: set_0 ).
tff(g_s8_8_type,type,
g_s8_8: set_0 ).
tff(g_s93_80_type,type,
g_s93_80: set_2 ).
tff(g_s94_77_type,type,
g_s94_77: set_2 ).
tff(g_s95_81_type,type,
g_s95_81: set_2 ).
tff(g_s96_82_type,type,
g_s96_82: set_2 ).
tff(g_s97_78_type,type,
g_s97_78: set_2 ).
tff(g_s98_83_type,type,
g_s98_83: set_2 ).
tff(g_s99_84_type,type,
g_s99_84: set_2 ).
tff(g_s9_9_type,type,
g_s9_9: set_0 ).
tff(mem2_type,type,
mem2: ( $int * $int * set_2 ) > $o ).
tff(prod_0_type,type,
prod_0: $tType ).
tff(prod_0_empty,type,
prod_0_empty: prod_0 ).
tff(prod_0_insert,type,
prod_0: ( $int * $int ) > prod_0 ).
tff(prod_0_in,type,
prod_0_in: ( $int * $int * prod_0 ) > $o ).
tff(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 ).
%----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: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_195: $int] :
( mem0(X_195,g_s10_10)
<=> $false )
& ! [X_198: $int] :
( mem0(X_198,g_s10_10)
=> $true )
& ? [X_196: $int,X_197: set_2] :
( ? [X_199: set_2] :
( ! [X_200: $int,X_201: $int] :
( mem2(X_201,X_200,X_199)
<=> mem2(X_201,X_200,X_197) )
& ! [X_202: $int,X_203: $int,X_204: $int] :
( ( mem2(X_202,X_203,X_199)
& mem2(X_202,X_204,X_199) )
=> ( X_203 = X_204 ) )
& ! [X_205: $int] :
( ( $greatereq(X_205,1)
& $lesseq(X_205,X_196) )
<=> ? [X_206: $int] : mem2(X_205,X_206,X_199) )
& ! [X_207: $int] :
( ? [X_208: $int] : mem2(X_208,X_207,X_199)
=> mem0(X_207,g_s10_10) ) )
& ! [X_209: $int] :
( mem0(X_209,g_s10_10)
=> ? [X_210: $int] : mem2(X_210,X_209,X_197) )
& ! [X_211: $int,X_212: $int,X_213: $int] :
( ( mem2(X_212,X_211,X_197)
& mem2(X_213,X_211,X_197) )
=> ( X_212 = X_213 ) ) ) ) ).
tff('Define:ctx:100',axiom,
~ mem0(g_s63_63,g_s66_66) ).
tff('Define:ctx:101',axiom,
( ! [X_635: $int,X_636: $int] :
( mem2(X_636,X_635,g_s67_67)
=> ( $greatereq(X_636,0)
& $lesseq(X_636,max_int)
& mem0(X_635,g_s65_65) ) )
& ! [X_637: $int,X_638: $int,X_639: $int] :
( ( mem2(X_637,X_638,g_s67_67)
& mem2(X_637,X_639,g_s67_67) )
=> ( X_638 = X_639 ) ) ) ).
tff('Define:ctx:102',axiom,
? [X_640: $int] :
( ? [X_641: set_2] :
( ! [X_642: $int,X_643: $int] :
( mem2(X_643,X_642,X_641)
<=> mem2(X_643,X_642,g_s67_67) )
& ! [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] :
( ( $greatereq(X_647,1)
& $lesseq(X_647,X_640) )
<=> ? [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_s66_66) ) )
& ! [X_651: $int] :
( mem0(X_651,g_s66_66)
=> ? [X_652: $int] : mem2(X_652,X_651,g_s67_67) )
& ! [X_653: $int,X_654: $int,X_655: $int] :
( ( mem2(X_654,X_653,g_s67_67)
& mem2(X_655,X_653,g_s67_67) )
=> ( X_654 = X_655 ) ) ) ).
tff('Define:ctx:103',axiom,
! [X_656: $int] :
( mem0(X_656,g_s68_68)
=> mem0(X_656,g_s12_12) ) ).
tff('Define:ctx:104',axiom,
mem0(g_s69_69,g_s12_12) ).
tff('Define:ctx:105',axiom,
~ mem0(g_s69_69,g_s68_68) ).
tff('Define:ctx:106',axiom,
( ! [X_657: $int,X_658: $int] :
( mem2(X_658,X_657,g_s70_70)
=> ( $greatereq(X_658,0)
& $lesseq(X_658,max_int)
& mem0(X_657,g_s12_12) ) )
& ! [X_659: $int,X_660: $int,X_661: $int] :
( ( mem2(X_659,X_660,g_s70_70)
& mem2(X_659,X_661,g_s70_70) )
=> ( X_660 = X_661 ) ) ) ).
tff('Define:ctx:107',axiom,
? [X_662: $int] :
( ? [X_663: set_2] :
( ! [X_664: $int,X_665: $int] :
( mem2(X_665,X_664,X_663)
<=> mem2(X_665,X_664,g_s70_70) )
& ! [X_666: $int,X_667: $int,X_668: $int] :
( ( mem2(X_666,X_667,X_663)
& mem2(X_666,X_668,X_663) )
=> ( X_667 = X_668 ) )
& ! [X_669: $int] :
( ( $greatereq(X_669,1)
& $lesseq(X_669,X_662) )
<=> ? [X_670: $int] : mem2(X_669,X_670,X_663) )
& ! [X_671: $int] :
( ? [X_672: $int] : mem2(X_672,X_671,X_663)
=> mem0(X_671,g_s68_68) ) )
& ! [X_673: $int] :
( mem0(X_673,g_s68_68)
=> ? [X_674: $int] : mem2(X_674,X_673,g_s70_70) )
& ! [X_675: $int,X_676: $int,X_677: $int] :
( ( mem2(X_676,X_675,g_s70_70)
& mem2(X_677,X_675,g_s70_70) )
=> ( X_676 = X_677 ) ) ) ).
tff('Define:ctx:108',axiom,
! [X_678: $int] :
( mem0(X_678,g_s71_71)
=> mem0(X_678,g_s13_13) ) ).
tff('Define:ctx:109',axiom,
mem0(g_s72_72,g_s13_13) ).
tff('Define:ctx:11',axiom,
( ~ ! [X_214: $int] :
( mem0(X_214,g_s11_11)
<=> $false )
& ! [X_217: $int] :
( mem0(X_217,g_s11_11)
=> $true )
& ? [X_215: $int,X_216: set_2] :
( ? [X_218: set_2] :
( ! [X_219: $int,X_220: $int] :
( mem2(X_220,X_219,X_218)
<=> mem2(X_220,X_219,X_216) )
& ! [X_221: $int,X_222: $int,X_223: $int] :
( ( mem2(X_221,X_222,X_218)
& mem2(X_221,X_223,X_218) )
=> ( X_222 = X_223 ) )
& ! [X_224: $int] :
( ( $greatereq(X_224,1)
& $lesseq(X_224,X_215) )
<=> ? [X_225: $int] : mem2(X_224,X_225,X_218) )
& ! [X_226: $int] :
( ? [X_227: $int] : mem2(X_227,X_226,X_218)
=> mem0(X_226,g_s11_11) ) )
& ! [X_228: $int] :
( mem0(X_228,g_s11_11)
=> ? [X_229: $int] : mem2(X_229,X_228,X_216) )
& ! [X_230: $int,X_231: $int,X_232: $int] :
( ( mem2(X_231,X_230,X_216)
& mem2(X_232,X_230,X_216) )
=> ( X_231 = X_232 ) ) ) ) ).
tff('Define:ctx:110',axiom,
~ mem0(g_s72_72,g_s71_71) ).
tff('Define:ctx:111',axiom,
( ! [X_679: $int,X_680: $int] :
( mem2(X_680,X_679,g_s73_73)
=> ( $greatereq(X_680,0)
& $lesseq(X_680,max_int)
& mem0(X_679,g_s13_13) ) )
& ! [X_681: $int,X_682: $int,X_683: $int] :
( ( mem2(X_681,X_682,g_s73_73)
& mem2(X_681,X_683,g_s73_73) )
=> ( X_682 = X_683 ) ) ) ).
tff('Define:ctx:112',axiom,
? [X_684: $int] :
( ? [X_685: set_2] :
( ! [X_686: $int,X_687: $int] :
( mem2(X_687,X_686,X_685)
<=> mem2(X_687,X_686,g_s73_73) )
& ! [X_688: $int,X_689: $int,X_690: $int] :
( ( mem2(X_688,X_689,X_685)
& mem2(X_688,X_690,X_685) )
=> ( X_689 = X_690 ) )
& ! [X_691: $int] :
( ( $greatereq(X_691,1)
& $lesseq(X_691,X_684) )
<=> ? [X_692: $int] : mem2(X_691,X_692,X_685) )
& ! [X_693: $int] :
( ? [X_694: $int] : mem2(X_694,X_693,X_685)
=> mem0(X_693,g_s71_71) ) )
& ! [X_695: $int] :
( mem0(X_695,g_s71_71)
=> ? [X_696: $int] : mem2(X_696,X_695,g_s73_73) )
& ! [X_697: $int,X_698: $int,X_699: $int] :
( ( mem2(X_698,X_697,g_s73_73)
& mem2(X_699,X_697,g_s73_73) )
=> ( X_698 = X_699 ) ) ) ).
tff('Define:ctx:113',axiom,
! [X_700: $int] :
( mem0(X_700,g_s74_74)
=> mem0(X_700,g_s14_14) ) ).
tff('Define:ctx:114',axiom,
mem0(g_s75_75,g_s14_14) ).
tff('Define:ctx:115',axiom,
~ mem0(g_s75_75,g_s74_74) ).
tff('Define:ctx:116',axiom,
( ! [X_701: $int,X_702: $int] :
( mem2(X_702,X_701,g_s76_76)
=> ( $greatereq(X_702,0)
& $lesseq(X_702,max_int)
& mem0(X_701,g_s14_14) ) )
& ! [X_703: $int,X_704: $int,X_705: $int] :
( ( mem2(X_703,X_704,g_s76_76)
& mem2(X_703,X_705,g_s76_76) )
=> ( X_704 = X_705 ) ) ) ).
tff('Define:ctx:117',axiom,
? [X_706: $int] :
( ? [X_707: set_2] :
( ! [X_708: $int,X_709: $int] :
( mem2(X_709,X_708,X_707)
<=> mem2(X_709,X_708,g_s76_76) )
& ! [X_710: $int,X_711: $int,X_712: $int] :
( ( mem2(X_710,X_711,X_707)
& mem2(X_710,X_712,X_707) )
=> ( X_711 = X_712 ) )
& ! [X_713: $int] :
( ( $greatereq(X_713,1)
& $lesseq(X_713,X_706) )
<=> ? [X_714: $int] : mem2(X_713,X_714,X_707) )
& ! [X_715: $int] :
( ? [X_716: $int] : mem2(X_716,X_715,X_707)
=> mem0(X_715,g_s74_74) ) )
& ! [X_717: $int] :
( mem0(X_717,g_s74_74)
=> ? [X_718: $int] : mem2(X_718,X_717,g_s76_76) )
& ! [X_719: $int,X_720: $int,X_721: $int] :
( ( mem2(X_720,X_719,g_s76_76)
& mem2(X_721,X_719,g_s76_76) )
=> ( X_720 = X_721 ) ) ) ).
tff('Define:ctx:12',axiom,
( ~ ! [X_233: $int] :
( mem0(X_233,g_s12_12)
<=> $false )
& ! [X_236: $int] :
( mem0(X_236,g_s12_12)
=> $true )
& ? [X_234: $int,X_235: set_2] :
( ? [X_237: set_2] :
( ! [X_238: $int,X_239: $int] :
( mem2(X_239,X_238,X_237)
<=> mem2(X_239,X_238,X_235) )
& ! [X_240: $int,X_241: $int,X_242: $int] :
( ( mem2(X_240,X_241,X_237)
& mem2(X_240,X_242,X_237) )
=> ( X_241 = X_242 ) )
& ! [X_243: $int] :
( ( $greatereq(X_243,1)
& $lesseq(X_243,X_234) )
<=> ? [X_244: $int] : mem2(X_243,X_244,X_237) )
& ! [X_245: $int] :
( ? [X_246: $int] : mem2(X_246,X_245,X_237)
=> mem0(X_245,g_s12_12) ) )
& ! [X_247: $int] :
( mem0(X_247,g_s12_12)
=> ? [X_248: $int] : mem2(X_248,X_247,X_235) )
& ! [X_249: $int,X_250: $int,X_251: $int] :
( ( mem2(X_250,X_249,X_235)
& mem2(X_251,X_249,X_235) )
=> ( X_250 = X_251 ) ) ) ) ).
tff('Define:ctx:13',axiom,
( ~ ! [X_252: $int] :
( mem0(X_252,g_s13_13)
<=> $false )
& ! [X_255: $int] :
( mem0(X_255,g_s13_13)
=> $true )
& ? [X_253: $int,X_254: set_2] :
( ? [X_256: set_2] :
( ! [X_257: $int,X_258: $int] :
( mem2(X_258,X_257,X_256)
<=> mem2(X_258,X_257,X_254) )
& ! [X_259: $int,X_260: $int,X_261: $int] :
( ( mem2(X_259,X_260,X_256)
& mem2(X_259,X_261,X_256) )
=> ( X_260 = X_261 ) )
& ! [X_262: $int] :
( ( $greatereq(X_262,1)
& $lesseq(X_262,X_253) )
<=> ? [X_263: $int] : mem2(X_262,X_263,X_256) )
& ! [X_264: $int] :
( ? [X_265: $int] : mem2(X_265,X_264,X_256)
=> mem0(X_264,g_s13_13) ) )
& ! [X_266: $int] :
( mem0(X_266,g_s13_13)
=> ? [X_267: $int] : mem2(X_267,X_266,X_254) )
& ! [X_268: $int,X_269: $int,X_270: $int] :
( ( mem2(X_269,X_268,X_254)
& mem2(X_270,X_268,X_254) )
=> ( X_269 = X_270 ) ) ) ) ).
tff('Define:ctx:14',axiom,
( ~ ! [X_271: $int] :
( mem0(X_271,g_s14_14)
<=> $false )
& ! [X_274: $int] :
( mem0(X_274,g_s14_14)
=> $true )
& ? [X_272: $int,X_273: set_2] :
( ? [X_275: set_2] :
( ! [X_276: $int,X_277: $int] :
( mem2(X_277,X_276,X_275)
<=> mem2(X_277,X_276,X_273) )
& ! [X_278: $int,X_279: $int,X_280: $int] :
( ( mem2(X_278,X_279,X_275)
& mem2(X_278,X_280,X_275) )
=> ( X_279 = X_280 ) )
& ! [X_281: $int] :
( ( $greatereq(X_281,1)
& $lesseq(X_281,X_272) )
<=> ? [X_282: $int] : mem2(X_281,X_282,X_275) )
& ! [X_283: $int] :
( ? [X_284: $int] : mem2(X_284,X_283,X_275)
=> mem0(X_283,g_s14_14) ) )
& ! [X_285: $int] :
( mem0(X_285,g_s14_14)
=> ? [X_286: $int] : mem2(X_286,X_285,X_273) )
& ! [X_287: $int,X_288: $int,X_289: $int] :
( ( mem2(X_288,X_287,X_273)
& mem2(X_289,X_287,X_273) )
=> ( X_288 = X_289 ) ) ) ) ).
tff('Define:ctx:15',axiom,
( ! [X_290: $int] :
( mem0(X_290,g_s15_15)
<=> ( ( X_290 = g_s16_16 )
| ( X_290 = g_s17_17 )
| ( X_290 = g_s18_18 ) ) )
& ( g_s16_16 != g_s17_17 )
& ( g_s17_17 != g_s18_18 ) ) ).
tff('Define:ctx:16',axiom,
! [X_291: $int] :
( mem0(X_291,g_s19_19)
=> mem0(X_291,g_s0_0) ) ).
tff('Define:ctx:17',axiom,
mem0(g_s20_20,g_s0_0) ).
tff('Define:ctx:18',axiom,
~ mem0(g_s20_20,g_s19_19) ).
tff('Define:ctx:19',axiom,
( ! [X_292: $int,X_293: $int] :
( mem2(X_293,X_292,g_s21_21)
=> ( $greatereq(X_293,0)
& $lesseq(X_293,max_int)
& mem0(X_292,g_s0_0) ) )
& ! [X_294: $int,X_295: $int,X_296: $int] :
( ( mem2(X_294,X_295,g_s21_21)
& mem2(X_294,X_296,g_s21_21) )
=> ( X_295 = X_296 ) ) ) ).
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_297: $int] :
( ? [X_298: set_2] :
( ! [X_299: $int,X_300: $int] :
( mem2(X_300,X_299,X_298)
<=> mem2(X_300,X_299,g_s21_21) )
& ! [X_301: $int,X_302: $int,X_303: $int] :
( ( mem2(X_301,X_302,X_298)
& mem2(X_301,X_303,X_298) )
=> ( X_302 = X_303 ) )
& ! [X_304: $int] :
( ( $greatereq(X_304,1)
& $lesseq(X_304,X_297) )
<=> ? [X_305: $int] : mem2(X_304,X_305,X_298) )
& ! [X_306: $int] :
( ? [X_307: $int] : mem2(X_307,X_306,X_298)
=> mem0(X_306,g_s19_19) ) )
& ! [X_308: $int] :
( mem0(X_308,g_s19_19)
=> ? [X_309: $int] : mem2(X_309,X_308,g_s21_21) )
& ! [X_310: $int,X_311: $int,X_312: $int] :
( ( mem2(X_311,X_310,g_s21_21)
& mem2(X_312,X_310,g_s21_21) )
=> ( X_311 = X_312 ) ) ) ).
tff('Define:ctx:21',axiom,
! [X_313: $int] :
( mem0(X_313,g_s22_22)
=> mem0(X_313,g_s1_1) ) ).
tff('Define:ctx:22',axiom,
mem0(g_s23_23,g_s1_1) ).
tff('Define:ctx:23',axiom,
~ mem0(g_s23_23,g_s22_22) ).
tff('Define:ctx:24',axiom,
( ! [X_314: $int,X_315: $int] :
( mem2(X_315,X_314,g_s24_24)
=> ( $greatereq(X_315,0)
& $lesseq(X_315,max_int)
& mem0(X_314,g_s1_1) ) )
& ! [X_316: $int,X_317: $int,X_318: $int] :
( ( mem2(X_316,X_317,g_s24_24)
& mem2(X_316,X_318,g_s24_24) )
=> ( X_317 = X_318 ) ) ) ).
tff('Define:ctx:25',axiom,
? [X_319: $int] :
( ? [X_320: set_2] :
( ! [X_321: $int,X_322: $int] :
( mem2(X_322,X_321,X_320)
<=> mem2(X_322,X_321,g_s24_24) )
& ! [X_323: $int,X_324: $int,X_325: $int] :
( ( mem2(X_323,X_324,X_320)
& mem2(X_323,X_325,X_320) )
=> ( X_324 = X_325 ) )
& ! [X_326: $int] :
( ( $greatereq(X_326,1)
& $lesseq(X_326,X_319) )
<=> ? [X_327: $int] : mem2(X_326,X_327,X_320) )
& ! [X_328: $int] :
( ? [X_329: $int] : mem2(X_329,X_328,X_320)
=> mem0(X_328,g_s22_22) ) )
& ! [X_330: $int] :
( mem0(X_330,g_s22_22)
=> ? [X_331: $int] : mem2(X_331,X_330,g_s24_24) )
& ! [X_332: $int,X_333: $int,X_334: $int] :
( ( mem2(X_333,X_332,g_s24_24)
& mem2(X_334,X_332,g_s24_24) )
=> ( X_333 = X_334 ) ) ) ).
tff('Define:ctx:26',axiom,
! [X_335: $int] :
( mem0(X_335,g_s25_25)
=> mem0(X_335,g_s2_2) ) ).
tff('Define:ctx:27',axiom,
mem0(g_s26_26,g_s2_2) ).
tff('Define:ctx:28',axiom,
~ mem0(g_s26_26,g_s25_25) ).
tff('Define:ctx:29',axiom,
( ! [X_336: $int,X_337: $int] :
( mem2(X_337,X_336,g_s27_27)
=> ( $greatereq(X_337,0)
& $lesseq(X_337,max_int)
& mem0(X_336,g_s2_2) ) )
& ! [X_338: $int,X_339: $int,X_340: $int] :
( ( mem2(X_338,X_339,g_s27_27)
& mem2(X_338,X_340,g_s27_27) )
=> ( X_339 = X_340 ) ) ) ).
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,
? [X_341: $int] :
( ? [X_342: set_2] :
( ! [X_343: $int,X_344: $int] :
( mem2(X_344,X_343,X_342)
<=> mem2(X_344,X_343,g_s27_27) )
& ! [X_345: $int,X_346: $int,X_347: $int] :
( ( mem2(X_345,X_346,X_342)
& mem2(X_345,X_347,X_342) )
=> ( X_346 = X_347 ) )
& ! [X_348: $int] :
( ( $greatereq(X_348,1)
& $lesseq(X_348,X_341) )
<=> ? [X_349: $int] : mem2(X_348,X_349,X_342) )
& ! [X_350: $int] :
( ? [X_351: $int] : mem2(X_351,X_350,X_342)
=> mem0(X_350,g_s25_25) ) )
& ! [X_352: $int] :
( mem0(X_352,g_s25_25)
=> ? [X_353: $int] : mem2(X_353,X_352,g_s27_27) )
& ! [X_354: $int,X_355: $int,X_356: $int] :
( ( mem2(X_355,X_354,g_s27_27)
& mem2(X_356,X_354,g_s27_27) )
=> ( X_355 = X_356 ) ) ) ).
tff('Define:ctx:31',axiom,
! [X_357: $int] :
( mem0(X_357,g_s28_28)
=> mem0(X_357,g_s3_3) ) ).
tff('Define:ctx:32',axiom,
mem0(g_s29_29,g_s3_3) ).
tff('Define:ctx:33',axiom,
~ mem0(g_s29_29,g_s28_28) ).
tff('Define:ctx:34',axiom,
( ! [X_358: $int,X_359: $int] :
( mem2(X_359,X_358,g_s30_30)
=> ( $greatereq(X_359,0)
& $lesseq(X_359,max_int)
& mem0(X_358,g_s3_3) ) )
& ! [X_360: $int,X_361: $int,X_362: $int] :
( ( mem2(X_360,X_361,g_s30_30)
& mem2(X_360,X_362,g_s30_30) )
=> ( X_361 = X_362 ) ) ) ).
tff('Define:ctx:35',axiom,
? [X_363: $int] :
( ? [X_364: set_2] :
( ! [X_365: $int,X_366: $int] :
( mem2(X_366,X_365,X_364)
<=> mem2(X_366,X_365,g_s30_30) )
& ! [X_367: $int,X_368: $int,X_369: $int] :
( ( mem2(X_367,X_368,X_364)
& mem2(X_367,X_369,X_364) )
=> ( X_368 = X_369 ) )
& ! [X_370: $int] :
( ( $greatereq(X_370,1)
& $lesseq(X_370,X_363) )
<=> ? [X_371: $int] : mem2(X_370,X_371,X_364) )
& ! [X_372: $int] :
( ? [X_373: $int] : mem2(X_373,X_372,X_364)
=> mem0(X_372,g_s28_28) ) )
& ! [X_374: $int] :
( mem0(X_374,g_s28_28)
=> ? [X_375: $int] : mem2(X_375,X_374,g_s30_30) )
& ! [X_376: $int,X_377: $int,X_378: $int] :
( ( mem2(X_377,X_376,g_s30_30)
& mem2(X_378,X_376,g_s30_30) )
=> ( X_377 = X_378 ) ) ) ).
tff('Define:ctx:36',axiom,
! [X_379: $int] :
( mem0(X_379,g_s31_31)
=> mem0(X_379,g_s4_4) ) ).
tff('Define:ctx:37',axiom,
mem0(g_s32_32,g_s4_4) ).
tff('Define:ctx:38',axiom,
~ mem0(g_s32_32,g_s31_31) ).
tff('Define:ctx:39',axiom,
( ! [X_380: $int,X_381: $int] :
( mem2(X_381,X_380,g_s33_33)
=> ( $greatereq(X_381,0)
& $lesseq(X_381,max_int)
& mem0(X_380,g_s4_4) ) )
& ! [X_382: $int,X_383: $int,X_384: $int] :
( ( mem2(X_382,X_383,g_s33_33)
& mem2(X_382,X_384,g_s33_33) )
=> ( X_383 = X_384 ) ) ) ).
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_385: $int] :
( ? [X_386: set_2] :
( ! [X_387: $int,X_388: $int] :
( mem2(X_388,X_387,X_386)
<=> mem2(X_388,X_387,g_s33_33) )
& ! [X_389: $int,X_390: $int,X_391: $int] :
( ( mem2(X_389,X_390,X_386)
& mem2(X_389,X_391,X_386) )
=> ( X_390 = X_391 ) )
& ! [X_392: $int] :
( ( $greatereq(X_392,1)
& $lesseq(X_392,X_385) )
<=> ? [X_393: $int] : mem2(X_392,X_393,X_386) )
& ! [X_394: $int] :
( ? [X_395: $int] : mem2(X_395,X_394,X_386)
=> mem0(X_394,g_s31_31) ) )
& ! [X_396: $int] :
( mem0(X_396,g_s31_31)
=> ? [X_397: $int] : mem2(X_397,X_396,g_s33_33) )
& ! [X_398: $int,X_399: $int,X_400: $int] :
( ( mem2(X_399,X_398,g_s33_33)
& mem2(X_400,X_398,g_s33_33) )
=> ( X_399 = X_400 ) ) ) ).
tff('Define:ctx:41',axiom,
! [X_401: $int] :
( mem0(X_401,g_s34_34)
=> mem0(X_401,g_s5_5) ) ).
tff('Define:ctx:42',axiom,
mem0(g_s35_35,g_s5_5) ).
tff('Define:ctx:43',axiom,
~ mem0(g_s35_35,g_s34_34) ).
tff('Define:ctx:44',axiom,
( ! [X_402: $int,X_403: $int] :
( mem2(X_403,X_402,g_s36_36)
=> ( $greatereq(X_403,0)
& $lesseq(X_403,max_int)
& mem0(X_402,g_s5_5) ) )
& ! [X_404: $int,X_405: $int,X_406: $int] :
( ( mem2(X_404,X_405,g_s36_36)
& mem2(X_404,X_406,g_s36_36) )
=> ( X_405 = X_406 ) ) ) ).
tff('Define:ctx:45',axiom,
? [X_407: $int] :
( ? [X_408: set_2] :
( ! [X_409: $int,X_410: $int] :
( mem2(X_410,X_409,X_408)
<=> mem2(X_410,X_409,g_s36_36) )
& ! [X_411: $int,X_412: $int,X_413: $int] :
( ( mem2(X_411,X_412,X_408)
& mem2(X_411,X_413,X_408) )
=> ( X_412 = X_413 ) )
& ! [X_414: $int] :
( ( $greatereq(X_414,1)
& $lesseq(X_414,X_407) )
<=> ? [X_415: $int] : mem2(X_414,X_415,X_408) )
& ! [X_416: $int] :
( ? [X_417: $int] : mem2(X_417,X_416,X_408)
=> mem0(X_416,g_s34_34) ) )
& ! [X_418: $int] :
( mem0(X_418,g_s34_34)
=> ? [X_419: $int] : mem2(X_419,X_418,g_s36_36) )
& ! [X_420: $int,X_421: $int,X_422: $int] :
( ( mem2(X_421,X_420,g_s36_36)
& mem2(X_422,X_420,g_s36_36) )
=> ( X_421 = X_422 ) ) ) ).
tff('Define:ctx:46',axiom,
! [X_423: $int] :
( mem0(X_423,g_s37_37)
=> mem0(X_423,g_s6_6) ) ).
tff('Define:ctx:47',axiom,
mem0(g_s38_38,g_s6_6) ).
tff('Define:ctx:48',axiom,
~ mem0(g_s38_38,g_s37_37) ).
tff('Define:ctx:49',axiom,
( ! [X_424: $int,X_425: $int] :
( mem2(X_425,X_424,g_s39_39)
=> ( $greatereq(X_425,0)
& $lesseq(X_425,max_int)
& mem0(X_424,g_s6_6) ) )
& ! [X_426: $int,X_427: $int,X_428: $int] :
( ( mem2(X_426,X_427,g_s39_39)
& mem2(X_426,X_428,g_s39_39) )
=> ( X_427 = X_428 ) ) ) ).
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_429: $int] :
( ? [X_430: set_2] :
( ! [X_431: $int,X_432: $int] :
( mem2(X_432,X_431,X_430)
<=> mem2(X_432,X_431,g_s39_39) )
& ! [X_433: $int,X_434: $int,X_435: $int] :
( ( mem2(X_433,X_434,X_430)
& mem2(X_433,X_435,X_430) )
=> ( X_434 = X_435 ) )
& ! [X_436: $int] :
( ( $greatereq(X_436,1)
& $lesseq(X_436,X_429) )
<=> ? [X_437: $int] : mem2(X_436,X_437,X_430) )
& ! [X_438: $int] :
( ? [X_439: $int] : mem2(X_439,X_438,X_430)
=> mem0(X_438,g_s37_37) ) )
& ! [X_440: $int] :
( mem0(X_440,g_s37_37)
=> ? [X_441: $int] : mem2(X_441,X_440,g_s39_39) )
& ! [X_442: $int,X_443: $int,X_444: $int] :
( ( mem2(X_443,X_442,g_s39_39)
& mem2(X_444,X_442,g_s39_39) )
=> ( X_443 = X_444 ) ) ) ).
tff('Define:ctx:51',axiom,
! [X_445: $int] :
( mem0(X_445,g_s40_40)
=> mem0(X_445,g_s7_7) ) ).
tff('Define:ctx:52',axiom,
mem0(g_s41_41,g_s7_7) ).
tff('Define:ctx:53',axiom,
~ mem0(g_s41_41,g_s40_40) ).
tff('Define:ctx:54',axiom,
( ! [X_446: $int,X_447: $int] :
( mem2(X_447,X_446,g_s42_42)
=> ( $greatereq(X_447,0)
& $lesseq(X_447,max_int)
& mem0(X_446,g_s7_7) ) )
& ! [X_448: $int,X_449: $int,X_450: $int] :
( ( mem2(X_448,X_449,g_s42_42)
& mem2(X_448,X_450,g_s42_42) )
=> ( X_449 = X_450 ) ) ) ).
tff('Define:ctx:55',axiom,
? [X_451: $int] :
( ? [X_452: set_2] :
( ! [X_453: $int,X_454: $int] :
( mem2(X_454,X_453,X_452)
<=> mem2(X_454,X_453,g_s42_42) )
& ! [X_455: $int,X_456: $int,X_457: $int] :
( ( mem2(X_455,X_456,X_452)
& mem2(X_455,X_457,X_452) )
=> ( X_456 = X_457 ) )
& ! [X_458: $int] :
( ( $greatereq(X_458,1)
& $lesseq(X_458,X_451) )
<=> ? [X_459: $int] : mem2(X_458,X_459,X_452) )
& ! [X_460: $int] :
( ? [X_461: $int] : mem2(X_461,X_460,X_452)
=> mem0(X_460,g_s40_40) ) )
& ! [X_462: $int] :
( mem0(X_462,g_s40_40)
=> ? [X_463: $int] : mem2(X_463,X_462,g_s42_42) )
& ! [X_464: $int,X_465: $int,X_466: $int] :
( ( mem2(X_465,X_464,g_s42_42)
& mem2(X_466,X_464,g_s42_42) )
=> ( X_465 = X_466 ) ) ) ).
tff('Define:ctx:56',axiom,
( ? [X_467: set_2] :
( ! [X_468: $int,X_469: $int] :
( mem2(X_469,X_468,X_467)
<=> mem2(X_469,X_468,g_s43_43) )
& ! [X_470: $int,X_471: $int,X_472: $int] :
( ( mem2(X_470,X_471,X_467)
& mem2(X_470,X_472,X_467) )
=> ( X_471 = X_472 ) )
& ! [X_473: $int] :
( mem0(X_473,g_s28_28)
<=> ? [X_474: $int] : mem2(X_473,X_474,X_467) )
& ! [X_475: $int] :
( ? [X_476: $int] : mem2(X_476,X_475,X_467)
=> mem0(X_475,g_s44_44) ) )
& ! [X_477: $int,X_478: $int,X_479: $int] :
( ( mem2(X_478,X_477,g_s43_43)
& mem2(X_479,X_477,g_s43_43) )
=> ( X_478 = X_479 ) ) ) ).
tff('Define:ctx:57',axiom,
( ? [X_480: set_2] :
( ! [X_481: $int,X_482: $int] :
( mem2(X_482,X_481,X_480)
<=> mem2(X_482,X_481,g_s45_45) )
& ! [X_483: $int,X_484: $int,X_485: $int] :
( ( mem2(X_483,X_484,X_480)
& mem2(X_483,X_485,X_480) )
=> ( X_484 = X_485 ) )
& ! [X_486: $int] :
( mem0(X_486,g_s31_31)
<=> ? [X_487: $int] : mem2(X_486,X_487,X_480) )
& ! [X_488: $int] :
( ? [X_489: $int] : mem2(X_489,X_488,X_480)
=> mem0(X_488,g_s44_44) ) )
& ! [X_490: $int,X_491: $int,X_492: $int] :
( ( mem2(X_491,X_490,g_s45_45)
& mem2(X_492,X_490,g_s45_45) )
=> ( X_491 = X_492 ) ) ) ).
tff('Define:ctx:58',axiom,
mem0(g_s46_47,g_s47_46) ).
tff('Define:ctx:59',axiom,
( ( g_s48_48 != 0 )
=> mem0(g_s46_47,g_s44_44) ) ).
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_493: set_2] :
( ! [X_494: $int,X_495: $int] :
( mem2(X_495,X_494,X_493)
<=> mem2(X_495,X_494,g_s49_49) )
& ! [X_496: $int,X_497: $int,X_498: $int] :
( ( mem2(X_496,X_497,X_493)
& mem2(X_496,X_498,X_493) )
=> ( X_497 = X_498 ) )
& ! [X_499: $int] :
( mem0(X_499,g_s37_37)
<=> ? [X_500: $int] : mem2(X_499,X_500,X_493) )
& ! [X_501: $int] :
( ? [X_502: $int] : mem2(X_502,X_501,X_493)
=> mem0(X_501,g_s44_44) ) )
& ! [X_503: $int,X_504: $int,X_505: $int] :
( ( mem2(X_504,X_503,g_s49_49)
& mem2(X_505,X_503,g_s49_49) )
=> ( X_504 = X_505 ) ) ) ).
tff('Define:ctx:61',axiom,
! [X_506: $int] :
( ( ? [X_507: $int] : mem2(X_507,X_506,g_s43_43)
& ? [X_508: $int] : mem2(X_508,X_506,g_s45_45) )
<=> $false ) ).
tff('Define:ctx:62',axiom,
! [X_509: $int] :
( ( ? [X_510: $int] : mem2(X_510,X_509,g_s43_43)
& ? [X_511: $int] : mem2(X_511,X_509,g_s49_49) )
<=> $false ) ).
tff('Define:ctx:63',axiom,
! [X_512: $int] :
( ( ? [X_513: $int] : mem2(X_513,X_512,g_s49_49)
& ? [X_514: $int] : mem2(X_514,X_512,g_s45_45) )
<=> $false ) ).
tff('Define:ctx:64',axiom,
( ( g_s48_48 != 0 )
=> ~ ? [X_515: $int] : mem2(X_515,g_s46_47,g_s43_43) ) ).
tff('Define:ctx:65',axiom,
( ( g_s48_48 != 0 )
=> ~ ? [X_516: $int] : mem2(X_516,g_s46_47,g_s45_45) ) ).
tff('Define:ctx:66',axiom,
( ( g_s48_48 != 0 )
=> ~ ? [X_517: $int] : mem2(X_517,g_s46_47,g_s49_49) ) ).
tff('Define:ctx:67',axiom,
! [X_518: $int] :
( mem0(X_518,g_s50_50)
=> mem0(X_518,g_s8_8) ) ).
tff('Define:ctx:68',axiom,
mem0(g_s51_51,g_s8_8) ).
tff('Define:ctx:69',axiom,
~ mem0(g_s51_51,g_s50_50) ).
tff('Define:ctx:7',axiom,
( ~ ! [X_138: $int] :
( mem0(X_138,g_s7_7)
<=> $false )
& ! [X_141: $int] :
( mem0(X_141,g_s7_7)
=> $true )
& ? [X_139: $int,X_140: set_2] :
( ? [X_142: set_2] :
( ! [X_143: $int,X_144: $int] :
( mem2(X_144,X_143,X_142)
<=> mem2(X_144,X_143,X_140) )
& ! [X_145: $int,X_146: $int,X_147: $int] :
( ( mem2(X_145,X_146,X_142)
& mem2(X_145,X_147,X_142) )
=> ( X_146 = X_147 ) )
& ! [X_148: $int] :
( ( $greatereq(X_148,1)
& $lesseq(X_148,X_139) )
<=> ? [X_149: $int] : mem2(X_148,X_149,X_142) )
& ! [X_150: $int] :
( ? [X_151: $int] : mem2(X_151,X_150,X_142)
=> mem0(X_150,g_s7_7) ) )
& ! [X_152: $int] :
( mem0(X_152,g_s7_7)
=> ? [X_153: $int] : mem2(X_153,X_152,X_140) )
& ! [X_154: $int,X_155: $int,X_156: $int] :
( ( mem2(X_155,X_154,X_140)
& mem2(X_156,X_154,X_140) )
=> ( X_155 = X_156 ) ) ) ) ).
tff('Define:ctx:70',axiom,
( ! [X_519: $int,X_520: $int] :
( mem2(X_520,X_519,g_s52_52)
=> ( $greatereq(X_520,0)
& $lesseq(X_520,max_int)
& mem0(X_519,g_s8_8) ) )
& ! [X_521: $int,X_522: $int,X_523: $int] :
( ( mem2(X_521,X_522,g_s52_52)
& mem2(X_521,X_523,g_s52_52) )
=> ( X_522 = X_523 ) ) ) ).
tff('Define:ctx:71',axiom,
? [X_524: $int] :
( ? [X_525: set_2] :
( ! [X_526: $int,X_527: $int] :
( mem2(X_527,X_526,X_525)
<=> mem2(X_527,X_526,g_s52_52) )
& ! [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] :
( ( $greatereq(X_531,1)
& $lesseq(X_531,X_524) )
<=> ? [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_s50_50) ) )
& ! [X_535: $int] :
( mem0(X_535,g_s50_50)
=> ? [X_536: $int] : mem2(X_536,X_535,g_s52_52) )
& ! [X_537: $int,X_538: $int,X_539: $int] :
( ( mem2(X_538,X_537,g_s52_52)
& mem2(X_539,X_537,g_s52_52) )
=> ( X_538 = X_539 ) ) ) ).
tff('Define:ctx:72',axiom,
! [X_540: $int] :
( mem0(X_540,g_s53_53)
=> mem0(X_540,g_s8_8) ) ).
tff('Define:ctx:73',axiom,
! [X_541: $int] :
( mem0(X_541,g_s54_54)
=> mem0(X_541,g_s53_53) ) ).
tff('Define:ctx:74',axiom,
! [X_542: $int] :
( mem0(X_542,g_s54_54)
=> mem0(X_542,g_s8_8) ) ).
tff('Define:ctx:75',axiom,
! [X_543: $int] :
( mem0(X_543,g_s54_54)
=> mem0(X_543,g_s50_50) ) ).
tff('Define:ctx:76',axiom,
mem0(g_s51_51,g_s53_53) ).
tff('Define:ctx:77',axiom,
~ mem0(g_s51_51,g_s54_54) ).
tff('Define:ctx:78',axiom,
( ! [X_544: $int,X_545: $int] :
( mem2(X_545,X_544,g_s55_55)
=> ( $greatereq(X_545,0)
& $lesseq(X_545,max_int)
& mem0(X_544,g_s53_53) ) )
& ! [X_546: $int,X_547: $int,X_548: $int] :
( ( mem2(X_546,X_547,g_s55_55)
& mem2(X_546,X_548,g_s55_55) )
=> ( X_547 = X_548 ) ) ) ).
tff('Define:ctx:79',axiom,
? [X_549: $int] :
( ? [X_550: set_2] :
( ! [X_551: $int,X_552: $int] :
( mem2(X_552,X_551,X_550)
<=> mem2(X_552,X_551,g_s55_55) )
& ! [X_553: $int,X_554: $int,X_555: $int] :
( ( mem2(X_553,X_554,X_550)
& mem2(X_553,X_555,X_550) )
=> ( X_554 = X_555 ) )
& ! [X_556: $int] :
( ( $greatereq(X_556,1)
& $lesseq(X_556,X_549) )
<=> ? [X_557: $int] : mem2(X_556,X_557,X_550) )
& ! [X_558: $int] :
( ? [X_559: $int] : mem2(X_559,X_558,X_550)
=> mem0(X_558,g_s54_54) ) )
& ! [X_560: $int] :
( mem0(X_560,g_s54_54)
=> ? [X_561: $int] : mem2(X_561,X_560,g_s55_55) )
& ! [X_562: $int,X_563: $int,X_564: $int] :
( ( mem2(X_563,X_562,g_s55_55)
& mem2(X_564,X_562,g_s55_55) )
=> ( X_563 = X_564 ) ) ) ).
tff('Define:ctx:8',axiom,
( ~ ! [X_157: $int] :
( mem0(X_157,g_s8_8)
<=> $false )
& ! [X_160: $int] :
( mem0(X_160,g_s8_8)
=> $true )
& ? [X_158: $int,X_159: set_2] :
( ? [X_161: set_2] :
( ! [X_162: $int,X_163: $int] :
( mem2(X_163,X_162,X_161)
<=> mem2(X_163,X_162,X_159) )
& ! [X_164: $int,X_165: $int,X_166: $int] :
( ( mem2(X_164,X_165,X_161)
& mem2(X_164,X_166,X_161) )
=> ( X_165 = X_166 ) )
& ! [X_167: $int] :
( ( $greatereq(X_167,1)
& $lesseq(X_167,X_158) )
<=> ? [X_168: $int] : mem2(X_167,X_168,X_161) )
& ! [X_169: $int] :
( ? [X_170: $int] : mem2(X_170,X_169,X_161)
=> mem0(X_169,g_s8_8) ) )
& ! [X_171: $int] :
( mem0(X_171,g_s8_8)
=> ? [X_172: $int] : mem2(X_172,X_171,X_159) )
& ! [X_173: $int,X_174: $int,X_175: $int] :
( ( mem2(X_174,X_173,X_159)
& mem2(X_175,X_173,X_159) )
=> ( X_174 = X_175 ) ) ) ) ).
tff('Define:ctx:80',axiom,
! [X_565: $int] :
( mem0(X_565,g_s56_56)
=> mem0(X_565,g_s9_9) ) ).
tff('Define:ctx:81',axiom,
mem0(g_s57_57,g_s9_9) ).
tff('Define:ctx:82',axiom,
~ mem0(g_s57_57,g_s56_56) ).
tff('Define:ctx:83',axiom,
( ! [X_566: $int,X_567: $int] :
( mem2(X_567,X_566,g_s58_58)
=> ( $greatereq(X_567,0)
& $lesseq(X_567,max_int)
& mem0(X_566,g_s9_9) ) )
& ! [X_568: $int,X_569: $int,X_570: $int] :
( ( mem2(X_568,X_569,g_s58_58)
& mem2(X_568,X_570,g_s58_58) )
=> ( X_569 = X_570 ) ) ) ).
tff('Define:ctx:84',axiom,
? [X_571: $int] :
( ? [X_572: set_2] :
( ! [X_573: $int,X_574: $int] :
( mem2(X_574,X_573,X_572)
<=> mem2(X_574,X_573,g_s58_58) )
& ! [X_575: $int,X_576: $int,X_577: $int] :
( ( mem2(X_575,X_576,X_572)
& mem2(X_575,X_577,X_572) )
=> ( X_576 = X_577 ) )
& ! [X_578: $int] :
( ( $greatereq(X_578,1)
& $lesseq(X_578,X_571) )
<=> ? [X_579: $int] : mem2(X_578,X_579,X_572) )
& ! [X_580: $int] :
( ? [X_581: $int] : mem2(X_581,X_580,X_572)
=> mem0(X_580,g_s56_56) ) )
& ! [X_582: $int] :
( mem0(X_582,g_s56_56)
=> ? [X_583: $int] : mem2(X_583,X_582,g_s58_58) )
& ! [X_584: $int,X_585: $int,X_586: $int] :
( ( mem2(X_585,X_584,g_s58_58)
& mem2(X_586,X_584,g_s58_58) )
=> ( X_585 = X_586 ) ) ) ).
tff('Define:ctx:85',axiom,
! [X_587: $int] :
( mem0(X_587,g_s59_59)
=> mem0(X_587,g_s10_10) ) ).
tff('Define:ctx:86',axiom,
mem0(g_s60_60,g_s10_10) ).
tff('Define:ctx:87',axiom,
~ mem0(g_s60_60,g_s59_59) ).
tff('Define:ctx:88',axiom,
( ! [X_588: $int,X_589: $int] :
( mem2(X_589,X_588,g_s61_61)
=> ( $greatereq(X_589,0)
& $lesseq(X_589,max_int)
& mem0(X_588,g_s10_10) ) )
& ! [X_590: $int,X_591: $int,X_592: $int] :
( ( mem2(X_590,X_591,g_s61_61)
& mem2(X_590,X_592,g_s61_61) )
=> ( X_591 = X_592 ) ) ) ).
tff('Define:ctx:89',axiom,
? [X_593: $int] :
( ? [X_594: set_2] :
( ! [X_595: $int,X_596: $int] :
( mem2(X_596,X_595,X_594)
<=> mem2(X_596,X_595,g_s61_61) )
& ! [X_597: $int,X_598: $int,X_599: $int] :
( ( mem2(X_597,X_598,X_594)
& mem2(X_597,X_599,X_594) )
=> ( X_598 = X_599 ) )
& ! [X_600: $int] :
( ( $greatereq(X_600,1)
& $lesseq(X_600,X_593) )
<=> ? [X_601: $int] : mem2(X_600,X_601,X_594) )
& ! [X_602: $int] :
( ? [X_603: $int] : mem2(X_603,X_602,X_594)
=> mem0(X_602,g_s59_59) ) )
& ! [X_604: $int] :
( mem0(X_604,g_s59_59)
=> ? [X_605: $int] : mem2(X_605,X_604,g_s61_61) )
& ! [X_606: $int,X_607: $int,X_608: $int] :
( ( mem2(X_607,X_606,g_s61_61)
& mem2(X_608,X_606,g_s61_61) )
=> ( X_607 = X_608 ) ) ) ).
tff('Define:ctx:9',axiom,
( ~ ! [X_176: $int] :
( mem0(X_176,g_s9_9)
<=> $false )
& ! [X_179: $int] :
( mem0(X_179,g_s9_9)
=> $true )
& ? [X_177: $int,X_178: set_2] :
( ? [X_180: set_2] :
( ! [X_181: $int,X_182: $int] :
( mem2(X_182,X_181,X_180)
<=> mem2(X_182,X_181,X_178) )
& ! [X_183: $int,X_184: $int,X_185: $int] :
( ( mem2(X_183,X_184,X_180)
& mem2(X_183,X_185,X_180) )
=> ( X_184 = X_185 ) )
& ! [X_186: $int] :
( ( $greatereq(X_186,1)
& $lesseq(X_186,X_177) )
<=> ? [X_187: $int] : mem2(X_186,X_187,X_180) )
& ! [X_188: $int] :
( ? [X_189: $int] : mem2(X_189,X_188,X_180)
=> mem0(X_188,g_s9_9) ) )
& ! [X_190: $int] :
( mem0(X_190,g_s9_9)
=> ? [X_191: $int] : mem2(X_191,X_190,X_178) )
& ! [X_192: $int,X_193: $int,X_194: $int] :
( ( mem2(X_193,X_192,X_178)
& mem2(X_194,X_192,X_178) )
=> ( X_193 = X_194 ) ) ) ) ).
tff('Define:ctx:90',axiom,
! [X_609: $int] :
( mem0(X_609,g_s62_62)
=> mem0(X_609,g_s11_11) ) ).
tff('Define:ctx:91',axiom,
mem0(g_s63_63,g_s11_11) ).
tff('Define:ctx:92',axiom,
~ mem0(g_s63_63,g_s62_62) ).
tff('Define:ctx:93',axiom,
( ! [X_610: $int,X_611: $int] :
( mem2(X_611,X_610,g_s64_64)
=> ( $greatereq(X_611,0)
& $lesseq(X_611,max_int)
& mem0(X_610,g_s11_11) ) )
& ! [X_612: $int,X_613: $int,X_614: $int] :
( ( mem2(X_612,X_613,g_s64_64)
& mem2(X_612,X_614,g_s64_64) )
=> ( X_613 = X_614 ) ) ) ).
tff('Define:ctx:94',axiom,
? [X_615: $int] :
( ? [X_616: set_2] :
( ! [X_617: $int,X_618: $int] :
( mem2(X_618,X_617,X_616)
<=> mem2(X_618,X_617,g_s64_64) )
& ! [X_619: $int,X_620: $int,X_621: $int] :
( ( mem2(X_619,X_620,X_616)
& mem2(X_619,X_621,X_616) )
=> ( X_620 = X_621 ) )
& ! [X_622: $int] :
( ( $greatereq(X_622,1)
& $lesseq(X_622,X_615) )
<=> ? [X_623: $int] : mem2(X_622,X_623,X_616) )
& ! [X_624: $int] :
( ? [X_625: $int] : mem2(X_625,X_624,X_616)
=> mem0(X_624,g_s62_62) ) )
& ! [X_626: $int] :
( mem0(X_626,g_s62_62)
=> ? [X_627: $int] : mem2(X_627,X_626,g_s64_64) )
& ! [X_628: $int,X_629: $int,X_630: $int] :
( ( mem2(X_629,X_628,g_s64_64)
& mem2(X_630,X_628,g_s64_64) )
=> ( X_629 = X_630 ) ) ) ).
tff('Define:ctx:95',axiom,
! [X_631: $int] :
( mem0(X_631,g_s65_65)
=> mem0(X_631,g_s11_11) ) ).
tff('Define:ctx:96',axiom,
! [X_632: $int] :
( mem0(X_632,g_s66_66)
=> mem0(X_632,g_s65_65) ) ).
tff('Define:ctx:97',axiom,
! [X_633: $int] :
( mem0(X_633,g_s66_66)
=> mem0(X_633,g_s11_11) ) ).
tff('Define:ctx:98',axiom,
! [X_634: $int] :
( mem0(X_634,g_s66_66)
=> mem0(X_634,g_s62_62) ) ).
tff('Define:ctx:99',axiom,
mem0(g_s63_63,g_s65_65) ).
tff('Define:imprp:0',axiom,
! [X_722: $int] :
( ? [X_723: $int] :
( mem2(X_722,X_723,g_s94_77)
& mem0(X_722,g_s22_22)
& mem0(X_723,g_s37_37) )
<=> mem0(X_722,g_s22_22) ) ).
tff('Define:imprp:1',axiom,
! [X_724: $int] :
( ? [X_725: $int] :
( mem2(X_724,X_725,g_s97_78)
& mem0(X_724,g_s25_25)
& mem0(X_725,g_s37_37) )
<=> mem0(X_724,g_s25_25) ) ).
tff('Define:imprp:10',axiom,
? [X_798: set_2] :
( ! [X_799: $int,X_800: $int] :
( mem2(X_800,X_799,X_798)
<=> mem2(X_800,X_799,g_s100_85) )
& ! [X_801: $int,X_802: $int,X_803: $int] :
( ( mem2(X_801,X_802,X_798)
& mem2(X_801,X_803,X_798) )
=> ( X_802 = X_803 ) )
& ! [X_804: $int] :
( mem0(X_804,g_s10_10)
<=> ? [X_805: $int] : mem2(X_804,X_805,X_798) )
& ! [X_806: $int] :
( ? [X_807: $int] : mem2(X_807,X_806,X_798)
=> mem0(X_806,g_s6_6) ) ) ).
tff('Define:imprp:11',axiom,
? [X_808: set_2] :
( ! [X_809: $int,X_810: $int] :
( mem2(X_810,X_809,X_808)
<=> mem2(X_810,X_809,g_s101_86) )
& ! [X_811: $int,X_812: $int,X_813: $int] :
( ( mem2(X_811,X_812,X_808)
& mem2(X_811,X_813,X_808) )
=> ( X_812 = X_813 ) )
& ! [X_814: $int] :
( mem0(X_814,g_s10_10)
<=> ? [X_815: $int] : mem2(X_814,X_815,X_808) )
& ! [X_816: $int] :
( ? [X_817: $int] : mem2(X_817,X_816,X_808)
=> mem0(X_816,g_s6_6) ) ) ).
tff('Define:imprp:12',axiom,
? [X_818: set_2] :
( ! [X_819: $int,X_820: $int] :
( mem2(X_820,X_819,X_818)
<=> mem2(X_820,X_819,g_s102_87) )
& ! [X_821: $int,X_822: $int,X_823: $int] :
( ( mem2(X_821,X_822,X_818)
& mem2(X_821,X_823,X_818) )
=> ( X_822 = X_823 ) )
& ! [X_824: $int] :
( mem0(X_824,g_s11_11)
<=> ? [X_825: $int] : mem2(X_824,X_825,X_818) )
& ! [X_826: $int] :
( ? [X_827: $int] : mem2(X_827,X_826,X_818)
=> mem0(X_826,g_s6_6) ) ) ).
tff('Define:imprp:13',axiom,
? [X_828: set_2] :
( ! [X_829: $int,X_830: $int] :
( mem2(X_830,X_829,X_828)
<=> mem2(X_830,X_829,g_s103_88) )
& ! [X_831: $int,X_832: $int,X_833: $int] :
( ( mem2(X_831,X_832,X_828)
& mem2(X_831,X_833,X_828) )
=> ( X_832 = X_833 ) )
& ! [X_834: $int] :
( mem0(X_834,g_s65_65)
<=> ? [X_835: $int] : mem2(X_834,X_835,X_828) )
& ! [X_836: $int] :
( ? [X_837: $int] : mem2(X_837,X_836,X_828)
=> mem0(X_836,g_s6_6) ) ) ).
tff('Define:imprp:14',axiom,
? [X_838: set_2] :
( ! [X_839: $int,X_840: $int] :
( mem2(X_840,X_839,X_838)
<=> mem2(X_840,X_839,g_s104_89) )
& ! [X_841: $int,X_842: $int,X_843: $int] :
( ( mem2(X_841,X_842,X_838)
& mem2(X_841,X_843,X_838) )
=> ( X_842 = X_843 ) )
& ! [X_844: $int] :
( mem0(X_844,g_s65_65)
<=> ? [X_845: $int] : mem2(X_844,X_845,X_838) )
& ! [X_846: $int] :
( ? [X_847: $int] : mem2(X_847,X_846,X_838)
=> mem0(X_846,g_s6_6) ) ) ).
tff('Define:imprp:15',axiom,
? [X_848: set_2] :
( ! [X_849: $int,X_850: $int] :
( mem2(X_850,X_849,X_848)
<=> mem2(X_850,X_849,g_s105_90) )
& ! [X_851: $int,X_852: $int,X_853: $int] :
( ( mem2(X_851,X_852,X_848)
& mem2(X_851,X_853,X_848) )
=> ( X_852 = X_853 ) )
& ! [X_854: $int] :
( mem0(X_854,g_s11_11)
<=> ? [X_855: $int] : mem2(X_854,X_855,X_848) )
& ! [X_856: $int] :
( ? [X_857: $int] : mem2(X_857,X_856,X_848)
=> mem0(X_856,g_s6_6) ) ) ).
tff('Define:imprp:16',axiom,
? [X_858: set_2] :
( ! [X_859: $int,X_860: $int] :
( mem2(X_860,X_859,X_858)
<=> mem2(X_860,X_859,g_s106_91) )
& ! [X_861: $int,X_862: $int,X_863: $int] :
( ( mem2(X_861,X_862,X_858)
& mem2(X_861,X_863,X_858) )
=> ( X_862 = X_863 ) )
& ! [X_864: $int] :
( mem0(X_864,g_s65_65)
<=> ? [X_865: $int] : mem2(X_864,X_865,X_858) )
& ! [X_866: $int] :
( ? [X_867: $int] : mem2(X_867,X_866,X_858)
=> mem0(X_866,g_s6_6) ) ) ).
tff('Define:imprp:17',axiom,
? [X_868: set_2] :
( ! [X_869: $int,X_870: $int] :
( mem2(X_870,X_869,X_868)
<=> mem2(X_870,X_869,g_s107_92) )
& ! [X_871: $int,X_872: $int,X_873: $int] :
( ( mem2(X_871,X_872,X_868)
& mem2(X_871,X_873,X_868) )
=> ( X_872 = X_873 ) )
& ! [X_874: $int] :
( mem0(X_874,g_s11_11)
<=> ? [X_875: $int] : mem2(X_874,X_875,X_868) )
& ! [X_876: $int] :
( ? [X_877: $int] : mem2(X_877,X_876,X_868)
=> mem0(X_876,g_s6_6) ) ) ).
tff('Define:imprp:18',axiom,
? [X_878: set_2] :
( ! [X_879: $int,X_880: $int] :
( mem2(X_880,X_879,X_878)
<=> mem2(X_880,X_879,g_s108_79) )
& ! [X_881: $int,X_882: $int,X_883: $int] :
( ( mem2(X_881,X_882,X_878)
& mem2(X_881,X_883,X_878) )
=> ( X_882 = X_883 ) )
& ! [X_884: $int] :
( mem0(X_884,g_s13_13)
<=> ? [X_885: $int] : mem2(X_884,X_885,X_878) )
& ! [X_886: $int] :
( ? [X_887: $int] : mem2(X_887,X_886,X_878)
=> mem0(X_886,g_s6_6) ) ) ).
tff('Define:imprp:2',axiom,
! [X_726: $int] :
( ? [X_727: $int] :
( mem2(X_726,X_727,g_s108_79)
& mem0(X_726,g_s71_71)
& mem0(X_727,g_s37_37) )
<=> mem0(X_726,g_s71_71) ) ).
tff('Define:imprp:3',axiom,
? [X_728: set_2] :
( ! [X_729: $int,X_730: $int] :
( mem2(X_730,X_729,X_728)
<=> mem2(X_730,X_729,g_s93_80) )
& ! [X_731: $int,X_732: $int,X_733: $int] :
( ( mem2(X_731,X_732,X_728)
& mem2(X_731,X_733,X_728) )
=> ( X_732 = X_733 ) )
& ! [X_734: $int] :
( mem0(X_734,g_s0_0)
<=> ? [X_735: $int] : mem2(X_734,X_735,X_728) )
& ! [X_736: $int] :
( ? [X_737: $int] : mem2(X_737,X_736,X_728)
=> mem0(X_736,g_s6_6) ) ) ).
tff('Define:imprp:4',axiom,
? [X_738: set_2] :
( ! [X_739: $int,X_740: $int] :
( mem2(X_740,X_739,X_738)
<=> mem2(X_740,X_739,g_s94_77) )
& ! [X_741: $int,X_742: $int,X_743: $int] :
( ( mem2(X_741,X_742,X_738)
& mem2(X_741,X_743,X_738) )
=> ( X_742 = X_743 ) )
& ! [X_744: $int] :
( mem0(X_744,g_s1_1)
<=> ? [X_745: $int] : mem2(X_744,X_745,X_738) )
& ! [X_746: $int] :
( ? [X_747: $int] : mem2(X_747,X_746,X_738)
=> mem0(X_746,g_s6_6) ) ) ).
tff('Define:imprp:5',axiom,
? [X_748: set_2] :
( ! [X_749: $int,X_750: $int] :
( mem2(X_750,X_749,X_748)
<=> mem2(X_750,X_749,g_s95_81) )
& ! [X_751: $int,X_752: $int,X_753: $int] :
( ( mem2(X_751,X_752,X_748)
& mem2(X_751,X_753,X_748) )
=> ( X_752 = X_753 ) )
& ! [X_754: $int] :
( mem0(X_754,g_s1_1)
<=> ? [X_755: $int] : mem2(X_754,X_755,X_748) )
& ! [X_756: $int] :
( ? [X_757: $int] : mem2(X_757,X_756,X_748)
=> mem0(X_756,g_s6_6) ) ) ).
tff('Define:imprp:6',axiom,
? [X_758: set_2] :
( ! [X_759: $int,X_760: $int] :
( mem2(X_760,X_759,X_758)
<=> mem2(X_760,X_759,g_s96_82) )
& ! [X_761: $int,X_762: $int,X_763: $int] :
( ( mem2(X_761,X_762,X_758)
& mem2(X_761,X_763,X_758) )
=> ( X_762 = X_763 ) )
& ! [X_764: $int] :
( mem0(X_764,g_s9_9)
<=> ? [X_765: $int] : mem2(X_764,X_765,X_758) )
& ! [X_766: $int] :
( ? [X_767: $int] : mem2(X_767,X_766,X_758)
=> mem0(X_766,g_s6_6) ) ) ).
tff('Define:imprp:7',axiom,
? [X_768: set_2] :
( ! [X_769: $int,X_770: $int] :
( mem2(X_770,X_769,X_768)
<=> mem2(X_770,X_769,g_s97_78) )
& ! [X_771: $int,X_772: $int,X_773: $int] :
( ( mem2(X_771,X_772,X_768)
& mem2(X_771,X_773,X_768) )
=> ( X_772 = X_773 ) )
& ! [X_774: $int] :
( mem0(X_774,g_s2_2)
<=> ? [X_775: $int] : mem2(X_774,X_775,X_768) )
& ! [X_776: $int] :
( ? [X_777: $int] : mem2(X_777,X_776,X_768)
=> mem0(X_776,g_s6_6) ) ) ).
tff('Define:imprp:8',axiom,
? [X_778: set_2] :
( ! [X_779: $int,X_780: $int] :
( mem2(X_780,X_779,X_778)
<=> mem2(X_780,X_779,g_s98_83) )
& ! [X_781: $int,X_782: $int,X_783: $int] :
( ( mem2(X_781,X_782,X_778)
& mem2(X_781,X_783,X_778) )
=> ( X_782 = X_783 ) )
& ! [X_784: $int] :
( mem0(X_784,g_s10_10)
<=> ? [X_785: $int] : mem2(X_784,X_785,X_778) )
& ! [X_786: $int] :
( ? [X_787: $int] : mem2(X_787,X_786,X_778)
=> mem0(X_786,g_s6_6) ) ) ).
tff('Define:imprp:9',axiom,
? [X_788: set_2] :
( ! [X_789: $int,X_790: $int] :
( mem2(X_790,X_789,X_788)
<=> mem2(X_790,X_789,g_s99_84) )
& ! [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_s10_10)
<=> ? [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_s6_6) ) ) ).
%Global hypotheses
%----Local hypotheses
%----Goal
tff('Goal',conjecture,
( ! [X_953: $int,X_954: $int] :
( ( mem2(X_954,X_953,g_s104_89)
& mem0(X_954,g_s66_66)
& mem0(X_953,g_s37_37) )
=> ( mem0(X_954,g_s66_66)
& mem0(X_953,g_s37_37) ) )
& ! [X_955: $int,X_956: $int,X_957: $int] :
( ( mem2(X_955,X_956,g_s104_89)
& mem0(X_955,g_s66_66)
& mem0(X_956,g_s37_37)
& mem2(X_955,X_957,g_s104_89)
& mem0(X_955,g_s66_66)
& mem0(X_957,g_s37_37) )
=> ( X_956 = X_957 ) ) ) ).
%------------------------------------------------------------------------------