TPTP Problem File: SWC540_1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWC540_1 : TPTP v9.0.0. Released v9.0.0.
% Domain : Software Creation
% Problem : Atelier-B Proof Obligation: PO 5 0 Group s94 Tag s88
% Version : Especial.
% English :
% Refs : [Deh22] Deharbe (2022), Proof Obligations from the B Formal Me
% : [Deh24] Deharbe (2024), Email to Geoff Sutcliffe
% Source : [Deh24]
% Names : 0015-00217-5-0.tptp [Deh24]
% Status : ContradictoryAxioms
% Rating : 0.50 v9.0.0
% Syntax : Number of formulae : 231 ( 20 unt; 112 typ; 0 def)
% Number of atoms : 678 ( 117 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 602 ( 43 ~; 22 |; 280 &)
% ( 79 <=>; 178 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 636 ( 96 atm; 17 fun; 52 num; 471 var)
% Number of types : 10 ( 7 usr; 2 ari)
% Number of type conns : 37 ( 19 >; 18 *; 0 +; 0 <<)
% Number of predicates : 14 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 109 ( 98 usr; 92 con; 0-2 aty)
% Number of variables : 529 ( 428 !; 101 ?; 529 :)
% SPC : TF0_CAX_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_s10_10_type,type,
g_s10_10: $int ).
tff(g_s11_11_type,type,
g_s11_11: $int ).
tff(g_s12_12_type,type,
g_s12_12: set_0 ).
tff(g_s13_13_type,type,
g_s13_13: $int ).
tff(g_s14_14_type,type,
g_s14_14: $int ).
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: set_0 ).
tff(g_s19_19_type,type,
g_s19_19: $int ).
tff(g_s1_1_type,type,
g_s1_1: $int ).
tff(g_s20_20_type,type,
g_s20_20: $int ).
tff(g_s21_21_type,type,
g_s21_21: $int ).
tff(g_s22_22_type,type,
g_s22_22: set_0 ).
tff(g_s23_23_type,type,
g_s23_23: $int ).
tff(g_s24_24_type,type,
g_s24_24: $int ).
tff(g_s25_25_type,type,
g_s25_25: set_0 ).
tff(g_s26_26_type,type,
g_s26_26: $int ).
tff(g_s27_27_type,type,
g_s27_27: $int ).
tff(g_s28_28_type,type,
g_s28_28: $int ).
tff(g_s29_29_type,type,
g_s29_29: set_0 ).
tff(g_s2_2_type,type,
g_s2_2: $int ).
tff(g_s30_30_type,type,
g_s30_30: set_0 ).
tff(g_s31_31_type,type,
g_s31_31: $int ).
tff(g_s32_32_type,type,
g_s32_32: $int ).
tff(g_s33_33_type,type,
g_s33_33: $int ).
tff(g_s34_34_type,type,
g_s34_34: set_0 ).
tff(g_s35_35_type,type,
g_s35_35: set_0 ).
tff(g_s36_36_type,type,
g_s36_36: set_0 ).
tff(g_s37_37_type,type,
g_s37_37: set_0 ).
tff(g_s38_38_type,type,
g_s38_38: set_0 ).
tff(g_s39_39_type,type,
g_s39_39: set_0 ).
tff(g_s3_3_type,type,
g_s3_3: $int ).
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_0 ).
tff(g_s44_44_type,type,
g_s44_44: set_2 ).
tff(g_s45_45_type,type,
g_s45_45: set_2 ).
tff(g_s46_46_type,type,
g_s46_46: set_0 ).
tff(g_s47_47_type,type,
g_s47_47: $int ).
tff(g_s48_48_type,type,
g_s48_48: set_2 ).
tff(g_s49_49_type,type,
g_s49_49: set_0 ).
tff(g_s4_4_type,type,
g_s4_4: set_0 ).
tff(g_s50_50_type,type,
g_s50_50: set_2 ).
tff(g_s51_51_type,type,
g_s51_51: $int ).
tff(g_s52_52_type,type,
g_s52_52: set_0 ).
tff(g_s53_53_type,type,
g_s53_53: $int ).
tff(g_s54_54_type,type,
g_s54_54: set_2 ).
tff(g_s55_55_type,type,
g_s55_55: set_0 ).
tff(g_s56_56_type,type,
g_s56_56: $int ).
tff(g_s57_57_type,type,
g_s57_57: set_2 ).
tff(g_s58_58_type,type,
g_s58_58: set_0 ).
tff(g_s59_59_type,type,
g_s59_59: $int ).
tff(g_s5_5_type,type,
g_s5_5: $int ).
tff(g_s60_60_type,type,
g_s60_60: set_2 ).
tff(g_s61_72_type,type,
g_s61_72: set_3 ).
tff(g_s62_73_type,type,
g_s62_73: set_2 ).
tff(g_s63_74_type,type,
g_s63_74: set_2 ).
tff(g_s64_75_type,type,
g_s64_75: set_4 ).
tff(g_s65_76_type,type,
g_s65_76: set_2 ).
tff(g_s68_1_77_type,type,
g_s68_1_77: $int ).
tff(g_s69_1_78_type,type,
g_s69_1_78: $int ).
tff(g_s6_6_type,type,
g_s6_6: $int ).
tff(g_s70_1_79_type,type,
g_s70_1_79: $int ).
tff(g_s71_1_80_type,type,
g_s71_1_80: $int ).
tff(g_s75_61_type,type,
g_s75_61: set_3 ).
tff(g_s76_67_type,type,
g_s76_67: set_2 ).
tff(g_s78_64_type,type,
g_s78_64: set_2 ).
tff(g_s79_65_type,type,
g_s79_65: set_2 ).
tff(g_s7_7_type,type,
g_s7_7: $int ).
tff(g_s80_66_type,type,
g_s80_66: set_2 ).
tff(g_s82_62_type,type,
g_s82_62: set_3 ).
tff(g_s83_63_type,type,
g_s83_63: set_0 ).
tff(g_s84_68_type,type,
g_s84_68: set_3 ).
tff(g_s8_8_type,type,
g_s8_8: set_0 ).
tff(g_s90_81_type,type,
g_s90_81: $int ).
tff(g_s9_9_type,type,
g_s9_9: $int ).
tff(mem2_type,type,
mem2: ( $int * $int * set_2 ) > $o ).
tff(mem3_type,type,
mem3: ( $int * $int * $int * set_3 ) > $o ).
tff(mem4_type,type,
mem4: ( $int * set_0 * set_4 ) > $o ).
tff(prod_0_type,type,
prod_0: $tType ).
tff(prod_0_empty,type,
prod_0_empty: prod_0 ).
tff(prod_0_insert,type,
prod_0: ( $int * $int ) > prod_0 ).
tff(prod_0_in,type,
prod_0_in: ( $int * $int * prod_0 ) > $o ).
tff(prod_1_type,type,
prod_1: $tType ).
tff(prod_1_empty,type,
prod_1_empty: prod_1 ).
tff(prod_1_insert,type,
prod_1: ( prod_0 * $int ) > prod_1 ).
tff(prod_1_in,type,
prod_1_in: ( prod_0 * $int * prod_1 ) > $o ).
tff(set_2_type,type,
set_2: $tType ).
tff(set_2_empty,type,
set_2_empty: set_2 ).
tff(set_2_insert,type,
set_2: prod_0 > set_2 ).
tff(set_3_type,type,
set_3: $tType ).
tff(set_3_empty,type,
set_3_empty: set_3 ).
tff(set_3_insert,type,
set_3: prod_1 > set_3 ).
tff(set_4_type,type,
set_4: $tType ).
tff(set_4_empty,type,
set_4_empty: set_4 ).
tff(set_4_insert,type,
set_4: prod_2 > set_4 ).
%----Defines
tff('Define:B definitions:0',axiom,
! [X_3: $int] :
( ( $greatereq(X_3,0)
& $lesseq(X_3,max_int) )
<=> ( $greatereq(X_3,0)
& $lesseq(X_3,max_int) ) ) ).
tff('Define:B definitions:1',axiom,
! [X_4: $int] :
( ( $greatereq(X_4,min_int)
& $lesseq(X_4,max_int) )
<=> ( $greatereq(X_4,min_int)
& $lesseq(X_4,max_int) ) ) ).
tff('Define:aprp:0',axiom,
( ! [X_513: $int,X_514: $int,X_515: $int] :
( mem3(X_515,X_514,X_513,g_s61_72)
=> ( mem0(X_515,g_s40_40)
& mem0(X_514,g_s43_43)
& mem0(X_513,g_s52_52) ) )
& ! [X_516: $int,X_517: $int,X_518: $int,X_519: $int] :
( ( mem3(X_517,X_516,X_518,g_s61_72)
& mem3(X_517,X_516,X_519,g_s61_72) )
=> ( X_518 = X_519 ) ) ) ).
tff('Define:aprp:1',axiom,
( ! [X_520: $int,X_521: $int] :
( mem2(X_521,X_520,g_s62_73)
=> ( mem0(X_521,g_s40_40)
& mem0(X_520,g_s58_58) ) )
& ! [X_522: $int,X_523: $int,X_524: $int] :
( ( mem2(X_522,X_523,g_s62_73)
& mem2(X_522,X_524,g_s62_73) )
=> ( X_523 = X_524 ) ) ) ).
tff('Define:aprp:2',axiom,
! [X_525: $int,X_526: $int] :
( mem2(X_526,X_525,g_s63_74)
=> ( mem0(X_526,g_s40_40)
& mem0(X_525,g_s55_55) ) ) ).
tff('Define:aprp:3',axiom,
? [X_527: set_4] :
( ! [X_528: set_0,X_529: $int] :
( mem4(X_529,X_528,X_527)
<=> mem4(X_529,X_528,g_s64_75) )
& ! [X_530: $int,X_531: set_0,X_532: set_0] :
( ( mem4(X_530,X_531,X_527)
& mem4(X_530,X_532,X_527) )
=> ! [X_533: $int] :
( mem0(X_533,X_531)
<=> mem0(X_533,X_532) ) )
& ! [X_534: $int] :
( mem0(X_534,g_s40_40)
<=> ? [X_535: set_0] : mem4(X_534,X_535,X_527) )
& ! [X_536: set_0] :
( ? [X_537: $int] : mem4(X_537,X_536,X_527)
=> ! [X_538: $int] :
( mem0(X_538,X_536)
=> mem0(X_538,g_s37_37) ) ) ) ).
tff('Define:aprp:4',axiom,
? [X_539: $int,X_540: set_2] :
( ! [X_541: $int,X_542: $int] :
( mem2(X_542,X_541,X_540)
<=> mem2(X_542,X_541,g_s65_76) )
& ! [X_543: $int,X_544: $int,X_545: $int] :
( ( mem2(X_543,X_544,X_540)
& mem2(X_543,X_545,X_540) )
=> ( X_544 = X_545 ) )
& ! [X_546: $int] :
( ( $greatereq(X_546,1)
& $lesseq(X_546,X_539) )
<=> ? [X_547: $int] : mem2(X_546,X_547,X_540) )
& ! [X_548: $int] :
( ? [X_549: $int] : mem2(X_549,X_548,X_540)
=> mem0(X_548,g_s55_55) ) ) ).
tff('Define:aprp:5',axiom,
! [L_s66: $int] :
( mem0(L_s66,g_s40_40)
=> ! [X_550: $int] :
( ? [X_551: $int] :
( ( X_551 = L_s66 )
& mem2(X_551,X_550,g_s63_74) )
<=> ? [X_552: $int] :
( ! [X_553: set_0] :
( mem4(L_s66,X_553,g_s64_75)
=> mem0(X_552,X_553) )
& mem2(X_552,X_550,g_s65_76) ) ) ) ).
tff('Define:aprp:6',axiom,
! [L_s66: $int] :
( mem0(L_s66,g_s40_40)
=> ! [X_554: $int] :
( ! [X_555: set_0] :
( mem4(L_s66,X_555,g_s64_75)
=> mem0(X_554,X_555) )
=> ? [X_556: $int] : mem2(X_554,X_556,g_s65_76) ) ) ).
tff('Define:aprp:7',axiom,
! [L_s66: $int] :
( mem0(L_s66,g_s40_40)
=> ( ! [X_557: $int,X_558: $int] :
( ( mem2(X_558,X_557,g_s65_76)
& ! [X_559: set_0] :
( mem4(L_s66,X_559,g_s64_75)
=> mem0(X_558,X_559) ) )
=> ( $greatereq(X_558,0)
& mem0(X_557,g_s55_55) ) )
& ! [X_560: $int,X_561: $int,X_562: $int] :
( ( mem2(X_560,X_561,g_s65_76)
& ! [X_563: set_0] :
( mem4(L_s66,X_563,g_s64_75)
=> mem0(X_560,X_563) )
& mem2(X_560,X_562,g_s65_76)
& ! [X_564: set_0] :
( mem4(L_s66,X_564,g_s64_75)
=> mem0(X_560,X_564) ) )
=> ( X_561 = X_562 ) )
& ! [X_565: $int,X_566: $int,X_567: $int] :
( ( mem2(X_566,X_565,g_s65_76)
& ! [X_568: set_0] :
( mem4(L_s66,X_568,g_s64_75)
=> mem0(X_566,X_568) )
& mem2(X_567,X_565,g_s65_76)
& ! [X_569: set_0] :
( mem4(L_s66,X_569,g_s64_75)
=> mem0(X_567,X_569) ) )
=> ( X_566 = X_567 ) ) ) ) ).
tff('Define:aprp:8',axiom,
! [L_s66: $int] :
( ( mem0(L_s66,g_s40_40)
& ~ ! [X_570: set_0] :
( ! [X_571: $int] :
( mem0(X_571,X_570)
<=> $false )
=> mem4(L_s66,X_570,g_s64_75) ) )
=> ! [X_572: set_0] :
( ! [X_573: $int] :
( mem0(X_573,X_572)
<=> ! [X_574: $int,X_575: $int] :
( ( ! [X_577: set_0] :
( mem4(L_s66,X_577,g_s64_75)
=> mem0(X_574,X_577) )
& ! [X_576: $int] :
( ! [X_578: set_0] :
( mem4(L_s66,X_578,g_s64_75)
=> mem0(X_576,X_578) )
=> $lesseq(X_574,X_576) )
& ! [X_580: set_0] :
( mem4(L_s66,X_580,g_s64_75)
=> mem0(X_575,X_580) )
& ! [X_579: $int] :
( ! [X_581: set_0] :
( mem4(L_s66,X_581,g_s64_75)
=> mem0(X_579,X_581) )
=> $greatereq(X_575,X_579) ) )
=> ( $greatereq(X_573,X_574)
& $lesseq(X_573,X_575) ) ) )
=> mem4(L_s66,X_572,g_s64_75) ) ) ).
tff('Define:ctx:0',axiom,
( ! [X_5: $int] :
( mem0(X_5,g_s0_0)
<=> ( ( X_5 = g_s1_1 )
| ( X_5 = g_s2_2 )
| ( X_5 = g_s3_3 ) ) )
& ( g_s1_1 != g_s2_2 )
& ( g_s2_2 != g_s3_3 ) ) ).
tff('Define:ctx:1',axiom,
( ! [X_6: $int] :
( mem0(X_6,g_s4_4)
<=> ( ( X_6 = g_s5_5 )
| ( X_6 = g_s6_6 )
| ( X_6 = g_s7_7 ) ) )
& ( g_s5_5 != g_s6_6 )
& ( g_s6_6 != g_s7_7 ) ) ).
tff('Define:ctx:10',axiom,
( ~ ! [X_33: $int] :
( mem0(X_33,g_s34_34)
<=> $false )
& ! [X_36: $int] :
( mem0(X_36,g_s34_34)
=> $true )
& ? [X_34: $int,X_35: set_2] :
( ? [X_37: set_2] :
( ! [X_38: $int,X_39: $int] :
( mem2(X_39,X_38,X_37)
<=> mem2(X_39,X_38,X_35) )
& ! [X_40: $int,X_41: $int,X_42: $int] :
( ( mem2(X_40,X_41,X_37)
& mem2(X_40,X_42,X_37) )
=> ( X_41 = X_42 ) )
& ! [X_43: $int] :
( ( $greatereq(X_43,1)
& $lesseq(X_43,X_34) )
<=> ? [X_44: $int] : mem2(X_43,X_44,X_37) )
& ! [X_45: $int] :
( ? [X_46: $int] : mem2(X_46,X_45,X_37)
=> mem0(X_45,g_s34_34) ) )
& ! [X_47: $int] :
( mem0(X_47,g_s34_34)
=> ? [X_48: $int] : mem2(X_48,X_47,X_35) )
& ! [X_49: $int,X_50: $int,X_51: $int] :
( ( mem2(X_50,X_49,X_35)
& mem2(X_51,X_49,X_35) )
=> ( X_50 = X_51 ) ) ) ) ).
tff('Define:ctx:11',axiom,
( ~ ! [X_52: $int] :
( mem0(X_52,g_s35_35)
<=> $false )
& ! [X_55: $int] :
( mem0(X_55,g_s35_35)
=> $true )
& ? [X_53: $int,X_54: set_2] :
( ? [X_56: set_2] :
( ! [X_57: $int,X_58: $int] :
( mem2(X_58,X_57,X_56)
<=> mem2(X_58,X_57,X_54) )
& ! [X_59: $int,X_60: $int,X_61: $int] :
( ( mem2(X_59,X_60,X_56)
& mem2(X_59,X_61,X_56) )
=> ( X_60 = X_61 ) )
& ! [X_62: $int] :
( ( $greatereq(X_62,1)
& $lesseq(X_62,X_53) )
<=> ? [X_63: $int] : mem2(X_62,X_63,X_56) )
& ! [X_64: $int] :
( ? [X_65: $int] : mem2(X_65,X_64,X_56)
=> mem0(X_64,g_s35_35) ) )
& ! [X_66: $int] :
( mem0(X_66,g_s35_35)
=> ? [X_67: $int] : mem2(X_67,X_66,X_54) )
& ! [X_68: $int,X_69: $int,X_70: $int] :
( ( mem2(X_69,X_68,X_54)
& mem2(X_70,X_68,X_54) )
=> ( X_69 = X_70 ) ) ) ) ).
tff('Define:ctx:12',axiom,
( ~ ! [X_71: $int] :
( mem0(X_71,g_s36_36)
<=> $false )
& ! [X_74: $int] :
( mem0(X_74,g_s36_36)
=> $true )
& ? [X_72: $int,X_73: set_2] :
( ? [X_75: set_2] :
( ! [X_76: $int,X_77: $int] :
( mem2(X_77,X_76,X_75)
<=> mem2(X_77,X_76,X_73) )
& ! [X_78: $int,X_79: $int,X_80: $int] :
( ( mem2(X_78,X_79,X_75)
& mem2(X_78,X_80,X_75) )
=> ( X_79 = X_80 ) )
& ! [X_81: $int] :
( ( $greatereq(X_81,1)
& $lesseq(X_81,X_72) )
<=> ? [X_82: $int] : mem2(X_81,X_82,X_75) )
& ! [X_83: $int] :
( ? [X_84: $int] : mem2(X_84,X_83,X_75)
=> mem0(X_83,g_s36_36) ) )
& ! [X_85: $int] :
( mem0(X_85,g_s36_36)
=> ? [X_86: $int] : mem2(X_86,X_85,X_73) )
& ! [X_87: $int,X_88: $int,X_89: $int] :
( ( mem2(X_88,X_87,X_73)
& mem2(X_89,X_87,X_73) )
=> ( X_88 = X_89 ) ) ) ) ).
tff('Define:ctx:13',axiom,
! [X_90: $int] :
( mem0(X_90,g_s37_37)
=> ( $greatereq(X_90,0)
& $lesseq(X_90,max_int) ) ) ).
tff('Define:ctx:14',axiom,
~ ! [X_91: $int] :
( mem0(X_91,g_s37_37)
<=> $false ) ).
tff('Define:ctx:15',axiom,
! [X_92: $int] :
( mem0(X_92,g_s37_37)
<=> ! [X_93: $int,X_94: $int] :
( ( mem0(X_93,g_s37_37)
& ! [X_95: $int] :
( mem0(X_95,g_s37_37)
=> $lesseq(X_93,X_95) )
& mem0(X_94,g_s37_37)
& ! [X_96: $int] :
( mem0(X_96,g_s37_37)
=> $greatereq(X_94,X_96) ) )
=> ( $greatereq(X_92,X_93)
& $lesseq(X_92,X_94) ) ) ) ).
tff('Define:ctx:16',axiom,
~ ! [X_97: $int] :
( ( X_97 = max_int )
=> mem0(X_97,g_s37_37) ) ).
tff('Define:ctx:17',axiom,
! [X_98: $int] :
( mem0(X_98,g_s38_38)
=> ( $greatereq(X_98,0)
& $lesseq(X_98,max_int) ) ) ).
tff('Define:ctx:18',axiom,
~ ! [X_99: $int] :
( mem0(X_99,g_s38_38)
<=> $false ) ).
tff('Define:ctx:19',axiom,
! [X_100: $int] :
( mem0(X_100,g_s38_38)
<=> ! [X_101: $int,X_102: $int] :
( ( mem0(X_101,g_s38_38)
& ! [X_103: $int] :
( mem0(X_103,g_s38_38)
=> $lesseq(X_101,X_103) )
& mem0(X_102,g_s38_38)
& ! [X_104: $int] :
( mem0(X_104,g_s38_38)
=> $greatereq(X_102,X_104) ) )
=> ( $greatereq(X_100,X_101)
& $lesseq(X_100,X_102) ) ) ) ).
tff('Define:ctx:2',axiom,
( ! [X_7: $int] :
( mem0(X_7,g_s8_8)
<=> ( ( X_7 = g_s9_9 )
| ( X_7 = g_s10_10 )
| ( X_7 = g_s11_11 ) ) )
& ( g_s9_9 != g_s10_10 )
& ( g_s10_10 != g_s11_11 ) ) ).
tff('Define:ctx:20',axiom,
~ ! [X_105: $int] :
( ( X_105 = max_int )
=> mem0(X_105,g_s38_38) ) ).
tff('Define:ctx:21',axiom,
! [X_106: $int] :
( mem0(X_106,g_s39_39)
=> ( $greatereq(X_106,0)
& $lesseq(X_106,max_int) ) ) ).
tff('Define:ctx:22',axiom,
~ ! [X_107: $int] :
( mem0(X_107,g_s39_39)
<=> $false ) ).
tff('Define:ctx:23',axiom,
! [X_108: $int] :
( mem0(X_108,g_s39_39)
<=> ! [X_109: $int,X_110: $int] :
( ( mem0(X_109,g_s39_39)
& ! [X_111: $int] :
( mem0(X_111,g_s39_39)
=> $lesseq(X_109,X_111) )
& mem0(X_110,g_s39_39)
& ! [X_112: $int] :
( mem0(X_112,g_s39_39)
=> $greatereq(X_110,X_112) ) )
=> ( $greatereq(X_108,X_109)
& $lesseq(X_108,X_110) ) ) ) ).
tff('Define:ctx:24',axiom,
~ ! [X_113: $int] :
( ( X_113 = max_int )
=> mem0(X_113,g_s39_39) ) ).
tff('Define:ctx:25',axiom,
! [X_114: $int] :
( mem0(X_114,g_s40_40)
=> mem0(X_114,g_s29_29) ) ).
tff('Define:ctx:26',axiom,
mem0(g_s41_41,g_s29_29) ).
tff('Define:ctx:27',axiom,
~ mem0(g_s41_41,g_s40_40) ).
tff('Define:ctx:28',axiom,
( ! [X_115: $int,X_116: $int] :
( mem2(X_116,X_115,g_s42_42)
=> ( $greatereq(X_116,0)
& $lesseq(X_116,max_int)
& mem0(X_115,g_s29_29) ) )
& ! [X_117: $int,X_118: $int,X_119: $int] :
( ( mem2(X_117,X_118,g_s42_42)
& mem2(X_117,X_119,g_s42_42) )
=> ( X_118 = X_119 ) ) ) ).
tff('Define:ctx:29',axiom,
? [X_120: $int] :
( ? [X_121: set_2] :
( ! [X_122: $int,X_123: $int] :
( mem2(X_123,X_122,X_121)
<=> mem2(X_123,X_122,g_s42_42) )
& ! [X_124: $int,X_125: $int,X_126: $int] :
( ( mem2(X_124,X_125,X_121)
& mem2(X_124,X_126,X_121) )
=> ( X_125 = X_126 ) )
& ! [X_127: $int] :
( ( $greatereq(X_127,1)
& $lesseq(X_127,X_120) )
<=> ? [X_128: $int] : mem2(X_127,X_128,X_121) )
& ! [X_129: $int] :
( ? [X_130: $int] : mem2(X_130,X_129,X_121)
=> mem0(X_129,g_s40_40) ) )
& ! [X_131: $int] :
( mem0(X_131,g_s40_40)
=> ? [X_132: $int] : mem2(X_132,X_131,g_s42_42) )
& ! [X_133: $int,X_134: $int,X_135: $int] :
( ( mem2(X_134,X_133,g_s42_42)
& mem2(X_135,X_133,g_s42_42) )
=> ( X_134 = X_135 ) ) ) ).
tff('Define:ctx:3',axiom,
( ! [X_8: $int] :
( mem0(X_8,g_s12_12)
<=> ( ( X_8 = g_s13_13 )
| ( X_8 = g_s14_14 ) ) )
& ( g_s13_13 != g_s14_14 ) ) ).
tff('Define:ctx:30',axiom,
! [X_136: $int] :
( mem0(X_136,g_s43_43)
=> mem0(X_136,g_s0_0) ) ).
tff('Define:ctx:31',axiom,
~ mem0(g_s1_1,g_s43_43) ).
tff('Define:ctx:32',axiom,
! [X_137: $int] :
( mem0(X_137,g_s43_43)
<=> ( ( X_137 = g_s2_2 )
| ( X_137 = g_s3_3 ) ) ) ).
tff('Define:ctx:33',axiom,
( ? [X_138: set_2] :
( ! [X_139: $int,X_140: $int] :
( mem2(X_140,X_139,X_138)
<=> mem2(X_140,X_139,g_s44_44) )
& ! [X_141: $int,X_142: $int,X_143: $int] :
( ( mem2(X_141,X_142,X_138)
& mem2(X_141,X_143,X_138) )
=> ( X_142 = X_143 ) )
& ! [X_144: $int] :
( mem0(X_144,g_s43_43)
<=> ? [X_145: $int] : mem2(X_144,X_145,X_138) )
& ! [X_146: $int] :
( ? [X_147: $int] : mem2(X_147,X_146,X_138)
=> mem0(X_146,g_s43_43) ) )
& ! [X_148: $int] :
( mem0(X_148,g_s43_43)
=> ? [X_149: $int] : mem2(X_149,X_148,g_s44_44) )
& ! [X_150: $int,X_151: $int,X_152: $int] :
( ( mem2(X_151,X_150,g_s44_44)
& mem2(X_152,X_150,g_s44_44) )
=> ( X_151 = X_152 ) ) ) ).
tff('Define:ctx:34',axiom,
! [X_153: $int,X_154: $int] :
( ( mem2(X_154,X_153,g_s44_44)
& ( X_154 = X_153 )
& mem0(X_154,g_s43_43) )
<=> $false ) ).
tff('Define:ctx:35',axiom,
( ? [X_155: set_2] :
( ! [X_156: $int,X_157: $int] :
( mem2(X_157,X_156,X_155)
<=> mem2(X_157,X_156,g_s45_45) )
& ! [X_158: $int,X_159: $int,X_160: $int] :
( ( mem2(X_158,X_159,X_155)
& mem2(X_158,X_160,X_155) )
=> ( X_159 = X_160 ) )
& ! [X_161: $int] :
( mem0(X_161,g_s46_46)
<=> ? [X_162: $int] : mem2(X_161,X_162,X_155) )
& ! [X_163: $int] :
( ? [X_164: $int] : mem2(X_164,X_163,X_155)
=> mem0(X_163,g_s0_0) ) )
& ! [X_165: $int] :
( mem0(X_165,g_s0_0)
=> ? [X_166: $int] : mem2(X_166,X_165,g_s45_45) )
& ! [X_167: $int,X_168: $int,X_169: $int] :
( ( mem2(X_168,X_167,g_s45_45)
& mem2(X_169,X_167,g_s45_45) )
=> ( X_168 = X_169 ) ) ) ).
tff('Define:ctx:36',axiom,
~ ! [X_170: $int] :
( mem2(g_s47_47,X_170,g_s45_45)
=> mem0(X_170,g_s43_43) ) ).
tff('Define:ctx:37',axiom,
( ? [X_171: set_2] :
( ! [X_172: $int,X_173: $int] :
( mem2(X_173,X_172,X_171)
<=> mem2(X_173,X_172,g_s48_48) )
& ! [X_174: $int,X_175: $int,X_176: $int] :
( ( mem2(X_174,X_175,X_171)
& mem2(X_174,X_176,X_171) )
=> ( X_175 = X_176 ) )
& ! [X_177: $int] :
( mem0(X_177,g_s49_49)
<=> ? [X_178: $int] : mem2(X_177,X_178,X_171) )
& ! [X_179: $int] :
( ? [X_180: $int] : mem2(X_180,X_179,X_171)
=> mem0(X_179,g_s0_0) ) )
& ! [X_181: $int] :
( mem0(X_181,g_s0_0)
=> ? [X_182: $int] : mem2(X_182,X_181,g_s48_48) )
& ! [X_183: $int,X_184: $int,X_185: $int] :
( ( mem2(X_184,X_183,g_s48_48)
& mem2(X_185,X_183,g_s48_48) )
=> ( X_184 = X_185 ) ) ) ).
tff('Define:ctx:38',axiom,
( ? [X_186: set_2] :
( ! [X_187: $int,X_188: $int] :
( mem2(X_188,X_187,X_186)
<=> mem2(X_188,X_187,g_s50_50) )
& ! [X_189: $int,X_190: $int,X_191: $int] :
( ( mem2(X_189,X_190,X_186)
& mem2(X_189,X_191,X_186) )
=> ( X_190 = X_191 ) )
& ! [X_192: $int] :
( mem0(X_192,g_s0_0)
<=> ? [X_193: $int] : mem2(X_192,X_193,X_186) )
& ! [X_194: $int] :
( ? [X_195: $int] : mem2(X_195,X_194,X_186)
=> mem0(X_194,g_s49_49) ) )
& ! [X_196: $int] :
( mem0(X_196,g_s49_49)
=> ? [X_197: $int] : mem2(X_197,X_196,g_s50_50) )
& ! [X_198: $int,X_199: $int,X_200: $int] :
( ( mem2(X_199,X_198,g_s50_50)
& mem2(X_200,X_198,g_s50_50) )
=> ( X_199 = X_200 ) ) ) ).
tff('Define:ctx:39',axiom,
! [X_201: $int,X_202: $int] :
( mem2(X_202,X_201,g_s48_48)
<=> mem2(X_201,X_202,g_s50_50) ) ).
tff('Define:ctx:4',axiom,
( ! [X_9: $int] :
( mem0(X_9,g_s15_15)
<=> ( ( X_9 = g_s16_16 )
| ( X_9 = g_s17_17 ) ) )
& ( g_s16_16 != g_s17_17 ) ) ).
tff('Define:ctx:40',axiom,
~ ! [X_203: $int] :
( mem2(g_s51_51,X_203,g_s48_48)
=> mem0(X_203,g_s43_43) ) ).
tff('Define:ctx:41',axiom,
! [X_204: $int] :
( mem0(X_204,g_s52_52)
=> mem0(X_204,g_s34_34) ) ).
tff('Define:ctx:42',axiom,
mem0(g_s53_53,g_s34_34) ).
tff('Define:ctx:43',axiom,
~ mem0(g_s53_53,g_s52_52) ).
tff('Define:ctx:44',axiom,
( ! [X_205: $int,X_206: $int] :
( mem2(X_206,X_205,g_s54_54)
=> ( $greatereq(X_206,0)
& $lesseq(X_206,max_int)
& mem0(X_205,g_s34_34) ) )
& ! [X_207: $int,X_208: $int,X_209: $int] :
( ( mem2(X_207,X_208,g_s54_54)
& mem2(X_207,X_209,g_s54_54) )
=> ( X_208 = X_209 ) ) ) ).
tff('Define:ctx:45',axiom,
? [X_210: $int] :
( ? [X_211: set_2] :
( ! [X_212: $int,X_213: $int] :
( mem2(X_213,X_212,X_211)
<=> mem2(X_213,X_212,g_s54_54) )
& ! [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] :
( ( $greatereq(X_217,1)
& $lesseq(X_217,X_210) )
<=> ? [X_218: $int] : mem2(X_217,X_218,X_211) )
& ! [X_219: $int] :
( ? [X_220: $int] : mem2(X_220,X_219,X_211)
=> mem0(X_219,g_s52_52) ) )
& ! [X_221: $int] :
( mem0(X_221,g_s52_52)
=> ? [X_222: $int] : mem2(X_222,X_221,g_s54_54) )
& ! [X_223: $int,X_224: $int,X_225: $int] :
( ( mem2(X_224,X_223,g_s54_54)
& mem2(X_225,X_223,g_s54_54) )
=> ( X_224 = X_225 ) ) ) ).
tff('Define:ctx:46',axiom,
! [X_226: $int] :
( mem0(X_226,g_s55_55)
=> mem0(X_226,g_s35_35) ) ).
tff('Define:ctx:47',axiom,
mem0(g_s56_56,g_s35_35) ).
tff('Define:ctx:48',axiom,
~ mem0(g_s56_56,g_s55_55) ).
tff('Define:ctx:49',axiom,
( ! [X_227: $int,X_228: $int] :
( mem2(X_228,X_227,g_s57_57)
=> ( $greatereq(X_228,0)
& $lesseq(X_228,max_int)
& mem0(X_227,g_s35_35) ) )
& ! [X_229: $int,X_230: $int,X_231: $int] :
( ( mem2(X_229,X_230,g_s57_57)
& mem2(X_229,X_231,g_s57_57) )
=> ( X_230 = X_231 ) ) ) ).
tff('Define:ctx:5',axiom,
( ! [X_10: $int] :
( mem0(X_10,g_s18_18)
<=> ( ( X_10 = g_s19_19 )
| ( X_10 = g_s20_20 )
| ( X_10 = g_s21_21 ) ) )
& ( g_s19_19 != g_s20_20 )
& ( g_s20_20 != g_s21_21 ) ) ).
tff('Define:ctx:50',axiom,
? [X_232: $int] :
( ? [X_233: set_2] :
( ! [X_234: $int,X_235: $int] :
( mem2(X_235,X_234,X_233)
<=> mem2(X_235,X_234,g_s57_57) )
& ! [X_236: $int,X_237: $int,X_238: $int] :
( ( mem2(X_236,X_237,X_233)
& mem2(X_236,X_238,X_233) )
=> ( X_237 = X_238 ) )
& ! [X_239: $int] :
( ( $greatereq(X_239,1)
& $lesseq(X_239,X_232) )
<=> ? [X_240: $int] : mem2(X_239,X_240,X_233) )
& ! [X_241: $int] :
( ? [X_242: $int] : mem2(X_242,X_241,X_233)
=> mem0(X_241,g_s55_55) ) )
& ! [X_243: $int] :
( mem0(X_243,g_s55_55)
=> ? [X_244: $int] : mem2(X_244,X_243,g_s57_57) )
& ! [X_245: $int,X_246: $int,X_247: $int] :
( ( mem2(X_246,X_245,g_s57_57)
& mem2(X_247,X_245,g_s57_57) )
=> ( X_246 = X_247 ) ) ) ).
tff('Define:ctx:51',axiom,
! [X_248: $int] :
( mem0(X_248,g_s58_58)
=> mem0(X_248,g_s36_36) ) ).
tff('Define:ctx:52',axiom,
mem0(g_s59_59,g_s36_36) ).
tff('Define:ctx:53',axiom,
~ mem0(g_s59_59,g_s58_58) ).
tff('Define:ctx:54',axiom,
( ! [X_249: $int,X_250: $int] :
( mem2(X_250,X_249,g_s60_60)
=> ( $greatereq(X_250,0)
& $lesseq(X_250,max_int)
& mem0(X_249,g_s36_36) ) )
& ! [X_251: $int,X_252: $int,X_253: $int] :
( ( mem2(X_251,X_252,g_s60_60)
& mem2(X_251,X_253,g_s60_60) )
=> ( X_252 = X_253 ) ) ) ).
tff('Define:ctx:55',axiom,
? [X_254: $int] :
( ? [X_255: set_2] :
( ! [X_256: $int,X_257: $int] :
( mem2(X_257,X_256,X_255)
<=> mem2(X_257,X_256,g_s60_60) )
& ! [X_258: $int,X_259: $int,X_260: $int] :
( ( mem2(X_258,X_259,X_255)
& mem2(X_258,X_260,X_255) )
=> ( X_259 = X_260 ) )
& ! [X_261: $int] :
( ( $greatereq(X_261,1)
& $lesseq(X_261,X_254) )
<=> ? [X_262: $int] : mem2(X_261,X_262,X_255) )
& ! [X_263: $int] :
( ? [X_264: $int] : mem2(X_264,X_263,X_255)
=> mem0(X_263,g_s58_58) ) )
& ! [X_265: $int] :
( mem0(X_265,g_s58_58)
=> ? [X_266: $int] : mem2(X_266,X_265,g_s60_60) )
& ! [X_267: $int,X_268: $int,X_269: $int] :
( ( mem2(X_268,X_267,g_s60_60)
& mem2(X_269,X_267,g_s60_60) )
=> ( X_268 = X_269 ) ) ) ).
tff('Define:ctx:6',axiom,
( ! [X_11: $int] :
( mem0(X_11,g_s22_22)
<=> ( ( X_11 = g_s23_23 )
| ( X_11 = g_s24_24 ) ) )
& ( g_s23_23 != g_s24_24 ) ) ).
tff('Define:ctx:7',axiom,
( ! [X_12: $int] :
( mem0(X_12,g_s25_25)
<=> ( ( X_12 = g_s26_26 )
| ( X_12 = g_s27_27 )
| ( X_12 = g_s28_28 ) ) )
& ( g_s26_26 != g_s27_27 )
& ( g_s27_27 != g_s28_28 ) ) ).
tff('Define:ctx:8',axiom,
( ~ ! [X_13: $int] :
( mem0(X_13,g_s29_29)
<=> $false )
& ! [X_16: $int] :
( mem0(X_16,g_s29_29)
=> $true )
& ? [X_14: $int,X_15: set_2] :
( ? [X_17: set_2] :
( ! [X_18: $int,X_19: $int] :
( mem2(X_19,X_18,X_17)
<=> mem2(X_19,X_18,X_15) )
& ! [X_20: $int,X_21: $int,X_22: $int] :
( ( mem2(X_20,X_21,X_17)
& mem2(X_20,X_22,X_17) )
=> ( X_21 = X_22 ) )
& ! [X_23: $int] :
( ( $greatereq(X_23,1)
& $lesseq(X_23,X_14) )
<=> ? [X_24: $int] : mem2(X_23,X_24,X_17) )
& ! [X_25: $int] :
( ? [X_26: $int] : mem2(X_26,X_25,X_17)
=> mem0(X_25,g_s29_29) ) )
& ! [X_27: $int] :
( mem0(X_27,g_s29_29)
=> ? [X_28: $int] : mem2(X_28,X_27,X_15) )
& ! [X_29: $int,X_30: $int,X_31: $int] :
( ( mem2(X_30,X_29,X_15)
& mem2(X_31,X_29,X_15) )
=> ( X_30 = X_31 ) ) ) ) ).
tff('Define:ctx:9',axiom,
( ! [X_32: $int] :
( mem0(X_32,g_s30_30)
<=> ( ( X_32 = g_s31_31 )
| ( X_32 = g_s32_32 )
| ( X_32 = g_s33_33 ) ) )
& ( g_s31_31 != g_s32_32 )
& ( g_s32_32 != g_s33_33 ) ) ).
tff('Define:imext:0',axiom,
! [X_599: $int] :
( ? [X_600: $int] :
( mem0(X_600,g_s55_55)
& mem2(X_599,X_600,g_s80_66) )
=> mem0(X_599,g_s37_37) ) ).
tff('Define:imext:1',axiom,
! [X_601: $int] :
( ? [X_602: $int] :
( mem0(X_602,g_s55_55)
& mem2(X_601,X_602,g_s80_66) )
=> $greatereq(X_601,0) ) ).
tff('Define:imlprp:0',axiom,
! [X_582: $int,X_583: $int,X_584: $int] :
( mem3(X_584,X_583,X_582,g_s61_72)
<=> ( mem3(X_584,X_583,X_582,g_s75_61)
& mem0(X_584,g_s40_40)
& mem0(X_583,g_s43_43)
& mem0(X_582,g_s52_52) ) ) ).
tff('Define:imlprp:1',axiom,
! [X_585: $int,X_586: $int] :
( mem2(X_586,X_585,g_s62_73)
<=> ( mem2(X_586,X_585,g_s76_67)
& mem0(X_586,g_s40_40)
& mem0(X_585,g_s58_58) ) ) ).
tff('Define:imlprp:2',axiom,
! [X_587: set_0,X_588: $int] :
( mem4(X_588,X_587,g_s64_75)
<=> ( mem0(X_588,g_s40_40)
& ! [X_589: $int] :
( mem0(X_589,X_587)
<=> ! [X_590: $int,X_591: $int] :
( ( mem2(X_588,X_590,g_s78_64)
& mem2(X_588,X_591,g_s79_65) )
=> ( $greatereq(X_589,X_590)
& $lesseq(X_589,X_591) ) ) ) ) ) ).
tff('Define:imlprp:3',axiom,
! [X_592: $int,X_593: $int] :
( mem2(X_593,X_592,g_s65_76)
<=> ( mem2(X_593,X_592,g_s80_66)
& mem0(X_592,g_s55_55) ) ) ).
tff('Define:imlprp:4',axiom,
! [X_594: $int,X_595: $int] :
( mem2(X_595,X_594,g_s63_74)
<=> ( mem0(X_595,g_s40_40)
& mem0(X_594,g_s55_55)
& ? [X_596: $int] :
( ! [X_597: $int,X_598: $int] :
( ( mem2(X_595,X_597,g_s78_64)
& mem2(X_595,X_598,g_s79_65) )
=> ( $greatereq(X_596,X_597)
& $lesseq(X_596,X_598) ) )
& mem2(X_596,X_594,g_s80_66) ) ) ) ).
tff('Define:imprp:0',axiom,
? [X_270: set_3] :
( ! [X_271: $int,X_272: $int,X_273: $int] :
( mem3(X_273,X_272,X_271,X_270)
<=> mem3(X_273,X_272,X_271,g_s75_61) )
& ! [X_274: $int,X_275: $int,X_276: $int,X_277: $int] :
( ( mem3(X_275,X_274,X_276,X_270)
& mem3(X_275,X_274,X_277,X_270) )
=> ( X_276 = X_277 ) )
& ! [X_278: $int,X_279: $int] :
( ( mem0(X_279,g_s29_29)
& mem0(X_278,g_s0_0) )
<=> ? [X_280: $int] : mem3(X_279,X_278,X_280,X_270) )
& ! [X_281: $int] :
( ? [X_282: $int,X_283: $int] : mem3(X_283,X_282,X_281,X_270)
=> mem0(X_281,g_s34_34) ) ) ).
tff('Define:imprp:1',axiom,
? [X_284: set_3] :
( ! [X_285: $int,X_286: $int,X_287: $int] :
( mem3(X_287,X_286,X_285,X_284)
<=> mem3(X_287,X_286,X_285,g_s82_62) )
& ! [X_288: $int,X_289: $int,X_290: $int,X_291: $int] :
( ( mem3(X_289,X_288,X_290,X_284)
& mem3(X_289,X_288,X_291,X_284) )
=> ( X_290 = X_291 ) )
& ! [X_292: $int,X_293: $int] :
( ( mem0(X_293,g_s29_29)
& mem0(X_292,g_s0_0) )
<=> ? [X_294: $int] : mem3(X_293,X_292,X_294,X_284) )
& ! [X_295: $int] :
( ? [X_296: $int,X_297: $int] : mem3(X_297,X_296,X_295,X_284)
=> mem0(X_295,g_s83_63) ) ) ).
tff('Define:imprp:10',axiom,
! [L_s77: $int] :
( mem0(L_s77,g_s40_40)
=> ( ! [X_368: $int,X_369: $int] :
( ( mem2(X_368,X_369,g_s80_66)
& mem0(X_369,g_s55_55)
& ! [X_370: $int,X_371: $int] :
( ( mem2(L_s77,X_370,g_s78_64)
& mem2(L_s77,X_371,g_s79_65) )
=> ( $greatereq(X_368,X_370)
& $lesseq(X_368,X_371) ) ) )
=> ( mem0(X_369,g_s55_55)
& $greatereq(X_368,0) ) )
& ! [X_372: $int,X_373: $int,X_374: $int] :
( ( mem2(X_373,X_372,g_s80_66)
& mem0(X_372,g_s55_55)
& ! [X_375: $int,X_376: $int] :
( ( mem2(L_s77,X_375,g_s78_64)
& mem2(L_s77,X_376,g_s79_65) )
=> ( $greatereq(X_373,X_375)
& $lesseq(X_373,X_376) ) )
& mem2(X_374,X_372,g_s80_66)
& mem0(X_372,g_s55_55)
& ! [X_377: $int,X_378: $int] :
( ( mem2(L_s77,X_377,g_s78_64)
& mem2(L_s77,X_378,g_s79_65) )
=> ( $greatereq(X_374,X_377)
& $lesseq(X_374,X_378) ) ) )
=> ( X_373 = X_374 ) ) ) ) ).
tff('Define:imprp:2',axiom,
? [X_298: set_2] :
( ! [X_299: $int,X_300: $int] :
( mem2(X_300,X_299,X_298)
<=> mem2(X_300,X_299,g_s78_64) )
& ! [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] :
( mem0(X_304,g_s29_29)
<=> ? [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_s37_37) ) ) ).
tff('Define:imprp:3',axiom,
? [X_308: set_2] :
( ! [X_309: $int,X_310: $int] :
( mem2(X_310,X_309,X_308)
<=> mem2(X_310,X_309,g_s79_65) )
& ! [X_311: $int,X_312: $int,X_313: $int] :
( ( mem2(X_311,X_312,X_308)
& mem2(X_311,X_313,X_308) )
=> ( X_312 = X_313 ) )
& ! [X_314: $int] :
( mem0(X_314,g_s29_29)
<=> ? [X_315: $int] : mem2(X_314,X_315,X_308) )
& ! [X_316: $int] :
( ? [X_317: $int] : mem2(X_317,X_316,X_308)
=> mem0(X_316,g_s37_37) ) ) ).
tff('Define:imprp:4',axiom,
? [X_318: set_2] :
( ! [X_319: $int,X_320: $int] :
( mem2(X_320,X_319,X_318)
<=> mem2(X_320,X_319,g_s80_66) )
& ! [X_321: $int,X_322: $int,X_323: $int] :
( ( mem2(X_321,X_322,X_318)
& mem2(X_321,X_323,X_318) )
=> ( X_322 = X_323 ) )
& ! [X_324: $int] :
( mem0(X_324,g_s37_37)
<=> ? [X_325: $int] : mem2(X_324,X_325,X_318) )
& ! [X_326: $int] :
( ? [X_327: $int] : mem2(X_327,X_326,X_318)
=> mem0(X_326,g_s35_35) ) ) ).
tff('Define:imprp:5',axiom,
? [X_328: set_2] :
( ! [X_329: $int,X_330: $int] :
( mem2(X_330,X_329,X_328)
<=> mem2(X_330,X_329,g_s76_67) )
& ! [X_331: $int,X_332: $int,X_333: $int] :
( ( mem2(X_331,X_332,X_328)
& mem2(X_331,X_333,X_328) )
=> ( X_332 = X_333 ) )
& ! [X_334: $int] :
( mem0(X_334,g_s29_29)
<=> ? [X_335: $int] : mem2(X_334,X_335,X_328) )
& ! [X_336: $int] :
( ? [X_337: $int] : mem2(X_337,X_336,X_328)
=> mem0(X_336,g_s36_36) ) ) ).
tff('Define:imprp:6',axiom,
? [X_338: set_3] :
( ! [X_339: $int,X_340: $int,X_341: $int] :
( mem3(X_341,X_340,X_339,X_338)
<=> mem3(X_341,X_340,X_339,g_s84_68) )
& ! [X_342: $int,X_343: $int,X_344: $int,X_345: $int] :
( ( mem3(X_343,X_342,X_344,X_338)
& mem3(X_343,X_342,X_345,X_338) )
=> ( X_344 = X_345 ) )
& ! [X_346: $int,X_347: $int] :
( ( mem0(X_347,g_s29_29)
& mem0(X_346,g_s0_0) )
<=> ? [X_348: $int] : mem3(X_347,X_346,X_348,X_338) )
& ! [X_349: $int] :
( ? [X_350: $int,X_351: $int] : mem3(X_351,X_350,X_349,X_338)
=> mem0(X_349,g_s25_25) ) ) ).
tff('Define:imprp:7',axiom,
? [X_352: $int,X_353: set_2] :
( ! [X_354: $int,X_355: $int] :
( mem2(X_355,X_354,X_353)
<=> ( mem2(X_355,X_354,g_s80_66)
& mem0(X_354,g_s55_55) ) )
& ! [X_356: $int,X_357: $int,X_358: $int] :
( ( mem2(X_356,X_357,X_353)
& mem2(X_356,X_358,X_353) )
=> ( X_357 = X_358 ) )
& ! [X_359: $int] :
( ( $greatereq(X_359,1)
& $lesseq(X_359,X_352) )
<=> ? [X_360: $int] : mem2(X_359,X_360,X_353) )
& ! [X_361: $int] :
( ? [X_362: $int] : mem2(X_362,X_361,X_353)
=> mem0(X_361,g_s55_55) ) ) ).
tff('Define:imprp:8',axiom,
! [L_s77: $int,L_s81: $int] :
( ( mem0(L_s77,g_s40_40)
& $true
& ! [X_363: $int] :
( mem2(L_s77,X_363,g_s78_64)
=> $lesseq(X_363,L_s81) )
& ! [X_364: $int] :
( mem2(L_s77,X_364,g_s79_65)
=> $lesseq(L_s81,X_364) ) )
=> mem0(L_s81,g_s37_37) ) ).
tff('Define:imprp:9',axiom,
! [L_s77: $int,L_s81: $int] :
( ( mem0(L_s77,g_s40_40)
& $true
& ! [X_365: $int] :
( mem2(L_s77,X_365,g_s78_64)
=> $lesseq(X_365,L_s81) )
& ! [X_366: $int] :
( mem2(L_s77,X_366,g_s79_65)
=> $lesseq(L_s81,X_366) ) )
=> ! [X_367: $int] :
( mem2(L_s81,X_367,g_s80_66)
=> mem0(X_367,g_s55_55) ) ) ).
tff('Define:inv:0',axiom,
$true ).
tff('Define:inv:1',axiom,
( $greatereq(g_s68_1_77,0)
& $lesseq(g_s68_1_77,max_int) ) ).
tff('Define:inv:2',axiom,
( $greatereq(g_s69_1_78,0)
& $lesseq(g_s69_1_78,max_int) ) ).
tff('Define:inv:3',axiom,
mem0(g_s70_1_79,g_s35_35) ).
tff('Define:inv:4',axiom,
mem0(g_s71_1_80,g_s35_35) ).
tff('Define:inv:5',axiom,
$true ).
tff('Define:inv:6',axiom,
$true ).
tff('Define:inv:7',axiom,
$true ).
tff('Define:seext:0',axiom,
! [X_603: $int] :
( ( $greatereq(X_603,0)
& $lesseq(X_603,max_int) )
=> $greatereq(X_603,0) ) ).
tff('Define:seext:1',axiom,
! [X_604: $int] :
( mem0(X_604,g_s37_37)
=> $greatereq(X_604,0) ) ).
tff('Define:seext:2',axiom,
! [X_605: $int] :
( mem0(X_605,g_s38_38)
=> $greatereq(X_605,0) ) ).
tff('Define:seext:3',axiom,
! [X_606: $int] :
( mem0(X_606,g_s39_39)
=> $greatereq(X_606,0) ) ).
%Global hypotheses
%----Local hypotheses
tff('Local_Hyp:0',hypothesis,
mem0(g_s90_81,g_s29_29) ).
tff('Local_Hyp:1',hypothesis,
mem0(g_s90_81,g_s40_40) ).
tff('Local_Hyp:2',hypothesis,
~ ! [X_651: set_0] :
( ! [X_652: $int] :
( mem0(X_652,X_651)
<=> $false )
=> mem4(g_s90_81,X_651,g_s64_75) ) ).
%----Goal
tff('Goal',conjecture,
! [X_653: $int,X_654: $int] :
( ( mem2(g_s90_81,X_653,g_s78_64)
& mem2(g_s90_81,X_654,g_s79_65) )
=> $lesseq(X_653,X_654) ) ).
%------------------------------------------------------------------------------