TSTP Solution File: NUM926^3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:43:47 EDT 2024
% Result : Theorem 5.56s 1.22s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1289
% Syntax : Number of formulae : 7070 (1633 unt; 118 typ; 0 def)
% Number of atoms : 97124 (13419 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 17752 (6478 ~;6796 |;1050 &; 0 @)
% ( 737 <=>;2691 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 458 ( 457 >; 1 *; 0 +; 0 <<)
% Number of symbols : 353 ( 350 usr; 260 con; 0-6 aty)
% Number of variables : 13058 ( 2 ^12860 !; 184 ?;13058 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
real: $tType ).
thf(type_def_9,type,
product_prod_int_int: $tType ).
thf(func_def_0,type,
int: $tType ).
thf(func_def_1,type,
nat: $tType ).
thf(func_def_2,type,
real: $tType ).
thf(func_def_3,type,
product_prod_int_int: $tType ).
thf(func_def_4,type,
div_mod_int: int > int > int ).
thf(func_def_5,type,
div_mod_nat: nat > nat > nat ).
thf(func_def_6,type,
minus_minus_int: int > int > int ).
thf(func_def_7,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_8,type,
minus_minus_real: real > real > real ).
thf(func_def_9,type,
one_one_int: int ).
thf(func_def_10,type,
one_one_nat: nat ).
thf(func_def_11,type,
one_one_real: real ).
thf(func_def_12,type,
plus_plus_int: int > int > int ).
thf(func_def_13,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_14,type,
plus_plus_real: real > real > real ).
thf(func_def_15,type,
times_times_int: int > int > int ).
thf(func_def_16,type,
times_times_nat: nat > nat > nat ).
thf(func_def_17,type,
times_times_real: real > real > real ).
thf(func_def_18,type,
zero_zero_int: int ).
thf(func_def_19,type,
zero_zero_nat: nat ).
thf(func_def_20,type,
zero_zero_real: real ).
thf(func_def_21,type,
multInv: int > int > int ).
thf(func_def_22,type,
d22set: int > int > $o ).
thf(func_def_23,type,
zfact: int > int ).
thf(func_def_24,type,
zcong: int > int > int > $o ).
thf(func_def_25,type,
zprime: int > $o ).
thf(func_def_26,type,
bit0: int > int ).
thf(func_def_27,type,
bit1: int > int ).
thf(func_def_28,type,
min: int ).
thf(func_def_29,type,
pls: int ).
thf(func_def_30,type,
number_number_of_int: int > int ).
thf(func_def_31,type,
number_number_of_nat: int > nat ).
thf(func_def_32,type,
number267125858f_real: int > real ).
thf(func_def_33,type,
ord_less_int: int > int > $o ).
thf(func_def_34,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_35,type,
ord_less_real: real > real > $o ).
thf(func_def_36,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_37,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_38,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_39,type,
power_power_int: int > nat > int ).
thf(func_def_40,type,
power_power_nat: nat > nat > nat ).
thf(func_def_41,type,
power_power_real: real > nat > real ).
thf(func_def_42,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(func_def_43,type,
legendre: int > int > int ).
thf(func_def_44,type,
quadRes: int > int > $o ).
thf(func_def_45,type,
sr: int > int > $o ).
thf(func_def_46,type,
standardRes: int > int > int ).
thf(func_def_47,type,
dvd_dvd_int: int > int > $o ).
thf(func_def_48,type,
dvd_dvd_nat: nat > nat > $o ).
thf(func_def_49,type,
dvd_dvd_real: real > real > $o ).
thf(func_def_50,type,
collect_int: ( int > $o ) > int > $o ).
thf(func_def_51,type,
twoSqu919416604sum2sq: int > $o ).
thf(func_def_52,type,
twoSqu2057625106sum2sq: product_prod_int_int > int ).
thf(func_def_53,type,
inv: int > int > int ).
thf(func_def_54,type,
wset: int > int > int > $o ).
thf(func_def_55,type,
member_int: int > ( int > $o ) > $o ).
thf(func_def_56,type,
m: int ).
thf(func_def_57,type,
s1: int ).
thf(func_def_58,type,
s: int ).
thf(func_def_59,type,
t: int ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_64,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_65,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_66,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_67,type,
sP0: nat > nat > ( nat > $o ) > $o ).
thf(func_def_68,type,
sP1: int > int > ( int > $o ) > $o ).
thf(func_def_69,type,
sP2: int > int > ( int > $o ) > $o ).
thf(func_def_70,type,
sK3: int ).
thf(func_def_71,type,
sK4: int ).
thf(func_def_72,type,
sK5: int ).
thf(func_def_73,type,
sK6: int ).
thf(func_def_74,type,
sK7: int ).
thf(func_def_75,type,
sK8: int ).
thf(func_def_76,type,
sK9: int ).
thf(func_def_77,type,
sK10: int > int ).
thf(func_def_78,type,
sK11: int > int ).
thf(func_def_79,type,
sK12: int > int ).
thf(func_def_80,type,
sK13: int > int ).
thf(func_def_81,type,
sK14: int > int > int ).
thf(func_def_82,type,
sK15: ( nat > $o ) > nat > nat ).
thf(func_def_83,type,
sK16: ( nat > $o ) > nat > nat ).
thf(func_def_84,type,
sK17: ( int > $o ) > int ).
thf(func_def_85,type,
sK18: nat > real > real ).
thf(func_def_86,type,
sK19: nat > real > real ).
thf(func_def_87,type,
sK20: int > int > int ).
thf(func_def_88,type,
sK21: nat > nat > nat ).
thf(func_def_89,type,
sK22: nat > nat > nat ).
thf(func_def_90,type,
sK23: int > int > int ).
thf(func_def_91,type,
sK24: nat > nat > nat ).
thf(func_def_92,type,
sK25: int > int > int ).
thf(func_def_93,type,
sK26: ( nat > nat ) > nat ).
thf(func_def_94,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_95,type,
sK28: int > ( int > $o ) > int ).
thf(func_def_96,type,
sK29: int > ( int > $o ) > int ).
thf(func_def_97,type,
sK30: int > ( int > $o ) > int ).
thf(func_def_98,type,
sK31: int > ( int > $o ) > int ).
thf(func_def_99,type,
sK32: int > ( int > $o ) > int ).
thf(func_def_100,type,
sK33: int > ( int > $o ) > int ).
thf(func_def_101,type,
sK34: nat > nat > ( nat > $o ) > nat ).
thf(func_def_102,type,
sK35: nat > nat > ( nat > $o ) > nat ).
thf(func_def_103,type,
sK36: nat > nat > ( nat > $o ) > nat ).
thf(func_def_104,type,
sK37: nat > nat > ( nat > $o ) > nat ).
thf(func_def_105,type,
sK38: int > int > ( int > $o ) > int ).
thf(func_def_106,type,
sK39: int > int > ( int > $o ) > int ).
thf(func_def_107,type,
sK40: int > int > ( int > $o ) > int ).
thf(func_def_108,type,
sK41: int > int > ( int > $o ) > int ).
thf(func_def_109,type,
sK42: int > int > int > int ).
thf(func_def_110,type,
sK43: int ).
thf(func_def_112,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_113,type,
vOR: $o > $o > $o ).
thf(func_def_114,type,
vIMP: $o > $o > $o ).
thf(func_def_115,type,
vNOT: $o > $o ).
thf(func_def_116,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f12606,plain,
$false,
inference(avatar_sat_refutation,[],[f7212,f7217,f7222,f7223,f7224,f7229,f7230,f7235,f7236,f7237,f7242,f7243,f7248,f7253,f7254,f7255,f7256,f7261,f7266,f7271,f7276,f7281,f7286,f7291,f7296,f7297,f7302,f7303,f7308,f7309,f7314,f7319,f7324,f7329,f7334,f7339,f7344,f7350,f7356,f7362,f7367,f7372,f7377,f7382,f7387,f7392,f7397,f7402,f7407,f7408,f7494,f7495,f7496,f7497,f7498,f7506,f7507,f7513,f7525,f7530,f7531,f7536,f7571,f7574,f7743,f7804,f7806,f7835,f7842,f7856,f7860,f7994,f8003,f8008,f8013,f8019,f8025,f8030,f8031,f8037,f8044,f8049,f8055,f8061,f8070,f8079,f8088,f8098,f8108,f8119,f8130,f8141,f8152,f8163,f8174,f8183,f8192,f8203,f8209,f8223,f8232,f8243,f8251,f8260,f8270,f8280,f8288,f8295,f8300,f8334,f8341,f8385,f8393,f8507,f8512,f8513,f8514,f8515,f8543,f8545,f8546,f8556,f8754,f8841,f8896,f8999,f9004,f9329,f9334,f9339,f9344,f9349,f9354,f9359,f9364,f9399,f9407,f9427,f9432,f9437,f9442,f9447,f9452,f9457,f9462,f9467,f9472,f9477,f9482,f9487,f9492,f9497,f9502,f9507,f9512,f9517,f9522,f9527,f9532,f9537,f9542,f9547,f9552,f9557,f9562,f9567,f9572,f9577,f9582,f9588,f9920,f9926,f9932,f9938,f9944,f9950,f9956,f9962,f9968,f9974,f9980,f9986,f9992,f9998,f10004,f10010,f10016,f10022,f10028,f10034,f10040,f10046,f10052,f10058,f10064,f10070,f10076,f10082,f10088,f10094,f10100,f10106,f10112,f10118,f10124,f10130,f10136,f10142,f10148,f10154,f10160,f10166,f10172,f10184,f10196,f10458,f10459,f10460,f10536,f10539,f10564,f10710,f10711,f10734,f10736,f10737,f10739,f10741,f10793,f10799,f10804,f10810,f10815,f10822,f10834,f10846,f10858,f10881,f10925,f10948,f10960,f11031,f11039,f11179,f11209,f11210,f11233,f11234,f11235,f11295,f11300,f11305,f11307,f11312,f11313,f11314,f11315,f11317,f11319,f11320,f11321,f11322,f11323,f11360,f11365,f11411,f11416,f11417,f11418,f11455,f11670,f11671,f11672,f11696,f11704,f11709,f11711,f11717,f11719,f11720,f11722,f11724,f11870,f11871,f12113,f12115,f12123,f12136,f12137,f12178,f12183,f12510,f12514,f12523,f12532,f12538,f12542,f12551,f12560,f12561,f12565,f12566,f12567,f12569,f12573,f12574,f12575,f12576,f12577,f12578,f12580,f12581,f12582,f12586,f12590,f12591,f12592,f12593,f12595,f12596,f12597,f12601,f12605]) ).
thf(f12605,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12604]) ).
thf(f12604,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12603]) ).
thf(f12603,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12602,f9931]) ).
thf(f9931,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ~ spl44_143 ),
inference(avatar_component_clause,[],[f9929]) ).
thf(f9929,plain,
( spl44_143
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_143])]) ).
thf(f12602,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| spl44_183
| ~ spl44_201 ),
inference(subsumption_resolution,[],[f12409,f10171]) ).
thf(f10171,plain,
( ( t != vAPP(int,int,zfact,zero_zero_int) )
| spl44_183 ),
inference(avatar_component_clause,[],[f10169]) ).
thf(f10169,plain,
( spl44_183
<=> ( t = vAPP(int,int,zfact,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_183])]) ).
thf(f12409,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12396]) ).
thf(f12396,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(superposition,[],[f10924,f4830]) ).
thf(f4830,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f1458]) ).
thf(f1458,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(fool_elimination,[],[f1457]) ).
thf(f1457,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
| ( X0 = X1 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X16: int,X17: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X17),X16)
| ( X16 = X17 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zless__linear) ).
thf(f10924,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_201 ),
inference(avatar_component_clause,[],[f10922]) ).
thf(f10922,plain,
( spl44_201
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_201])]) ).
thf(f12601,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12600]) ).
thf(f12600,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12599]) ).
thf(f12599,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12598,f10924]) ).
thf(f12598,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143
| spl44_183 ),
inference(subsumption_resolution,[],[f12412,f10171]) ).
thf(f12412,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f12393]) ).
thf(f12393,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(superposition,[],[f9931,f4830]) ).
thf(f12597,plain,
( spl44_237
| spl44_238
| ~ spl44_199 ),
inference(avatar_split_clause,[],[f12414,f10855,f12557,f12553]) ).
thf(f12553,plain,
( spl44_237
<=> ( zero_zero_int = sK43 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_237])]) ).
thf(f12557,plain,
( spl44_238
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_238])]) ).
thf(f10855,plain,
( spl44_199
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_199])]) ).
thf(f12414,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(trivial_inequality_removal,[],[f12391]) ).
thf(f12391,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(superposition,[],[f10857,f4830]) ).
thf(f10857,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) )
| ~ spl44_199 ),
inference(avatar_component_clause,[],[f10855]) ).
thf(f12596,plain,
( spl44_235
| spl44_236
| ~ spl44_198 ),
inference(avatar_split_clause,[],[f12415,f10843,f12548,f12544]) ).
thf(f12544,plain,
( spl44_235
<=> ( zero_zero_int = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_235])]) ).
thf(f12548,plain,
( spl44_236
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_236])]) ).
thf(f10843,plain,
( spl44_198
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_198])]) ).
thf(f12415,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(trivial_inequality_removal,[],[f12390]) ).
thf(f12390,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(superposition,[],[f10845,f4830]) ).
thf(f10845,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) )
| ~ spl44_198 ),
inference(avatar_component_clause,[],[f10843]) ).
thf(f12595,plain,
( spl44_234
| ~ spl44_203 ),
inference(avatar_split_clause,[],[f12594,f10957,f12535]) ).
thf(f12535,plain,
( spl44_234
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_234])]) ).
thf(f10957,plain,
( spl44_203
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_203])]) ).
thf(f12594,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_203 ),
inference(subsumption_resolution,[],[f12417,f6031]) ).
thf(f6031,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,bit1,X0) ),
inference(definition_unfolding,[],[f4460,f4404]) ).
thf(f4404,plain,
pls = zero_zero_int,
inference(cnf_transformation,[],[f359]) ).
thf(f359,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_Pls__def) ).
thf(f4460,plain,
! [X0: int] : ( pls != vAPP(int,int,bit1,X0) ),
inference(cnf_transformation,[],[f2723]) ).
thf(f2723,plain,
! [X0: int] : ( pls != vAPP(int,int,bit1,X0) ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X18: int] : ( pls != vAPP(int,int,bit1,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_rel__simps_I46_J) ).
thf(f12417,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(trivial_inequality_removal,[],[f12388]) ).
thf(f12388,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(superposition,[],[f10959,f4830]) ).
thf(f10959,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| ~ spl44_203 ),
inference(avatar_component_clause,[],[f10957]) ).
thf(f12593,plain,
( spl44_232
| spl44_233
| ~ spl44_227 ),
inference(avatar_split_clause,[],[f12418,f12180,f12529,f12525]) ).
thf(f12525,plain,
( spl44_232
<=> ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_232])]) ).
thf(f12529,plain,
( spl44_233
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_233])]) ).
thf(f12180,plain,
( spl44_227
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_227])]) ).
thf(f12418,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(trivial_inequality_removal,[],[f12387]) ).
thf(f12387,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(superposition,[],[f12182,f4830]) ).
thf(f12182,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))),zero_zero_int) )
| ~ spl44_227 ),
inference(avatar_component_clause,[],[f12180]) ).
thf(f12592,plain,
( spl44_230
| spl44_231
| ~ spl44_202 ),
inference(avatar_split_clause,[],[f12419,f10945,f12520,f12516]) ).
thf(f12516,plain,
( spl44_230
<=> ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_230])]) ).
thf(f12520,plain,
( spl44_231
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_231])]) ).
thf(f10945,plain,
( spl44_202
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_202])]) ).
thf(f12419,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(trivial_inequality_removal,[],[f12386]) ).
thf(f12386,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(superposition,[],[f10947,f4830]) ).
thf(f10947,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| ~ spl44_202 ),
inference(avatar_component_clause,[],[f10945]) ).
thf(f12591,plain,
( spl44_228
| spl44_229
| ~ spl44_197 ),
inference(avatar_split_clause,[],[f12421,f10831,f12507,f12503]) ).
thf(f12503,plain,
( spl44_228
<=> ( s = zero_zero_int ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_228])]) ).
thf(f12507,plain,
( spl44_229
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_229])]) ).
thf(f10831,plain,
( spl44_197
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_197])]) ).
thf(f12421,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(trivial_inequality_removal,[],[f12384]) ).
thf(f12384,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(superposition,[],[f10833,f4830]) ).
thf(f10833,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) )
| ~ spl44_197 ),
inference(avatar_component_clause,[],[f10831]) ).
thf(f12590,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12589]) ).
thf(f12589,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12588]) ).
thf(f12588,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12587,f9931]) ).
thf(f12587,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| spl44_183
| ~ spl44_201 ),
inference(subsumption_resolution,[],[f12437,f10171]) ).
thf(f12437,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12367]) ).
thf(f12367,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(superposition,[],[f10924,f4830]) ).
thf(f12586,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12585]) ).
thf(f12585,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12584]) ).
thf(f12584,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12583,f10924]) ).
thf(f12583,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143
| spl44_183 ),
inference(subsumption_resolution,[],[f12440,f10171]) ).
thf(f12440,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f12364]) ).
thf(f12364,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(superposition,[],[f9931,f4830]) ).
thf(f12582,plain,
( spl44_237
| spl44_238
| ~ spl44_199 ),
inference(avatar_split_clause,[],[f12442,f10855,f12557,f12553]) ).
thf(f12442,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(trivial_inequality_removal,[],[f12362]) ).
thf(f12362,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(superposition,[],[f10857,f4830]) ).
thf(f12581,plain,
( spl44_235
| spl44_236
| ~ spl44_198 ),
inference(avatar_split_clause,[],[f12443,f10843,f12548,f12544]) ).
thf(f12443,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(trivial_inequality_removal,[],[f12361]) ).
thf(f12361,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(superposition,[],[f10845,f4830]) ).
thf(f12580,plain,
( spl44_234
| ~ spl44_203 ),
inference(avatar_split_clause,[],[f12579,f10957,f12535]) ).
thf(f12579,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_203 ),
inference(subsumption_resolution,[],[f12445,f6031]) ).
thf(f12445,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(trivial_inequality_removal,[],[f12359]) ).
thf(f12359,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(superposition,[],[f10959,f4830]) ).
thf(f12578,plain,
( spl44_232
| spl44_233
| ~ spl44_227 ),
inference(avatar_split_clause,[],[f12446,f12180,f12529,f12525]) ).
thf(f12446,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(trivial_inequality_removal,[],[f12358]) ).
thf(f12358,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(superposition,[],[f12182,f4830]) ).
thf(f12577,plain,
( spl44_230
| spl44_231
| ~ spl44_202 ),
inference(avatar_split_clause,[],[f12447,f10945,f12520,f12516]) ).
thf(f12447,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(trivial_inequality_removal,[],[f12357]) ).
thf(f12357,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(superposition,[],[f10947,f4830]) ).
thf(f12576,plain,
( spl44_228
| spl44_229
| ~ spl44_197 ),
inference(avatar_split_clause,[],[f12449,f10831,f12507,f12503]) ).
thf(f12449,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(trivial_inequality_removal,[],[f12355]) ).
thf(f12355,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(superposition,[],[f10833,f4830]) ).
thf(f12575,plain,
( spl44_237
| spl44_238
| ~ spl44_199 ),
inference(avatar_split_clause,[],[f12461,f10855,f12557,f12553]) ).
thf(f12461,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(trivial_inequality_removal,[],[f12342]) ).
thf(f12342,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(superposition,[],[f4830,f10857]) ).
thf(f12574,plain,
( spl44_235
| spl44_236
| ~ spl44_198 ),
inference(avatar_split_clause,[],[f12462,f10843,f12548,f12544]) ).
thf(f12462,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(trivial_inequality_removal,[],[f12341]) ).
thf(f12341,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(superposition,[],[f4830,f10845]) ).
thf(f12573,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12572]) ).
thf(f12572,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12571]) ).
thf(f12571,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12570,f10924]) ).
thf(f12570,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143
| spl44_183 ),
inference(subsumption_resolution,[],[f12464,f10171]) ).
thf(f12464,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f12339]) ).
thf(f12339,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(superposition,[],[f4830,f9931]) ).
thf(f12569,plain,
( spl44_234
| ~ spl44_203 ),
inference(avatar_split_clause,[],[f12568,f10957,f12535]) ).
thf(f12568,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_203 ),
inference(subsumption_resolution,[],[f12466,f6031]) ).
thf(f12466,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(trivial_inequality_removal,[],[f12337]) ).
thf(f12337,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(superposition,[],[f4830,f10959]) ).
thf(f12567,plain,
( spl44_232
| spl44_233
| ~ spl44_227 ),
inference(avatar_split_clause,[],[f12467,f12180,f12529,f12525]) ).
thf(f12467,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(trivial_inequality_removal,[],[f12336]) ).
thf(f12336,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(superposition,[],[f4830,f12182]) ).
thf(f12566,plain,
( spl44_230
| spl44_231
| ~ spl44_202 ),
inference(avatar_split_clause,[],[f12468,f10945,f12520,f12516]) ).
thf(f12468,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(trivial_inequality_removal,[],[f12335]) ).
thf(f12335,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(superposition,[],[f4830,f10947]) ).
thf(f12565,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12564]) ).
thf(f12564,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12563]) ).
thf(f12563,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12562,f9931]) ).
thf(f12562,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| spl44_183
| ~ spl44_201 ),
inference(subsumption_resolution,[],[f12470,f10171]) ).
thf(f12470,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12333]) ).
thf(f12333,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(superposition,[],[f4830,f10924]) ).
thf(f12561,plain,
( spl44_228
| spl44_229
| ~ spl44_197 ),
inference(avatar_split_clause,[],[f12471,f10831,f12507,f12503]) ).
thf(f12471,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(trivial_inequality_removal,[],[f12332]) ).
thf(f12332,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(superposition,[],[f4830,f10833]) ).
thf(f12560,plain,
( spl44_237
| spl44_238
| ~ spl44_199 ),
inference(avatar_split_clause,[],[f12482,f10855,f12557,f12553]) ).
thf(f12482,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(trivial_inequality_removal,[],[f12320]) ).
thf(f12320,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK43) )
| ( zero_zero_int = sK43 )
| ~ spl44_199 ),
inference(superposition,[],[f4830,f10857]) ).
thf(f12551,plain,
( spl44_235
| spl44_236
| ~ spl44_198 ),
inference(avatar_split_clause,[],[f12483,f10843,f12548,f12544]) ).
thf(f12483,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(trivial_inequality_removal,[],[f12319]) ).
thf(f12319,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),sK8) )
| ( zero_zero_int = sK8 )
| ~ spl44_198 ),
inference(superposition,[],[f4830,f10845]) ).
thf(f12542,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12541]) ).
thf(f12541,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12540]) ).
thf(f12540,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12539,f10924]) ).
thf(f12539,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143
| spl44_183 ),
inference(subsumption_resolution,[],[f12485,f10171]) ).
thf(f12485,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f12317]) ).
thf(f12317,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_143 ),
inference(superposition,[],[f4830,f9931]) ).
thf(f12538,plain,
( spl44_234
| ~ spl44_203 ),
inference(avatar_split_clause,[],[f12533,f10957,f12535]) ).
thf(f12533,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_203 ),
inference(subsumption_resolution,[],[f12487,f6031]) ).
thf(f12487,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(trivial_inequality_removal,[],[f12315]) ).
thf(f12315,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_203 ),
inference(superposition,[],[f4830,f10959]) ).
thf(f12532,plain,
( spl44_232
| spl44_233
| ~ spl44_227 ),
inference(avatar_split_clause,[],[f12488,f12180,f12529,f12525]) ).
thf(f12488,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(trivial_inequality_removal,[],[f12314]) ).
thf(f12314,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_227 ),
inference(superposition,[],[f4830,f12182]) ).
thf(f12523,plain,
( spl44_230
| spl44_231
| ~ spl44_202 ),
inference(avatar_split_clause,[],[f12489,f10945,f12520,f12516]) ).
thf(f12489,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(trivial_inequality_removal,[],[f12313]) ).
thf(f12313,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_202 ),
inference(superposition,[],[f4830,f10947]) ).
thf(f12514,plain,
( ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(avatar_contradiction_clause,[],[f12513]) ).
thf(f12513,plain,
( $false
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12512]) ).
thf(f12512,plain,
( ( $true = $false )
| ~ spl44_143
| spl44_183
| ~ spl44_201 ),
inference(forward_demodulation,[],[f12511,f9931]) ).
thf(f12511,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| spl44_183
| ~ spl44_201 ),
inference(subsumption_resolution,[],[f12491,f10171]) ).
thf(f12491,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(trivial_inequality_removal,[],[f12311]) ).
thf(f12311,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ( t = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_201 ),
inference(superposition,[],[f4830,f10924]) ).
thf(f12510,plain,
( spl44_228
| spl44_229
| ~ spl44_197 ),
inference(avatar_split_clause,[],[f12492,f10831,f12507,f12503]) ).
thf(f12492,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(trivial_inequality_removal,[],[f12310]) ).
thf(f12310,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),s) )
| ( s = zero_zero_int )
| ~ spl44_197 ),
inference(superposition,[],[f4830,f10833]) ).
thf(f12183,plain,
( spl44_227
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f12163,f9585,f9001,f12180]) ).
thf(f9001,plain,
( spl44_97
<=> ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_97])]) ).
thf(f9585,plain,
( spl44_140
<=> ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_140])]) ).
thf(f12163,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))),zero_zero_int) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f8536,f9706]) ).
thf(f9706,plain,
( ! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),X0) )
| ~ spl44_97
| ~ spl44_140 ),
inference(backward_demodulation,[],[f9140,f9587]) ).
thf(f9587,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,min) )
| ~ spl44_140 ),
inference(avatar_component_clause,[],[f9585]) ).
thf(f9140,plain,
( ! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,zfact,min))),X0) )
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7427,f9003]) ).
thf(f9003,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,min) )
| ~ spl44_97 ),
inference(avatar_component_clause,[],[f9001]) ).
thf(f7427,plain,
! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(forward_demodulation,[],[f7426,f4526]) ).
thf(f4526,plain,
! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ),
inference(cnf_transformation,[],[f2789]) ).
thf(f2789,plain,
! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ),
inference(rectify,[],[f207]) ).
thf(f207,axiom,
! [X18: int] : ( vAPP(int,int,bit0,X18) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Bit0__def) ).
thf(f7426,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(forward_demodulation,[],[f7425,f4464]) ).
thf(f4464,plain,
! [X0: int] : ( vAPP(int,int,number_number_of_int,X0) = X0 ),
inference(cnf_transformation,[],[f2727]) ).
thf(f2727,plain,
! [X0: int] : ( vAPP(int,int,number_number_of_int,X0) = X0 ),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X18: int] : ( vAPP(int,int,number_number_of_int,X18) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_number__of__is__id) ).
thf(f7425,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(forward_demodulation,[],[f6096,f4526]) ).
thf(f6096,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4543,f5971,f5971]) ).
thf(f5971,plain,
one_one_int = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4424,f4404]) ).
thf(f4424,plain,
one_one_int = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f261]) ).
thf(f261,axiom,
one_one_int = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
thf(f4543,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int)),X0) ),
inference(cnf_transformation,[],[f2806]) ).
thf(f2806,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int)),X0) ),
inference(rectify,[],[f233]) ).
thf(f233,axiom,
! [X137: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X137),X137) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int)),X137) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(f8536,plain,
! [X0: int] : ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),zero_zero_int) ),
inference(trivial_inequality_removal,[],[f8535]) ).
thf(f8535,plain,
! [X0: int] :
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),zero_zero_int) ) ),
inference(superposition,[],[f4717,f1202]) ).
thf(f1202,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f4717,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),zero_zero_int) ),
inference(cnf_transformation,[],[f2876]) ).
thf(f2876,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),zero_zero_int) ),
inference(flattening,[],[f1384]) ).
thf(f1384,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),zero_zero_int) ),
inference(fool_elimination,[],[f1383]) ).
thf(f1383,plain,
! [X0: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),zero_zero_int),
inference(rectify,[],[f857]) ).
thf(f857,axiom,
! [X485: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X485),X485)),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_not__square__less__zero) ).
thf(f12178,plain,
( spl44_226
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f12162,f9585,f9001,f12175]) ).
thf(f12175,plain,
( spl44_226
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_226])]) ).
thf(f12162,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f4739,f9706]) ).
thf(f4739,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)) ),
inference(cnf_transformation,[],[f1428]) ).
thf(f1428,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)) ),
inference(fool_elimination,[],[f1427]) ).
thf(f1427,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),
inference(rectify,[],[f814]) ).
thf(f814,axiom,
! [X443: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X443),X443)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_zero__le__square) ).
thf(f12137,plain,
( spl44_225
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f12131,f9585,f9001,f12133]) ).
thf(f12133,plain,
( spl44_225
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_225])]) ).
thf(f12131,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f6254,f9594]) ).
thf(f9594,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))) = X0 )
| ~ spl44_97
| ~ spl44_140 ),
inference(backward_demodulation,[],[f9010,f9587]) ).
thf(f9010,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,min))) = X0 )
| ~ spl44_97 ),
inference(backward_demodulation,[],[f6059,f9003]) ).
thf(f6059,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) = X0 ),
inference(definition_unfolding,[],[f4498,f5973]) ).
thf(f5973,plain,
one_one_real = vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4418,f4404]) ).
thf(f4418,plain,
one_one_real = vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f265]) ).
thf(f265,axiom,
one_one_real = vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_numeral__1__eq__1) ).
thf(f4498,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),one_one_real) = X0 ),
inference(cnf_transformation,[],[f2761]) ).
thf(f2761,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),one_one_real) = X0 ),
inference(rectify,[],[f188]) ).
thf(f188,axiom,
! [X118: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X118),one_one_real) = X118 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(f6254,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) ),
inference(definition_unfolding,[],[f4738,f5970]) ).
thf(f5970,plain,
zero_zero_real = vAPP(int,real,number267125858f_real,zero_zero_int),
inference(definition_unfolding,[],[f4410,f4404]) ).
thf(f4410,plain,
vAPP(int,real,number267125858f_real,pls) = zero_zero_real,
inference(cnf_transformation,[],[f398]) ).
thf(f398,axiom,
vAPP(int,real,number267125858f_real,pls) = zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_semiring__numeral__0__eq__0) ).
thf(f4738,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) ),
inference(cnf_transformation,[],[f1426]) ).
thf(f1426,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) ),
inference(fool_elimination,[],[f1425]) ).
thf(f1425,plain,
! [X0: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),
inference(rectify,[],[f813]) ).
thf(f813,axiom,
! [X443: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X443),X443)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_zero__le__square) ).
thf(f12136,plain,
( spl44_225
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f12129,f9585,f9001,f12133]) ).
thf(f12129,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f6254,f9593]) ).
thf(f9593,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),X0) = X0 )
| ~ spl44_97
| ~ spl44_140 ),
inference(backward_demodulation,[],[f9009,f9587]) ).
thf(f9009,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,min))),X0) = X0 )
| ~ spl44_97 ),
inference(backward_demodulation,[],[f6056,f9003]) ).
thf(f6056,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X0) = X0 ),
inference(definition_unfolding,[],[f4495,f5973]) ).
thf(f4495,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,one_one_real),X0) = X0 ),
inference(cnf_transformation,[],[f2758]) ).
thf(f2758,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,one_one_real),X0) = X0 ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X119: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,one_one_real),X119) = X119 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(f12123,plain,
( spl44_224
| spl44_223 ),
inference(avatar_split_clause,[],[f12118,f12110,f12120]) ).
thf(f12120,plain,
( spl44_224
<=> ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_224])]) ).
thf(f12110,plain,
( spl44_223
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_223])]) ).
thf(f12118,plain,
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| spl44_223 ),
inference(trivial_inequality_removal,[],[f12117]) ).
thf(f12117,plain,
( ( $true != $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| spl44_223 ),
inference(superposition,[],[f12112,f1202]) ).
thf(f12112,plain,
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| spl44_223 ),
inference(avatar_component_clause,[],[f12110]) ).
thf(f12115,plain,
( ~ spl44_223
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f12105,f9585,f9001,f12110]) ).
thf(f12105,plain,
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f6242,f9594]) ).
thf(f6242,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4716,f5970]) ).
thf(f4716,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f2875]) ).
thf(f2875,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),zero_zero_real) ),
inference(flattening,[],[f1382]) ).
thf(f1382,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),zero_zero_real) ),
inference(fool_elimination,[],[f1381]) ).
thf(f1381,plain,
! [X0: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),zero_zero_real),
inference(rectify,[],[f856]) ).
thf(f856,axiom,
! [X485: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X485),X485)),zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_not__square__less__zero) ).
thf(f12113,plain,
( ~ spl44_223
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f12103,f9585,f9001,f12110]) ).
thf(f12103,plain,
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f6242,f9593]) ).
thf(f11871,plain,
( spl44_222
| ~ spl44_214 ),
inference(avatar_split_clause,[],[f11855,f11357,f11867]) ).
thf(f11867,plain,
( spl44_222
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_222])]) ).
thf(f11357,plain,
( spl44_214
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_214])]) ).
thf(f11855,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))) )
| ~ spl44_214 ),
inference(trivial_inequality_removal,[],[f11854]) ).
thf(f11854,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))) )
| ~ spl44_214 ),
inference(superposition,[],[f8441,f11359]) ).
thf(f11359,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_214 ),
inference(avatar_component_clause,[],[f11357]) ).
thf(f8441,plain,
! [X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $false = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,sK17,X0)) ) ),
inference(trivial_inequality_removal,[],[f8440]) ).
thf(f8440,plain,
! [X0: int > $o,X1: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,X0,X1) )
| ( $false = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,sK17,X0)) ) ),
inference(superposition,[],[f4889,f1202]) ).
thf(f4889,plain,
! [X0: int,X1: int > $o] :
( ( $true != vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,sK17,X1)) )
| ( $true = vAPP(int,$o,X1,X0) ) ),
inference(cnf_transformation,[],[f4132]) ).
thf(f4132,plain,
! [X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,X0) )
| ( ( $true != vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,sK17,X1)) )
& ( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,sK17,X1)),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(sTfun(int,$o),int,sK17,X1)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f3315,f4131]) ).
thf(f4131,plain,
! [X1: int > $o] :
( ? [X2: int] :
( ( $true != vAPP(int,$o,X1,X2) )
& ( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ) )
=> ( ( $true != vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,sK17,X1)) )
& ( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,sK17,X1)),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(sTfun(int,$o),int,sK17,X1)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3315,plain,
! [X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,X0) )
| ? [X2: int] :
( ( $true != vAPP(int,$o,X1,X2) )
& ( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ) ) ),
inference(ennf_transformation,[],[f1520]) ).
thf(f1520,plain,
! [X0: int,X1: int > $o] :
( ! [X2: int] :
( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) ) )
=> ( $true = vAPP(int,$o,X1,X2) ) )
=> ( $true = vAPP(int,$o,X1,X0) ) ),
inference(fool_elimination,[],[f1519]) ).
thf(f1519,plain,
! [X0: int,X1: int > $o] :
( ! [X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> vAPP(int,$o,X1,X2) )
=> vAPP(int,$o,X1,X0) ),
inference(rectify,[],[f1107]) ).
thf(f1107,axiom,
! [X16: int,X490: int > $o] :
( ! [X495: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X495)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X495),one_one_int)) )
=> vAPP(int,$o,X490,X495) )
=> vAPP(int,$o,X490,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_d22set__induct__old) ).
thf(f11870,plain,
( spl44_222
| ~ spl44_214 ),
inference(avatar_split_clause,[],[f11861,f11357,f11867]) ).
thf(f11861,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))) )
| ~ spl44_214 ),
inference(trivial_inequality_removal,[],[f11847]) ).
thf(f11847,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))) )
| ~ spl44_214 ),
inference(superposition,[],[f11359,f8441]) ).
thf(f11724,plain,
( spl44_181
| ~ spl44_219 ),
inference(avatar_contradiction_clause,[],[f11723]) ).
thf(f11723,plain,
( $false
| spl44_181
| ~ spl44_219 ),
inference(subsumption_resolution,[],[f11691,f10159]) ).
thf(f10159,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_181 ),
inference(avatar_component_clause,[],[f10157]) ).
thf(f10157,plain,
( spl44_181
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_181])]) ).
thf(f11691,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11686]) ).
thf(f11686,plain,
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(superposition,[],[f6177,f11665]) ).
thf(f11665,plain,
( ! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ~ spl44_219 ),
inference(avatar_component_clause,[],[f11664]) ).
thf(f11664,plain,
( spl44_219
<=> ! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_219])]) ).
thf(f6177,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f4630,f5969,f4404]) ).
thf(f5969,plain,
zero_zero_nat = vAPP(int,nat,number_number_of_nat,zero_zero_int),
inference(definition_unfolding,[],[f4406,f4404]) ).
thf(f4406,plain,
zero_zero_nat = vAPP(int,nat,number_number_of_nat,pls),
inference(cnf_transformation,[],[f397]) ).
thf(f397,axiom,
zero_zero_nat = vAPP(int,nat,number_number_of_nat,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_semiring__numeral__0__eq__0) ).
thf(f4630,plain,
! [X0: int] :
( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) ),
inference(cnf_transformation,[],[f4100]) ).
thf(f4100,plain,
! [X0: int] :
( ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ) ),
inference(nnf_transformation,[],[f1266]) ).
thf(f1266,plain,
! [X0: int] :
( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) ),
inference(fool_elimination,[],[f1265]) ).
thf(f1265,plain,
! [X0: int] :
( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ),
inference(rectify,[],[f561]) ).
thf(f561,axiom,
! [X40: int] :
( ( vAPP(int,nat,number_number_of_nat,X40) = zero_zero_nat )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X40),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_eq__number__of__0) ).
thf(f11722,plain,
( spl44_181
| ~ spl44_219 ),
inference(avatar_contradiction_clause,[],[f11721]) ).
thf(f11721,plain,
( $false
| spl44_181
| ~ spl44_219 ),
inference(subsumption_resolution,[],[f11692,f10159]) ).
thf(f11692,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11685]) ).
thf(f11685,plain,
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(superposition,[],[f8889,f11665]) ).
thf(f8889,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(trivial_inequality_removal,[],[f8888]) ).
thf(f8888,plain,
! [X0: int] :
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(superposition,[],[f6177,f1202]) ).
thf(f11720,plain,
( spl44_221
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(avatar_split_clause,[],[f11693,f11664,f9585,f9001,f11706]) ).
thf(f11706,plain,
( spl44_221
<=> ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_221])]) ).
thf(f11693,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11684]) ).
thf(f11684,plain,
( ( $true != $true )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(superposition,[],[f9714,f11665]) ).
thf(f9714,plain,
( ! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,zfact,zero_zero_int) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(backward_demodulation,[],[f9148,f9587]) ).
thf(f9148,plain,
( ! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,zfact,min) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7461,f9003]) ).
thf(f7461,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,bit1,zero_zero_int) ) ),
inference(forward_demodulation,[],[f6148,f4464]) ).
thf(f6148,plain,
! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4596,f5971]) ).
thf(f4596,plain,
! [X0: int] :
( ( one_one_int = vAPP(int,int,zfact,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3215]) ).
thf(f3215,plain,
! [X0: int] :
( ( ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
& ( ( one_one_int = vAPP(int,int,zfact,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ) ),
inference(ennf_transformation,[],[f2852]) ).
thf(f2852,plain,
! [X0: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( one_one_int = vAPP(int,int,zfact,X0) ) ) ),
inference(flattening,[],[f1226]) ).
thf(f1226,plain,
! [X0: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( one_one_int = vAPP(int,int,zfact,X0) ) ) ),
inference(fool_elimination,[],[f1225]) ).
thf(f1225,plain,
! [X0: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
=> ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
=> ( one_one_int = vAPP(int,int,zfact,X0) ) ) ),
inference(rectify,[],[f1072]) ).
thf(f1072,axiom,
! [X191: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X191),zero_zero_int)
=> ( vAPP(int,int,zfact,X191) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X191),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X191),one_one_int))) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X191),zero_zero_int)
=> ( one_one_int = vAPP(int,int,zfact,X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_zfact_Osimps) ).
thf(f11719,plain,
( spl44_221
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(avatar_split_clause,[],[f11694,f11664,f9585,f9001,f11706]) ).
thf(f11694,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11683]) ).
thf(f11683,plain,
( ( $true = $false )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(superposition,[],[f9806,f11665]) ).
thf(f9806,plain,
( ! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,zfact,zero_zero_int) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(backward_demodulation,[],[f9313,f9587]) ).
thf(f9313,plain,
( ! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,zfact,min) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8991,f9003]) ).
thf(f8991,plain,
! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,bit1,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(trivial_inequality_removal,[],[f8990]) ).
thf(f8990,plain,
! [X0: int] :
( ( $true != $true )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,bit1,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(superposition,[],[f7461,f1202]) ).
thf(f11717,plain,
( ~ spl44_168
| ~ spl44_219 ),
inference(avatar_contradiction_clause,[],[f11716]) ).
thf(f11716,plain,
( $false
| ~ spl44_168
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11715]) ).
thf(f11715,plain,
( ( $true = $false )
| ~ spl44_168
| ~ spl44_219 ),
inference(backward_demodulation,[],[f10081,f11700]) ).
thf(f11700,plain,
( ! [X0: int] : ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11678]) ).
thf(f11678,plain,
( ! [X0: int] :
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,zfact,zero_zero_int)) ) )
| ~ spl44_219 ),
inference(superposition,[],[f11665,f11169]) ).
thf(f11169,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f11168]) ).
thf(f11168,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(superposition,[],[f10771,f1202]) ).
thf(f10771,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10770]) ).
thf(f10770,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(superposition,[],[f7782,f1202]) ).
thf(f7782,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) ) ),
inference(forward_demodulation,[],[f7781,f4464]) ).
thf(f7781,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) ) ),
inference(forward_demodulation,[],[f7780,f4464]) ).
thf(f7780,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7779,f4464]) ).
thf(f7779,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f5227,f4464]) ).
thf(f5227,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(cnf_transformation,[],[f4248]) ).
thf(f4248,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ) ),
inference(nnf_transformation,[],[f3034]) ).
thf(f3034,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
<=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(flattening,[],[f1902]) ).
thf(f1902,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
<=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(fool_elimination,[],[f1901]) ).
thf(f1901,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1))
<=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X25: int,X26: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X25)),vAPP(int,int,number_number_of_int,X26))
<=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X26)),vAPP(int,int,number_number_of_int,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
thf(f10081,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_168 ),
inference(avatar_component_clause,[],[f10079]) ).
thf(f10079,plain,
( spl44_168
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_168])]) ).
thf(f11711,plain,
( spl44_181
| ~ spl44_219 ),
inference(avatar_contradiction_clause,[],[f11710]) ).
thf(f11710,plain,
( $false
| spl44_181
| ~ spl44_219 ),
inference(subsumption_resolution,[],[f11701,f10159]) ).
thf(f11701,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11677]) ).
thf(f11677,plain,
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_219 ),
inference(superposition,[],[f11665,f8889]) ).
thf(f11709,plain,
( spl44_221
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(avatar_split_clause,[],[f11702,f11664,f9585,f9001,f11706]) ).
thf(f11702,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11676]) ).
thf(f11676,plain,
( ( $true = $false )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_219 ),
inference(superposition,[],[f11665,f9806]) ).
thf(f11704,plain,
( ~ spl44_207
| ~ spl44_219 ),
inference(avatar_contradiction_clause,[],[f11703]) ).
thf(f11703,plain,
( $false
| ~ spl44_207
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11675]) ).
thf(f11675,plain,
( ( $true = $false )
| ~ spl44_207
| ~ spl44_219 ),
inference(superposition,[],[f11665,f11178]) ).
thf(f11178,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) )
| ~ spl44_207 ),
inference(avatar_component_clause,[],[f11176]) ).
thf(f11176,plain,
( spl44_207
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_207])]) ).
thf(f11696,plain,
( ~ spl44_207
| ~ spl44_219 ),
inference(avatar_contradiction_clause,[],[f11695]) ).
thf(f11695,plain,
( $false
| ~ spl44_207
| ~ spl44_219 ),
inference(trivial_inequality_removal,[],[f11682]) ).
thf(f11682,plain,
( ( $true = $false )
| ~ spl44_207
| ~ spl44_219 ),
inference(superposition,[],[f11178,f11665]) ).
thf(f11672,plain,
( spl44_220
| spl44_219
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11649,f9585,f9001,f11664,f11667]) ).
thf(f11667,plain,
( spl44_220
<=> ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_220])]) ).
thf(f11649,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11648]) ).
thf(f11648,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f4889,f11282]) ).
thf(f11282,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11267]) ).
thf(f11267,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f5207,f11024]) ).
thf(f11024,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11023]) ).
thf(f11023,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f9726,f1202]) ).
thf(f9726,plain,
( ! [X0: int] :
( ( $true != vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(backward_demodulation,[],[f9165,f9587]) ).
thf(f9165,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) )
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7520,f9003]) ).
thf(f7520,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f6196,f4464]) ).
thf(f6196,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(definition_unfolding,[],[f4651,f5971]) ).
thf(f4651,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(cnf_transformation,[],[f4118]) ).
thf(f4118,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,zprime,X0) )
| ( ( vAPP(int,int,sK13,X0) != X0 )
& ( one_one_int != vAPP(int,int,sK13,X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK13,X0)),X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,sK13,X0)) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
& ( ( ! [X2: int] :
( ( X0 = X2 )
| ( one_one_int = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
| ( $true != vAPP(int,$o,zprime,X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f4116,f4117]) ).
thf(f4117,plain,
! [X0: int] :
( ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) )
=> ( ( vAPP(int,int,sK13,X0) != X0 )
& ( one_one_int != vAPP(int,int,sK13,X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK13,X0)),X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,sK13,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4116,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,zprime,X0) )
| ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
& ( ( ! [X2: int] :
( ( X0 = X2 )
| ( one_one_int = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
| ( $true != vAPP(int,$o,zprime,X0) ) ) ),
inference(rectify,[],[f4115]) ).
thf(f4115,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,zprime,X0) )
| ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
& ( ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
| ( $true != vAPP(int,$o,zprime,X0) ) ) ),
inference(flattening,[],[f4114]) ).
thf(f4114,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,zprime,X0) )
| ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
& ( ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) )
| ( $true != vAPP(int,$o,zprime,X0) ) ) ),
inference(nnf_transformation,[],[f3235]) ).
thf(f3235,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
<=> ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ) ),
inference(flattening,[],[f3234]) ).
thf(f3234,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
<=> ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ) ),
inference(ennf_transformation,[],[f1274]) ).
thf(f1274,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
<=> ( ! [X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) )
=> ( ( X0 = X1 )
| ( one_one_int = X1 ) ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ) ),
inference(fool_elimination,[],[f1273]) ).
thf(f1273,plain,
! [X0: int] :
( vAPP(int,$o,zprime,X0)
<=> ( ! [X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) )
=> ( ( X0 = X1 )
| ( one_one_int = X1 ) ) )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(rectify,[],[f509]) ).
thf(f509,axiom,
! [X163: int] :
( vAPP(int,$o,zprime,X163)
<=> ( ! [X305: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X305),X163)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X305) )
=> ( ( X163 = X305 )
| ( one_one_int = X305 ) ) )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X163) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_zprime__def) ).
thf(f5207,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4240]) ).
thf(f4240,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) )
& ( ( ( X0 != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ),
inference(flattening,[],[f4239]) ).
thf(f4239,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) )
& ( ( ( X0 != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1882]) ).
thf(f1882,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
<=> ( ( X0 != X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1881]) ).
thf(f1881,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
<=> ( ( X0 != X1 )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(rectify,[],[f38]) ).
thf(f38,axiom,
! [X15: int,X14: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X15),X14)
<=> ( ( X14 != X15 )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X15),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(f11671,plain,
( spl44_220
| spl44_219
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11650,f9585,f9001,f11664,f11667]) ).
thf(f11650,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11647]) ).
thf(f11647,plain,
( ! [X0: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f8441,f11282]) ).
thf(f11670,plain,
( spl44_219
| spl44_220
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11658,f9585,f9001,f11667,f11664]) ).
thf(f11658,plain,
( ! [X0: int] :
( ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11639]) ).
thf(f11639,plain,
( ! [X0: int] :
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f11282,f8441]) ).
thf(f11455,plain,
( spl44_218
| ~ spl44_204 ),
inference(avatar_split_clause,[],[f11444,f11028,f11452]) ).
thf(f11452,plain,
( spl44_218
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_218])]) ).
thf(f11028,plain,
( spl44_204
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_204])]) ).
thf(f11444,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_204 ),
inference(trivial_inequality_removal,[],[f11436]) ).
thf(f11436,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_204 ),
inference(superposition,[],[f11113,f11030]) ).
thf(f11030,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_204 ),
inference(avatar_component_clause,[],[f11028]) ).
thf(f11113,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f11098]) ).
thf(f11098,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(superposition,[],[f7782,f10587]) ).
thf(f10587,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10586]) ).
thf(f10586,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(superposition,[],[f5207,f1202]) ).
thf(f11418,plain,
( spl44_217
| ~ spl44_90 ),
inference(avatar_split_clause,[],[f11395,f8509,f11413]) ).
thf(f11413,plain,
( spl44_217
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_217])]) ).
thf(f8509,plain,
( spl44_90
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_90])]) ).
thf(f11395,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) )
| ~ spl44_90 ),
inference(trivial_inequality_removal,[],[f11387]) ).
thf(f11387,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) )
| ~ spl44_90 ),
inference(superposition,[],[f7778,f8511]) ).
thf(f8511,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_90 ),
inference(avatar_component_clause,[],[f8509]) ).
thf(f7778,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7777,f4464]) ).
thf(f7777,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7776,f4464]) ).
thf(f7776,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(forward_demodulation,[],[f7775,f4464]) ).
thf(f7775,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(forward_demodulation,[],[f5228,f4464]) ).
thf(f5228,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(cnf_transformation,[],[f4248]) ).
thf(f11417,plain,
( spl44_216
| ~ spl44_90 ),
inference(avatar_split_clause,[],[f11396,f8509,f11408]) ).
thf(f11408,plain,
( spl44_216
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_216])]) ).
thf(f11396,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_90 ),
inference(trivial_inequality_removal,[],[f11385]) ).
thf(f11385,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_90 ),
inference(superposition,[],[f10587,f8511]) ).
thf(f11416,plain,
( spl44_217
| ~ spl44_90 ),
inference(avatar_split_clause,[],[f11403,f8509,f11413]) ).
thf(f11403,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) )
| ~ spl44_90 ),
inference(trivial_inequality_removal,[],[f11378]) ).
thf(f11378,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) )
| ~ spl44_90 ),
inference(superposition,[],[f8511,f7778]) ).
thf(f11411,plain,
( spl44_216
| ~ spl44_90 ),
inference(avatar_split_clause,[],[f11404,f8509,f11408]) ).
thf(f11404,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_90 ),
inference(trivial_inequality_removal,[],[f11377]) ).
thf(f11377,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_90 ),
inference(superposition,[],[f8511,f10587]) ).
thf(f11365,plain,
( spl44_215
| ~ spl44_204 ),
inference(avatar_split_clause,[],[f11354,f11028,f11362]) ).
thf(f11362,plain,
( spl44_215
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_215])]) ).
thf(f11354,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_204 ),
inference(trivial_inequality_removal,[],[f11353]) ).
thf(f11353,plain,
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_204 ),
inference(superposition,[],[f5207,f11030]) ).
thf(f11360,plain,
( spl44_214
| ~ spl44_204 ),
inference(avatar_split_clause,[],[f11355,f11028,f11357]) ).
thf(f11355,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_204 ),
inference(trivial_inequality_removal,[],[f11352]) ).
thf(f11352,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_204 ),
inference(superposition,[],[f10771,f11030]) ).
thf(f11323,plain,
( spl44_213
| spl44_206
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11275,f9585,f9001,f11037,f11309]) ).
thf(f11309,plain,
( spl44_213
<=> ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_213])]) ).
thf(f11037,plain,
( spl44_206
<=> ! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_206])]) ).
thf(f11275,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11274]) ).
thf(f11274,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f4889,f11024]) ).
thf(f11322,plain,
( spl44_213
| spl44_206
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11276,f9585,f9001,f11037,f11309]) ).
thf(f11276,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11273]) ).
thf(f11273,plain,
( ! [X0: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f8441,f11024]) ).
thf(f11321,plain,
( spl44_213
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11277,f9585,f9001,f11309]) ).
thf(f11277,plain,
( ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11272]) ).
thf(f11272,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f8495,f11024]) ).
thf(f8495,plain,
! [X0: int] : ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,X0))) ),
inference(trivial_inequality_removal,[],[f8458]) ).
thf(f8458,plain,
! [X0: int] :
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,X0))) ) ),
inference(superposition,[],[f8441,f8359]) ).
thf(f8359,plain,
! [X0: int] : ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X0) ),
inference(trivial_inequality_removal,[],[f8358]) ).
thf(f8358,plain,
! [X0: int] :
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X0) ) ),
inference(superposition,[],[f6878,f1202]) ).
thf(f6878,plain,
! [X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X1) ),
inference(equality_resolution,[],[f5208]) ).
thf(f5208,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4240]) ).
thf(f11320,plain,
( spl44_211
| ~ spl44_97
| ~ spl44_140
| ~ spl44_143 ),
inference(avatar_split_clause,[],[f11278,f9929,f9585,f9001,f11297]) ).
thf(f11297,plain,
( spl44_211
<=> ( $false = vAPP(int,$o,zprime,t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_211])]) ).
thf(f11278,plain,
( ( $false = vAPP(int,$o,zprime,t) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f11271]) ).
thf(f11271,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,t) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_143 ),
inference(superposition,[],[f9931,f11024]) ).
thf(f11319,plain,
( spl44_210
| ~ spl44_97
| ~ spl44_140
| spl44_181 ),
inference(avatar_split_clause,[],[f11318,f10157,f9585,f9001,f11292]) ).
thf(f11292,plain,
( spl44_210
<=> ( $false = vAPP(int,$o,zprime,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_210])]) ).
thf(f11318,plain,
( ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| spl44_181 ),
inference(subsumption_resolution,[],[f11279,f10159]) ).
thf(f11279,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11270]) ).
thf(f11270,plain,
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f10784,f11024]) ).
thf(f10784,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(trivial_inequality_removal,[],[f10755]) ).
thf(f10755,plain,
! [X0: int] :
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(superposition,[],[f7782,f10437]) ).
thf(f10437,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(trivial_inequality_removal,[],[f10402]) ).
thf(f10402,plain,
! [X0: int] :
( ( $true = $false )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(superposition,[],[f4829,f8889]) ).
thf(f4829,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f1456]) ).
thf(f1456,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(fool_elimination,[],[f1455]) ).
thf(f1455,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X15: int,X14: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X14),X15)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X15),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(f11317,plain,
( spl44_210
| ~ spl44_97
| ~ spl44_140
| spl44_181 ),
inference(avatar_split_clause,[],[f11316,f10157,f9585,f9001,f11292]) ).
thf(f11316,plain,
( ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| spl44_181 ),
inference(subsumption_resolution,[],[f11280,f10159]) ).
thf(f11280,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11269]) ).
thf(f11269,plain,
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f10997,f11024]) ).
thf(f10997,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(trivial_inequality_removal,[],[f10996]) ).
thf(f10996,plain,
! [X0: int] :
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) ),
inference(superposition,[],[f10784,f1202]) ).
thf(f11315,plain,
( spl44_210
| ~ spl44_97
| ~ spl44_140
| ~ spl44_142 ),
inference(avatar_split_clause,[],[f11281,f9923,f9585,f9001,f11292]) ).
thf(f9923,plain,
( spl44_142
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_142])]) ).
thf(f11281,plain,
( ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_142 ),
inference(trivial_inequality_removal,[],[f11268]) ).
thf(f11268,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_142 ),
inference(superposition,[],[f9925,f11024]) ).
thf(f9925,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) )
| ~ spl44_142 ),
inference(avatar_component_clause,[],[f9923]) ).
thf(f11314,plain,
( spl44_212
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11284,f9585,f9001,f11302]) ).
thf(f11302,plain,
( spl44_212
<=> ( $false = vAPP(int,$o,zprime,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_212])]) ).
thf(f11284,plain,
( ( $false = vAPP(int,$o,zprime,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11265]) ).
thf(f11265,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f8359,f11024]) ).
thf(f11313,plain,
( spl44_206
| spl44_213
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11285,f9585,f9001,f11309,f11037]) ).
thf(f11285,plain,
( ! [X0: int] :
( ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11264]) ).
thf(f11264,plain,
( ! [X0: int] :
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f11024,f8441]) ).
thf(f11312,plain,
( spl44_213
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11286,f9585,f9001,f11309]) ).
thf(f11286,plain,
( ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11263]) ).
thf(f11263,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f11024,f8495]) ).
thf(f11307,plain,
( spl44_210
| ~ spl44_97
| ~ spl44_140
| spl44_181 ),
inference(avatar_split_clause,[],[f11306,f10157,f9585,f9001,f11292]) ).
thf(f11306,plain,
( ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| spl44_181 ),
inference(subsumption_resolution,[],[f11287,f10159]) ).
thf(f11287,plain,
( ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11262]) ).
thf(f11262,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f11024,f10997]) ).
thf(f11305,plain,
( spl44_212
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11288,f9585,f9001,f11302]) ).
thf(f11288,plain,
( ( $false = vAPP(int,$o,zprime,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11261]) ).
thf(f11261,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f11024,f8359]) ).
thf(f11300,plain,
( spl44_211
| ~ spl44_97
| ~ spl44_140
| ~ spl44_143 ),
inference(avatar_split_clause,[],[f11289,f9929,f9585,f9001,f11297]) ).
thf(f11289,plain,
( ( $false = vAPP(int,$o,zprime,t) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f11260]) ).
thf(f11260,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,t) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_143 ),
inference(superposition,[],[f11024,f9931]) ).
thf(f11295,plain,
( spl44_210
| ~ spl44_97
| ~ spl44_140
| ~ spl44_142 ),
inference(avatar_split_clause,[],[f11290,f9923,f9585,f9001,f11292]) ).
thf(f11290,plain,
( ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_142 ),
inference(trivial_inequality_removal,[],[f11259]) ).
thf(f11259,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,zprime,zero_zero_int) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_142 ),
inference(superposition,[],[f11024,f9925]) ).
thf(f11235,plain,
( spl44_209
| spl44_186
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11223,f9585,f9001,f10452,f11230]) ).
thf(f11230,plain,
( spl44_209
<=> ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_209])]) ).
thf(f10452,plain,
( spl44_186
<=> ! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_186])]) ).
thf(f11223,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11222]) ).
thf(f11222,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f4889,f10875]) ).
thf(f10875,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,zfact,zero_zero_int) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f10863]) ).
thf(f10863,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,zfact,zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f9714,f4829]) ).
thf(f11234,plain,
( spl44_209
| spl44_186
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11224,f9585,f9001,f10452,f11230]) ).
thf(f11224,plain,
( ! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11221]) ).
thf(f11221,plain,
( ! [X0: int] :
( ( $true = $false )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f8441,f10875]) ).
thf(f11233,plain,
( spl44_186
| spl44_209
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11227,f9585,f9001,f11230,f10452]) ).
thf(f11227,plain,
( ! [X0: int] :
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11214]) ).
thf(f11214,plain,
( ! [X0: int] :
( ( $true = $false )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f10875,f8441]) ).
thf(f11210,plain,
( spl44_208
| ~ spl44_207 ),
inference(avatar_split_clause,[],[f11194,f11176,f11206]) ).
thf(f11206,plain,
( spl44_208
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_208])]) ).
thf(f11194,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_207 ),
inference(trivial_inequality_removal,[],[f11193]) ).
thf(f11193,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_207 ),
inference(superposition,[],[f8441,f11178]) ).
thf(f11209,plain,
( spl44_208
| ~ spl44_207 ),
inference(avatar_split_clause,[],[f11200,f11176,f11206]) ).
thf(f11200,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_207 ),
inference(trivial_inequality_removal,[],[f11184]) ).
thf(f11184,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_207 ),
inference(superposition,[],[f11178,f8441]) ).
thf(f11179,plain,
( spl44_207
| ~ spl44_168 ),
inference(avatar_split_clause,[],[f11173,f10079,f11176]) ).
thf(f11173,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) )
| ~ spl44_168 ),
inference(trivial_inequality_removal,[],[f11154]) ).
thf(f11154,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) )
| ~ spl44_168 ),
inference(superposition,[],[f10771,f10081]) ).
thf(f11039,plain,
( spl44_205
| spl44_206
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f11025,f9585,f9001,f11037,f11033]) ).
thf(f11033,plain,
( spl44_205
<=> ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,zprime)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_205])]) ).
thf(f11025,plain,
( ! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,zprime)) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f11021]) ).
thf(f11021,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,zprime,vAPP(sTfun(int,$o),int,sK17,zprime)) ) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f9726,f8441]) ).
thf(f11031,plain,
( spl44_204
| ~ spl44_97
| ~ spl44_140
| ~ spl44_167 ),
inference(avatar_split_clause,[],[f11026,f10073,f9585,f9001,f11028]) ).
thf(f10073,plain,
( spl44_167
<=> ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_167])]) ).
thf(f11026,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_167 ),
inference(trivial_inequality_removal,[],[f11020]) ).
thf(f11020,plain,
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_97
| ~ spl44_140
| ~ spl44_167 ),
inference(superposition,[],[f9726,f10075]) ).
thf(f10075,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_167 ),
inference(avatar_component_clause,[],[f10073]) ).
thf(f10960,plain,
( spl44_203
| spl44_193 ),
inference(avatar_split_clause,[],[f10953,f10801,f10957]) ).
thf(f10801,plain,
( spl44_193
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_193])]) ).
thf(f10953,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| spl44_193 ),
inference(trivial_inequality_removal,[],[f10952]) ).
thf(f10952,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| spl44_193 ),
inference(superposition,[],[f10803,f1202]) ).
thf(f10803,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| spl44_193 ),
inference(avatar_component_clause,[],[f10801]) ).
thf(f10948,plain,
( spl44_202
| spl44_192 ),
inference(avatar_split_clause,[],[f10941,f10796,f10945]) ).
thf(f10796,plain,
( spl44_192
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_192])]) ).
thf(f10941,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| spl44_192 ),
inference(trivial_inequality_removal,[],[f10940]) ).
thf(f10940,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| spl44_192 ),
inference(superposition,[],[f10798,f1202]) ).
thf(f10798,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| spl44_192 ),
inference(avatar_component_clause,[],[f10796]) ).
thf(f10925,plain,
( spl44_201
| spl44_196 ),
inference(avatar_split_clause,[],[f10918,f10819,f10922]) ).
thf(f10819,plain,
( spl44_196
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_196])]) ).
thf(f10918,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| spl44_196 ),
inference(trivial_inequality_removal,[],[f10917]) ).
thf(f10917,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| spl44_196 ),
inference(superposition,[],[f10821,f1202]) ).
thf(f10821,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| spl44_196 ),
inference(avatar_component_clause,[],[f10819]) ).
thf(f10881,plain,
( spl44_200
| ~ spl44_97
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10872,f9585,f9001,f10878]) ).
thf(f10878,plain,
( spl44_200
<=> ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_200])]) ).
thf(f10872,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(trivial_inequality_removal,[],[f10867]) ).
thf(f10867,plain,
( ( $true != $true )
| ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) )
| ~ spl44_97
| ~ spl44_140 ),
inference(superposition,[],[f9714,f10704]) ).
thf(f10704,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,X0))),X0) ),
inference(trivial_inequality_removal,[],[f10659]) ).
thf(f10659,plain,
! [X0: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,X0))),X0) ) ),
inference(superposition,[],[f7778,f8495]) ).
thf(f10858,plain,
( spl44_199
| spl44_195 ),
inference(avatar_split_clause,[],[f10851,f10812,f10855]) ).
thf(f10812,plain,
( spl44_195
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_195])]) ).
thf(f10851,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) )
| spl44_195 ),
inference(trivial_inequality_removal,[],[f10850]) ).
thf(f10850,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) )
| spl44_195 ),
inference(superposition,[],[f10814,f1202]) ).
thf(f10814,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) )
| spl44_195 ),
inference(avatar_component_clause,[],[f10812]) ).
thf(f10846,plain,
( spl44_198
| spl44_194 ),
inference(avatar_split_clause,[],[f10839,f10807,f10843]) ).
thf(f10807,plain,
( spl44_194
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_194])]) ).
thf(f10839,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) )
| spl44_194 ),
inference(trivial_inequality_removal,[],[f10838]) ).
thf(f10838,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) )
| spl44_194 ),
inference(superposition,[],[f10809,f1202]) ).
thf(f10809,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) )
| spl44_194 ),
inference(avatar_component_clause,[],[f10807]) ).
thf(f10834,plain,
( spl44_197
| spl44_191 ),
inference(avatar_split_clause,[],[f10827,f10790,f10831]) ).
thf(f10790,plain,
( spl44_191
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_191])]) ).
thf(f10827,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) )
| spl44_191 ),
inference(trivial_inequality_removal,[],[f10826]) ).
thf(f10826,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) )
| spl44_191 ),
inference(superposition,[],[f10792,f1202]) ).
thf(f10792,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) )
| spl44_191 ),
inference(avatar_component_clause,[],[f10790]) ).
thf(f10822,plain,
( ~ spl44_196
| ~ spl44_170 ),
inference(avatar_split_clause,[],[f10774,f10091,f10819]) ).
thf(f10091,plain,
( spl44_170
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_170])]) ).
thf(f10774,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_170 ),
inference(trivial_inequality_removal,[],[f10766]) ).
thf(f10766,plain,
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_170 ),
inference(superposition,[],[f7782,f10093]) ).
thf(f10093,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ~ spl44_170 ),
inference(avatar_component_clause,[],[f10091]) ).
thf(f10815,plain,
( ~ spl44_195
| ~ spl44_49 ),
inference(avatar_split_clause,[],[f10777,f8005,f10812]) ).
thf(f8005,plain,
( spl44_49
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_49])]) ).
thf(f10777,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) )
| ~ spl44_49 ),
inference(trivial_inequality_removal,[],[f10763]) ).
thf(f10763,plain,
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),zero_zero_int) )
| ~ spl44_49 ),
inference(superposition,[],[f7782,f8007]) ).
thf(f8007,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK43) )
| ~ spl44_49 ),
inference(avatar_component_clause,[],[f8005]) ).
thf(f10810,plain,
( ~ spl44_194
| ~ spl44_32 ),
inference(avatar_split_clause,[],[f10778,f7379,f10807]) ).
thf(f7379,plain,
( spl44_32
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_32])]) ).
thf(f10778,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) )
| ~ spl44_32 ),
inference(trivial_inequality_removal,[],[f10762]) ).
thf(f10762,plain,
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),zero_zero_int) )
| ~ spl44_32 ),
inference(superposition,[],[f7782,f7381]) ).
thf(f7381,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK8) )
| ~ spl44_32 ),
inference(avatar_component_clause,[],[f7379]) ).
thf(f10804,plain,
( ~ spl44_193
| ~ spl44_164 ),
inference(avatar_split_clause,[],[f10780,f10055,f10801]) ).
thf(f10055,plain,
( spl44_164
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_164])]) ).
thf(f10780,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| ~ spl44_164 ),
inference(trivial_inequality_removal,[],[f10760]) ).
thf(f10760,plain,
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| ~ spl44_164 ),
inference(superposition,[],[f7782,f10057]) ).
thf(f10057,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_164 ),
inference(avatar_component_clause,[],[f10055]) ).
thf(f10799,plain,
( ~ spl44_192
| ~ spl44_165 ),
inference(avatar_split_clause,[],[f10781,f10061,f10796]) ).
thf(f10061,plain,
( spl44_165
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_165])]) ).
thf(f10781,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| ~ spl44_165 ),
inference(trivial_inequality_removal,[],[f10759]) ).
thf(f10759,plain,
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))),zero_zero_int) )
| ~ spl44_165 ),
inference(superposition,[],[f7782,f10063]) ).
thf(f10063,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_165 ),
inference(avatar_component_clause,[],[f10061]) ).
thf(f10793,plain,
( ~ spl44_191
| ~ spl44_25 ),
inference(avatar_split_clause,[],[f10783,f7341,f10790]) ).
thf(f7341,plain,
( spl44_25
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),s) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_25])]) ).
thf(f10783,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) )
| ~ spl44_25 ),
inference(trivial_inequality_removal,[],[f10757]) ).
thf(f10757,plain,
( ( $true != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),zero_zero_int) )
| ~ spl44_25 ),
inference(superposition,[],[f7782,f7343]) ).
thf(f7343,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),s) = $true )
| ~ spl44_25 ),
inference(avatar_component_clause,[],[f7341]) ).
thf(f10741,plain,
spl44_190,
inference(avatar_split_clause,[],[f10740,f10731]) ).
thf(f10731,plain,
( spl44_190
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_190])]) ).
thf(f10740,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))),
inference(global_subsumption,[],[f5974,f1202,f1201,f5975,f5976,f5977,f5978,f5979,f5980,f5981,f5982,f5983,f5984,f5985,f4405,f5988,f5991,f5992,f5993,f5994,f6002,f6003,f6004,f6005,f6006,f6007,f6008,f6009,f6010,f6011,f6012,f6013,f6014,f6015,f6016,f6017,f6018,f6019,f4444,f7345,f6021,f7351,f7357,f6023,f6024,f6025,f4451,f6026,f6027,f4456,f6028,f6029,f6030,f6031,f4462,f4464,f7410,f6033,f6034,f6036,f6037,f7411,f7412,f6042,f6044,f6046,f6047,f6050,f6053,f6054,f4487,f4490,f4492,f4493,f6055,f6056,f6058,f6059,f6060,f6062,f6064,f6066,f6067,f6069,f6071,f6073,f6075,f7414,f6078,f6079,f7416,f7418,f4526,f7423,f7424,f4537,f4538,f6092,f6093,f6094,f6095,f7427,f6097,f6098,f6099,f6100,f6101,f7429,f6102,f6105,f6112,f7435,f7443,f6121,f7449,f7450,f7451,f6126,f6127,f6128,f6132,f6133,f6134,f4583,f6135,f6137,f6139,f6142,f6144,f7459,f7460,f7461,f7464,f6150,f7465,f7468,f7470,f6154,f6155,f6157,f4607,f7472,f7473,f7474,f7475,f7477,f7484,f7489,f6167,f6170,f6770,f6771,f6174,f6772,f6177,f6178,f6773,f4633,f6774,f6182,f4639,f7501,f7505,f6777,f6186,f6778,f6188,f7508,f6190,f6780,f4649,f7514,f7516,f7517,f7518,f7519,f7520,f6781,f6782,f6783,f6784,f6204,f7537,f7538,f7204,f7205,f7202,f7203,f7200,f7201,f7198,f7199,f7196,f7197,f7194,f7195,f7192,f7193,f7190,f7191,f7188,f7189,f7186,f7187,f7184,f7185,f7174,f7175,f7172,f7173,f7168,f7169,f7158,f7159,f7156,f7157,f7154,f7155,f7152,f7153,f7146,f7147,f7144,f7145,f7140,f7141,f7138,f7139,f7134,f7135,f6233,f7570,f6235,f7573,f6237,f6238,f6239,f4714,f6242,f4717,f6243,f6244,f6245,f6246,f6247,f6249,f6251,f7575,f4729,f4730,f4731,f4732,f4734,f4735,f4736,f4737,f6254,f4740,f4741,f6255,f6256,f6257,f6258,f4746,f6259,f4749,f4750,f4752,f4754,f4756,f4757,f7576,f7578,f4759,f7579,f4761,f4762,f4763,f7583,f4764,f4765,f4766,f4770,f4771,f4774,f4775,f4778,f4779,f7597,f4782,f6260,f6261,f6262,f6263,f7602,f7603,f6266,f6267,f6268,f6269,f6270,f6271,f7609,f6273,f6274,f6275,f6276,f6278,f7612,f7615,f7618,f7621,f7623,f7625,f6285,f6287,f6290,f6292,f6293,f4821,f4820,f7634,f7645,f7646,f4824,f4827,f4828,f4829,f4830,f4831,f4832,f4835,f6297,f6298,f6299,f4839,f4840,f7649,f6302,f4847,f6304,f6305,f6306,f7651,f6308,f6309,f6310,f6311,f6312,f7652,f7653,f6316,f6318,f6320,f4878,f6321,f6322,f6323,f7655,f6325,f6326,f4886,f4889,f7657,f4890,f7660,f7662,f7664,f7667,f7670,f7673,f7676,f7677,f7680,f7681,f6338,f6342,f6343,f6344,f6345,f6346,f6348,f6349,f6350,f6351,f6355,f6356,f6361,f6362,f6363,f6364,f6365,f6366,f6367,f6368,f7682,f6370,f6371,f6372,f6373,f6374,f6377,f6378,f6380,f6382,f6383,f6384,f6385,f7686,f7697,f7699,f7700,f7701,f7703,f7704,f4978,f4979,f7705,f4981,f4982,f7707,f4984,f4985,f4986,f4987,f7710,f7712,f4993,f4992,f4997,f4998,f7719,f5003,f5005,f5004,f5007,f5010,f5011,f6407,f6408,f6410,f6411,f5025,f5026,f5027,f5028,f5029,f5031,f5037,f6413,f5039,f5040,f5041,f5042,f5043,f7720,f6415,f6416,f6417,f6418,f5049,f7721,f5052,f7722,f5054,f7723,f7725,f7729,f7730,f7731,f7734,f6428,f6429,f6430,f6431,f7735,f7736,f6434,f6435,f5082,f5084,f5086,f5088,f6438,f6440,f6441,f7738,f7747,f7750,f7753,f6835,f6458,f6460,f6462,f6837,f6468,f6469,f6845,f5131,f5130,f6846,f5132,f6476,f6851,f5144,f6483,f6486,f6489,f6491,f6492,f5162,f5161,f6497,f6498,f6500,f6501,f5187,f7128,f7129,f6873,f6876,f5200,f6506,f6507,f6878,f5207,f7126,f7127,f7124,f7125,f5213,f5212,f7122,f7123,f7120,f7121,f6508,f5217,f6509,f5220,f5219,f6510,f5222,f7766,f7770,f7774,f7778,f7782,f7114,f7115,f7110,f7111,f7106,f7107,f7102,f7103,f7094,f7095,f7090,f7091,f7086,f7087,f7082,f7083,f7078,f7079,f6879,f5251,f6515,f6516,f6521,f6522,f7074,f7075,f7799,f6527,f7805,f6531,f6532,f6533,f6535,f7807,f7808,f7809,f7810,f7811,f7812,f7813,f7814,f7815,f7816,f5291,f7066,f7067,f6544,f7818,f7820,f6547,f6548,f6551,f6552,f5309,f5308,f7830,f7837,f5311,f5310,f6553,f6554,f6557,f6558,f6559,f6560,f7855,f7859,f6563,f6564,f5325,f5326,f6565,f5328,f6566,f6567,f7861,f5332,f5333,f5334,f5335,f5336,f5337,f5339,f5340,f5341,f5342,f5343,f5344,f6569,f6570,f6571,f6572,f6573,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f7862,f7863,f7864,f7865,f5363,f5365,f5366,f5368,f5369,f5370,f7866,f5371,f7867,f7868,f7869,f5380,f5383,f7870,f5385,f5386,f5387,f7877,f7878,f7873,f7874,f7879,f7880,f5394,f5395,f5398,f5399,f5401,f5402,f5403,f5404,f5406,f5408,f5409,f5410,f5413,f5415,f5417,f5418,f7881,f5420,f5421,f5423,f5424,f5433,f5434,f5435,f5436,f5437,f7884,f5441,f5443,f6574,f6575,f6577,f6579,f6580,f7062,f7063,f7060,f7061,f7058,f7059,f6906,f6583,f7892,f5471,f5475,f5474,f5478,f5477,f6586,f5505,f5504,f5506,f7894,f7896,f7898,f6590,f5513,f5514,f7899,f7903,f7905,f6594,f6595,f6597,f7048,f7049,f7046,f7047,f6600,f7044,f7045,f7042,f7043,f7040,f7041,f7038,f7039,f7036,f7037,f6606,f6607,f6609,f7034,f7035,f7032,f7033,f6612,f6613,f6614,f6615,f7030,f7031,f7028,f7029,f7026,f7027,f7907,f7908,f7909,f7911,f7912,f7913,f7914,f7915,f7916,f7917,f7918,f5562,f5563,f5564,f5566,f5565,f5567,f7020,f7021,f7018,f7019,f5571,f5572,f5573,f5574,f5575,f5576,f6631,f6632,f6634,f6635,f6636,f5583,f5584,f6637,f6639,f6641,f6642,f5592,f5594,f5596,f5597,f5598,f5599,f5600,f5601,f5603,f5604,f5605,f5606,f5608,f6643,f6644,f6645,f7920,f7921,f7922,f7923,f7924,f7925,f5620,f5621,f7015,f7016,f7013,f7014,f5625,f7011,f7012,f5629,f5630,f5631,f5632,f5633,f5634,f5635,f5636,f5639,f6653,f6654,f7926,f6656,f6657,f6658,f6659,f7927,f7928,f5652,f5653,f5654,f5655,f5656,f5657,f5658,f5659,f5660,f5661,f5662,f5663,f5664,f7929,f5666,f5665,f7931,f5669,f5668,f5675,f5676,f5677,f5678,f5680,f5682,f5684,f5685,f7933,f7934,f7935,f7938,f7939,f7940,f5693,f5694,f5695,f5696,f5697,f5698,f5699,f5701,f5700,f5704,f5705,f5706,f5707,f5708,f7941,f7942,f7945,f7946,f6678,f6679,f6680,f6681,f7947,f6683,f5721,f5723,f5725,f6685,f6687,f5737,f5736,f5747,f6690,f5745,f6691,f5743,f6692,f6946,f6948,f6949,f5749,f5748,f6697,f5754,f6698,f5752,f6699,f6700,f5760,f6701,f5758,f5767,f5766,f5765,f5764,f5763,f6952,f5773,f5772,f5771,f5769,f5778,f5777,f5776,f5775,f6954,f6955,f5779,f7009,f7007,f7008,f7005,f7006,f7003,f7004,f7001,f7002,f5789,f6705,f6706,f6707,f5795,f6710,f6711,f6712,f6714,f6716,f6999,f7000,f6717,f6718,f6719,f6720,f6997,f6998,f5813,f6722,f5816,f6724,f6995,f6996,f5822,f5821,f5820,f5819,f5828,f5827,f5826,f5825,f5831,f5832,f7955,f7956,f7957,f7958,f7959,f7960,f7961,f5846,f5847,f5849,f5850,f6958,f6960,f5856,f5857,f6726,f5861,f5862,f5863,f5864,f6727,f6728,f5867,f5868,f7963,f5871,f5873,f5874,f5875,f5876,f5879,f5880,f5881,f5882,f5883,f5884,f5885,f5886,f5887,f7964,f7965,f7967,f7970,f7971,f7973,f5896,f5899,f5902,f6975,f6976,f6977,f6739,f5918,f5919,f6978,f5920,f6993,f6994,f6991,f6992,f6989,f6990,f6987,f6988,f7975,f7976,f7977,f5931,f5932,f5933,f6983,f6984,f6981,f6982,f5937,f5940,f7985,f7989,f7998,f5941,f6744,f8014,f8020,f6748,f5952,f8032,f8039,f6752,f8050,f8056,f8065,f8074,f8083,f8093,f8103,f8114,f8125,f8136,f8147,f8158,f8353,f8356,f8359,f8368,f8402,f8419,f8424,f8434,f8444,f8441,f8495,f8492,f8485,f8484,f8530,f8533,f8536,f8579,f8608,f8633,f8642,f8688,f8698,f8769,f8770,f8775,f8777,f8786,f8789,f8792,f8795,f8828,f8830,f8834,f8836,f8864,f8863,f8874,f8882,f8890,f8889,f8909,f8907,f8921,f8948,f8929,f8959,f8974,f8975,f8976,f8994,f8992,f8991,f10380,f10435,f10449,f10447,f10446,f5561,f6291,f6289,f7167,f5292,f7166,f7178,f7180,f10437,f7181,f7179,f4739,f4977,f4869,f4995,f4991,f5346,f5770,f4868,f4870,f4871,f4959,f4960,f4961,f4966,f4967,f4969,f4971,f4994,f5546,f5557,f5558,f5559,f5671,f5672,f5674,f5714,f5722,f5859,f5860,f5877,f5878,f5936,f5938,f5939,f6391,f6392,f6585,f6667,f6953,f6959,f6961,f7479,f7481,f7644,f7919,f5279,f5280,f5713,f10571,f10575,f10587,f10591,f10593,f10602,f10622,f10624,f10628,f10651,f10650,f10704,f10698,f10696,f10728,f10727,f10735,f10724,f10723,f10738,f10722]) ).
thf(f10722,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
inference(trivial_inequality_removal,[],[f10721]) ).
thf(f10721,plain,
! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
inference(superposition,[],[f4889,f10698]) ).
thf(f10738,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))),
inference(global_subsumption,[],[f5974,f1202,f1201,f5975,f5976,f5977,f5978,f5979,f5980,f5981,f5982,f5983,f5984,f5985,f4405,f5988,f5991,f5992,f5993,f5994,f6002,f6003,f6004,f6005,f6006,f6007,f6008,f6009,f6010,f6011,f6012,f6013,f6014,f6015,f6016,f6017,f6018,f6019,f4444,f7345,f6021,f7351,f7357,f6023,f6024,f6025,f4451,f6026,f6027,f4456,f6028,f6029,f6030,f6031,f4462,f4464,f7410,f6033,f6034,f6036,f6037,f7411,f7412,f6042,f6044,f6046,f6047,f6050,f6053,f6054,f4487,f4490,f4492,f4493,f6055,f6056,f6058,f6059,f6060,f6062,f6064,f6066,f6067,f6069,f6071,f6073,f6075,f7414,f6078,f6079,f7416,f7418,f4526,f7423,f7424,f4537,f4538,f6092,f6093,f6094,f6095,f7427,f6097,f6098,f6099,f6100,f6101,f7429,f6102,f6105,f6112,f7435,f7443,f6121,f7449,f7450,f7451,f6126,f6127,f6128,f6132,f6133,f6134,f4583,f6135,f6137,f6139,f6142,f6144,f7459,f7460,f7461,f7464,f6150,f7465,f7468,f7470,f6154,f6155,f6157,f4607,f7472,f7473,f7474,f7475,f7477,f7484,f7489,f6167,f6170,f6770,f6771,f6174,f6772,f6177,f6178,f6773,f4633,f6774,f6182,f4639,f7501,f7505,f6777,f6186,f6778,f6188,f7508,f6190,f6780,f4649,f7514,f7516,f7517,f7518,f7519,f7520,f6781,f6782,f6783,f6784,f6204,f7537,f7538,f7204,f7205,f7202,f7203,f7200,f7201,f7198,f7199,f7196,f7197,f7194,f7195,f7192,f7193,f7190,f7191,f7188,f7189,f7186,f7187,f7184,f7185,f7174,f7175,f7172,f7173,f7168,f7169,f7158,f7159,f7156,f7157,f7154,f7155,f7152,f7153,f7146,f7147,f7144,f7145,f7140,f7141,f7138,f7139,f7134,f7135,f6233,f7570,f6235,f7573,f6237,f6238,f6239,f4714,f6242,f4717,f6243,f6244,f6245,f6246,f6247,f6249,f6251,f7575,f4729,f4730,f4731,f4732,f4734,f4735,f4736,f4737,f6254,f4740,f4741,f6255,f6256,f6257,f6258,f4746,f6259,f4749,f4750,f4752,f4754,f4756,f4757,f7576,f7578,f4759,f7579,f4761,f4762,f4763,f7583,f4764,f4765,f4766,f4770,f4771,f4774,f4775,f4778,f4779,f7597,f4782,f6260,f6261,f6262,f6263,f7602,f7603,f6266,f6267,f6268,f6269,f6270,f6271,f7609,f6273,f6274,f6275,f6276,f6278,f7612,f7615,f7618,f7621,f7623,f7625,f6285,f6287,f6290,f6292,f6293,f4821,f4820,f7634,f7645,f7646,f4824,f4827,f4828,f4829,f4830,f4831,f4832,f4835,f6297,f6298,f6299,f4839,f4840,f7649,f6302,f4847,f6304,f6305,f6306,f7651,f6308,f6309,f6310,f6311,f6312,f7652,f7653,f6316,f6318,f6320,f4878,f6321,f6322,f6323,f7655,f6325,f6326,f4886,f4889,f7657,f4890,f7660,f7662,f7664,f7667,f7670,f7673,f7676,f7677,f7680,f7681,f6338,f6342,f6343,f6344,f6345,f6346,f6348,f6349,f6350,f6351,f6355,f6356,f6361,f6362,f6363,f6364,f6365,f6366,f6367,f6368,f7682,f6370,f6371,f6372,f6373,f6374,f6377,f6378,f6380,f6382,f6383,f6384,f6385,f7686,f7697,f7699,f7700,f7701,f7703,f7704,f4978,f4979,f7705,f4981,f4982,f7707,f4984,f4985,f4986,f4987,f7710,f7712,f4993,f4992,f4997,f4998,f7719,f5003,f5005,f5004,f5007,f5010,f5011,f6407,f6408,f6410,f6411,f5025,f5026,f5027,f5028,f5029,f5031,f5037,f6413,f5039,f5040,f5041,f5042,f5043,f7720,f6415,f6416,f6417,f6418,f5049,f7721,f5052,f7722,f5054,f7723,f7725,f7729,f7730,f7731,f7734,f6428,f6429,f6430,f6431,f7735,f7736,f6434,f6435,f5082,f5084,f5086,f5088,f6438,f6440,f6441,f7738,f7747,f7750,f7753,f6835,f6458,f6460,f6462,f6837,f6468,f6469,f6845,f5131,f5130,f6846,f5132,f6476,f6851,f5144,f6483,f6486,f6489,f6491,f6492,f5162,f5161,f6497,f6498,f6500,f6501,f5187,f7128,f7129,f6873,f6876,f5200,f6506,f6507,f6878,f5207,f7126,f7127,f7124,f7125,f5213,f5212,f7122,f7123,f7120,f7121,f6508,f5217,f6509,f5220,f5219,f6510,f5222,f7766,f7770,f7774,f7778,f7782,f7114,f7115,f7110,f7111,f7106,f7107,f7102,f7103,f7094,f7095,f7090,f7091,f7086,f7087,f7082,f7083,f7078,f7079,f6879,f5251,f6515,f6516,f6521,f6522,f7074,f7075,f7799,f6527,f7805,f6531,f6532,f6533,f6535,f7807,f7808,f7809,f7810,f7811,f7812,f7813,f7814,f7815,f7816,f5291,f7066,f7067,f6544,f7818,f7820,f6547,f6548,f6551,f6552,f5309,f5308,f7830,f7837,f5311,f5310,f6553,f6554,f6557,f6558,f6559,f6560,f7855,f7859,f6563,f6564,f5325,f5326,f6565,f5328,f6566,f6567,f7861,f5332,f5333,f5334,f5335,f5336,f5337,f5339,f5340,f5341,f5342,f5343,f5344,f6569,f6570,f6571,f6572,f6573,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f7862,f7863,f7864,f7865,f5363,f5365,f5366,f5368,f5369,f5370,f7866,f5371,f7867,f7868,f7869,f5380,f5383,f7870,f5385,f5386,f5387,f7877,f7878,f7873,f7874,f7879,f7880,f5394,f5395,f5398,f5399,f5401,f5402,f5403,f5404,f5406,f5408,f5409,f5410,f5413,f5415,f5417,f5418,f7881,f5420,f5421,f5423,f5424,f5433,f5434,f5435,f5436,f5437,f7884,f5441,f5443,f6574,f6575,f6577,f6579,f6580,f7062,f7063,f7060,f7061,f7058,f7059,f6906,f6583,f7892,f5471,f5475,f5474,f5478,f5477,f6586,f5505,f5504,f5506,f7894,f7896,f7898,f6590,f5513,f5514,f7899,f7903,f7905,f6594,f6595,f6597,f7048,f7049,f7046,f7047,f6600,f7044,f7045,f7042,f7043,f7040,f7041,f7038,f7039,f7036,f7037,f6606,f6607,f6609,f7034,f7035,f7032,f7033,f6612,f6613,f6614,f6615,f7030,f7031,f7028,f7029,f7026,f7027,f7907,f7908,f7909,f7911,f7912,f7913,f7914,f7915,f7916,f7917,f7918,f5562,f5563,f5564,f5566,f5565,f5567,f7020,f7021,f7018,f7019,f5571,f5572,f5573,f5574,f5575,f5576,f6631,f6632,f6634,f6635,f6636,f5583,f5584,f6637,f6639,f6641,f6642,f5592,f5594,f5596,f5597,f5598,f5599,f5600,f5601,f5603,f5604,f5605,f5606,f5608,f6643,f6644,f6645,f7920,f7921,f7922,f7923,f7924,f7925,f5620,f5621,f7015,f7016,f7013,f7014,f5625,f7011,f7012,f5629,f5630,f5631,f5632,f5633,f5634,f5635,f5636,f5639,f6653,f6654,f7926,f6656,f6657,f6658,f6659,f7927,f7928,f5652,f5653,f5654,f5655,f5656,f5657,f5658,f5659,f5660,f5661,f5662,f5663,f5664,f7929,f5666,f5665,f7931,f5669,f5668,f5675,f5676,f5677,f5678,f5680,f5682,f5684,f5685,f7933,f7934,f7935,f7938,f7939,f7940,f5693,f5694,f5695,f5696,f5697,f5698,f5699,f5701,f5700,f5704,f5705,f5706,f5707,f5708,f7941,f7942,f7945,f7946,f6678,f6679,f6680,f6681,f7947,f6683,f5721,f5723,f5725,f6685,f6687,f5737,f5736,f5747,f6690,f5745,f6691,f5743,f6692,f6946,f6948,f6949,f5749,f5748,f6697,f5754,f6698,f5752,f6699,f6700,f5760,f6701,f5758,f5767,f5766,f5765,f5764,f5763,f6952,f5773,f5772,f5771,f5769,f5778,f5777,f5776,f5775,f6954,f6955,f5779,f7009,f7007,f7008,f7005,f7006,f7003,f7004,f7001,f7002,f5789,f6705,f6706,f6707,f5795,f6710,f6711,f6712,f6714,f6716,f6999,f7000,f6717,f6718,f6719,f6720,f6997,f6998,f5813,f6722,f5816,f6724,f6995,f6996,f5822,f5821,f5820,f5819,f5828,f5827,f5826,f5825,f5831,f5832,f7955,f7956,f7957,f7958,f7959,f7960,f7961,f5846,f5847,f5849,f5850,f6958,f6960,f5856,f5857,f6726,f5861,f5862,f5863,f5864,f6727,f6728,f5867,f5868,f7963,f5871,f5873,f5874,f5875,f5876,f5879,f5880,f5881,f5882,f5883,f5884,f5885,f5886,f5887,f7964,f7965,f7967,f7970,f7971,f7973,f5896,f5899,f5902,f6975,f6976,f6977,f6739,f5918,f5919,f6978,f5920,f6993,f6994,f6991,f6992,f6989,f6990,f6987,f6988,f7975,f7976,f7977,f5931,f5932,f5933,f6983,f6984,f6981,f6982,f5937,f5940,f7985,f7989,f7998,f5941,f6744,f8014,f8020,f6748,f5952,f8032,f8039,f6752,f8050,f8056,f8065,f8074,f8083,f8093,f8103,f8114,f8125,f8136,f8147,f8158,f8353,f8356,f8359,f8368,f8402,f8419,f8424,f8434,f8444,f8441,f8495,f8492,f8485,f8484,f8530,f8533,f8536,f8579,f8608,f8633,f8642,f8688,f8698,f8769,f8770,f8775,f8777,f8786,f8789,f8792,f8795,f8828,f8830,f8834,f8836,f8864,f8863,f8874,f8882,f8890,f8889,f8909,f8907,f8921,f8948,f8929,f8959,f8974,f8975,f8976,f8994,f8992,f8991,f10380,f10435,f10449,f10447,f10446,f5561,f6291,f6289,f7167,f5292,f7166,f7178,f7180,f10437,f7181,f7179,f4739,f4977,f4869,f4995,f4991,f5346,f5770,f4868,f4870,f4871,f4959,f4960,f4961,f4966,f4967,f4969,f4971,f4994,f5546,f5557,f5558,f5559,f5671,f5672,f5674,f5714,f5722,f5859,f5860,f5877,f5878,f5936,f5938,f5939,f6391,f6392,f6585,f6667,f6953,f6959,f6961,f7479,f7481,f7644,f7919,f5279,f5280,f5713,f10571,f10575,f10587,f10591,f10593,f10602,f10622,f10624,f10628,f10651,f10650,f10704,f10698,f10696,f10728,f10727,f10735,f10724,f10723]) ).
thf(f10723,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
inference(trivial_inequality_removal,[],[f10720]) ).
thf(f10720,plain,
! [X0: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
inference(superposition,[],[f8441,f10698]) ).
thf(f10724,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))),
inference(trivial_inequality_removal,[],[f10719]) ).
thf(f10719,plain,
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
inference(superposition,[],[f8495,f10698]) ).
thf(f10735,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))),
inference(global_subsumption,[],[f5974,f1202,f1201,f5975,f5976,f5977,f5978,f5979,f5980,f5981,f5982,f5983,f5984,f5985,f4405,f5988,f5991,f5992,f5993,f5994,f6002,f6003,f6004,f6005,f6006,f6007,f6008,f6009,f6010,f6011,f6012,f6013,f6014,f6015,f6016,f6017,f6018,f6019,f4444,f7345,f6021,f7351,f7357,f6023,f6024,f6025,f4451,f6026,f6027,f4456,f6028,f6029,f6030,f6031,f4462,f4464,f7410,f6033,f6034,f6036,f6037,f7411,f7412,f6042,f6044,f6046,f6047,f6050,f6053,f6054,f4487,f4490,f4492,f4493,f6055,f6056,f6058,f6059,f6060,f6062,f6064,f6066,f6067,f6069,f6071,f6073,f6075,f7414,f6078,f6079,f7416,f7418,f4526,f7423,f7424,f4537,f4538,f6092,f6093,f6094,f6095,f7427,f6097,f6098,f6099,f6100,f6101,f7429,f6102,f6105,f6112,f7435,f7443,f6121,f7449,f7450,f7451,f6126,f6127,f6128,f6132,f6133,f6134,f4583,f6135,f6137,f6139,f6142,f6144,f7459,f7460,f7461,f7464,f6150,f7465,f7468,f7470,f6154,f6155,f6157,f4607,f7472,f7473,f7474,f7475,f7477,f7484,f7489,f6167,f6170,f6770,f6771,f6174,f6772,f6177,f6178,f6773,f4633,f6774,f6182,f4639,f7501,f7505,f6777,f6186,f6778,f6188,f7508,f6190,f6780,f4649,f7514,f7516,f7517,f7518,f7519,f7520,f6781,f6782,f6783,f6784,f6204,f7537,f7538,f7204,f7205,f7202,f7203,f7200,f7201,f7198,f7199,f7196,f7197,f7194,f7195,f7192,f7193,f7190,f7191,f7188,f7189,f7186,f7187,f7184,f7185,f7174,f7175,f7172,f7173,f7168,f7169,f7158,f7159,f7156,f7157,f7154,f7155,f7152,f7153,f7146,f7147,f7144,f7145,f7140,f7141,f7138,f7139,f7134,f7135,f6233,f7570,f6235,f7573,f6237,f6238,f6239,f4714,f6242,f4717,f6243,f6244,f6245,f6246,f6247,f6249,f6251,f7575,f4729,f4730,f4731,f4732,f4734,f4735,f4736,f4737,f6254,f4740,f4741,f6255,f6256,f6257,f6258,f4746,f6259,f4749,f4750,f4752,f4754,f4756,f4757,f7576,f7578,f4759,f7579,f4761,f4762,f4763,f7583,f4764,f4765,f4766,f4770,f4771,f4774,f4775,f4778,f4779,f7597,f4782,f6260,f6261,f6262,f6263,f7602,f7603,f6266,f6267,f6268,f6269,f6270,f6271,f7609,f6273,f6274,f6275,f6276,f6278,f7612,f7615,f7618,f7621,f7623,f7625,f6285,f6287,f6290,f6292,f6293,f4821,f4820,f7634,f7645,f7646,f4824,f4827,f4828,f4829,f4830,f4831,f4832,f4835,f6297,f6298,f6299,f4839,f4840,f7649,f6302,f4847,f6304,f6305,f6306,f7651,f6308,f6309,f6310,f6311,f6312,f7652,f7653,f6316,f6318,f6320,f4878,f6321,f6322,f6323,f7655,f6325,f6326,f4886,f4889,f7657,f4890,f7660,f7662,f7664,f7667,f7670,f7673,f7676,f7677,f7680,f7681,f6338,f6342,f6343,f6344,f6345,f6346,f6348,f6349,f6350,f6351,f6355,f6356,f6361,f6362,f6363,f6364,f6365,f6366,f6367,f6368,f7682,f6370,f6371,f6372,f6373,f6374,f6377,f6378,f6380,f6382,f6383,f6384,f6385,f7686,f7697,f7699,f7700,f7701,f7703,f7704,f4978,f4979,f7705,f4981,f4982,f7707,f4984,f4985,f4986,f4987,f7710,f7712,f4993,f4992,f4997,f4998,f7719,f5003,f5005,f5004,f5007,f5010,f5011,f6407,f6408,f6410,f6411,f5025,f5026,f5027,f5028,f5029,f5031,f5037,f6413,f5039,f5040,f5041,f5042,f5043,f7720,f6415,f6416,f6417,f6418,f5049,f7721,f5052,f7722,f5054,f7723,f7725,f7729,f7730,f7731,f7734,f6428,f6429,f6430,f6431,f7735,f7736,f6434,f6435,f5082,f5084,f5086,f5088,f6438,f6440,f6441,f7738,f7747,f7750,f7753,f6835,f6458,f6460,f6462,f6837,f6468,f6469,f6845,f5131,f5130,f6846,f5132,f6476,f6851,f5144,f6483,f6486,f6489,f6491,f6492,f5162,f5161,f6497,f6498,f6500,f6501,f5187,f7128,f7129,f6873,f6876,f5200,f6506,f6507,f6878,f5207,f7126,f7127,f7124,f7125,f5213,f5212,f7122,f7123,f7120,f7121,f6508,f5217,f6509,f5220,f5219,f6510,f5222,f7766,f7770,f7774,f7778,f7782,f7114,f7115,f7110,f7111,f7106,f7107,f7102,f7103,f7094,f7095,f7090,f7091,f7086,f7087,f7082,f7083,f7078,f7079,f6879,f5251,f6515,f6516,f6521,f6522,f7074,f7075,f7799,f6527,f7805,f6531,f6532,f6533,f6535,f7807,f7808,f7809,f7810,f7811,f7812,f7813,f7814,f7815,f7816,f5291,f7066,f7067,f6544,f7818,f7820,f6547,f6548,f6551,f6552,f5309,f5308,f7830,f7837,f5311,f5310,f6553,f6554,f6557,f6558,f6559,f6560,f7855,f7859,f6563,f6564,f5325,f5326,f6565,f5328,f6566,f6567,f7861,f5332,f5333,f5334,f5335,f5336,f5337,f5339,f5340,f5341,f5342,f5343,f5344,f6569,f6570,f6571,f6572,f6573,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f7862,f7863,f7864,f7865,f5363,f5365,f5366,f5368,f5369,f5370,f7866,f5371,f7867,f7868,f7869,f5380,f5383,f7870,f5385,f5386,f5387,f7877,f7878,f7873,f7874,f7879,f7880,f5394,f5395,f5398,f5399,f5401,f5402,f5403,f5404,f5406,f5408,f5409,f5410,f5413,f5415,f5417,f5418,f7881,f5420,f5421,f5423,f5424,f5433,f5434,f5435,f5436,f5437,f7884,f5441,f5443,f6574,f6575,f6577,f6579,f6580,f7062,f7063,f7060,f7061,f7058,f7059,f6906,f6583,f7892,f5471,f5475,f5474,f5478,f5477,f6586,f5505,f5504,f5506,f7894,f7896,f7898,f6590,f5513,f5514,f7899,f7903,f7905,f6594,f6595,f6597,f7048,f7049,f7046,f7047,f6600,f7044,f7045,f7042,f7043,f7040,f7041,f7038,f7039,f7036,f7037,f6606,f6607,f6609,f7034,f7035,f7032,f7033,f6612,f6613,f6614,f6615,f7030,f7031,f7028,f7029,f7026,f7027,f7907,f7908,f7909,f7911,f7912,f7913,f7914,f7915,f7916,f7917,f7918,f5562,f5563,f5564,f5566,f5565,f5567,f7020,f7021,f7018,f7019,f5571,f5572,f5573,f5574,f5575,f5576,f6631,f6632,f6634,f6635,f6636,f5583,f5584,f6637,f6639,f6641,f6642,f5592,f5594,f5596,f5597,f5598,f5599,f5600,f5601,f5603,f5604,f5605,f5606,f5608,f6643,f6644,f6645,f7920,f7921,f7922,f7923,f7924,f7925,f5620,f5621,f7015,f7016,f7013,f7014,f5625,f7011,f7012,f5629,f5630,f5631,f5632,f5633,f5634,f5635,f5636,f5639,f6653,f6654,f7926,f6656,f6657,f6658,f6659,f7927,f7928,f5652,f5653,f5654,f5655,f5656,f5657,f5658,f5659,f5660,f5661,f5662,f5663,f5664,f7929,f5666,f5665,f7931,f5669,f5668,f5675,f5676,f5677,f5678,f5680,f5682,f5684,f5685,f7933,f7934,f7935,f7938,f7939,f7940,f5693,f5694,f5695,f5696,f5697,f5698,f5699,f5701,f5700,f5704,f5705,f5706,f5707,f5708,f7941,f7942,f7945,f7946,f6678,f6679,f6680,f6681,f7947,f6683,f5721,f5723,f5725,f6685,f6687,f5737,f5736,f5747,f6690,f5745,f6691,f5743,f6692,f6946,f6948,f6949,f5749,f5748,f6697,f5754,f6698,f5752,f6699,f6700,f5760,f6701,f5758,f5767,f5766,f5765,f5764,f5763,f6952,f5773,f5772,f5771,f5769,f5778,f5777,f5776,f5775,f6954,f6955,f5779,f7009,f7007,f7008,f7005,f7006,f7003,f7004,f7001,f7002,f5789,f6705,f6706,f6707,f5795,f6710,f6711,f6712,f6714,f6716,f6999,f7000,f6717,f6718,f6719,f6720,f6997,f6998,f5813,f6722,f5816,f6724,f6995,f6996,f5822,f5821,f5820,f5819,f5828,f5827,f5826,f5825,f5831,f5832,f7955,f7956,f7957,f7958,f7959,f7960,f7961,f5846,f5847,f5849,f5850,f6958,f6960,f5856,f5857,f6726,f5861,f5862,f5863,f5864,f6727,f6728,f5867,f5868,f7963,f5871,f5873,f5874,f5875,f5876,f5879,f5880,f5881,f5882,f5883,f5884,f5885,f5886,f5887,f7964,f7965,f7967,f7970,f7971,f7973,f5896,f5899,f5902,f6975,f6976,f6977,f6739,f5918,f5919,f6978,f5920,f6993,f6994,f6991,f6992,f6989,f6990,f6987,f6988,f7975,f7976,f7977,f5931,f5932,f5933,f6983,f6984,f6981,f6982,f5937,f5940,f7985,f7989,f7998,f5941,f6744,f8014,f8020,f6748,f5952,f8032,f8039,f6752,f8050,f8056,f8065,f8074,f8083,f8093,f8103,f8114,f8125,f8136,f8147,f8158,f8353,f8356,f8359,f8368,f8402,f8419,f8424,f8434,f8444,f8441,f8495,f8492,f8485,f8484,f8530,f8533,f8536,f8579,f8608,f8633,f8642,f8688,f8698,f8769,f8770,f8775,f8777,f8786,f8789,f8792,f8795,f8828,f8830,f8834,f8836,f8864,f8863,f8874,f8882,f8890,f8889,f8909,f8907,f8921,f8948,f8929,f8959,f8974,f8975,f8976,f8994,f8992,f8991,f10380,f10435,f10449,f10447,f10446,f5561,f6291,f6289,f7167,f5292,f7166,f7178,f7180,f10437,f7181,f7179,f4739,f4977,f4869,f4995,f4991,f5346,f5770,f4868,f4870,f4871,f4959,f4960,f4961,f4966,f4967,f4969,f4971,f4994,f5546,f5557,f5558,f5559,f5671,f5672,f5674,f5714,f5722,f5859,f5860,f5877,f5878,f5936,f5938,f5939,f6391,f6392,f6585,f6667,f6953,f6959,f6961,f7479,f7481,f7644,f7919,f5279,f5280,f5713,f10571,f10575,f10587,f10591,f10593,f10602,f10622,f10624,f10628,f10651,f10650,f10704,f10698,f10696,f10728,f10727]) ).
thf(f10727,plain,
! [X0: int] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(trivial_inequality_removal,[],[f10715]) ).
thf(f10715,plain,
! [X0: int] :
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(superposition,[],[f10698,f8441]) ).
thf(f10728,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))),
inference(trivial_inequality_removal,[],[f10714]) ).
thf(f10714,plain,
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int))) ) ),
inference(superposition,[],[f10698,f8495]) ).
thf(f10696,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10667]) ).
thf(f10667,plain,
! [X0: int,X1: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(superposition,[],[f7778,f8441]) ).
thf(f10698,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(trivial_inequality_removal,[],[f10665]) ).
thf(f10665,plain,
! [X0: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(superposition,[],[f7778,f8889]) ).
thf(f10650,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10649]) ).
thf(f10649,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(superposition,[],[f7774,f1202]) ).
thf(f10651,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0))) ) ),
inference(trivial_inequality_removal,[],[f10647]) ).
thf(f10647,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0))) ) ),
inference(superposition,[],[f7774,f8441]) ).
thf(f10628,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),X0) ),
inference(trivial_inequality_removal,[],[f10625]) ).
thf(f10625,plain,
! [X0: int] :
( ( zero_zero_int != zero_zero_int )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),X0) ) ),
inference(superposition,[],[f7770,f7418]) ).
thf(f10624,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0) ) ),
inference(superposition,[],[f7770,f8921]) ).
thf(f10622,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) ) ),
inference(superposition,[],[f7770,f4756]) ).
thf(f10602,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) != X1 )
| ( X0 = X1 ) ),
inference(superposition,[],[f10591,f4752]) ).
thf(f10593,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) )
| ( X1 = X2 ) ),
inference(superposition,[],[f5723,f4752]) ).
thf(f10591,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) != X0 )
| ( X0 = X1 ) ),
inference(superposition,[],[f5723,f6062]) ).
thf(f10575,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10574]) ).
thf(f10574,plain,
! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(superposition,[],[f5187,f1202]) ).
thf(f10571,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10570]) ).
thf(f10570,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(superposition,[],[f4878,f1202]) ).
thf(f5713,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)) ) ),
inference(cnf_transformation,[],[f3933]) ).
thf(f3933,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)) ) ),
inference(flattening,[],[f3932]) ).
thf(f3932,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)) ) ),
inference(ennf_transformation,[],[f2470]) ).
thf(f2470,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) ) ) ),
inference(fool_elimination,[],[f2469]) ).
thf(f2469,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) ) ) ),
inference(rectify,[],[f603]) ).
thf(f603,axiom,
! [X322: int,X323: int,X324: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X322),X323)),X324))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X324),X322)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X322)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X323) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_q__pos__lemma) ).
thf(f5280,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(cnf_transformation,[],[f4263]) ).
thf(f4263,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
& ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ) ),
inference(flattening,[],[f4262]) ).
thf(f4262,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
& ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1964]) ).
thf(f1964,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
<=> ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ) ) ),
inference(fool_elimination,[],[f1963]) ).
thf(f1963,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) ) ) ),
inference(rectify,[],[f812]) ).
thf(f812,axiom,
! [X441: int,X442: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X441),X442))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X442),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X441),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X442)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X441) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_zero__le__mult__iff) ).
thf(f5279,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(cnf_transformation,[],[f4263]) ).
thf(f7919,plain,
! [X2: int,X3: int,X0: int,X1: int > $o] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1))) )
| ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(forward_demodulation,[],[f5560,f4757]) ).
thf(f5560,plain,
! [X2: int,X3: int,X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1)),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4303]) ).
thf(f4303,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X3: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1)),X2)) )
& ( $true = vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1)) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f4301,f4302]) ).
thf(f4302,plain,
! [X1: int > $o,X2: int] :
( ? [X4: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),X2)) )
& ( $true = vAPP(int,$o,X1,X4) ) )
=> ( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1)),X2)) )
& ( $true = vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4301,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X3: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ? [X4: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),X2)) )
& ( $true = vAPP(int,$o,X1,X4) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(rectify,[],[f3707]) ).
thf(f3707,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X4: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X4) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
& ( $true = vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3706]) ).
thf(f3706,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X4: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X4) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
& ( $true = vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2192]) ).
thf(f2192,plain,
! [X0: int,X1: int > $o,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ! [X3: int] :
( ( $true = vAPP(int,$o,X1,X3) )
=> ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) ) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ! [X4: int] :
( ( $true = vAPP(int,$o,X1,X4) )
=> ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ) ) ) ) ),
inference(fool_elimination,[],[f2191]) ).
thf(f2191,plain,
! [X0: int,X1: int > $o,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ! [X3: int] :
( vAPP(int,$o,X1,X3)
=> vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ! [X4: int] :
( vAPP(int,$o,X1,X4)
=> vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ) ) ) ),
inference(rectify,[],[f1067]) ).
thf(f1067,axiom,
! [X18: int,X490: int > $o,X218: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X218)
=> ( ! [X0: int] :
( vAPP(int,$o,X490,X0)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X218)) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X18)
=> ! [X0: int] :
( vAPP(int,$o,X490,X0)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X218))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_incr__mult__lemma) ).
thf(f7644,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ) ),
inference(forward_demodulation,[],[f7643,f4464]) ).
thf(f7643,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7642,f4464]) ).
thf(f7642,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7641,f4464]) ).
thf(f7641,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7640,f6079]) ).
thf(f7640,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7639,f4771]) ).
thf(f7639,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7638,f7427]) ).
thf(f7638,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7637,f4464]) ).
thf(f7637,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7636,f4464]) ).
thf(f7636,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7635,f4464]) ).
thf(f7635,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f6295,f4464]) ).
thf(f6295,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(definition_unfolding,[],[f4822,f4404,f5971]) ).
thf(f4822,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(cnf_transformation,[],[f3244]) ).
thf(f3244,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),one_one_int)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) )
& ( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ) ),
inference(ennf_transformation,[],[f2949]) ).
thf(f2949,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),one_one_int)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) ) ) ),
inference(flattening,[],[f1448]) ).
thf(f1448,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),one_one_int)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) ) ) ),
inference(fool_elimination,[],[f1447]) ).
thf(f1447,plain,
! [X0: int,X1: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),one_one_int)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) ) ) ),
inference(rectify,[],[f1136]) ).
thf(f1136,axiom,
! [X40: int,X14: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X14))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X40))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X14))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X40)),one_one_int)),vAPP(int,int,number_number_of_int,X14)))),one_one_int) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X14))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X40))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X14))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X40)),vAPP(int,int,number_number_of_int,X14)))),one_one_int) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1135_zmod__number__of__Bit1) ).
thf(f7481,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,X0)) ) ),
inference(forward_demodulation,[],[f7480,f4464]) ).
thf(f7480,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(forward_demodulation,[],[f4613,f4464]) ).
thf(f4613,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(cnf_transformation,[],[f3231]) ).
thf(f3231,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(ennf_transformation,[],[f1254]) ).
thf(f1254,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))) ) ) ),
inference(fool_elimination,[],[f1253]) ).
thf(f1253,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0)))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))) ) ),
inference(rectify,[],[f1060]) ).
thf(f1060,axiom,
! [X191: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X191))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X191)))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X191))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_number__of1) ).
thf(f7479,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,X0)) ) ),
inference(forward_demodulation,[],[f7478,f4464]) ).
thf(f7478,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(forward_demodulation,[],[f4614,f4464]) ).
thf(f4614,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(cnf_transformation,[],[f3231]) ).
thf(f6961,plain,
! [X2: int,X3: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3)),X1) = X3 )
| ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) ),
inference(equality_resolution,[],[f5853]) ).
thf(f5853,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 )
| ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) != X0 ) ),
inference(cnf_transformation,[],[f3963]) ).
thf(f3963,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 )
| ( zero_zero_int = X1 )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) )
& ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) != X0 ) ),
inference(flattening,[],[f3962]) ).
thf(f3962,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 )
| ( zero_zero_int = X1 )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) )
& ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) != X0 ) ),
inference(ennf_transformation,[],[f3185]) ).
thf(f3185,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) = X0 )
=> ( ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) = $true ) ) ) )
=> ( ( zero_zero_int != X1 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 ) ) ) ),
inference(flattening,[],[f2542]) ).
thf(f2542,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) = X0 )
=> ( ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) = $true ) ) ) )
=> ( ( zero_zero_int != X1 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 ) ) ) ),
inference(fool_elimination,[],[f2541]) ).
thf(f2541,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) = X0 )
=> ( ( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) ) ) )
=> ( ( zero_zero_int != X1 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 ) ) ) ),
inference(rectify,[],[f1172]) ).
thf(f1172,axiom,
! [X503: int,X504: int,X505: int,X17: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X504),X505)),X17) = X503 )
=> ( ( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X504)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X17),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X504),X17) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X504)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X17),X504)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X17) ) ) )
=> ( ( zero_zero_int != X504 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X503),X504) = X17 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_divmod__int__rel__mod__eq) ).
thf(f6959,plain,
! [X2: int,X3: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3)),X1) = X3 )
| ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) ),
inference(equality_resolution,[],[f5855]) ).
thf(f5855,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 )
| ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) != X0 ) ),
inference(cnf_transformation,[],[f3963]) ).
thf(f6953,plain,
! [X2: int,X0: int > $o,X6: int,X5: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6)),X0) ) ),
inference(equality_resolution,[],[f5768]) ).
thf(f5768,plain,
! [X2: int,X0: int > $o,X1: int,X6: int,X5: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f4350]) ).
thf(f4350,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( ( $true != vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK40,X2),X1),X0))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true ) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f4348,f4349]) ).
thf(f4349,plain,
! [X0: int > $o,X1: int,X2: int] :
( ? [X3: int,X4: int] :
( ( $true != vAPP(int,$o,X0,X4) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X4) ) )
=> ( ( $true != vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK40,X2),X1),X0))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4348,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( ? [X3: int,X4: int] :
( ( $true != vAPP(int,$o,X0,X4) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X4) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true ) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) ) ) ),
inference(rectify,[],[f4347]) ).
thf(f4347,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( ? [X5: int,X6: int] :
( ( $true != vAPP(int,$o,X0,X6) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true ) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) ) ) ),
inference(flattening,[],[f4346]) ).
thf(f4346,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( ? [X5: int,X6: int] :
( ( $true != vAPP(int,$o,X0,X6) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true ) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f4078]) ).
thf(f4078,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
<=> ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f6667,plain,
! [X2: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5679,f5969]) ).
thf(f5679,plain,
! [X2: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3887]) ).
thf(f3887,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3886]) ).
thf(f3886,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2412]) ).
thf(f2412,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) ) ) ) ),
inference(fool_elimination,[],[f2411]) ).
thf(f2411,plain,
! [X0: nat,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) ) ) ),
inference(rectify,[],[f339]) ).
thf(f339,axiom,
! [X199: nat,X200: int,X201: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X200),X201)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X200)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X199)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X200),X199)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X201),X199)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_power__strict__mono) ).
thf(f6585,plain,
! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(definition_unfolding,[],[f5470,f5969]) ).
thf(f5470,plain,
! [X2: int,X0: int,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(cnf_transformation,[],[f3611]) ).
thf(f3611,plain,
! [X0: int,X1: nat,X2: int] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(flattening,[],[f3610]) ).
thf(f3610,plain,
! [X0: int,X1: nat,X2: int] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) ) ),
inference(ennf_transformation,[],[f2074]) ).
thf(f2074,plain,
! [X0: int,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f2073]) ).
thf(f2073,plain,
! [X0: int,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f324]) ).
thf(f324,axiom,
! [X188: int,X189: nat,X190: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X188),X189) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X190),X189) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X188)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X190)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X189)
=> ( X188 = X190 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
thf(f6392,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(definition_unfolding,[],[f4955,f4404,f4404]) ).
thf(f4955,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) ) ),
inference(cnf_transformation,[],[f3419]) ).
thf(f3419,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) ) ),
inference(flattening,[],[f3418]) ).
thf(f3418,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) ) ),
inference(ennf_transformation,[],[f1642]) ).
thf(f1642,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(fool_elimination,[],[f1641]) ).
thf(f1641,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0)
=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f215]) ).
thf(f215,axiom,
! [X123: int,X124: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X124)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X123)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X124)),vAPP(int,nat,number_number_of_nat,X123)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X124),X123)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_semiring__mult__number__of) ).
thf(f6391,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(definition_unfolding,[],[f4954,f4404,f4404]) ).
thf(f4954,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) ) ),
inference(cnf_transformation,[],[f3417]) ).
thf(f3417,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) ) ),
inference(flattening,[],[f3416]) ).
thf(f3416,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) ) ),
inference(ennf_transformation,[],[f1640]) ).
thf(f1640,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1639]) ).
thf(f1639,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ) ),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X125: int,X126: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X126)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X125)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X126)),vAPP(int,nat,number_number_of_nat,X125)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X126),X125)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_semiring__add__number__of) ).
thf(f5939,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int,X5: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X5) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)),zero_zero_int) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) ) ),
inference(cnf_transformation,[],[f4073]) ).
thf(f4073,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X5) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)),zero_zero_int) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) ) ),
inference(flattening,[],[f4072]) ).
thf(f4072,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X5) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)),zero_zero_int) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) ) ),
inference(ennf_transformation,[],[f2664]) ).
thf(f2664,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X5) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),X1) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f2663]) ).
thf(f2663,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X5)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),X1) ) ) ) ) ) ),
inference(rectify,[],[f598]) ).
thf(f598,axiom,
! [X3: int,X307: int,X306: int,X322: int,X323: int,X324: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X307)),X306) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X322),X323)),X324) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X322),X323)),X324)),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X306),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X324)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X322)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X322),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X323),X307) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_zdiv__mono2__neg__lemma) ).
thf(f5938,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int,X5: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X5),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) ) ),
inference(cnf_transformation,[],[f4071]) ).
thf(f4071,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X5),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) ) ),
inference(flattening,[],[f4070]) ).
thf(f4070,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X5),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) ) ),
inference(ennf_transformation,[],[f2662]) ).
thf(f2662,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X5),X3) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X4) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f2661]) ).
thf(f2661,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X4)),X5))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X5),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X4) ) ) ) ) ) ),
inference(rectify,[],[f600]) ).
thf(f600,axiom,
! [X3: int,X307: int,X306: int,X322: int,X323: int,X324: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X307)),X306) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X322),X323)),X324) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X322),X323)),X324))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X324),X322)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X306)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X322)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X322),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X307),X323) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_zdiv__mono2__lemma) ).
thf(f5936,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) ) ),
inference(cnf_transformation,[],[f4067]) ).
thf(f4067,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) ) ),
inference(flattening,[],[f4066]) ).
thf(f4066,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) ) ),
inference(ennf_transformation,[],[f2658]) ).
thf(f2658,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) ) ) ) ) ),
inference(fool_elimination,[],[f2657]) ).
thf(f2657,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X4),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) ) ) ) ),
inference(rectify,[],[f601]) ).
thf(f601,axiom,
! [X3: int,X323: int,X324: int,X307: int,X306: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X323)),X324)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X307)),X306))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X324)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X324),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X306),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X323),X307) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_unique__quotient__lemma) ).
thf(f5878,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f4009]) ).
thf(f4009,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) != $true ) ),
inference(flattening,[],[f4008]) ).
thf(f4008,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2588]) ).
thf(f2588,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) ) ) ) ) ),
inference(fool_elimination,[],[f2587]) ).
thf(f2587,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) ) ) ) ),
inference(rectify,[],[f781]) ).
thf(f781,axiom,
! [X410: int,X411: int,X412: int,X413: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X412),X413)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X410),X411)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X412)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X410)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X412),X410)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X413),X411)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_mult__mono_H) ).
thf(f5877,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f4007]) ).
thf(f4007,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) != $true ) ),
inference(flattening,[],[f4006]) ).
thf(f4006,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2586]) ).
thf(f2586,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) ) ) ) ) ),
inference(fool_elimination,[],[f2585]) ).
thf(f2585,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) ) ) ) ),
inference(rectify,[],[f778]) ).
thf(f778,axiom,
! [X406: int,X407: int,X408: int,X409: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X408),X409)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X406),X407)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X409)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X406)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X408),X406)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X409),X407)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_mult__mono) ).
thf(f5860,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(cnf_transformation,[],[f3973]) ).
thf(f3973,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(flattening,[],[f3972]) ).
thf(f3972,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(ennf_transformation,[],[f2552]) ).
thf(f2552,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) ) ) ) ),
inference(fool_elimination,[],[f2551]) ).
thf(f2551,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) ) ) ),
inference(rectify,[],[f1169]) ).
thf(f1169,axiom,
! [X307: int,X3: int,X306: int,X216: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X216)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X306)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X306),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X307),X216))),X306)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X216)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_zmult2__lemma__aux4) ).
thf(f5859,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(cnf_transformation,[],[f3971]) ).
thf(f3971,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(flattening,[],[f3970]) ).
thf(f3970,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(ennf_transformation,[],[f2550]) ).
thf(f2550,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) ) ) ) ),
inference(fool_elimination,[],[f2549]) ).
thf(f2549,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) ) ) ),
inference(rectify,[],[f1168]) ).
thf(f1168,axiom,
! [X307: int,X3: int,X306: int,X216: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X216)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X306)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X306),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X307),X216))),X306)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_zmult2__lemma__aux3) ).
thf(f5722,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f3951]) ).
thf(f3951,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(flattening,[],[f3950]) ).
thf(f3950,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(ennf_transformation,[],[f2488]) ).
thf(f2488,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) ) ) ),
inference(fool_elimination,[],[f2487]) ).
thf(f2487,plain,
! [X0: int,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) ) ),
inference(rectify,[],[f375]) ).
thf(f375,axiom,
! [X219: int,X220: nat,X221: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X219),X220)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X221),X220))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X221)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X219),X221) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base) ).
thf(f5714,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3935]) ).
thf(f3935,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),zero_zero_int) ) ),
inference(flattening,[],[f3934]) ).
thf(f3934,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),zero_zero_int) ) ),
inference(ennf_transformation,[],[f2472]) ).
thf(f2472,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),zero_zero_int) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ) ) ),
inference(fool_elimination,[],[f2471]) ).
thf(f2471,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ) ),
inference(rectify,[],[f602]) ).
thf(f602,axiom,
! [X322: int,X323: int,X324: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X322),X323)),X324)),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X324)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X322)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X323),zero_zero_int) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_q__neg__lemma) ).
thf(f5674,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3878]) ).
thf(f3878,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3877]) ).
thf(f3877,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2402]) ).
thf(f2402,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2401]) ).
thf(f2401,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) ) ),
inference(rectify,[],[f794]) ).
thf(f794,axiom,
! [X426: int,X427: int,X428: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X427),X428)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X426)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X427),X426)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X428),X426)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_mult__right__mono) ).
thf(f5672,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3874]) ).
thf(f3874,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3873]) ).
thf(f3873,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2398]) ).
thf(f2398,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2397]) ).
thf(f2397,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(rectify,[],[f788]) ).
thf(f788,axiom,
! [X420: int,X421: int,X422: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X421),X422)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X420)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X420),X421)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X420),X422)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_comm__mult__left__mono) ).
thf(f5671,plain,
! [X2: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3872]) ).
thf(f3872,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3871]) ).
thf(f3871,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2396]) ).
thf(f2396,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2395]) ).
thf(f2395,plain,
! [X0: nat,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) ) ),
inference(rectify,[],[f366]) ).
thf(f366,axiom,
! [X211: nat,X212: int,X213: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X212),X213)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X212)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X212),X211)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X213),X211)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_power__mono) ).
thf(f5559,plain,
! [X2: int,X3: int,X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK29,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4303]) ).
thf(f5558,plain,
! [X2: int,X3: int,X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK28,X2),X1)),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4300]) ).
thf(f4300,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X3: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK28,X2),X1)),X2)) )
& ( $true = vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK28,X2),X1)) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f4298,f4299]) ).
thf(f4299,plain,
! [X1: int > $o,X2: int] :
( ? [X4: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),X2)) )
& ( $true = vAPP(int,$o,X1,X4) ) )
=> ( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK28,X2),X1)),X2)) )
& ( $true = vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK28,X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4298,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X3: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ? [X4: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),X2)) )
& ( $true = vAPP(int,$o,X1,X4) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(rectify,[],[f3705]) ).
thf(f3705,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X4: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X4) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) )
& ( $true = vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3704]) ).
thf(f3704,plain,
! [X0: int,X1: int > $o,X2: int] :
( ! [X4: int] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X4) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) )
& ( $true = vAPP(int,$o,X1,X3) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2190]) ).
thf(f2190,plain,
! [X0: int,X1: int > $o,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ! [X3: int] :
( ( $true = vAPP(int,$o,X1,X3) )
=> ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) ) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ! [X4: int] :
( ( $true = vAPP(int,$o,X1,X4) )
=> ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ) ) ) ) ),
inference(fool_elimination,[],[f2189]) ).
thf(f2189,plain,
! [X0: int,X1: int > $o,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ! [X3: int] :
( vAPP(int,$o,X1,X3)
=> vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ! [X4: int] :
( vAPP(int,$o,X1,X4)
=> vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ) ) ) ),
inference(rectify,[],[f1066]) ).
thf(f1066,axiom,
! [X18: int,X490: int > $o,X218: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X218)
=> ( ! [X0: int] :
( vAPP(int,$o,X490,X0)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X218)) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X18)
=> ! [X0: int] :
( vAPP(int,$o,X490,X0)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X218))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_decr__mult__lemma) ).
thf(f5557,plain,
! [X2: int,X3: int,X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) )
| ( $true != vAPP(int,$o,X1,X3) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true = vAPP(int,$o,X1,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK28,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4300]) ).
thf(f5546,plain,
! [X2: int,X0: int,X1: int] :
( ( X0 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3688]) ).
thf(f3688,plain,
! [X0: int,X1: int,X2: int] :
( ( X0 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3687]) ).
thf(f3687,plain,
! [X0: int,X1: int,X2: int] :
( ( X0 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2170]) ).
thf(f2170,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
=> ( X0 = X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f2169]) ).
thf(f2169,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1)
=> ( X0 = X2 ) ) ) ) ) ),
inference(rectify,[],[f595]) ).
thf(f595,axiom,
! [X3: int,X192: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_zcong__zless__imp__eq) ).
thf(f4994,plain,
! [X3: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0) = X3 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f4142]) ).
thf(f4142,plain,
! [X0: int,X1: int] :
( ( ! [X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0) = X3 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f3476,f4141]) ).
thf(f4141,plain,
! [X0: int,X1: int] :
( ? [X2: int] :
( ! [X3: int] :
( ( X2 = X3 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true ) )
=> ( ! [X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0) = X3 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3476,plain,
! [X0: int,X1: int] :
( ? [X2: int] :
( ! [X3: int] :
( ( X2 = X3 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3475]) ).
thf(f3475,plain,
! [X0: int,X1: int] :
( ? [X2: int] :
( ! [X3: int] :
( ( X2 = X3 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1708]) ).
thf(f1708,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ? [X2: int] :
( ! [X3: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) = $true ) )
=> ( X2 = X3 ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) = $true ) ) ),
inference(fool_elimination,[],[f1707]) ).
thf(f1707,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ? [X2: int] :
( ! [X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X3),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X3) )
=> ( X2 = X3 ) )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) ) ),
inference(rectify,[],[f1069]) ).
thf(f1069,axiom,
! [X2: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ? [X0: int] :
( ! [X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X1),X192)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X192)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) )
=> ( X0 = X1 ) )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X192)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X192)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_zcong__zless__unique) ).
thf(f4971,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3447]) ).
thf(f3447,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1674]) ).
thf(f1674,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)),X1) ) ),
inference(fool_elimination,[],[f1673]) ).
thf(f1673,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)),X1) ),
inference(rectify,[],[f1141]) ).
thf(f1141,axiom,
! [X18: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X192),X18)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_zmod__le__nonneg__dividend) ).
thf(f4969,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3445]) ).
thf(f3445,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1670]) ).
thf(f1670,plain,
! [X0: nat,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ),
inference(fool_elimination,[],[f1669]) ).
thf(f1669,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ),
inference(rectify,[],[f590]) ).
thf(f590,axiom,
! [X191: nat,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X16)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),X191)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(f4967,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3442]) ).
thf(f3442,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(flattening,[],[f3441]) ).
thf(f3441,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1666]) ).
thf(f1666,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
=> ( zero_zero_int = X1 ) ) ) ),
inference(fool_elimination,[],[f1665]) ).
thf(f1665,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0)
=> ( zero_zero_int = X1 ) ) ) ),
inference(rectify,[],[f596]) ).
thf(f596,axiom,
! [X192: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X192)
=> ( zero_zero_int = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_zcong__zless__0) ).
thf(f4966,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3440]) ).
thf(f3440,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(flattening,[],[f3439]) ).
thf(f3439,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1664]) ).
thf(f1664,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 ) ) ),
inference(fool_elimination,[],[f1663]) ).
thf(f1663,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 ) ) ),
inference(rectify,[],[f1161]) ).
thf(f1161,axiom,
! [X3: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_mod__pos__pos__trivial) ).
thf(f4961,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3430]) ).
thf(f3430,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(flattening,[],[f3429]) ).
thf(f3429,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1654]) ).
thf(f1654,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1653]) ).
thf(f1653,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ),
inference(rectify,[],[f588]) ).
thf(f588,axiom,
! [X17: int,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X17)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X16),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(f4960,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3428]) ).
thf(f3428,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(flattening,[],[f3427]) ).
thf(f3427,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1652]) ).
thf(f1652,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1651]) ).
thf(f1651,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0)) ) ),
inference(rectify,[],[f1140]) ).
thf(f1140,axiom,
! [X17: int,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X17)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(f4959,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3426]) ).
thf(f3426,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(flattening,[],[f3425]) ).
thf(f3425,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1650]) ).
thf(f1650,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
=> ( X0 = X1 ) ) ) ) ),
inference(fool_elimination,[],[f1649]) ).
thf(f1649,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1)
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f328]) ).
thf(f328,axiom,
! [X191: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X191)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X192),X191)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X191),X192)
=> ( X191 = X192 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_zdvd__antisym__nonneg) ).
thf(f4871,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3304]) ).
thf(f3304,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) )
| ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ) ) ),
inference(ennf_transformation,[],[f1502]) ).
thf(f1502,plain,
! [X0: int,X1: int] :
( ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) ) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) ) ),
inference(fool_elimination,[],[f1501]) ).
thf(f1501,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) ) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) ),
inference(rectify,[],[f773]) ).
thf(f773,axiom,
! [X402: int,X403: int] :
( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X402)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X403),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X402),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X403) ) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X403),X402)),zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_split__mult__neg__le) ).
thf(f4870,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3304]) ).
thf(f4868,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3303]) ).
thf(f3303,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) )
& ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ) ) ),
inference(ennf_transformation,[],[f1500]) ).
thf(f1500,plain,
! [X0: int,X1: int] :
( ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) )
| ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) ) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ),
inference(fool_elimination,[],[f1499]) ).
thf(f1499,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) ) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ),
inference(rectify,[],[f775]) ).
thf(f775,axiom,
! [X404: int,X405: int] :
( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X404),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X405),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X404)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X405) ) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X405),X404)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_split__mult__pos__le) ).
thf(f5770,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f4350]) ).
thf(f5346,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) ),
inference(cnf_transformation,[],[f2040]) ).
thf(f2040,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) ),
inference(fool_elimination,[],[f2039]) ).
thf(f2039,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),
inference(rectify,[],[f412]) ).
thf(f412,axiom,
! [X238: int,X239: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X238),X238)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X239),X239))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_sum__squares__ge__zero) ).
thf(f4991,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f4142]) ).
thf(f4995,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3477]) ).
thf(f3477,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1710]) ).
thf(f1710,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)) ) ),
inference(fool_elimination,[],[f1709]) ).
thf(f1709,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)) ),
inference(rectify,[],[f1197]) ).
thf(f1197,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X163),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_StandardRes__lbound) ).
thf(f4869,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3303]) ).
thf(f4977,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3455]) ).
thf(f3455,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1686]) ).
thf(f1686,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ) ) ),
inference(fool_elimination,[],[f1685]) ).
thf(f1685,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ) ),
inference(rectify,[],[f1160]) ).
thf(f1160,axiom,
! [X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3)),X3)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_pos__mod__conj) ).
thf(f7179,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,X0)) ) ),
inference(binary_proxy_clausification,[],[f6217]) ).
thf(f6217,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,X0)) ),
inference(definition_unfolding,[],[f4679,f4404,f4404]) ).
thf(f4679,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit1,X0)) ),
inference(cnf_transformation,[],[f1312]) ).
thf(f1312,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit1,X0)) ),
inference(fool_elimination,[],[f1311]) ).
thf(f1311,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit1,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit1,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rel__simps_I22_J) ).
thf(f7181,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,X0)) ) ),
inference(binary_proxy_clausification,[],[f6216]) ).
thf(f6216,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,X0)) ),
inference(definition_unfolding,[],[f4678,f4404,f4404]) ).
thf(f4678,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit0,X0)) ),
inference(cnf_transformation,[],[f1310]) ).
thf(f1310,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit0,X0)) ),
inference(fool_elimination,[],[f1309]) ).
thf(f1309,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit0,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) ),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),vAPP(int,int,bit0,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_rel__simps_I21_J) ).
thf(f7180,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,X0)) ) ),
inference(binary_proxy_clausification,[],[f6216]) ).
thf(f7178,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,X0)) ) ),
inference(binary_proxy_clausification,[],[f6217]) ).
thf(f7166,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,X0)) ) ),
inference(binary_proxy_clausification,[],[f6221]) ).
thf(f6221,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,X0)) ),
inference(definition_unfolding,[],[f4685,f4404,f4404]) ).
thf(f4685,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit1,X0)) ),
inference(cnf_transformation,[],[f1324]) ).
thf(f1324,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit1,X0)) ),
inference(fool_elimination,[],[f1323]) ).
thf(f1323,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit1,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit1,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J) ).
thf(f5292,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4267]) ).
thf(f4267,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) )
| ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ) )
& ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) ) ) ),
inference(flattening,[],[f4266]) ).
thf(f4266,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) )
| ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ) ) )
& ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) ) ) ),
inference(nnf_transformation,[],[f1974]) ).
thf(f1974,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) )
<=> ( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ) ) ),
inference(fool_elimination,[],[f1973]) ).
thf(f1973,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int)
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) ) ) ),
inference(rectify,[],[f810]) ).
thf(f810,axiom,
! [X439: int,X440: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X439),X440)),zero_zero_int)
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X440)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X439),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X440),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X439) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_mult__le__0__iff) ).
thf(f7167,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,X0)) ) ),
inference(binary_proxy_clausification,[],[f6221]) ).
thf(f6289,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4816,f4404]) ).
thf(f4816,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ),
inference(cnf_transformation,[],[f3241]) ).
thf(f3241,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) )
& ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ) ),
inference(ennf_transformation,[],[f2946]) ).
thf(f2946,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(flattening,[],[f1442]) ).
thf(f1442,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(fool_elimination,[],[f1441]) ).
thf(f1441,plain,
! [X0: int,X1: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls)
=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f568]) ).
thf(f568,axiom,
! [X39: int,X40: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),pls)
=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X40),X39)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39)) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),pls)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_mult__nat__number__of) ).
thf(f6291,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4819,f4404,f4404]) ).
thf(f4819,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ),
inference(cnf_transformation,[],[f3242]) ).
thf(f3242,plain,
! [X0: int,X1: int] :
( ( ( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ) )
& ( ( vAPP(int,nat,number_number_of_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ) ) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) )
& ( ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ) ),
inference(ennf_transformation,[],[f2947]) ).
thf(f2947,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) )
=> ( vAPP(int,nat,number_number_of_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(flattening,[],[f1444]) ).
thf(f1444,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) )
=> ( vAPP(int,nat,number_number_of_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) )
=> ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(fool_elimination,[],[f1443]) ).
thf(f1443,plain,
! [X0: int,X1: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls)
=> ( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls)
=> ( vAPP(int,nat,number_number_of_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls)
=> ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f78]) ).
thf(f78,axiom,
! [X39: int,X40: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),pls)
=> ( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X39),pls)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39)) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X40),X39)) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X39),pls)
=> ( vAPP(int,nat,number_number_of_nat,X40) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39)) ) ) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),pls)
=> ( vAPP(int,nat,number_number_of_nat,X39) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__nat__number__of) ).
thf(f5561,plain,
! [X2: int,X0: int,X1: int] :
( ( X1 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3709]) ).
thf(f3709,plain,
! [X0: int,X1: int,X2: int] :
( ( X1 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3708]) ).
thf(f3708,plain,
! [X0: int,X1: int,X2: int] :
( ( X1 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2194]) ).
thf(f2194,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X1),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( X1 = X2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f2193]) ).
thf(f2193,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X1),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ( X1 = X2 ) ) ) ) ) ) ),
inference(rectify,[],[f653]) ).
thf(f653,axiom,
! [X192: int,X17: int,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X17)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),X17),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X17),X192)
=> ( X16 = X17 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_zcong__less__eq) ).
thf(f10446,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
inference(trivial_inequality_removal,[],[f10445]) ).
thf(f10445,plain,
! [X0: int] :
( ( $true != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
inference(superposition,[],[f4889,f10437]) ).
thf(f10447,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
inference(trivial_inequality_removal,[],[f10444]) ).
thf(f10444,plain,
! [X0: int] :
( ( $true = $false )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
inference(superposition,[],[f8441,f10437]) ).
thf(f10449,plain,
! [X0: int] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(trivial_inequality_removal,[],[f10440]) ).
thf(f10440,plain,
! [X0: int] :
( ( $true = $false )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(superposition,[],[f10437,f8441]) ).
thf(f10435,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10404]) ).
thf(f10404,plain,
! [X0: int,X1: int] :
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(superposition,[],[f4829,f8441]) ).
thf(f10380,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f10379]) ).
thf(f10379,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(superposition,[],[f4820,f1202]) ).
thf(f8992,plain,
! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,bit1,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))) ) ),
inference(trivial_inequality_removal,[],[f8989]) ).
thf(f8989,plain,
! [X0: int] :
( ( $true != $true )
| ( vAPP(int,int,zfact,X0) = vAPP(int,int,bit1,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))) ) ),
inference(superposition,[],[f7461,f8441]) ).
thf(f8994,plain,
vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,zero_zero_int),
inference(trivial_inequality_removal,[],[f8987]) ).
thf(f8987,plain,
( ( $true != $true )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,zero_zero_int) ) ),
inference(superposition,[],[f7461,f4736]) ).
thf(f8976,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),zero_zero_int) = X1 ) ),
inference(superposition,[],[f8948,f8770]) ).
thf(f8975,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,zero_zero_int),X0) != X1 )
| ( X0 = X1 ) ),
inference(superposition,[],[f8948,f4756]) ).
thf(f8974,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),X0) = X1 ) ),
inference(superposition,[],[f8948,f6846]) ).
thf(f8959,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,zero_zero_int),X0) = X0 ),
inference(superposition,[],[f8921,f4756]) ).
thf(f8929,plain,
! [X0: int,X1: int > $o] :
( ( $true != vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,zero_zero_int),X0)) )
| ( $true = vAPP(int,$o,X1,X0) ) ),
inference(superposition,[],[f6954,f4756]) ).
thf(f8948,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),zero_zero_int) != X0 )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f8947]) ).
thf(f8947,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),zero_zero_int) != X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f8925]) ).
thf(f8925,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(primitive_instantiation,[],[f6954]) ).
thf(f8921,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),zero_zero_int) = X0 ),
inference(leibniz_equality_elimination,[],[f6954]) ).
thf(f8907,plain,
! [X0: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(trivial_inequality_removal,[],[f8906]) ).
thf(f8906,plain,
! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(superposition,[],[f6204,f1202]) ).
thf(f8909,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ),
inference(trivial_inequality_removal,[],[f8904]) ).
thf(f8904,plain,
! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(superposition,[],[f6204,f5339]) ).
thf(f8890,plain,
! [X0: int] :
( ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))) ) ),
inference(trivial_inequality_removal,[],[f8887]) ).
thf(f8887,plain,
! [X0: int] :
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0))) ) ),
inference(superposition,[],[f6177,f8441]) ).
thf(f8882,plain,
! [X0: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(trivial_inequality_removal,[],[f8881]) ).
thf(f8881,plain,
! [X0: nat] :
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(superposition,[],[f6155,f1202]) ).
thf(f8874,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 ) ),
inference(trivial_inequality_removal,[],[f8873]) ).
thf(f8873,plain,
! [X0: real] :
( ( $true != $true )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) ) ),
inference(superposition,[],[f6154,f1202]) ).
thf(f8863,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f8862]) ).
thf(f8862,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( X0 = X1 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) ) ),
inference(superposition,[],[f5251,f1202]) ).
thf(f8864,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1))) ) ),
inference(trivial_inequality_removal,[],[f8861]) ).
thf(f8861,plain,
! [X0: int,X1: int] :
( ( $true != $true )
| ( X0 = X1 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1))) ) ),
inference(superposition,[],[f5251,f8441]) ).
thf(f8836,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X0) ),
inference(superposition,[],[f8775,f7416]) ).
thf(f8834,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),zero_zero_int) ),
inference(superposition,[],[f8775,f4490]) ).
thf(f8830,plain,
zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,zero_zero_int),zero_zero_int),
inference(superposition,[],[f8775,f6054]) ).
thf(f8828,plain,
! [X0: int,X1: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ),
inference(superposition,[],[f8770,f4756]) ).
thf(f8795,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X0) ),
inference(equality_resolution,[],[f8789]) ).
thf(f8792,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != X0 )
| ( zero_zero_int = X1 ) ),
inference(superposition,[],[f5144,f6906]) ).
thf(f8789,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) ) ),
inference(superposition,[],[f8642,f6906]) ).
thf(f8786,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = X0 ),
inference(superposition,[],[f6906,f4757]) ).
thf(f8777,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,vAPP(int,int,bit1,zero_zero_int)),X0) ),
inference(superposition,[],[f8769,f4756]) ).
thf(f8775,plain,
! [X0: int,X1: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ),
inference(superposition,[],[f6846,f4756]) ).
thf(f8770,plain,
! [X0: int,X1: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),X0) ),
inference(superposition,[],[f6846,f4759]) ).
thf(f8769,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit1,zero_zero_int)) ),
inference(superposition,[],[f6846,f7414]) ).
thf(f8698,plain,
! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
inference(trivial_inequality_removal,[],[f8697]) ).
thf(f8697,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
inference(superposition,[],[f5326,f1202]) ).
thf(f8688,plain,
! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
inference(trivial_inequality_removal,[],[f8687]) ).
thf(f8687,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ) ),
inference(superposition,[],[f5325,f1202]) ).
thf(f8642,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) != X0 )
| ( zero_zero_int = X1 ) ),
inference(superposition,[],[f5144,f4757]) ).
thf(f8633,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,min),X0) ),
inference(superposition,[],[f4756,f7418]) ).
thf(f8608,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) != X0 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 ) ),
inference(superposition,[],[f6304,f4752]) ).
thf(f8579,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) != X0 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 ) ),
inference(superposition,[],[f6476,f4749]) ).
thf(f8533,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int),
inference(superposition,[],[f4717,f7416]) ).
thf(f8530,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int),
inference(superposition,[],[f4717,f7414]) ).
thf(f8484,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) ) ),
inference(trivial_inequality_removal,[],[f8469]) ).
thf(f8469,plain,
! [X0: int] :
( ( $true != $true )
| ( zero_zero_int = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) ) ),
inference(superposition,[],[f4607,f8441]) ).
thf(f8485,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) ) ),
inference(trivial_inequality_removal,[],[f8468]) ).
thf(f8468,plain,
! [X0: int] :
( ( $true = $false )
| ( zero_zero_int = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) ) ),
inference(superposition,[],[f8402,f8441]) ).
thf(f8492,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) )
| ( zero_zero_int = X0 ) ),
inference(trivial_inequality_removal,[],[f8461]) ).
thf(f8461,plain,
! [X0: int] :
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) )
| ( zero_zero_int = X0 ) ),
inference(superposition,[],[f8441,f8402]) ).
thf(f8444,plain,
! [X0: int,X1: int] :
( ( vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),vEQ(int),X0)) != X0 )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f8443]) ).
thf(f8443,plain,
! [X0: int,X1: int] :
( ( vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),vEQ(int),X0)) != X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f8437]) ).
thf(f8437,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),vEQ(int),X0))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) ) ),
inference(primitive_instantiation,[],[f4889]) ).
thf(f8434,plain,
! [X0: int] : ( vAPP(sTfun(int,$o),int,sK17,vAPP(sTfun(int,$o),sTfun(int,$o),vAPP(sTfun($o,$o),sTfun(sTfun(int,$o),sTfun(int,$o)),bCOMB,vNOT),vAPP(int,sTfun(int,$o),vEQ(int),X0))) = X0 ),
inference(leibniz_equality_elimination,[],[f4889]) ).
thf(f8424,plain,
! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(trivial_inequality_removal,[],[f8423]) ).
thf(f8423,plain,
! [X0: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(superposition,[],[f6239,f1202]) ).
thf(f8419,plain,
! [X0: int] :
( ( vAPP(int,int,bit0,X0) != X0 )
| ( zero_zero_int = X0 ) ),
inference(superposition,[],[f5144,f4526]) ).
thf(f8402,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0) )
| ( zero_zero_int = X0 ) ),
inference(trivial_inequality_removal,[],[f8401]) ).
thf(f8401,plain,
! [X0: int] :
( ( $true != $true )
| ( zero_zero_int = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0) ) ),
inference(superposition,[],[f4607,f1202]) ).
thf(f8368,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,X1) != X0 )
| ( X0 = X1 ) ),
inference(superposition,[],[f5084,f4464]) ).
thf(f8356,plain,
! [X0: real] : ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ),
inference(trivial_inequality_removal,[],[f8355]) ).
thf(f8355,plain,
! [X0: real] :
( ( $true != $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ) ),
inference(superposition,[],[f6873,f1202]) ).
thf(f8353,plain,
! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(trivial_inequality_removal,[],[f8352]) ).
thf(f8352,plain,
! [X0: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ) ),
inference(superposition,[],[f4714,f1202]) ).
thf(f8158,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8157,f6100]) ).
thf(f8157,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8156,f6100]) ).
thf(f8156,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8155,f4464]) ).
thf(f8155,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8154,f4464]) ).
thf(f8154,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8153,f4759]) ).
thf(f8153,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6764,f4757]) ).
thf(f6764,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5968,f4404,f4404,f4404,f5971]) ).
thf(f5968,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f2714]) ).
thf(f2714,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(fool_elimination,[],[f2713]) ).
thf(f2713,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f307]) ).
thf(f307,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(f8147,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)),
inference(forward_demodulation,[],[f8146,f4464]) ).
thf(f8146,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)),
inference(forward_demodulation,[],[f8145,f4464]) ).
thf(f8145,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)),
inference(forward_demodulation,[],[f8144,f4759]) ).
thf(f8144,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)),
inference(forward_demodulation,[],[f8143,f4757]) ).
thf(f8143,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)),
inference(forward_demodulation,[],[f8142,f6100]) ).
thf(f8142,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),min)),
inference(forward_demodulation,[],[f6763,f4464]) ).
thf(f6763,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min))),
inference(definition_unfolding,[],[f5967,f4404,f5971,f4404]) ).
thf(f5967,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min))) = $true,
inference(cnf_transformation,[],[f2712]) ).
thf(f2712,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min))) = $true,
inference(fool_elimination,[],[f2711]) ).
thf(f2711,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min))),
inference(rectify,[],[f606]) ).
thf(f606,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(f8136,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8135,f6100]) ).
thf(f8135,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8134,f4464]) ).
thf(f8134,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8133,f4464]) ).
thf(f8133,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8132,f4464]) ).
thf(f8132,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8131,f4759]) ).
thf(f8131,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6762,f4757]) ).
thf(f6762,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5966,f4404,f4404,f5971]) ).
thf(f5966,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f2710]) ).
thf(f2710,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(fool_elimination,[],[f2709]) ).
thf(f2709,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f504]) ).
thf(f504,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_s) ).
thf(f8125,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8124,f6100]) ).
thf(f8124,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8123,f4464]) ).
thf(f8123,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8122,f4464]) ).
thf(f8122,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8121,f4464]) ).
thf(f8121,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8120,f4759]) ).
thf(f8120,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6761,f4757]) ).
thf(f6761,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5965,f4404,f4404,f5971]) ).
thf(f5965,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f2708]) ).
thf(f2708,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(fool_elimination,[],[f2707]) ).
thf(f2707,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f311]) ).
thf(f311,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_s1) ).
thf(f8114,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))),
inference(forward_demodulation,[],[f8113,f4464]) ).
thf(f8113,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))),
inference(forward_demodulation,[],[f8112,f4759]) ).
thf(f8112,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))),
inference(forward_demodulation,[],[f8111,f4757]) ).
thf(f8111,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))),
inference(forward_demodulation,[],[f8110,f4464]) ).
thf(f8110,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))),
inference(forward_demodulation,[],[f8109,f6100]) ).
thf(f8109,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f6760,f4757]) ).
thf(f6760,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5964,f4404,f5971,f4404,f5971]) ).
thf(f5964,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int)) = $true,
inference(cnf_transformation,[],[f2706]) ).
thf(f2706,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int)) = $true,
inference(fool_elimination,[],[f2705]) ).
thf(f2705,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int)),
inference(rectify,[],[f290]) ).
thf(f290,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(f8103,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),min),
inference(forward_demodulation,[],[f8102,f4464]) ).
thf(f8102,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),min),
inference(forward_demodulation,[],[f8101,f4464]) ).
thf(f8101,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),min),
inference(forward_demodulation,[],[f8100,f4759]) ).
thf(f8100,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),min),
inference(forward_demodulation,[],[f8099,f4757]) ).
thf(f8099,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),min),
inference(forward_demodulation,[],[f6759,f4464]) ).
thf(f6759,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,number_number_of_int,min)),
inference(definition_unfolding,[],[f5963,f4404,f5971]) ).
thf(f5963,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)) = $true,
inference(cnf_transformation,[],[f2704]) ).
thf(f2704,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)) = $true,
inference(fool_elimination,[],[f2703]) ).
thf(f2703,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)),
inference(rectify,[],[f605]) ).
thf(f605,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(f8093,plain,
$true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8092,f4464]) ).
thf(f8092,plain,
$true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8091,f4464]) ).
thf(f8091,plain,
$true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))))),
inference(forward_demodulation,[],[f8090,f4759]) ).
thf(f8090,plain,
$true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)))),
inference(forward_demodulation,[],[f8089,f4757]) ).
thf(f8089,plain,
$true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),
inference(forward_demodulation,[],[f6758,f4759]) ).
thf(f6758,plain,
$true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t)),
inference(definition_unfolding,[],[f5962,f4404,f5971]) ).
thf(f5962,plain,
vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t)) = $true,
inference(cnf_transformation,[],[f2702]) ).
thf(f2702,plain,
vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t)) = $true,
inference(fool_elimination,[],[f2701]) ).
thf(f2701,plain,
vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t)),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(f8083,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8082,f4464]) ).
thf(f8082,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8081,f4464]) ).
thf(f8081,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8080,f4759]) ).
thf(f8080,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6757,f4757]) ).
thf(f6757,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5961,f4404,f5971]) ).
thf(f5961,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f2700]) ).
thf(f2700,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(fool_elimination,[],[f2699]) ).
thf(f2699,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f289]) ).
thf(f289,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_p0) ).
thf(f8074,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8073,f4464]) ).
thf(f8073,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8072,f4464]) ).
thf(f8072,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8071,f4759]) ).
thf(f8071,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6756,f4757]) ).
thf(f6756,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5960,f4404,f5971]) ).
thf(f5960,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f2698]) ).
thf(f2698,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(fool_elimination,[],[f2697]) ).
thf(f2697,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(f8065,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8064,f4464]) ).
thf(f8064,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f8063,f4464]) ).
thf(f8063,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f8062,f4759]) ).
thf(f8062,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6755,f4757]) ).
thf(f6755,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5959,f4404,f5971]) ).
thf(f5959,plain,
vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f2696]) ).
thf(f2696,plain,
vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(fool_elimination,[],[f2695]) ).
thf(f2695,plain,
vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_p) ).
thf(f8056,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),
inference(forward_demodulation,[],[f6754,f4464]) ).
thf(f6754,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5958,f4404]) ).
thf(f5958,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = $true,
inference(cnf_transformation,[],[f2694]) ).
thf(f2694,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = $true,
inference(fool_elimination,[],[f2693]) ).
thf(f2693,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),
inference(rectify,[],[f597]) ).
thf(f597,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(f8050,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),
inference(forward_demodulation,[],[f6753,f4464]) ).
thf(f6753,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5957,f4404]) ).
thf(f5957,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = $true,
inference(cnf_transformation,[],[f2692]) ).
thf(f2692,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = $true,
inference(fool_elimination,[],[f2691]) ).
thf(f2691,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(rectify,[],[f512]) ).
thf(f512,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(f6752,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5956,f5969,f4404]) ).
thf(f5956,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = $true,
inference(cnf_transformation,[],[f2690]) ).
thf(f2690,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = $true,
inference(fool_elimination,[],[f2689]) ).
thf(f2689,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(rectify,[],[f566]) ).
thf(f566,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_pos2) ).
thf(f8039,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),
inference(forward_demodulation,[],[f6751,f4464]) ).
thf(f6751,plain,
$true = vAPP(int,$o,zprime,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5955,f4404]) ).
thf(f5955,plain,
vAPP(int,$o,zprime,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = $true,
inference(cnf_transformation,[],[f2688]) ).
thf(f2688,plain,
vAPP(int,$o,zprime,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = $true,
inference(fool_elimination,[],[f2687]) ).
thf(f2687,plain,
vAPP(int,$o,zprime,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
vAPP(int,$o,zprime,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zprime__2) ).
thf(f8032,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,zero_zero_int)),
inference(forward_demodulation,[],[f6749,f4464]) ).
thf(f6749,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f5953,f5971]) ).
thf(f5953,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int) = $true,
inference(cnf_transformation,[],[f2684]) ).
thf(f2684,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int) = $true,
inference(fool_elimination,[],[f2683]) ).
thf(f2683,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int),
inference(rectify,[],[f403]) ).
thf(f403,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_int__0__less__1) ).
thf(f5952,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),zero_zero_int) = $true,
inference(cnf_transformation,[],[f2682]) ).
thf(f2682,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),zero_zero_int) = $true,
inference(fool_elimination,[],[f2681]) ).
thf(f2681,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),zero_zero_int),
inference(rectify,[],[f534]) ).
thf(f534,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_bin__less__0__simps_I2_J) ).
thf(f6748,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),zero_zero_int) = $true,
inference(definition_unfolding,[],[f5951,f4404]) ).
thf(f5951,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),pls) = $true,
inference(cnf_transformation,[],[f2680]) ).
thf(f2680,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),pls) = $true,
inference(fool_elimination,[],[f2679]) ).
thf(f2679,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),pls),
inference(rectify,[],[f532]) ).
thf(f532,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_rel__simps_I6_J) ).
thf(f8020,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,zero_zero_int)),
inference(forward_demodulation,[],[f6747,f4464]) ).
thf(f6747,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f5949,f5971]) ).
thf(f5949,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),one_one_int) = $true,
inference(cnf_transformation,[],[f2676]) ).
thf(f2676,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),one_one_int) = $true,
inference(fool_elimination,[],[f2675]) ).
thf(f2675,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),one_one_int),
inference(rectify,[],[f586]) ).
thf(f586,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(f8014,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),t),
inference(forward_demodulation,[],[f6745,f4464]) ).
thf(f6745,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t),
inference(definition_unfolding,[],[f5947,f5971]) ).
thf(f5947,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),t) = $true,
inference(cnf_transformation,[],[f2672]) ).
thf(f2672,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),t) = $true,
inference(fool_elimination,[],[f2671]) ).
thf(f2671,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),t),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(f6744,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),zero_zero_int),
inference(definition_unfolding,[],[f5946,f4404]) ).
thf(f5946,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),pls) = $true,
inference(cnf_transformation,[],[f2670]) ).
thf(f2670,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),pls) = $true,
inference(fool_elimination,[],[f2669]) ).
thf(f2669,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),pls),
inference(rectify,[],[f538]) ).
thf(f538,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_rel__simps_I23_J) ).
thf(f5941,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK43),
inference(cnf_transformation,[],[f4392]) ).
thf(f4392,plain,
( ! [X1: int] :
( ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK43) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f4075,f4391]) ).
thf(f4391,plain,
( ? [X0: int] :
( ! [X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
=> ( ! [X1: int] :
( ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK43) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4075,plain,
? [X0: int] :
( ! [X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(flattening,[],[f4074]) ).
thf(f4074,plain,
? [X0: int] :
( ! [X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(ennf_transformation,[],[f2666]) ).
thf(f2666,plain,
? [X0: int] :
( ! [X1: int] :
( ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true ) )
=> ( X0 = X1 ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(fool_elimination,[],[f2665]) ).
thf(f2665,plain,
? [X0: int] :
( ! [X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) )
=> ( X0 = X1 ) )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) ),
inference(rectify,[],[f309]) ).
thf(f309,axiom,
? [X0: int] :
( ! [X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) )
=> ( X0 = X1 ) )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).
thf(f7998,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f7997,f4464]) ).
thf(f7997,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f7996,f4464]) ).
thf(f7996,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f7995,f4759]) ).
thf(f7995,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6743,f4757]) ).
thf(f6743,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5942,f4404,f5971]) ).
thf(f5942,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(cnf_transformation,[],[f4392]) ).
thf(f7989,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f7988,f4464]) ).
thf(f7988,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f7987,f4464]) ).
thf(f7987,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),
inference(forward_demodulation,[],[f7986,f4759]) ).
thf(f7986,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),
inference(forward_demodulation,[],[f6742,f4757]) ).
thf(f6742,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f5943,f4404,f5971]) ).
thf(f5943,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(cnf_transformation,[],[f4392]) ).
thf(f7985,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7984,f4464]) ).
thf(f7984,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7983,f4464]) ).
thf(f7983,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7982,f4759]) ).
thf(f7982,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7981,f4757]) ).
thf(f7981,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( sK43 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7980,f4464]) ).
thf(f7980,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( sK43 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7979,f4464]) ).
thf(f7979,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ( sK43 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7978,f4759]) ).
thf(f7978,plain,
! [X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ( sK43 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f6741,f4757]) ).
thf(f6741,plain,
! [X1: int] :
( ( sK43 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(definition_unfolding,[],[f5944,f4404,f5971,f4404,f5971]) ).
thf(f5944,plain,
! [X1: int] :
( ( sK43 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f4392]) ).
thf(f5940,plain,
! [X2: int,X3: int,X0: int,X1: int,X6: int,X4: int,X5: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2))),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X5))),X6)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X6))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X5),X6)))) ),
inference(cnf_transformation,[],[f3201]) ).
thf(f3201,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int,X5: int,X6: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2))),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X4),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X5))),X6)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X6))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X5),X6)))) ),
inference(rectify,[],[f629]) ).
thf(f629,axiom,
! [X2: int,X306: int,X3: int,X192: int,X216: int,X218: int,X191: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X306),X3))),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X216),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X306),X218))),X191)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X216),X191))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X306),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X218),X191)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_xzgcda__linear__aux1) ).
thf(f5937,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) ) ),
inference(cnf_transformation,[],[f4069]) ).
thf(f4069,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) ) ),
inference(flattening,[],[f4068]) ).
thf(f4068,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) ) ),
inference(ennf_transformation,[],[f2660]) ).
thf(f2660,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X4) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X1) ) ) ) ) ),
inference(fool_elimination,[],[f2659]) ).
thf(f2659,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),X4))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X1) ) ) ) ),
inference(rectify,[],[f599]) ).
thf(f599,axiom,
! [X3: int,X323: int,X324: int,X307: int,X306: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X323)),X324)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X307)),X306))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X306),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X306)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X324)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X307),X323) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_unique__quotient__lemma__neg) ).
thf(f6982,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),X4) ) ),
inference(binary_proxy_clausification,[],[f5935]) ).
thf(f5935,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X4) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(cnf_transformation,[],[f4065]) ).
thf(f4065,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X4) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(ennf_transformation,[],[f2656]) ).
thf(f2656,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X4) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),X4) ) ),
inference(fool_elimination,[],[f2655]) ).
thf(f2655,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X4)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),X4) ) ),
inference(rectify,[],[f646]) ).
thf(f646,axiom,
! [X216: int,X218: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X218),X2)),X192)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X218),X3)),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_zcong__zmult__prop2) ).
thf(f6981,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),X4) ) ),
inference(binary_proxy_clausification,[],[f5935]) ).
thf(f6984,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) ) ),
inference(binary_proxy_clausification,[],[f5934]) ).
thf(f5934,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X4) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(cnf_transformation,[],[f4064]) ).
thf(f4064,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X4) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(ennf_transformation,[],[f2654]) ).
thf(f2654,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X4) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) ) ),
inference(fool_elimination,[],[f2653]) ).
thf(f2653,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X4)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) ) ),
inference(rectify,[],[f645]) ).
thf(f645,axiom,
! [X216: int,X218: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X218)),X192)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X218)),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_zcong__zmult__prop1) ).
thf(f6983,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) ) ),
inference(binary_proxy_clausification,[],[f5934]) ).
thf(f5933,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(cnf_transformation,[],[f4063]) ).
thf(f4063,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(flattening,[],[f4062]) ).
thf(f4062,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(ennf_transformation,[],[f2652]) ).
thf(f2652,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) ) ) ),
inference(fool_elimination,[],[f2651]) ).
thf(f2651,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)),X4) ) ),
inference(rectify,[],[f576]) ).
thf(f576,axiom,
! [X216: int,X218: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),X218),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X216)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X218)),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_zcong__zmult) ).
thf(f5932,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(cnf_transformation,[],[f4061]) ).
thf(f4061,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(flattening,[],[f4060]) ).
thf(f4060,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(ennf_transformation,[],[f2650]) ).
thf(f2650,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)),X4) ) ) ),
inference(fool_elimination,[],[f2649]) ).
thf(f2649,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)),X4) ) ),
inference(rectify,[],[f580]) ).
thf(f580,axiom,
! [X216: int,X218: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),X218),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X216)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X218)),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_zcong__zadd) ).
thf(f5931,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(cnf_transformation,[],[f4059]) ).
thf(f4059,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(flattening,[],[f4058]) ).
thf(f4058,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) ) ),
inference(ennf_transformation,[],[f2648]) ).
thf(f2648,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)),X4) ) ) ),
inference(fool_elimination,[],[f2647]) ).
thf(f2647,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X4)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)),X4) ) ),
inference(rectify,[],[f619]) ).
thf(f619,axiom,
! [X216: int,X218: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X216),X218),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X216)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X218)),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_zcong__zdiff) ).
thf(f7977,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4) ) ),
inference(forward_demodulation,[],[f6740,f4464]) ).
thf(f6740,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4) ) ),
inference(definition_unfolding,[],[f5929,f5971]) ).
thf(f5929,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4) ) ),
inference(cnf_transformation,[],[f4055]) ).
thf(f4055,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4) ) ),
inference(flattening,[],[f4054]) ).
thf(f4054,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4) ) ),
inference(ennf_transformation,[],[f2644]) ).
thf(f2644,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) ) ) ) ) ) ),
inference(fool_elimination,[],[f2643]) ).
thf(f2643,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))),X4) ) ) ) ) ),
inference(rectify,[],[f672]) ).
thf(f672,axiom,
! [X338: int,X339: int,X340: int,X341: int,X342: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X341),X342)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X340),X342)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X339)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X338)
=> ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X339),X338) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X339),X341)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X338),X340))),X342) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_convex__bound__lt) ).
thf(f7976,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4)),X2))) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) ) ),
inference(forward_demodulation,[],[f6986,f5385]) ).
thf(f6986,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4))),X2)) ) ),
inference(binary_proxy_clausification,[],[f5928]) ).
thf(f5928,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4))),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) ) ),
inference(cnf_transformation,[],[f4053]) ).
thf(f4053,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4))),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) ) ),
inference(ennf_transformation,[],[f2642]) ).
thf(f2642,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4))),X2)) ) ),
inference(fool_elimination,[],[f2641]) ).
thf(f2641,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4))),X2)) ) ),
inference(rectify,[],[f374]) ).
thf(f374,axiom,
! [X216: int,X16: int,X217: int,X2: int,X218: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X218)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X16),X217))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X16),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X216),X218))),X217)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_zdvd__period) ).
thf(f7975,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4)),X2))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) ) ),
inference(forward_demodulation,[],[f6985,f5385]) ).
thf(f6985,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X4) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X4))),X2)) ) ),
inference(binary_proxy_clausification,[],[f5928]) ).
thf(f6988,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(binary_proxy_clausification,[],[f5927]) ).
thf(f5927,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4052]) ).
thf(f4052,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2640]) ).
thf(f2640,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(fool_elimination,[],[f2639]) ).
thf(f2639,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(rectify,[],[f1059]) ).
thf(f1059,axiom,
! [X494: nat,X192: nat,X191: nat,X20: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),X19)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),X20)),X494)),X192)),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_nat__less__add__iff1) ).
thf(f6987,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(binary_proxy_clausification,[],[f5927]) ).
thf(f6990,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(binary_proxy_clausification,[],[f5926]) ).
thf(f5926,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4051]) ).
thf(f4051,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2638]) ).
thf(f2638,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(fool_elimination,[],[f2637]) ).
thf(f2637,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(rectify,[],[f1045]) ).
thf(f1045,axiom,
! [X494: nat,X192: nat,X191: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X19)),X494)),X191)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_nat__less__add__iff2) ).
thf(f6989,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(binary_proxy_clausification,[],[f5926]) ).
thf(f6992,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(binary_proxy_clausification,[],[f5925]) ).
thf(f5925,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4050]) ).
thf(f4050,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2636]) ).
thf(f2636,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(fool_elimination,[],[f2635]) ).
thf(f2635,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(rectify,[],[f1053]) ).
thf(f1053,axiom,
! [X494: nat,X192: nat,X191: nat,X20: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),X19)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),X20)),X494)),X192)),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_nat__le__add__iff1) ).
thf(f6991,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(binary_proxy_clausification,[],[f5925]) ).
thf(f6994,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(binary_proxy_clausification,[],[f5924]) ).
thf(f5924,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4049]) ).
thf(f4049,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2634]) ).
thf(f2634,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(fool_elimination,[],[f2633]) ).
thf(f2633,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(rectify,[],[f1056]) ).
thf(f1056,axiom,
! [X494: nat,X192: nat,X191: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X19)),X494)),X191)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_nat__le__add__iff2) ).
thf(f6993,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(binary_proxy_clausification,[],[f5924]) ).
thf(f5920,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4389]) ).
thf(f4389,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) != X1 ) )
& ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(nnf_transformation,[],[f4047]) ).
thf(f4047,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) )
<=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2630]) ).
thf(f2630,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) )
<=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) = X1 ) ) ),
inference(fool_elimination,[],[f2629]) ).
thf(f2629,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) )
<=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) = X1 ) ) ),
inference(rectify,[],[f1058]) ).
thf(f1058,axiom,
! [X494: nat,X192: nat,X191: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191) )
<=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X19)),X494)),X191) = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_nat__eq__add__iff2) ).
thf(f6978,plain,
! [X2: nat,X3: nat,X0: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(equality_resolution,[],[f5921]) ).
thf(f5921,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4389]) ).
thf(f5919,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4046]) ).
thf(f4046,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2628]) ).
thf(f2628,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(fool_elimination,[],[f2627]) ).
thf(f2627,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X1)),X2) ) ),
inference(rectify,[],[f1054]) ).
thf(f1054,axiom,
! [X494: nat,X192: nat,X191: nat,X20: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),X19)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),X20)),X494)),X192)),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_nat__diff__add__eq1) ).
thf(f5918,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(cnf_transformation,[],[f4045]) ).
thf(f4045,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ),
inference(ennf_transformation,[],[f2626]) ).
thf(f2626,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(fool_elimination,[],[f2625]) ).
thf(f2625,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X4),X3)),X0)),X2)) ) ),
inference(rectify,[],[f1057]) ).
thf(f1057,axiom,
! [X494: nat,X192: nat,X191: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X494)),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X494)),X191)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X19)),X494)),X191)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_nat__diff__add__eq2) ).
thf(f6739,plain,
! [X2: real,X3: real,X0: real,X1: real,X4: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))),X4) )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) != vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X4) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X3),X4) ) ),
inference(definition_unfolding,[],[f5917,f5973,f5970,f5970]) ).
thf(f5917,plain,
! [X2: real,X3: real,X0: real,X1: real,X4: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))),X4) )
| ( one_one_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X4) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X3),X4) ) ),
inference(cnf_transformation,[],[f4044]) ).
thf(f4044,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))),X4) )
| ( one_one_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X4) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X3),X4) ) ),
inference(flattening,[],[f4043]) ).
thf(f4043,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))),X4) )
| ( one_one_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X4) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X3),X4) ) ),
inference(ennf_transformation,[],[f2624]) ).
thf(f2624,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X3),X4) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X4) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( ( one_one_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))),X4) ) ) ) ) ) ),
inference(fool_elimination,[],[f2623]) ).
thf(f2623,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X3),X4)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X4)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( ( one_one_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))),X4) ) ) ) ) ),
inference(rectify,[],[f671]) ).
thf(f671,axiom,
! [X338: real,X339: real,X340: real,X341: real,X342: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X341),X342)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X340),X342)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X339)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X338)
=> ( ( one_one_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X339),X338) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X339),X341)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X338),X340))),X342) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_convex__bound__lt) ).
thf(f6977,plain,
! [X3: int,X0: int,X1: int,X4: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X1)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X0)) )
| ( X0 = X1 )
| ( zero_zero_int = X4 ) ),
inference(equality_resolution,[],[f5916]) ).
thf(f5916,plain,
! [X2: int,X3: int,X0: int,X1: int,X4: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X0)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_int = X4 ) ),
inference(cnf_transformation,[],[f4042]) ).
thf(f4042,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X0)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_int = X4 ) ),
inference(flattening,[],[f4041]) ).
thf(f4041,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X0)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_int = X4 ) ),
inference(ennf_transformation,[],[f3200]) ).
thf(f3200,plain,
! [X0: int,X1: int,X2: int,X3: int,X4: int] :
( ( zero_zero_int != X4 )
=> ( ( ( X0 != X1 )
& ( X2 = X3 ) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X0)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X4),X1)) ) ) ),
inference(rectify,[],[f388]) ).
thf(f388,axiom,
! [X231: int,X232: int,X233: int,X234: int,X235: int] :
( ( zero_zero_int != X235 )
=> ( ( ( X231 != X232 )
& ( X233 = X234 ) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X233),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X235),X231)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X234),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X235),X232)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq) ).
thf(f6976,plain,
! [X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X1)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)) )
| ( X0 = X1 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X4 ) ),
inference(equality_resolution,[],[f6738]) ).
thf(f6738,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X4 ) ),
inference(definition_unfolding,[],[f5915,f5969]) ).
thf(f5915,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_nat = X4 ) ),
inference(cnf_transformation,[],[f4040]) ).
thf(f4040,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_nat = X4 ) ),
inference(flattening,[],[f4039]) ).
thf(f4039,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_nat = X4 ) ),
inference(ennf_transformation,[],[f3199]) ).
thf(f3199,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat,X4: nat] :
( ( zero_zero_nat != X4 )
=> ( ( ( X0 != X1 )
& ( X2 = X3 ) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X0)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X4),X1)) ) ) ),
inference(rectify,[],[f389]) ).
thf(f389,axiom,
! [X231: nat,X232: nat,X233: nat,X234: nat,X235: nat] :
( ( zero_zero_nat != X235 )
=> ( ( ( X231 != X232 )
& ( X233 = X234 ) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X233),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X235),X231)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X234),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X235),X232)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_add__scale__eq__noteq) ).
thf(f6975,plain,
! [X3: real,X0: real,X1: real,X4: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X1)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X0)) )
| ( X0 = X1 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X4 ) ),
inference(equality_resolution,[],[f6737]) ).
thf(f6737,plain,
! [X2: real,X3: real,X0: real,X1: real,X4: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X0)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X4 ) ),
inference(definition_unfolding,[],[f5914,f5970]) ).
thf(f5914,plain,
! [X2: real,X3: real,X0: real,X1: real,X4: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X0)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_real = X4 ) ),
inference(cnf_transformation,[],[f4038]) ).
thf(f4038,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X0)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_real = X4 ) ),
inference(flattening,[],[f4037]) ).
thf(f4037,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X0)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X1)) )
| ( X0 = X1 )
| ( X2 != X3 )
| ( zero_zero_real = X4 ) ),
inference(ennf_transformation,[],[f3198]) ).
thf(f3198,plain,
! [X0: real,X1: real,X2: real,X3: real,X4: real] :
( ( zero_zero_real != X4 )
=> ( ( ( X0 != X1 )
& ( X2 = X3 ) )
=> ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X0)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X3),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X4),X1)) ) ) ),
inference(rectify,[],[f390]) ).
thf(f390,axiom,
! [X231: real,X232: real,X233: real,X234: real,X235: real] :
( ( zero_zero_real != X235 )
=> ( ( ( X231 != X232 )
& ( X233 = X234 ) )
=> ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X233),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X235),X231)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X234),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X235),X232)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_add__scale__eq__noteq) ).
thf(f5902,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f4382]) ).
thf(f4382,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ) ),
inference(flattening,[],[f4381]) ).
thf(f4381,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f3194]) ).
thf(f3194,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) ),
inference(rectify,[],[f171]) ).
thf(f171,axiom,
! [X101: int,X102: int,X103: int,X104: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X101),X102)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X103),X104)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X101),X104)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X103),X102)) )
<=> ( ( X102 = X104 )
| ( X101 = X103 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_crossproduct__eq) ).
thf(f5899,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f4380]) ).
thf(f4380,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(flattening,[],[f4379]) ).
thf(f4379,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f3193]) ).
thf(f3193,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) ),
inference(rectify,[],[f172]) ).
thf(f172,axiom,
! [X101: nat,X102: nat,X103: nat,X104: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X101),X102)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X103),X104)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X101),X104)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X103),X102)) )
<=> ( ( X102 = X104 )
| ( X101 = X103 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_crossproduct__eq) ).
thf(f5896,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f4378]) ).
thf(f4378,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ) ),
inference(flattening,[],[f4377]) ).
thf(f4377,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f3192]) ).
thf(f3192,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) ),
inference(rectify,[],[f173]) ).
thf(f173,axiom,
! [X101: real,X102: real,X103: real,X104: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X101),X102)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X103),X104)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X101),X104)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X103),X102)) )
<=> ( ( X102 = X104 )
| ( X101 = X103 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_crossproduct__eq) ).
thf(f7973,plain,
! [X2: nat,X3: int,X0: nat,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),vAPP(int,int,bit1,zero_zero_int)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),vAPP(int,int,bit1,zero_zero_int)),X3) ) ),
inference(forward_demodulation,[],[f7972,f4464]) ).
thf(f7972,plain,
! [X2: nat,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),vAPP(int,int,bit1,zero_zero_int)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X3) ) ),
inference(forward_demodulation,[],[f6736,f4464]) ).
thf(f6736,plain,
! [X2: nat,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X3) ) ),
inference(definition_unfolding,[],[f5893,f5971,f5971]) ).
thf(f5893,plain,
! [X2: nat,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),one_one_int),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),one_one_int),X3) ) ),
inference(cnf_transformation,[],[f4034]) ).
thf(f4034,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),one_one_int),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),one_one_int),X3) ) ),
inference(ennf_transformation,[],[f2618]) ).
thf(f2618,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),one_one_int),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),one_one_int),X3) ) ),
inference(fool_elimination,[],[f2617]) ).
thf(f2617,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),one_one_int),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0))),one_one_int),X3) ),
inference(rectify,[],[f372]) ).
thf(f372,axiom,
! [X15: nat,X16: int,X17: nat,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),X17)),one_one_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X17),X15))),one_one_int),X163) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_zcong__zpower__zmult) ).
thf(f7971,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(forward_demodulation,[],[f6735,f4464]) ).
thf(f6735,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(definition_unfolding,[],[f5892,f4404]) ).
thf(f5892,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(cnf_transformation,[],[f4033]) ).
thf(f4033,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(flattening,[],[f4032]) ).
thf(f4032,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(ennf_transformation,[],[f2616]) ).
thf(f2616,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) ) ) ),
inference(fool_elimination,[],[f2615]) ).
thf(f2615,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) ) ),
inference(rectify,[],[f1084]) ).
thf(f1084,axiom,
! [X2: int,X20: int,X18: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),X18),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X18))),X163) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_MultInv__zcong__prop1) ).
thf(f7970,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(forward_demodulation,[],[f7969,f4464]) ).
thf(f7969,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(forward_demodulation,[],[f7968,f5386]) ).
thf(f7968,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(forward_demodulation,[],[f6734,f5387]) ).
thf(f6734,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(definition_unfolding,[],[f5891,f4404]) ).
thf(f5891,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(cnf_transformation,[],[f4031]) ).
thf(f4031,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(flattening,[],[f4030]) ).
thf(f4030,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(ennf_transformation,[],[f3191]) ).
thf(f3191,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) ) ) ) ) ),
inference(flattening,[],[f2614]) ).
thf(f2614,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) ) ) ) ) ),
inference(fool_elimination,[],[f2613]) ).
thf(f2613,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3)
=> ( vAPP(int,$o,zprime,X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X2)),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)),X1)),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) ) ) ) ),
inference(rectify,[],[f1089]) ).
thf(f1089,axiom,
! [X18: int,X2: int,X20: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),zero_zero_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20)),X20)),X18)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20)),X2)),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X18),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20))),X163) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_aux______4) ).
thf(f7967,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(forward_demodulation,[],[f7966,f4464]) ).
thf(f7966,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2)))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(forward_demodulation,[],[f6733,f4759]) ).
thf(f6733,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(definition_unfolding,[],[f5890,f4404]) ).
thf(f5890,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(cnf_transformation,[],[f4029]) ).
thf(f4029,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(flattening,[],[f4028]) ).
thf(f4028,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(ennf_transformation,[],[f3190]) ).
thf(f3190,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) ) ) ) ) ),
inference(flattening,[],[f2612]) ).
thf(f2612,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) ) ) ) ) ),
inference(fool_elimination,[],[f2611]) ).
thf(f2611,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3)
=> ( vAPP(int,$o,zprime,X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X2)),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1),X3) ) ) ) ),
inference(rectify,[],[f1090]) ).
thf(f1090,axiom,
! [X20: int,X2: int,X18: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X18),zero_zero_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X20),X18)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X18))),X18)),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X20),X18)),X2),X163) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_aux______2) ).
thf(f7965,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(forward_demodulation,[],[f6732,f4464]) ).
thf(f6732,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(definition_unfolding,[],[f5889,f4404]) ).
thf(f5889,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(cnf_transformation,[],[f4027]) ).
thf(f4027,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(flattening,[],[f4026]) ).
thf(f4026,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(ennf_transformation,[],[f3189]) ).
thf(f3189,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) ) ) ) ) ) ),
inference(flattening,[],[f2610]) ).
thf(f2610,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) ) ) ) ) ) ),
inference(fool_elimination,[],[f2609]) ).
thf(f2609,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3)
=> ( vAPP(int,$o,zprime,X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X2))),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) ) ) ) ) ),
inference(rectify,[],[f1091]) ).
thf(f1091,axiom,
! [X2: int,X20: int,X18: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X18),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),zero_zero_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X18))),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X18),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20))),X163) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_MultInv__zcong__prop2) ).
thf(f7964,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(forward_demodulation,[],[f6731,f4464]) ).
thf(f6731,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X3) ) ),
inference(definition_unfolding,[],[f5888,f4404]) ).
thf(f5888,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(cnf_transformation,[],[f4025]) ).
thf(f4025,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(flattening,[],[f4024]) ).
thf(f4024,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
| ( $true != vAPP(int,$o,zprime,X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) ) ),
inference(ennf_transformation,[],[f3188]) ).
thf(f3188,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) ) ) ) ) ) ) ),
inference(flattening,[],[f2608]) ).
thf(f2608,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3) )
=> ( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f2607]) ).
thf(f2607,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3)
=> ( vAPP(int,$o,zprime,X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X3),X1))),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X3) ) ) ) ) ) ),
inference(rectify,[],[f1092]) ).
thf(f1092,axiom,
! [X20: int,X18: int,X2: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X18),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),zero_zero_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X18))),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),X18),X163) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_MultInv__zcong__prop3) ).
thf(f5887,plain,
! [X2: nat,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X3) ) ),
inference(cnf_transformation,[],[f4023]) ).
thf(f4023,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X3) ) ),
inference(flattening,[],[f4022]) ).
thf(f4022,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X3) ) ),
inference(ennf_transformation,[],[f2606]) ).
thf(f2606,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),X3) ) ) ),
inference(fool_elimination,[],[f2605]) ).
thf(f2605,plain,
! [X0: nat,X1: int,X2: nat,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),X3) ) ),
inference(rectify,[],[f322]) ).
thf(f322,axiom,
! [X184: nat,X185: int,X186: nat,X187: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X185),X186)),X187)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X184),X186)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X185),X184)),X187) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_power__le__dvd) ).
thf(f5886,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)),X3) ) ),
inference(cnf_transformation,[],[f4021]) ).
thf(f4021,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)),X3) ) ),
inference(flattening,[],[f4020]) ).
thf(f4020,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)),X3) ) ),
inference(ennf_transformation,[],[f2604]) ).
thf(f2604,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),X3) ) ) ),
inference(fool_elimination,[],[f2603]) ).
thf(f2603,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),X3) ) ),
inference(rectify,[],[f323]) ).
thf(f323,axiom,
! [X184: nat,X185: nat,X186: nat,X187: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X185),X186)),X187)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X184),X186)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X185),X184)),X187) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_power__le__dvd) ).
thf(f5885,plain,
! [X2: nat,X3: real,X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)),X3) ) ),
inference(cnf_transformation,[],[f4019]) ).
thf(f4019,plain,
! [X0: nat,X1: real,X2: nat,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)),X3) ) ),
inference(flattening,[],[f4018]) ).
thf(f4018,plain,
! [X0: nat,X1: real,X2: nat,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)),X3) ) ),
inference(ennf_transformation,[],[f2602]) ).
thf(f2602,plain,
! [X0: nat,X1: real,X2: nat,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),X3) ) ) ),
inference(fool_elimination,[],[f2601]) ).
thf(f2601,plain,
! [X0: nat,X1: real,X2: nat,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),X3) ) ),
inference(rectify,[],[f321]) ).
thf(f321,axiom,
! [X184: nat,X185: real,X186: nat,X187: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X185),X186)),X187)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X184),X186)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X185),X184)),X187) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_power__le__dvd) ).
thf(f5884,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(cnf_transformation,[],[f4017]) ).
thf(f4017,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(ennf_transformation,[],[f2600]) ).
thf(f2600,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X3) ) ),
inference(fool_elimination,[],[f2599]) ).
thf(f2599,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X3) ),
inference(rectify,[],[f577]) ).
thf(f577,axiom,
! [X18: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X3)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_zcong__scalar2) ).
thf(f5883,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(cnf_transformation,[],[f4016]) ).
thf(f4016,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(ennf_transformation,[],[f2598]) ).
thf(f2598,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),X3) ) ),
inference(fool_elimination,[],[f2597]) ).
thf(f2597,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),X3) ),
inference(rectify,[],[f578]) ).
thf(f578,axiom,
! [X18: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X18)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X18)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_zcong__scalar) ).
thf(f5882,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(cnf_transformation,[],[f4015]) ).
thf(f4015,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(ennf_transformation,[],[f2596]) ).
thf(f2596,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),X3) ) ),
inference(fool_elimination,[],[f2595]) ).
thf(f2595,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),X3) ),
inference(rectify,[],[f647]) ).
thf(f647,axiom,
! [X216: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X216)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X216)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_zcong__shift) ).
thf(f5881,plain,
! [X2: int,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(cnf_transformation,[],[f4014]) ).
thf(f4014,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(ennf_transformation,[],[f2594]) ).
thf(f2594,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),X3) ) ),
inference(fool_elimination,[],[f2593]) ).
thf(f2593,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),X3) ),
inference(rectify,[],[f648]) ).
thf(f648,axiom,
! [X15: nat,X16: int,X17: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),X17),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),X15)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X17),X15)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_zcong__zpower) ).
thf(f5880,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(cnf_transformation,[],[f4013]) ).
thf(f4013,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(flattening,[],[f4012]) ).
thf(f4012,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X3) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) ) ),
inference(ennf_transformation,[],[f2592]) ).
thf(f2592,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X3) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X3) ) ) ),
inference(fool_elimination,[],[f2591]) ).
thf(f2591,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X2),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X3)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X3) ) ),
inference(rectify,[],[f565]) ).
thf(f565,axiom,
! [X216: int,X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X3),X216),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X216),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_zcong__trans) ).
thf(f5879,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f4011]) ).
thf(f4011,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3) != $true ) ),
inference(flattening,[],[f4010]) ).
thf(f4010,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2590]) ).
thf(f2590,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2589]) ).
thf(f2589,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
! [X31: int,X15: int,X32: int,X14: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X32),X14)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X31),X15)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X32),X31)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X14),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_zadd__zless__mono) ).
thf(f5876,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f4005]) ).
thf(f4005,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) != $true ) ),
inference(flattening,[],[f4004]) ).
thf(f4004,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2584]) ).
thf(f2584,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2583]) ).
thf(f2583,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X1)) ) ),
inference(rectify,[],[f741]) ).
thf(f741,axiom,
! [X381: int,X382: int,X383: int,X384: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X383),X384)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X381),X382)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X383),X381)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X384),X382)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_mult__dvd__mono) ).
thf(f5875,plain,
! [X2: int,X3: int,X0: nat,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f4003]) ).
thf(f4003,plain,
! [X0: nat,X1: nat,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) != $true ) ),
inference(flattening,[],[f4002]) ).
thf(f4002,plain,
! [X0: nat,X1: nat,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2582]) ).
thf(f2582,plain,
! [X0: nat,X1: nat,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2581]) ).
thf(f2581,plain,
! [X0: nat,X1: nat,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X1)) ) ),
inference(rectify,[],[f319]) ).
thf(f319,axiom,
! [X180: nat,X181: nat,X182: int,X183: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X182),X183)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X180),X181)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X182),X180)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X183),X181)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_dvd__power__le) ).
thf(f5874,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f4001]) ).
thf(f4001,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
inference(flattening,[],[f4000]) ).
thf(f4000,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2580]) ).
thf(f2580,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2579]) ).
thf(f2579,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) ) ),
inference(rectify,[],[f981]) ).
thf(f981,axiom,
! [X18: nat,X38: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X18),X38)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_add__less__mono) ).
thf(f5873,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f3999]) ).
thf(f3999,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
inference(flattening,[],[f3998]) ).
thf(f3998,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2578]) ).
thf(f2578,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2577]) ).
thf(f2577,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f982]) ).
thf(f982,axiom,
! [X192: nat,X191: nat,X18: nat,X38: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X18),X38)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X38) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_less__add__eq__less) ).
thf(f5871,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f3995]) ).
thf(f3995,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(flattening,[],[f3994]) ).
thf(f3994,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2574]) ).
thf(f2574,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2573]) ).
thf(f2573,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X1)) ) ),
inference(rectify,[],[f1003]) ).
thf(f1003,axiom,
! [X18: nat,X38: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X38)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_add__le__mono) ).
thf(f7963,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(subsumption_resolution,[],[f7962,f6249]) ).
thf(f7962,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(subsumption_resolution,[],[f6729,f6249]) ).
thf(f6729,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(definition_unfolding,[],[f5869,f5969,f5969]) ).
thf(f5869,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f3991]) ).
thf(f3991,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(flattening,[],[f3990]) ).
thf(f3990,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2570]) ).
thf(f2570,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) ) ) ) ) ),
inference(fool_elimination,[],[f2569]) ).
thf(f2569,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) ) ) ) ),
inference(rectify,[],[f777]) ).
thf(f777,axiom,
! [X406: nat,X407: nat,X408: nat,X409: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X408),X409)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X406),X407)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X409)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X406)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X408),X406)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X409),X407)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_mult__mono) ).
thf(f5868,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f3989]) ).
thf(f3989,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) != $true ) ),
inference(flattening,[],[f3988]) ).
thf(f3988,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2568]) ).
thf(f2568,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2567]) ).
thf(f2567,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X1)) ) ),
inference(rectify,[],[f320]) ).
thf(f320,axiom,
! [X180: nat,X181: nat,X182: nat,X183: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X182),X183)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X180),X181)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X182),X180)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X183),X181)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_dvd__power__le) ).
thf(f5867,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) != $true ) ),
inference(cnf_transformation,[],[f3987]) ).
thf(f3987,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) != $true ) ),
inference(flattening,[],[f3986]) ).
thf(f3986,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) != $true ) ),
inference(ennf_transformation,[],[f2566]) ).
thf(f2566,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) = $true )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2565]) ).
thf(f2565,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X1)) ) ),
inference(rectify,[],[f740]) ).
thf(f740,axiom,
! [X381: nat,X382: nat,X383: nat,X384: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X383),X384)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X381),X382)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X383),X381)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X384),X382)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_mult__dvd__mono) ).
thf(f6728,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(definition_unfolding,[],[f5866,f5970,f5970]) ).
thf(f5866,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(cnf_transformation,[],[f3985]) ).
thf(f3985,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(flattening,[],[f3984]) ).
thf(f3984,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(ennf_transformation,[],[f2564]) ).
thf(f2564,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) ) ) ) ) ),
inference(fool_elimination,[],[f2563]) ).
thf(f2563,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) ) ) ) ),
inference(rectify,[],[f779]) ).
thf(f779,axiom,
! [X410: real,X411: real,X412: real,X413: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X412),X413)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X410),X411)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X412)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X410)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X412),X410)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X413),X411)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_mult__mono_H) ).
thf(f6727,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(definition_unfolding,[],[f5865,f5970,f5970]) ).
thf(f5865,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(cnf_transformation,[],[f3983]) ).
thf(f3983,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(flattening,[],[f3982]) ).
thf(f3982,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) ) ),
inference(ennf_transformation,[],[f2562]) ).
thf(f2562,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X3) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) ) ) ) ) ),
inference(fool_elimination,[],[f2561]) ).
thf(f2561,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X3)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X3)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) ) ) ) ),
inference(rectify,[],[f776]) ).
thf(f776,axiom,
! [X406: real,X407: real,X408: real,X409: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X408),X409)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X406),X407)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X409)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X406)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X408),X406)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X409),X407)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_mult__mono) ).
thf(f5864,plain,
! [X2: real,X3: real,X0: nat,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) ) ),
inference(cnf_transformation,[],[f3981]) ).
thf(f3981,plain,
! [X0: nat,X1: nat,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) ) ),
inference(flattening,[],[f3980]) ).
thf(f3980,plain,
! [X0: nat,X1: nat,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) ) ),
inference(ennf_transformation,[],[f2560]) ).
thf(f2560,plain,
! [X0: nat,X1: nat,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2559]) ).
thf(f2559,plain,
! [X0: nat,X1: nat,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) ) ),
inference(rectify,[],[f318]) ).
thf(f318,axiom,
! [X180: nat,X181: nat,X182: real,X183: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X182),X183)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X180),X181)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X182),X180)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X183),X181)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_dvd__power__le) ).
thf(f5863,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) ) ),
inference(cnf_transformation,[],[f3979]) ).
thf(f3979,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) ) ),
inference(flattening,[],[f3978]) ).
thf(f3978,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) ) ),
inference(ennf_transformation,[],[f2558]) ).
thf(f2558,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) ) ) ),
inference(fool_elimination,[],[f2557]) ).
thf(f2557,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X3)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X1)) ) ),
inference(rectify,[],[f739]) ).
thf(f739,axiom,
! [X381: real,X382: real,X383: real,X384: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X383),X384)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X381),X382)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X383),X381)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X384),X382)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_mult__dvd__mono) ).
thf(f5862,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(cnf_transformation,[],[f3977]) ).
thf(f3977,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(flattening,[],[f3976]) ).
thf(f3976,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(ennf_transformation,[],[f2556]) ).
thf(f2556,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) ) ) ) ),
inference(fool_elimination,[],[f2555]) ).
thf(f2555,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)) ) ) ),
inference(rectify,[],[f1170]) ).
thf(f1170,axiom,
! [X307: int,X3: int,X306: int,X216: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X216)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X306)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X306),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X216)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X307),X216))),X306)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_zmult2__lemma__aux1) ).
thf(f5861,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(cnf_transformation,[],[f3975]) ).
thf(f3975,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(flattening,[],[f3974]) ).
thf(f3974,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) != $true ) ),
inference(ennf_transformation,[],[f2554]) ).
thf(f2554,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),zero_zero_int) ) ) ) ),
inference(fool_elimination,[],[f2553]) ).
thf(f2553,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X3))),X2)),zero_zero_int) ) ) ),
inference(rectify,[],[f1171]) ).
thf(f1171,axiom,
! [X307: int,X3: int,X306: int,X216: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X216)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X306)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X306),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X307),X216))),X306)),zero_zero_int) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_zmult2__lemma__aux2) ).
thf(f6726,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X3))),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X3) ) ),
inference(definition_unfolding,[],[f5858,f5969]) ).
thf(f5858,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X3))),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) ) ),
inference(cnf_transformation,[],[f3969]) ).
thf(f3969,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X3))),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) ) ),
inference(flattening,[],[f3968]) ).
thf(f3968,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X3))),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) ) ),
inference(ennf_transformation,[],[f2548]) ).
thf(f2548,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X3))),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) ) ) ),
inference(fool_elimination,[],[f2547]) ).
thf(f2547,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X3))),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) ) ),
inference(rectify,[],[f1196]) ).
thf(f1196,axiom,
! [X307: nat,X306: nat,X3: nat,X216: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X216)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X306),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X307),X216))),X306)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X216)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_mod__lemma) ).
thf(f5857,plain,
! [X2: int,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(cnf_transformation,[],[f3967]) ).
thf(f3967,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(flattening,[],[f3966]) ).
thf(f3966,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(ennf_transformation,[],[f3187]) ).
thf(f3187,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) ) ) ) ),
inference(flattening,[],[f2546]) ).
thf(f2546,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) ) ) ) ),
inference(fool_elimination,[],[f2545]) ).
thf(f2545,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( vAPP(int,$o,zprime,X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) ) ) ),
inference(rectify,[],[f410]) ).
thf(f410,axiom,
! [X191: nat,X3: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X163),X191)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X163),X191)),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_zprime__power__zdvd__cancel__left) ).
thf(f5856,plain,
! [X2: int,X3: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(cnf_transformation,[],[f3965]) ).
thf(f3965,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(flattening,[],[f3964]) ).
thf(f3964,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
| ( $true != vAPP(int,$o,zprime,X3) ) ),
inference(ennf_transformation,[],[f3186]) ).
thf(f3186,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) ) ) ) ),
inference(flattening,[],[f2544]) ).
thf(f2544,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( ( $true = vAPP(int,$o,zprime,X3) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) ) ) ) ),
inference(fool_elimination,[],[f2543]) ).
thf(f2543,plain,
! [X0: nat,X1: int,X2: int,X3: int] :
( vAPP(int,$o,zprime,X3)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X3),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X0)),X1) ) ) ),
inference(rectify,[],[f411]) ).
thf(f411,axiom,
! [X191: nat,X2: int,X3: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X163),X191)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X163),X191)),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_zprime__power__zdvd__cancel__right) ).
thf(f6960,plain,
! [X2: int,X3: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3)),X1) = X3 )
| ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(equality_resolution,[],[f5854]) ).
thf(f5854,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = X3 )
| ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X3) != X0 ) ),
inference(cnf_transformation,[],[f3963]) ).
thf(f6958,plain,
! [X2: nat,X3: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X3) ) ),
inference(equality_resolution,[],[f6725]) ).
thf(f6725,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) != X0 ) ),
inference(definition_unfolding,[],[f5851,f5969]) ).
thf(f5851,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) != X0 ) ),
inference(cnf_transformation,[],[f3961]) ).
thf(f3961,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) != X0 ) ),
inference(flattening,[],[f3960]) ).
thf(f3960,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) != X0 ) ),
inference(ennf_transformation,[],[f3184]) ).
thf(f3184,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) = X0 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) ) ) ),
inference(flattening,[],[f2540]) ).
thf(f2540,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) = X0 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f2539]) ).
thf(f2539,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X3) = X0 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) ) ),
inference(rectify,[],[f871]) ).
thf(f871,axiom,
! [X16: nat,X307: nat,X191: nat,X306: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X307),X191)),X306) = X16 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X306)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X306),X191)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X191),X16) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_divides__div__not) ).
thf(f5850,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X0),X1))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X2),X3))) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)))) ),
inference(cnf_transformation,[],[f3183]) ).
thf(f3183,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X0),X1))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X2),X3))) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)))) ),
inference(rectify,[],[f640]) ).
thf(f640,axiom,
! [X2: int,X3: int,X163: int,X307: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X2),X3))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X163),X307))) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X163)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X307))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X307)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X163)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_mult__sum2sq) ).
thf(f5849,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1)),X3) ),
inference(cnf_transformation,[],[f3182]) ).
thf(f3182,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1)),X3) ),
inference(rectify,[],[f721]) ).
thf(f721,axiom,
! [X360: int,X361: int,X362: int,X363: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X360),X361)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X362),X361)),X363)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X360),X362)),X361)),X363) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_combine__common__factor) ).
thf(f5847,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1)),X3) ),
inference(cnf_transformation,[],[f3180]) ).
thf(f3180,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1)),X3) ),
inference(rectify,[],[f720]) ).
thf(f720,axiom,
! [X360: nat,X361: nat,X362: nat,X363: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X360),X361)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X362),X361)),X363)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X360),X362)),X361)),X363) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_combine__common__factor) ).
thf(f5846,plain,
! [X2: real,X3: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1)),X3) ),
inference(cnf_transformation,[],[f3179]) ).
thf(f3179,plain,
! [X0: real,X1: real,X2: real,X3: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1)),X3) ),
inference(rectify,[],[f719]) ).
thf(f719,axiom,
! [X360: real,X361: real,X362: real,X363: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X360),X361)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X362),X361)),X363)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X360),X362)),X361)),X363) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_combine__common__factor) ).
thf(f7961,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3))) ),
inference(forward_demodulation,[],[f5845,f5387]) ).
thf(f5845,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) ),
inference(cnf_transformation,[],[f3178]) ).
thf(f3178,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3)) ),
inference(rectify,[],[f92]) ).
thf(f92,axiom,
! [X41: int,X42: int,X43: int,X44: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X41),X42)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X43),X44)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X41),X43)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X42),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(f7960,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) ),
inference(forward_demodulation,[],[f5842,f5385]) ).
thf(f5842,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3)) ),
inference(cnf_transformation,[],[f3175]) ).
thf(f3175,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3)) ),
inference(rectify,[],[f116]) ).
thf(f116,axiom,
! [X67: int,X68: int,X69: int,X70: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X67),X68)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X69),X70)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X67),X69)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X68),X70)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(f7959,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) ),
inference(forward_demodulation,[],[f5841,f7884]) ).
thf(f5841,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3)) ),
inference(cnf_transformation,[],[f3174]) ).
thf(f3174,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3)) ),
inference(rectify,[],[f729]) ).
thf(f729,axiom,
! [X368: int,X369: int,X370: int,X371: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X368),X369)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X370),X371)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X368),X370)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X369),X371)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_add__diff__add) ).
thf(f7958,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3))) ),
inference(forward_demodulation,[],[f5840,f5370]) ).
thf(f5840,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) ),
inference(cnf_transformation,[],[f3173]) ).
thf(f3173,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3)) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
! [X41: nat,X42: nat,X43: nat,X44: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X41),X42)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X43),X44)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X41),X43)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X42),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(f7957,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3))) ),
inference(forward_demodulation,[],[f5837,f5368]) ).
thf(f5837,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
inference(cnf_transformation,[],[f3170]) ).
thf(f3170,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
inference(rectify,[],[f117]) ).
thf(f117,axiom,
! [X67: nat,X68: nat,X69: nat,X70: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X67),X68)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X69),X70)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X67),X69)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X68),X70)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(f7956,plain,
! [X2: real,X3: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3))) ),
inference(forward_demodulation,[],[f5836,f5357]) ).
thf(f5836,plain,
! [X2: real,X3: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)) ),
inference(cnf_transformation,[],[f3169]) ).
thf(f3169,plain,
! [X0: real,X1: real,X2: real,X3: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X3)) ),
inference(rectify,[],[f94]) ).
thf(f94,axiom,
! [X41: real,X42: real,X43: real,X44: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X41),X42)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X43),X44)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X41),X43)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X42),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(f7955,plain,
! [X2: real,X3: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3))) ),
inference(forward_demodulation,[],[f5833,f5355]) ).
thf(f5833,plain,
! [X2: real,X3: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) ),
inference(cnf_transformation,[],[f3166]) ).
thf(f3166,plain,
! [X0: real,X1: real,X2: real,X3: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) ),
inference(rectify,[],[f118]) ).
thf(f118,axiom,
! [X67: real,X68: real,X69: real,X70: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X67),X68)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X69),X70)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X67),X69)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X68),X70)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(f5832,plain,
! [X2: real,X3: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X3)) ),
inference(cnf_transformation,[],[f3165]) ).
thf(f3165,plain,
! [X0: real,X1: real,X2: real,X3: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X3)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X3)) ),
inference(rectify,[],[f728]) ).
thf(f728,axiom,
! [X368: real,X369: real,X370: real,X371: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X368),X369)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X370),X371)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X368),X370)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X369),X371)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_add__diff__add) ).
thf(f5831,plain,
! [X2: int,X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X1) ),
inference(cnf_transformation,[],[f2538]) ).
thf(f2538,plain,
! [X0: int,X1: int,X2: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X1) ),
inference(fool_elimination,[],[f2537]) ).
thf(f2537,plain,
! [X0: int,X1: int,X2: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)),X1),
inference(rectify,[],[f579]) ).
thf(f579,axiom,
! [X2: int,X192: int,X3: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X3),X192)),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_zcong__zmult__self) ).
thf(f5825,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f4376]) ).
thf(f4376,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ) ),
inference(flattening,[],[f4375]) ).
thf(f4375,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f2536]) ).
thf(f2536,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
<=> ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ) ) ),
inference(fool_elimination,[],[f2535]) ).
thf(f2535,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ) ),
inference(rectify,[],[f855]) ).
thf(f855,axiom,
! [X482: int,X483: int,X484: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X482),X483)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X484),X483))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X484),X482)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X483),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X482),X484)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X483) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_mult__less__cancel__right__disj) ).
thf(f5826,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f4376]) ).
thf(f5827,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f4376]) ).
thf(f5828,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f4376]) ).
thf(f5819,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(cnf_transformation,[],[f4374]) ).
thf(f4374,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ) ),
inference(flattening,[],[f4373]) ).
thf(f4373,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) )
& ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ) ),
inference(nnf_transformation,[],[f2534]) ).
thf(f2534,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
<=> ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) )
| ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ) ) ),
inference(fool_elimination,[],[f2533]) ).
thf(f2533,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ) ),
inference(rectify,[],[f853]) ).
thf(f853,axiom,
! [X479: int,X480: int,X481: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X479),X480)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X479),X481))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X481),X480)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X479),zero_zero_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X480),X481)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X479) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_mult__less__cancel__left__disj) ).
thf(f5820,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(cnf_transformation,[],[f4374]) ).
thf(f5821,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(cnf_transformation,[],[f4374]) ).
thf(f5822,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(cnf_transformation,[],[f4374]) ).
thf(f6996,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ) ),
inference(binary_proxy_clausification,[],[f5818]) ).
thf(f5818,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ),
inference(cnf_transformation,[],[f2532]) ).
thf(f2532,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ),
inference(fool_elimination,[],[f2531]) ).
thf(f2531,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ),
inference(rectify,[],[f373]) ).
thf(f373,axiom,
! [X18: int,X191: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X191),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X192)))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_zdvd__reduce) ).
thf(f6995,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))) ) ),
inference(binary_proxy_clausification,[],[f5818]) ).
thf(f6724,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(definition_unfolding,[],[f5815,f5969]) ).
thf(f5815,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f4372]) ).
thf(f4372,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
& ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(flattening,[],[f4371]) ).
thf(f4371,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
& ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f2530]) ).
thf(f2530,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) ),
inference(fool_elimination,[],[f2529]) ).
thf(f2529,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(rectify,[],[f1036]) ).
thf(f1036,axiom,
! [X192: nat,X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1035_mult__less__cancel2) ).
thf(f5816,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f4372]) ).
thf(f6722,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(definition_unfolding,[],[f5812,f5969]) ).
thf(f5812,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(cnf_transformation,[],[f4370]) ).
thf(f4370,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
& ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(flattening,[],[f4369]) ).
thf(f4369,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
& ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(nnf_transformation,[],[f2528]) ).
thf(f2528,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(fool_elimination,[],[f2527]) ).
thf(f2527,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f1037]) ).
thf(f1037,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_mult__less__cancel1) ).
thf(f5813,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(cnf_transformation,[],[f4370]) ).
thf(f6998,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f5811]) ).
thf(f5811,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(cnf_transformation,[],[f2526]) ).
thf(f2526,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(fool_elimination,[],[f2525]) ).
thf(f2525,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ),
inference(rectify,[],[f977]) ).
thf(f977,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_nat__add__left__cancel__less) ).
thf(f6997,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f5811]) ).
thf(f6720,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(definition_unfolding,[],[f5808,f5969]) ).
thf(f5808,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f4368]) ).
thf(f4368,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(flattening,[],[f4367]) ).
thf(f4367,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f3959]) ).
thf(f3959,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) ),
inference(ennf_transformation,[],[f2524]) ).
thf(f2524,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f2523]) ).
thf(f2523,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
inference(rectify,[],[f1043]) ).
thf(f1043,axiom,
! [X192: nat,X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_mult__le__cancel2) ).
thf(f6719,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f5809,f5969]) ).
thf(f5809,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4368]) ).
thf(f6718,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(definition_unfolding,[],[f5805,f5969]) ).
thf(f5805,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(cnf_transformation,[],[f4366]) ).
thf(f4366,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(flattening,[],[f4365]) ).
thf(f4365,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(nnf_transformation,[],[f3958]) ).
thf(f3958,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(ennf_transformation,[],[f2522]) ).
thf(f2522,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ) ),
inference(fool_elimination,[],[f2521]) ).
thf(f2521,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(rectify,[],[f1042]) ).
thf(f1042,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_mult__le__cancel1) ).
thf(f6717,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(definition_unfolding,[],[f5806,f5969]) ).
thf(f5806,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(cnf_transformation,[],[f4366]) ).
thf(f7000,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f5804]) ).
thf(f5804,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(cnf_transformation,[],[f2520]) ).
thf(f2520,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(fool_elimination,[],[f2519]) ).
thf(f2519,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ),
inference(rectify,[],[f999]) ).
thf(f999,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_998_nat__add__left__cancel__le) ).
thf(f6999,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f5804]) ).
thf(f6716,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(definition_unfolding,[],[f5801,f5969]) ).
thf(f5801,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(cnf_transformation,[],[f4364]) ).
thf(f4364,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
& ( zero_zero_nat != X0 ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(flattening,[],[f4363]) ).
thf(f4363,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
& ( zero_zero_nat != X0 ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(nnf_transformation,[],[f2518]) ).
thf(f2518,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( zero_zero_nat = X0 ) ) ),
inference(fool_elimination,[],[f2517]) ).
thf(f2517,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
| ( zero_zero_nat = X0 ) ) ),
inference(rectify,[],[f1050]) ).
thf(f1050,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X192),X191)
| ( zero_zero_nat = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_nat__mult__dvd__cancel__disj) ).
thf(f6714,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(definition_unfolding,[],[f5798,f5969]) ).
thf(f5798,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f4362]) ).
thf(f4362,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
& ( zero_zero_nat != X1 ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(flattening,[],[f4361]) ).
thf(f4361,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
& ( zero_zero_nat != X1 ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f2516]) ).
thf(f2516,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 ) ) ),
inference(fool_elimination,[],[f2515]) ).
thf(f2515,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2)
| ( zero_zero_nat = X1 ) ) ),
inference(rectify,[],[f861]) ).
thf(f861,axiom,
! [X192: nat,X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X192),X191)
| ( zero_zero_nat = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_nat__mult__dvd__cancel__disj_H) ).
thf(f6712,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(definition_unfolding,[],[f5792,f5970,f5970]) ).
thf(f5792,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(cnf_transformation,[],[f4360]) ).
thf(f4360,plain,
! [X0: real,X1: real,X2: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ) ),
inference(flattening,[],[f4359]) ).
thf(f4359,plain,
! [X0: real,X1: real,X2: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ) ),
inference(nnf_transformation,[],[f2514]) ).
thf(f2514,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
<=> ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true ) ) ) ),
inference(fool_elimination,[],[f2513]) ).
thf(f2513,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2))
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ) ),
inference(rectify,[],[f852]) ).
thf(f852,axiom,
! [X479: real,X480: real,X481: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X479),X480)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X479),X481))
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X481),X480)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X479),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X480),X481)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X479) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_mult__less__cancel__left__disj) ).
thf(f6711,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(definition_unfolding,[],[f5793,f5970]) ).
thf(f5793,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(cnf_transformation,[],[f4360]) ).
thf(f6710,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(definition_unfolding,[],[f5794,f5970]) ).
thf(f5794,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(cnf_transformation,[],[f4360]) ).
thf(f5795,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(cnf_transformation,[],[f4360]) ).
thf(f6707,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(definition_unfolding,[],[f5786,f5970,f5970]) ).
thf(f5786,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f4358]) ).
thf(f4358,plain,
! [X0: real,X1: real,X2: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ) ),
inference(flattening,[],[f4357]) ).
thf(f4357,plain,
! [X0: real,X1: real,X2: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ) ),
inference(nnf_transformation,[],[f2512]) ).
thf(f2512,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
<=> ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true ) ) ) ),
inference(fool_elimination,[],[f2511]) ).
thf(f2511,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1))
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) ) ),
inference(rectify,[],[f854]) ).
thf(f854,axiom,
! [X482: real,X483: real,X484: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X482),X483)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X484),X483))
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X484),X482)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X483),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X482),X484)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X483) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_mult__less__cancel__right__disj) ).
thf(f6706,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(definition_unfolding,[],[f5787,f5970]) ).
thf(f5787,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f4358]) ).
thf(f6705,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(definition_unfolding,[],[f5788,f5970]) ).
thf(f5788,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f4358]) ).
thf(f5789,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f4358]) ).
thf(f7002,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5785]) ).
thf(f5785,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(cnf_transformation,[],[f2510]) ).
thf(f2510,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(fool_elimination,[],[f2509]) ).
thf(f2509,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2)
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(rectify,[],[f1008]) ).
thf(f1008,axiom,
! [X20: nat,X18: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X18)),X19)
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_le__diff__conv) ).
thf(f7001,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5785]) ).
thf(f7004,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f5784]) ).
thf(f5784,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ),
inference(cnf_transformation,[],[f2508]) ).
thf(f2508,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ),
inference(fool_elimination,[],[f2507]) ).
thf(f2507,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ),
inference(rectify,[],[f985]) ).
thf(f985,axiom,
! [X19: nat,X20: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X18))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_less__diff__conv) ).
thf(f7003,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f5784]) ).
thf(f7006,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)),X2) ) ),
inference(binary_proxy_clausification,[],[f5783]) ).
thf(f5783,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)),X2) ),
inference(cnf_transformation,[],[f2506]) ).
thf(f2506,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)),X2) ),
inference(fool_elimination,[],[f2505]) ).
thf(f2505,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)),X2) ),
inference(rectify,[],[f1146]) ).
thf(f1146,axiom,
! [X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X3),X192)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_zcong__zmod) ).
thf(f7005,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)),X2) ) ),
inference(binary_proxy_clausification,[],[f5783]) ).
thf(f7008,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f5782]) ).
thf(f5782,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ),
inference(cnf_transformation,[],[f2504]) ).
thf(f2504,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ),
inference(fool_elimination,[],[f2503]) ).
thf(f2503,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ),
inference(rectify,[],[f630]) ).
thf(f630,axiom,
! [X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X192),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_zcong__def) ).
thf(f7007,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f5782]) ).
thf(f7009,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f5781]) ).
thf(f5781,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ),
inference(cnf_transformation,[],[f2502]) ).
thf(f2502,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ),
inference(fool_elimination,[],[f2501]) ).
thf(f2501,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ),
inference(rectify,[],[f563]) ).
thf(f563,axiom,
! [X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X3),X2),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_zcong__sym) ).
thf(f5779,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),vAPP(int,sTfun(int,sTfun(int,int)),sK42,X2),X1),X0))) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f4356]) ).
thf(f4356,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ! [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != X1 ) )
& ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),vAPP(int,sTfun(int,sTfun(int,int)),sK42,X2),X1),X0))) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f4354,f4355]) ).
thf(f4355,plain,
! [X0: int,X1: int,X2: int] :
( ? [X4: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X4)) = X1 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),vAPP(int,sTfun(int,sTfun(int,int)),sK42,X2),X1),X0))) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f4354,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ! [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != X1 ) )
& ( ? [X4: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X4)) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ) ),
inference(rectify,[],[f4353]) ).
thf(f4353,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ! [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != X1 ) )
& ( ? [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ) ),
inference(nnf_transformation,[],[f2500]) ).
thf(f2500,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
<=> ? [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = X1 ) ),
inference(fool_elimination,[],[f2499]) ).
thf(f2499,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2)
<=> ? [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) = X1 ) ),
inference(rectify,[],[f591]) ).
thf(f591,axiom,
! [X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
<=> ? [X320: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X192),X320)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_zcong__iff__lin) ).
thf(f6955,plain,
! [X2: int,X3: int,X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3))),X2) ),
inference(equality_resolution,[],[f5780]) ).
thf(f5780,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)) != X1 ) ),
inference(cnf_transformation,[],[f4356]) ).
thf(f6954,plain,
! [X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),zero_zero_int)) )
| ( $true = vAPP(int,$o,X0,X1) ) ),
inference(equality_resolution,[],[f5774]) ).
thf(f5774,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( zero_zero_int != X2 )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ),
inference(cnf_transformation,[],[f4352]) ).
thf(f4352,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( ( $true != vAPP(int,$o,X0,X1) )
& ( zero_zero_int = X2 ) ) )
& ( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
& ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
& ( ( $true = vAPP(int,$o,X0,X1) )
| ( zero_zero_int != X2 ) ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ) ),
inference(flattening,[],[f4351]) ).
thf(f4351,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( ( $true != vAPP(int,$o,X0,X1) )
& ( zero_zero_int = X2 ) ) )
& ( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
& ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
& ( ( $true = vAPP(int,$o,X0,X1) )
| ( zero_zero_int != X2 ) ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ) ),
inference(nnf_transformation,[],[f4080]) ).
thf(f4080,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
<=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
& ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
& ( ( $true = vAPP(int,$o,X0,X1) )
| ( zero_zero_int != X2 ) ) ) ),
inference(definition_folding,[],[f3957,f4079,f4078]) ).
thf(f4079,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
<=> ( ! [X3: int,X4: int] :
( ( $true = vAPP(int,$o,X0,X4) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3957,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
<=> ( ( ! [X3: int,X4: int] :
( ( $true = vAPP(int,$o,X0,X4) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) )
& ( ( $true = vAPP(int,$o,X0,X1) )
| ( zero_zero_int != X2 ) ) ) ),
inference(flattening,[],[f3956]) ).
thf(f3956,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
<=> ( ( ! [X3: int,X4: int] :
( ( $true = vAPP(int,$o,X0,X4) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) )
& ( ( $true = vAPP(int,$o,X0,X1) )
| ( zero_zero_int != X2 ) ) ) ),
inference(ennf_transformation,[],[f2498]) ).
thf(f2498,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
<=> ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
=> ! [X3: int,X4: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
=> ( $true = vAPP(int,$o,X0,X4) ) ) )
& ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ! [X5: int,X6: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) ) )
=> ( $true = vAPP(int,$o,X0,X6) ) ) )
& ( ( zero_zero_int = X2 )
=> ( $true = vAPP(int,$o,X0,X1) ) ) ) ),
inference(fool_elimination,[],[f2497]) ).
thf(f2497,plain,
! [X0: int > $o,X1: int,X2: int] :
( vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int)
=> ! [X3: int,X4: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) )
=> vAPP(int,$o,X0,X4) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ! [X5: int,X6: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) = X1 )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X6),X2)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X6) )
=> vAPP(int,$o,X0,X6) ) )
& ( ( zero_zero_int = X2 )
=> vAPP(int,$o,X0,X1) ) ) ),
inference(rectify,[],[f1167]) ).
thf(f1167,axiom,
! [X490: int > $o,X191: int,X18: int] :
( vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X191),X18))
<=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),zero_zero_int)
=> ! [X493: int,X502: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X493)),X502) = X191 )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X502),zero_zero_int)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X502) )
=> vAPP(int,$o,X490,X502) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X18)
=> ! [X493: int,X502: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X493)),X502) = X191 )
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X502),X18)
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X502) )
=> vAPP(int,$o,X490,X502) ) )
& ( ( zero_zero_int = X18 )
=> vAPP(int,$o,X490,X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_split__zmod) ).
thf(f5775,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ),
inference(cnf_transformation,[],[f4352]) ).
thf(f5776,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ),
inference(cnf_transformation,[],[f4352]) ).
thf(f5777,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( zero_zero_int = X2 ) ),
inference(cnf_transformation,[],[f4352]) ).
thf(f5778,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( $true != vAPP(int,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f4352]) ).
thf(f5769,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true ) ),
inference(cnf_transformation,[],[f4350]) ).
thf(f5771,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)),X2) ) ),
inference(cnf_transformation,[],[f4350]) ).
thf(f5772,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK40,X2),X1),X0))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) = X1 ) ),
inference(cnf_transformation,[],[f4350]) ).
thf(f5773,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP1,X2),X1),X0) )
| ( $true != vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK41,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f4350]) ).
thf(f6952,plain,
! [X2: int,X0: int > $o,X6: int,X5: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X6),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X6) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6)),X0) ) ),
inference(equality_resolution,[],[f5762]) ).
thf(f5762,plain,
! [X2: int,X0: int > $o,X1: int,X6: int,X5: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X6),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X6) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f4345]) ).
thf(f4345,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( ( $true != vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK38,X2),X1),X0))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X6),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X6) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f4343,f4344]) ).
thf(f4344,plain,
! [X0: int > $o,X1: int,X2: int] :
( ? [X3: int,X4: int] :
( ( $true != vAPP(int,$o,X0,X4) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
=> ( ( $true != vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK38,X2),X1),X0))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4343,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( ? [X3: int,X4: int] :
( ( $true != vAPP(int,$o,X0,X4) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ) )
& ( ! [X5: int,X6: int] :
( ( $true = vAPP(int,$o,X0,X6) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X5)),X6) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X6),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X6) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) ) ) ),
inference(rectify,[],[f4342]) ).
thf(f4342,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( ? [X3: int,X4: int] :
( ( $true != vAPP(int,$o,X0,X4) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ) )
& ( ! [X3: int,X4: int] :
( ( $true = vAPP(int,$o,X0,X4) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) ) ) ),
inference(flattening,[],[f4341]) ).
thf(f4341,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( ? [X3: int,X4: int] :
( ( $true != vAPP(int,$o,X0,X4) )
& ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) = X1 )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ) )
& ( ! [X3: int,X4: int] :
( ( $true = vAPP(int,$o,X0,X4) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X4) != X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X4),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X4) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f4079]) ).
thf(f5763,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4345]) ).
thf(f5764,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f4345]) ).
thf(f5765,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4345]) ).
thf(f5766,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK38,X2),X1),X0))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) = X1 ) ),
inference(cnf_transformation,[],[f4345]) ).
thf(f5767,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),$o)),sP2,X2),X1),X0) )
| ( $true != vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),vAPP(int,sTfun(int,sTfun(sTfun(int,$o),int)),sK39,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f4345]) ).
thf(f5758,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f4340]) ).
thf(f4340,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X4) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f4338,f4339]) ).
thf(f4339,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f4338,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X4) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(rectify,[],[f4337]) ).
thf(f4337,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(flattening,[],[f4336]) ).
thf(f4336,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(nnf_transformation,[],[f3955]) ).
thf(f3955,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
<=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) ) ),
inference(ennf_transformation,[],[f3164]) ).
thf(f3164,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
<=> ~ ( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) ) ),
inference(flattening,[],[f2496]) ).
thf(f2496,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
<=> ~ ( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f2495]) ).
thf(f2495,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2))
<=> ~ ( ? [X3: nat] :
( ~ vAPP(nat,$o,X0,X3)
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ~ vAPP(nat,$o,X0,zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) ),
inference(rectify,[],[f1033]) ).
thf(f1033,axiom,
! [X490: nat > $o,X2: nat,X3: nat] :
( vAPP(nat,$o,X490,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X3))
<=> ~ ( ? [X492: nat] :
( ~ vAPP(nat,$o,X490,X492)
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X492) = X2 ) )
| ( ~ vAPP(nat,$o,X490,zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_nat__diff__split__asm) ).
thf(f6701,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,X0,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5759,f5969]) ).
thf(f5759,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4340]) ).
thf(f5760,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f4340]) ).
thf(f6700,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X0,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5761,f5969]) ).
thf(f5761,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK37,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4340]) ).
thf(f6699,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f5750,f5969]) ).
thf(f5750,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f4335]) ).
thf(f4335,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X4) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f4333,f4334]) ).
thf(f4334,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f4333,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X4) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(rectify,[],[f4332]) ).
thf(f4332,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(flattening,[],[f4331]) ).
thf(f4331,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 ) )
| ( ( $true != vAPP(nat,$o,X0,zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
& ( ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(nnf_transformation,[],[f3954]) ).
thf(f3954,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
<=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) != X1 ) )
& ( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ) ) ),
inference(ennf_transformation,[],[f2494]) ).
thf(f2494,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
<=> ( ! [X3: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 )
=> ( $true = vAPP(nat,$o,X0,X3) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ) ),
inference(fool_elimination,[],[f2493]) ).
thf(f2493,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2))
<=> ( ! [X3: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3) = X1 )
=> vAPP(nat,$o,X0,X3) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
inference(rectify,[],[f1032]) ).
thf(f1032,axiom,
! [X490: nat > $o,X2: nat,X3: nat] :
( vAPP(nat,$o,X490,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X3))
<=> ( ! [X492: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X492) = X2 )
=> vAPP(nat,$o,X490,X492) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
=> vAPP(nat,$o,X490,zero_zero_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_nat__diff__split) ).
thf(f5752,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f4335]) ).
thf(f6698,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,X0,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5753,f5969]) ).
thf(f5753,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4335]) ).
thf(f5754,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f4335]) ).
thf(f6697,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X0,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5755,f5969]) ).
thf(f5755,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK36,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4335]) ).
thf(f5748,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f4330]) ).
thf(f4330,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) )
& ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) ) ) ),
inference(nnf_transformation,[],[f4077]) ).
thf(f4077,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) )
<=> ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ),
inference(definition_folding,[],[f3953,f4076]) ).
thf(f4076,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
<=> ( ( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3953,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) )
<=> ( ( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) ) ),
inference(flattening,[],[f3952]) ).
thf(f3952,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) )
<=> ( ( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) ) ),
inference(ennf_transformation,[],[f2492]) ).
thf(f2492,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) )
<=> ( ( ( zero_zero_nat != X2 )
=> ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) = X1 )
=> ( $true = vAPP(nat,$o,X0,X4) ) ) ) )
& ( ( zero_zero_nat = X2 )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ) ),
inference(fool_elimination,[],[f2491]) ).
thf(f2491,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2))
<=> ( ( ( zero_zero_nat != X2 )
=> ! [X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) = X1 )
=> vAPP(nat,$o,X0,X4) ) ) )
& ( ( zero_zero_nat = X2 )
=> vAPP(nat,$o,X0,X1) ) ) ),
inference(rectify,[],[f1195]) ).
thf(f1195,axiom,
! [X490: nat > $o,X191: nat,X18: nat] :
( vAPP(nat,$o,X490,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X191),X18))
<=> ( ( ( zero_zero_nat != X18 )
=> ! [X493: nat,X502: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X502),X18)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X493)),X502) = X191 )
=> vAPP(nat,$o,X490,X502) ) ) )
& ( ( zero_zero_nat = X18 )
=> vAPP(nat,$o,X490,X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_split__mod) ).
thf(f5749,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f4330]) ).
thf(f6949,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1),X0) ) ),
inference(equality_resolution,[],[f6696]) ).
thf(f6696,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X2 )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f5738,f5969]) ).
thf(f5738,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f4329,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK34,X2),X1),X0))),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)),X2) )
& ( zero_zero_nat != X2 ) )
| ( ( $true != vAPP(nat,$o,X0,X1) )
& ( zero_zero_nat = X2 ) ) )
& ( ( ( ! [X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,X0,X6) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X5)),X6) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35])],[f4327,f4328]) ).
thf(f4328,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,X0,X4) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK34,X2),X1),X0))),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)),X2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f4327,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,X0,X4) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
& ( zero_zero_nat != X2 ) )
| ( ( $true != vAPP(nat,$o,X0,X1) )
& ( zero_zero_nat = X2 ) ) )
& ( ( ( ! [X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,X0,X6) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X5)),X6) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ) ),
inference(rectify,[],[f4326]) ).
thf(f4326,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,X0,X4) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
& ( zero_zero_nat != X2 ) )
| ( ( $true != vAPP(nat,$o,X0,X1) )
& ( zero_zero_nat = X2 ) ) )
& ( ( ( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ) ),
inference(flattening,[],[f4325]) ).
thf(f4325,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,X0,X4) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
& ( zero_zero_nat != X2 ) )
| ( ( $true != vAPP(nat,$o,X0,X1) )
& ( zero_zero_nat = X2 ) ) )
& ( ( ( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X3)),X4) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X2) ) )
| ( zero_zero_nat = X2 ) )
& ( ( $true = vAPP(nat,$o,X0,X1) )
| ( zero_zero_nat != X2 ) ) )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f4076]) ).
thf(f6948,plain,
! [X2: nat,X0: nat > $o,X6: nat,X5: nat] :
( ( $true = vAPP(nat,$o,X0,X6) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X5)),X6)),X0) ) ),
inference(equality_resolution,[],[f6695]) ).
thf(f6695,plain,
! [X2: nat,X0: nat > $o,X1: nat,X6: nat,X5: nat] :
( ( $true = vAPP(nat,$o,X0,X6) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X5)),X6) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f5739,f5969]) ).
thf(f5739,plain,
! [X2: nat,X0: nat > $o,X1: nat,X6: nat,X5: nat] :
( ( $true = vAPP(nat,$o,X0,X6) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X5)),X6) != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X2) )
| ( zero_zero_nat = X2 )
| ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f6946,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1),X0) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(equality_resolution,[],[f6693]) ).
thf(f6693,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X2 )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(definition_unfolding,[],[f5741,f5969]) ).
thf(f5741,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( zero_zero_nat != X2 )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f6692,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5742,f5969]) ).
thf(f5742,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)),X2) )
| ( zero_zero_nat = X2 ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f5743,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f6691,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK34,X2),X1),X0))),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) = X1 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5744,f5969]) ).
thf(f5744,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK34,X2),X1),X0))),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) = X1 )
| ( zero_zero_nat = X2 ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f5745,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK34,X2),X1),X0))),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f6690,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5746,f5969]) ).
thf(f5746,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) )
| ( zero_zero_nat = X2 ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f5747,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK35,X2),X1),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f4329]) ).
thf(f5736,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) ) ),
inference(cnf_transformation,[],[f4324]) ).
thf(f4324,plain,
! [X0: int,X1: int,X2: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) ) ) ),
inference(nnf_transformation,[],[f2490]) ).
thf(f2490,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) )
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) ) ),
inference(fool_elimination,[],[f2489]) ).
thf(f2489,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) ),
inference(rectify,[],[f1143]) ).
thf(f1143,axiom,
! [X16: int,X191: int,X17: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X191) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X17),X191) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X191),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X16),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_zmod__eq__dvd__iff) ).
thf(f5737,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) ) ),
inference(cnf_transformation,[],[f4324]) ).
thf(f6687,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) ) ),
inference(definition_unfolding,[],[f5730,f5969]) ).
thf(f5730,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) ) ),
inference(cnf_transformation,[],[f4321]) ).
thf(f4321,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( ( zero_zero_nat != X1 )
& ( X0 != X2 ) ) )
& ( ( zero_zero_nat = X1 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) ) ) ),
inference(flattening,[],[f4320]) ).
thf(f4320,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
| ( ( zero_zero_nat != X1 )
& ( X0 != X2 ) ) )
& ( ( zero_zero_nat = X1 )
| ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) ) ) ),
inference(nnf_transformation,[],[f3162]) ).
thf(f3162,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) )
<=> ( ( zero_zero_nat = X1 )
| ( X0 = X2 ) ) ),
inference(rectify,[],[f974]) ).
thf(f974,axiom,
! [X192: nat,X18: nat,X191: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18) )
<=> ( ( zero_zero_nat = X18 )
| ( X191 = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_mult__cancel2) ).
thf(f6685,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) ) ),
inference(definition_unfolding,[],[f5727,f5969]) ).
thf(f5727,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) ) ),
inference(cnf_transformation,[],[f4319]) ).
thf(f4319,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( ( zero_zero_nat != X0 )
& ( X1 != X2 ) ) )
& ( ( zero_zero_nat = X0 )
| ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) ) ) ),
inference(flattening,[],[f4318]) ).
thf(f4318,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
| ( ( zero_zero_nat != X0 )
& ( X1 != X2 ) ) )
& ( ( zero_zero_nat = X0 )
| ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) ) ) ),
inference(nnf_transformation,[],[f3161]) ).
thf(f3161,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2) )
<=> ( ( zero_zero_nat = X0 )
| ( X1 = X2 ) ) ),
inference(rectify,[],[f973]) ).
thf(f973,axiom,
! [X18: nat,X192: nat,X191: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191) )
<=> ( ( zero_zero_nat = X18 )
| ( X191 = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_mult__cancel1) ).
thf(f5725,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f4317]) ).
thf(f4317,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) ) ) ),
inference(nnf_transformation,[],[f3160]) ).
thf(f3160,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f932]) ).
thf(f932,axiom,
! [X192: nat,X18: nat,X191: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X18) )
<=> ( X191 = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_931_nat__add__right__cancel) ).
thf(f5723,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f4316]) ).
thf(f4316,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3159]) ).
thf(f3159,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
<=> ( X1 = X2 ) ),
inference(rectify,[],[f931]) ).
thf(f931,axiom,
! [X18: nat,X192: nat,X191: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X192) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X191) )
<=> ( X191 = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_nat__add__left__cancel) ).
thf(f5721,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(cnf_transformation,[],[f3949]) ).
thf(f3949,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(flattening,[],[f3948]) ).
thf(f3948,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(ennf_transformation,[],[f2486]) ).
thf(f2486,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
=> ( ( zero_zero_int != X0 )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ) ),
inference(fool_elimination,[],[f2485]) ).
thf(f2485,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2))
=> ( ( zero_zero_int != X0 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(rectify,[],[f329]) ).
thf(f329,axiom,
! [X18: int,X192: int,X191: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X191))
=> ( ( zero_zero_int != X18 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_zdvd__mult__cancel) ).
thf(f6683,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(definition_unfolding,[],[f5720,f5969]) ).
thf(f5720,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(cnf_transformation,[],[f3947]) ).
thf(f3947,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(flattening,[],[f3946]) ).
thf(f3946,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(ennf_transformation,[],[f2484]) ).
thf(f2484,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
=> ( ( zero_zero_nat != X1 )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) ) ) ),
inference(fool_elimination,[],[f2483]) ).
thf(f2483,plain,
! [X0: int,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
=> ( ( zero_zero_nat != X1 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) ) ),
inference(rectify,[],[f1131]) ).
thf(f1131,axiom,
! [X2: int,X191: nat,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X191)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X191))
=> ( ( zero_zero_nat != X191 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1130_pow__divides__pow__int) ).
thf(f7947,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(subsumption_resolution,[],[f6682,f6249]) ).
thf(f6682,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(definition_unfolding,[],[f5719,f5969]) ).
thf(f5719,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f3945]) ).
thf(f3945,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(flattening,[],[f3944]) ).
thf(f3944,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(ennf_transformation,[],[f2482]) ).
thf(f2482,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f2481]) ).
thf(f2481,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
inference(rectify,[],[f376]) ).
thf(f376,axiom,
! [X219: nat,X220: nat,X221: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X219),X220)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X221),X220))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X221)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X219),X221) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_power__less__imp__less__base) ).
thf(f6681,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(definition_unfolding,[],[f5718,f5969]) ).
thf(f5718,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(cnf_transformation,[],[f3943]) ).
thf(f3943,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(flattening,[],[f3942]) ).
thf(f3942,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(ennf_transformation,[],[f2480]) ).
thf(f2480,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ) ),
inference(fool_elimination,[],[f2479]) ).
thf(f2479,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(rectify,[],[f1041]) ).
thf(f1041,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_dvd__mult__cancel) ).
thf(f6680,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(definition_unfolding,[],[f5717,f5972]) ).
thf(f5972,plain,
one_one_nat = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4421,f4404]) ).
thf(f4421,plain,
one_one_nat = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f79]) ).
thf(f79,axiom,
one_one_nat = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(f5717,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(cnf_transformation,[],[f3941]) ).
thf(f3941,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(flattening,[],[f3940]) ).
thf(f3940,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(ennf_transformation,[],[f2478]) ).
thf(f2478,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ) ),
inference(fool_elimination,[],[f2477]) ).
thf(f2477,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(rectify,[],[f541]) ).
thf(f541,axiom,
! [X19: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X19),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X19),X191))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X19)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_power__dvd__imp__le) ).
thf(f6679,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(definition_unfolding,[],[f5716,f5969]) ).
thf(f5716,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(cnf_transformation,[],[f3939]) ).
thf(f3939,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(flattening,[],[f3938]) ).
thf(f3938,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(ennf_transformation,[],[f2476]) ).
thf(f2476,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
=> ( ( zero_zero_nat != X1 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f2475]) ).
thf(f2475,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
=> ( ( zero_zero_nat != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) ) ),
inference(rectify,[],[f869]) ).
thf(f869,axiom,
! [X2: nat,X191: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X191)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X191))
=> ( ( zero_zero_nat != X191 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_divides__rev) ).
thf(f6678,plain,
! [X2: real,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(definition_unfolding,[],[f5715,f5970]) ).
thf(f5715,plain,
! [X2: real,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f3937]) ).
thf(f3937,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(flattening,[],[f3936]) ).
thf(f3936,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(ennf_transformation,[],[f2474]) ).
thf(f2474,plain,
! [X0: real,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ) ) ),
inference(fool_elimination,[],[f2473]) ).
thf(f2473,plain,
! [X0: real,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ) ),
inference(rectify,[],[f377]) ).
thf(f377,axiom,
! [X219: real,X220: nat,X221: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X219),X220)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X221),X220))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X221)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X219),X221) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_power__less__imp__less__base) ).
thf(f7946,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ) ),
inference(forward_demodulation,[],[f6677,f4464]) ).
thf(f6677,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) ) ),
inference(definition_unfolding,[],[f5712,f4404]) ).
thf(f5712,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(cnf_transformation,[],[f3931]) ).
thf(f3931,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(ennf_transformation,[],[f2468]) ).
thf(f2468,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ) ),
inference(fool_elimination,[],[f2467]) ).
thf(f2467,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ),
inference(rectify,[],[f1177]) ).
thf(f1177,axiom,
! [X16: int,X17: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X192)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X16)),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X17))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X16),X17)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_StandardRes__prop4) ).
thf(f7945,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X1)),X2) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X1) ) ),
inference(forward_demodulation,[],[f7944,f4464]) ).
thf(f7944,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X1)),X2) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) ) ),
inference(forward_demodulation,[],[f7943,f4464]) ).
thf(f7943,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) ) ),
inference(forward_demodulation,[],[f6676,f4464]) ).
thf(f6676,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) ) ),
inference(definition_unfolding,[],[f5711,f4404]) ).
thf(f5711,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(cnf_transformation,[],[f3930]) ).
thf(f3930,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(flattening,[],[f3929]) ).
thf(f3929,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(ennf_transformation,[],[f2466]) ).
thf(f2466,plain,
! [X0: nat,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2) )
=> ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1) ) ) ),
inference(fool_elimination,[],[f2465]) ).
thf(f2465,plain,
! [X0: nat,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1)),X2)
=> ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X1) ) ) ),
inference(rectify,[],[f607]) ).
thf(f607,axiom,
! [X20: nat,X18: nat,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X20)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X18)),X192)
=> ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X20) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_neg__one__power__eq__mod__m) ).
thf(f7942,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ),
inference(forward_demodulation,[],[f6675,f4464]) ).
thf(f6675,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) ) ),
inference(definition_unfolding,[],[f5710,f4404]) ).
thf(f5710,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(cnf_transformation,[],[f3928]) ).
thf(f3928,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(flattening,[],[f3927]) ).
thf(f3927,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(ennf_transformation,[],[f2464]) ).
thf(f2464,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) ) ) ),
inference(fool_elimination,[],[f2463]) ).
thf(f2463,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),X2) ) ),
inference(rectify,[],[f1082]) ).
thf(f1082,axiom,
! [X16: int,X17: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),X17),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X17)),X163) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_MultInv__prop1) ).
thf(f7941,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6674,f4464]) ).
thf(f6674,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) ) ),
inference(definition_unfolding,[],[f5709,f4404]) ).
thf(f5709,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(cnf_transformation,[],[f3926]) ).
thf(f3926,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(flattening,[],[f3925]) ).
thf(f3925,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) ) ),
inference(ennf_transformation,[],[f3158]) ).
thf(f3158,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ) ) ) ) ) ),
inference(flattening,[],[f2462]) ).
thf(f2462,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ) ) ) ) ) ),
inference(fool_elimination,[],[f2461]) ).
thf(f2461,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)
=> ( vAPP(int,$o,zprime,X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0)),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X0),X2) ) ) ) ) ),
inference(rectify,[],[f1085]) ).
thf(f1085,axiom,
! [X17: int,X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X17),zero_zero_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X17)),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),X17),X163) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_MultInv__prop5) ).
thf(f5708,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3924]) ).
thf(f3924,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2460]) ).
thf(f2460,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) ) ),
inference(fool_elimination,[],[f2459]) ).
thf(f2459,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) ),
inference(rectify,[],[f735]) ).
thf(f735,axiom,
! [X375: int,X376: int,X377: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X375),X376)),X377)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X375),X377) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_dvd__mult__left) ).
thf(f5707,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3923]) ).
thf(f3923,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2458]) ).
thf(f2458,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(fool_elimination,[],[f2457]) ).
thf(f2457,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ),
inference(rectify,[],[f732]) ).
thf(f732,axiom,
! [X372: int,X373: int,X374: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X372),X373)),X374)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X373),X374) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_dvd__mult__right) ).
thf(f5706,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ) ),
inference(cnf_transformation,[],[f3922]) ).
thf(f3922,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ) ),
inference(flattening,[],[f3921]) ).
thf(f3921,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ) ),
inference(ennf_transformation,[],[f2456]) ).
thf(f2456,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f2455]) ).
thf(f2455,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(rectify,[],[f620]) ).
thf(f620,axiom,
! [X18: int,X192: int,X191: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X192),X191))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),X191)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_zdvd__zdiffD) ).
thf(f5705,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ),
inference(cnf_transformation,[],[f3920]) ).
thf(f3920,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ),
inference(flattening,[],[f3919]) ).
thf(f3919,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) ) ),
inference(ennf_transformation,[],[f2454]) ).
thf(f2454,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f2453]) ).
thf(f2453,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(rectify,[],[f1147]) ).
thf(f1147,axiom,
! [X18: int,X192: int,X191: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X192),X191))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),X191)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X18),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_zdvd__zmod__imp__zdvd) ).
thf(f5704,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3918]) ).
thf(f3918,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2452]) ).
thf(f2452,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
inference(fool_elimination,[],[f2451]) ).
thf(f2451,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ),
inference(rectify,[],[f983]) ).
thf(f983,axiom,
! [X19: nat,X20: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X20)),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_add__lessD1) ).
thf(f5700,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3915]) ).
thf(f3915,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f3157]) ).
thf(f3157,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ) ),
inference(flattening,[],[f2446]) ).
thf(f2446,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ) ),
inference(fool_elimination,[],[f2445]) ).
thf(f2445,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2)
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(rectify,[],[f1006]) ).
thf(f1006,axiom,
! [X192: nat,X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X18)),X191)
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_add__leE) ).
thf(f5701,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3915]) ).
thf(f5699,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3914]) ).
thf(f3914,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2444]) ).
thf(f2444,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) ) ),
inference(fool_elimination,[],[f2443]) ).
thf(f2443,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) ),
inference(rectify,[],[f734]) ).
thf(f734,axiom,
! [X375: nat,X376: nat,X377: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X375),X376)),X377)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X375),X377) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_dvd__mult__left) ).
thf(f5698,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3913]) ).
thf(f3913,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2442]) ).
thf(f2442,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(fool_elimination,[],[f2441]) ).
thf(f2441,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ),
inference(rectify,[],[f731]) ).
thf(f731,axiom,
! [X372: nat,X373: nat,X374: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X372),X373)),X374)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X373),X374) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_dvd__mult__right) ).
thf(f5697,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f3912]) ).
thf(f3912,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(flattening,[],[f3911]) ).
thf(f3911,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f2440]) ).
thf(f2440,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f2439]) ).
thf(f2439,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) ) ) ),
inference(rectify,[],[f994]) ).
thf(f994,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_dvd__diffD1) ).
thf(f5696,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f3910]) ).
thf(f3910,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(flattening,[],[f3909]) ).
thf(f3909,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f2438]) ).
thf(f2438,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ) ),
inference(fool_elimination,[],[f2437]) ).
thf(f2437,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ),
inference(rectify,[],[f995]) ).
thf(f995,axiom,
! [X18: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X192) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_dvd__diffD) ).
thf(f5695,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3908]) ).
thf(f3908,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2436]) ).
thf(f2436,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X2) ) ),
inference(fool_elimination,[],[f2435]) ).
thf(f2435,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X2) ),
inference(rectify,[],[f733]) ).
thf(f733,axiom,
! [X375: real,X376: real,X377: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X375),X376)),X377)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X375),X377) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_dvd__mult__left) ).
thf(f5694,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f3907]) ).
thf(f3907,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f2434]) ).
thf(f2434,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(fool_elimination,[],[f2433]) ).
thf(f2433,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ),
inference(rectify,[],[f730]) ).
thf(f730,axiom,
! [X372: real,X373: real,X374: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X372),X373)),X374)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X373),X374) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_dvd__mult__right) ).
thf(f5693,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3906]) ).
thf(f3906,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2432]) ).
thf(f2432,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
inference(fool_elimination,[],[f2431]) ).
thf(f2431,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X18: int,X19: int,X20: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X19),X20)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X19),X18)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X20),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono) ).
thf(f7940,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6673,f4464]) ).
thf(f6673,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5690,f5971]) ).
thf(f5690,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4315]) ).
thf(f4315,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f3905,f4314]) ).
thf(f4314,plain,
! [X0: int > $o,X1: int] :
( ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) )
=> ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3905,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3904]) ).
thf(f3904,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2430]) ).
thf(f2430,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
=> ( ! [X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3) )
=> ( ( $true = vAPP(int,$o,X0,X3) )
=> ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) ) ) )
=> ( $true = vAPP(int,$o,X0,X2) ) ) ) ),
inference(fool_elimination,[],[f2429]) ).
thf(f2429,plain,
! [X0: int > $o,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int))
=> ( ! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X3)
=> ( vAPP(int,$o,X0,X3)
=> vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) ) )
=> vAPP(int,$o,X0,X2) ) ) ),
inference(rectify,[],[f1109]) ).
thf(f1109,axiom,
! [X490: int > $o,X18: int,X19: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X19)
=> ( vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),one_one_int))
=> ( ! [X493: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X493)
=> ( vAPP(int,$o,X490,X493)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X493),one_one_int)) ) )
=> vAPP(int,$o,X490,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_int__gr__induct) ).
thf(f7939,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6672,f4464]) ).
thf(f6672,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5691,f5971]) ).
thf(f5691,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4315]) ).
thf(f7938,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f7937,f4464]) ).
thf(f7937,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f7936,f4464]) ).
thf(f7936,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6671,f4757]) ).
thf(f6671,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5692,f5971,f5971]) ).
thf(f5692,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK33,X1),X0)),one_one_int)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4315]) ).
thf(f7935,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6670,f4464]) ).
thf(f6670,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5687,f5971]) ).
thf(f5687,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4313]) ).
thf(f4313,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),X2) ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f3903,f4312]) ).
thf(f4312,plain,
! [X0: int > $o,X2: int] :
( ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2) = $true ) )
=> ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),X2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3903,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2) = $true ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3902]) ).
thf(f3902,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2) = $true ) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2428]) ).
thf(f2428,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ! [X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2) = $true )
=> ( ( $true = vAPP(int,$o,X0,X3) )
=> ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) ) ) )
=> ( $true = vAPP(int,$o,X0,X1) ) ) ) ),
inference(fool_elimination,[],[f2427]) ).
thf(f2427,plain,
! [X0: int > $o,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( ! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2)
=> ( vAPP(int,$o,X0,X3)
=> vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) ) )
=> vAPP(int,$o,X0,X1) ) ) ),
inference(rectify,[],[f1106]) ).
thf(f1106,axiom,
! [X490: int > $o,X19: int,X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X19),X18)
=> ( vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X18),one_one_int))
=> ( ! [X493: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X493),X18)
=> ( vAPP(int,$o,X490,X493)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X493),one_one_int)) ) )
=> vAPP(int,$o,X490,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_int__less__induct) ).
thf(f7934,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6669,f4464]) ).
thf(f6669,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5688,f5971]) ).
thf(f5688,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4313]) ).
thf(f7933,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f7932,f4464]) ).
thf(f7932,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6668,f4464]) ).
thf(f6668,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5689,f5971,f5971]) ).
thf(f5689,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK32,X2),X0)),one_one_int)) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4313]) ).
thf(f5685,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3899]) ).
thf(f3899,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3898]) ).
thf(f3898,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2424]) ).
thf(f2424,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f2423]) ).
thf(f2423,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ),
inference(rectify,[],[f818]) ).
thf(f818,axiom,
! [X447: int,X448: int,X449: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X448),X449)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X447),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X449),X447)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X448),X447)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_mult__strict__right__mono__neg) ).
thf(f5684,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3897]) ).
thf(f3897,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3896]) ).
thf(f3896,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2422]) ).
thf(f2422,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2421]) ).
thf(f2421,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(rectify,[],[f816]) ).
thf(f816,axiom,
! [X444: int,X445: int,X446: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X445),X446)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X444),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X444),X446)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X444),X445)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_mult__strict__left__mono__neg) ).
thf(f5682,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3893]) ).
thf(f3893,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3892]) ).
thf(f3892,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2418]) ).
thf(f2418,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2417]) ).
thf(f2417,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) ) ),
inference(rectify,[],[f827]) ).
thf(f827,axiom,
! [X456: int,X457: int,X458: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X457),X458)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X456)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X457),X456)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X458),X456)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_mult__strict__right__mono) ).
thf(f5680,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3889]) ).
thf(f3889,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(flattening,[],[f3888]) ).
thf(f3888,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2414]) ).
thf(f2414,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2413]) ).
thf(f2413,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(rectify,[],[f824]) ).
thf(f824,axiom,
! [X453: int,X454: int,X455: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X454),X455)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X453)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X453),X454)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X453),X455)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_mult__strict__left__mono) ).
thf(f5678,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3885]) ).
thf(f3885,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2410]) ).
thf(f2410,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ) ),
inference(fool_elimination,[],[f2409]) ).
thf(f2409,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X18: int,X19: int,X20: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X19),X20)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),X19)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zadd__left__mono) ).
thf(f5677,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3884]) ).
thf(f3884,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3883]) ).
thf(f3883,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2408]) ).
thf(f2408,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) ) ) ),
inference(fool_elimination,[],[f2407]) ).
thf(f2407,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) ) ),
inference(rectify,[],[f40]) ).
thf(f40,axiom,
! [X18: int,X19: int,X20: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X19),X20)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X20),X18)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X19),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zle__trans) ).
thf(f5676,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3882]) ).
thf(f3882,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3881]) ).
thf(f3881,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2406]) ).
thf(f2406,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f2405]) ).
thf(f2405,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ),
inference(rectify,[],[f785]) ).
thf(f785,axiom,
! [X417: int,X418: int,X419: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X418),X419)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X417),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X419),X417)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X418),X417)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_mult__right__mono__neg) ).
thf(f5675,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3880]) ).
thf(f3880,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3879]) ).
thf(f3879,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2404]) ).
thf(f2404,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2403]) ).
thf(f2403,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(rectify,[],[f783]) ).
thf(f783,axiom,
! [X414: int,X415: int,X416: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X415),X416)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X414),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X414),X416)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X414),X415)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_mult__left__mono__neg) ).
thf(f5668,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4311]) ).
thf(f4311,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)) ) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f3870,f4310]) ).
thf(f4310,plain,
! [X0: int > $o,X1: int] :
( ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) ) )
=> ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3870,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) ) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3869]) ).
thf(f3869,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) ) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2394]) ).
thf(f2394,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,X0,X1) )
=> ( ! [X3: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3) )
=> ( ( $true = vAPP(int,$o,X0,X3) )
=> ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) ) ) )
=> ( $true = vAPP(int,$o,X0,X2) ) ) ) ),
inference(fool_elimination,[],[f2393]) ).
thf(f2393,plain,
! [X0: int > $o,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,X0,X1)
=> ( ! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X3)
=> ( vAPP(int,$o,X0,X3)
=> vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)) ) )
=> vAPP(int,$o,X0,X2) ) ) ),
inference(rectify,[],[f1108]) ).
thf(f1108,axiom,
! [X490: int > $o,X18: int,X19: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),X19)
=> ( vAPP(int,$o,X490,X18)
=> ( ! [X493: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),X493)
=> ( vAPP(int,$o,X490,X493)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X493),one_one_int)) ) )
=> vAPP(int,$o,X490,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_int__ge__induct) ).
thf(f5669,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4311]) ).
thf(f7931,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(forward_demodulation,[],[f7930,f4464]) ).
thf(f7930,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0))) )
| ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6666,f4757]) ).
thf(f6666,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5670,f5971]) ).
thf(f5670,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK31,X1),X0)),one_one_int)) )
| ( $true != vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4311]) ).
thf(f5665,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),X2) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4309]) ).
thf(f4309,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),X2) ) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f3868,f4308]) ).
thf(f4308,plain,
! [X0: int > $o,X2: int] :
( ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2) = $true ) )
=> ( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),one_one_int)) )
& ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),X2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3868,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2) = $true ) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(flattening,[],[f3867]) ).
thf(f3867,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ? [X3: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) )
& ( $true = vAPP(int,$o,X0,X3) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2) = $true ) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2392]) ).
thf(f2392,plain,
! [X0: int > $o,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,X0,X2) )
=> ( ! [X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2) = $true )
=> ( ( $true = vAPP(int,$o,X0,X3) )
=> ( $true = vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) ) ) )
=> ( $true = vAPP(int,$o,X0,X1) ) ) ) ),
inference(fool_elimination,[],[f2391]) ).
thf(f2391,plain,
! [X0: int > $o,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2)
=> ( vAPP(int,$o,X0,X2)
=> ( ! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2)
=> ( vAPP(int,$o,X0,X3)
=> vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int)) ) )
=> vAPP(int,$o,X0,X1) ) ) ),
inference(rectify,[],[f1105]) ).
thf(f1105,axiom,
! [X490: int > $o,X19: int,X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X19),X18)
=> ( vAPP(int,$o,X490,X18)
=> ( ! [X493: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X493),X18)
=> ( vAPP(int,$o,X490,X493)
=> vAPP(int,$o,X490,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X493),one_one_int)) ) )
=> vAPP(int,$o,X490,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_int__le__induct) ).
thf(f5666,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true = vAPP(int,$o,X0,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4309]) ).
thf(f7929,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(forward_demodulation,[],[f6665,f4464]) ).
thf(f6665,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(definition_unfolding,[],[f5667,f5971]) ).
thf(f5667,plain,
! [X2: int,X0: int > $o,X1: int] :
( ( $true = vAPP(int,$o,X0,X1) )
| ( $true != vAPP(int,$o,X0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,vAPP(int,sTfun(sTfun(int,$o),int),sK30,X2),X0)),one_one_int)) )
| ( $true != vAPP(int,$o,X0,X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X2) ) ),
inference(cnf_transformation,[],[f4309]) ).
thf(f5664,plain,
! [X2: int,X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3866]) ).
thf(f3866,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2390]) ).
thf(f2390,plain,
! [X0: nat,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) ) ),
inference(fool_elimination,[],[f2389]) ).
thf(f2389,plain,
! [X0: nat,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)) ),
inference(rectify,[],[f331]) ).
thf(f331,axiom,
! [X193: nat,X194: int,X195: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X194),X195)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X194),X193)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X195),X193)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_dvd__power__same) ).
thf(f5663,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3865]) ).
thf(f3865,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2388]) ).
thf(f2388,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) ) ),
inference(fool_elimination,[],[f2387]) ).
thf(f2387,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)) ),
inference(rectify,[],[f747]) ).
thf(f747,axiom,
! [X388: int,X389: int,X390: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X389),X390)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X389),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X390),X388)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_dvd__mult2) ).
thf(f5662,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3864]) ).
thf(f3864,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2386]) ).
thf(f2386,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ) ),
inference(fool_elimination,[],[f2385]) ).
thf(f2385,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(rectify,[],[f744]) ).
thf(f744,axiom,
! [X385: int,X386: int,X387: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X386),X387)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X386),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X385),X387)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_dvd__mult) ).
thf(f5661,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3863]) ).
thf(f3863,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(flattening,[],[f3862]) ).
thf(f3862,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2384]) ).
thf(f2384,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2383]) ).
thf(f2383,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
inference(rectify,[],[f756]) ).
thf(f756,axiom,
! [X395: int,X396: int,X397: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X396),X397)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X396),X395)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X396),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X397),X395)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_dvd__add) ).
thf(f5660,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3861]) ).
thf(f3861,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(flattening,[],[f3860]) ).
thf(f3860,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2382]) ).
thf(f2382,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2381]) ).
thf(f2381,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) ) ),
inference(rectify,[],[f761]) ).
thf(f761,axiom,
! [X399: int,X400: int,X401: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X400),X401)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X400),X399)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X400),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X401),X399)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_dvd__diff) ).
thf(f5659,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3859]) ).
thf(f3859,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(flattening,[],[f3858]) ).
thf(f3858,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2380]) ).
thf(f2380,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2379]) ).
thf(f2379,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X0)) ) ),
inference(rectify,[],[f1148]) ).
thf(f1148,axiom,
! [X191: int,X499: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X499),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X499),X191)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X499),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X192),X191)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_zdvd__zmod) ).
thf(f5658,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(cnf_transformation,[],[f3857]) ).
thf(f3857,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(flattening,[],[f3856]) ).
thf(f3856,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) ) ),
inference(ennf_transformation,[],[f2378]) ).
thf(f2378,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) ) ) ),
inference(fool_elimination,[],[f2377]) ).
thf(f2377,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) ) ),
inference(rectify,[],[f684]) ).
thf(f684,axiom,
! [X347: int,X348: int,X349: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X348),X349)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X349),X347)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X348),X347) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_dvd__trans) ).
thf(f5657,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3855]) ).
thf(f3855,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2376]) ).
thf(f2376,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2375]) ).
thf(f2375,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ),
inference(rectify,[],[f980]) ).
thf(f980,axiom,
! [X18: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_add__less__mono1) ).
thf(f5656,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3854]) ).
thf(f3854,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2374]) ).
thf(f2374,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X2) ) ),
inference(fool_elimination,[],[f2373]) ).
thf(f2373,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X2) ),
inference(rectify,[],[f897]) ).
thf(f897,axiom,
! [X191: nat,X20: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X191)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_less__imp__diff__less) ).
thf(f5655,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3853]) ).
thf(f3853,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2372]) ).
thf(f2372,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2371]) ).
thf(f2371,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ),
inference(rectify,[],[f978]) ).
thf(f978,axiom,
! [X192: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X192)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_trans__less__add1) ).
thf(f5654,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3852]) ).
thf(f3852,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2370]) ).
thf(f2370,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
inference(fool_elimination,[],[f2369]) ).
thf(f2369,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(rectify,[],[f979]) ).
thf(f979,axiom,
! [X192: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_trans__less__add2) ).
thf(f5653,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3851]) ).
thf(f3851,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3850]) ).
thf(f3850,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2368]) ).
thf(f2368,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2367]) ).
thf(f2367,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(rectify,[],[f896]) ).
thf(f896,axiom,
! [X38: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X38)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X38),X191)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X38),X192)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_diff__less__mono2) ).
thf(f5652,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3849]) ).
thf(f3849,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3848]) ).
thf(f3848,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2366]) ).
thf(f2366,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2365]) ).
thf(f2365,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) ) ),
inference(rectify,[],[f992]) ).
thf(f992,axiom,
! [X216: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X216),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X216)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),X216)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_diff__less__mono) ).
thf(f7928,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(forward_demodulation,[],[f6664,f4464]) ).
thf(f6664,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5651,f5971]) ).
thf(f5651,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3847]) ).
thf(f3847,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3846]) ).
thf(f3846,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2364]) ).
thf(f2364,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),one_one_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f2363]) ).
thf(f2363,plain,
! [X0: int,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),one_one_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ) ),
inference(rectify,[],[f381]) ).
thf(f381,axiom,
! [X225: int,X226: nat,X227: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X226),X227)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X225)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X225),one_one_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X225),X227)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X225),X226)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_power__strict__decreasing) ).
thf(f7927,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(forward_demodulation,[],[f6663,f4464]) ).
thf(f6663,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5650,f5971]) ).
thf(f5650,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3845]) ).
thf(f3845,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3844]) ).
thf(f3844,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2362]) ).
thf(f2362,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2361]) ).
thf(f2361,plain,
! [X0: int,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ) ),
inference(rectify,[],[f503]) ).
thf(f503,axiom,
! [X300: int,X301: nat,X302: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X301),X302)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X300)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X300),X301)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X300),X302)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_power__strict__increasing) ).
thf(f6659,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5646,f5969]) ).
thf(f5646,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3837]) ).
thf(f3837,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3836]) ).
thf(f3836,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2354]) ).
thf(f2354,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2353]) ).
thf(f2353,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ),
inference(rectify,[],[f1035]) ).
thf(f1035,axiom,
! [X18: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X19),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X20),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_mult__less__mono1) ).
thf(f6658,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5645,f5969]) ).
thf(f5645,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3835]) ).
thf(f3835,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3834]) ).
thf(f3834,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2352]) ).
thf(f2352,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2351]) ).
thf(f2351,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(rectify,[],[f1034]) ).
thf(f1034,axiom,
! [X18: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X19)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_mult__less__mono2) ).
thf(f6657,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5644,f5972,f5969]) ).
thf(f5644,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3833]) ).
thf(f3833,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3832]) ).
thf(f3832,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2350]) ).
thf(f2350,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),one_one_nat) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f2349]) ).
thf(f2349,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),one_one_nat)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ),
inference(rectify,[],[f382]) ).
thf(f382,axiom,
! [X225: nat,X226: nat,X227: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X226),X227)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X225)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X225),one_one_nat)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X225),X227)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X225),X226)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_power__strict__decreasing) ).
thf(f6656,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5643,f5972]) ).
thf(f5643,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3831]) ).
thf(f3831,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3830]) ).
thf(f3830,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2348]) ).
thf(f2348,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2347]) ).
thf(f2347,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(rectify,[],[f502]) ).
thf(f502,axiom,
! [X300: nat,X301: nat,X302: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X301),X302)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X300)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X300),X301)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X300),X302)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_power__strict__increasing) ).
thf(f7926,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(subsumption_resolution,[],[f6655,f6249]) ).
thf(f6655,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5642,f5969,f5969]) ).
thf(f5642,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3829]) ).
thf(f3829,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3828]) ).
thf(f3828,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2346]) ).
thf(f2346,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) ) ) ) ),
inference(fool_elimination,[],[f2345]) ).
thf(f2345,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) ) ) ),
inference(rectify,[],[f340]) ).
thf(f340,axiom,
! [X199: nat,X200: nat,X201: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X200),X201)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X200)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X199)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X200),X199)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X201),X199)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_power__strict__mono) ).
thf(f6654,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5641,f5973,f5970]) ).
thf(f5641,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),one_one_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3827]) ).
thf(f3827,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),one_one_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3826]) ).
thf(f3826,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),one_one_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2344]) ).
thf(f2344,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),one_one_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f2343]) ).
thf(f2343,plain,
! [X0: real,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),one_one_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ) ),
inference(rectify,[],[f383]) ).
thf(f383,axiom,
! [X225: real,X226: nat,X227: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X226),X227)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X225)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X225),one_one_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X225),X227)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X225),X226)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_power__strict__decreasing) ).
thf(f6653,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5640,f5973]) ).
thf(f5640,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3825]) ).
thf(f3825,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(flattening,[],[f3824]) ).
thf(f3824,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2342]) ).
thf(f2342,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2341]) ).
thf(f2341,plain,
! [X0: real,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ) ),
inference(rectify,[],[f501]) ).
thf(f501,axiom,
! [X300: real,X301: nat,X302: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X301),X302)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X300)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X300),X301)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X300),X302)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_power__strict__increasing) ).
thf(f5639,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3823]) ).
thf(f3823,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2340]) ).
thf(f2340,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ) ),
inference(fool_elimination,[],[f2339]) ).
thf(f2339,plain,
! [X0: int,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ),
inference(rectify,[],[f316]) ).
thf(f316,axiom,
! [X177: int,X178: nat,X179: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X178),X179)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X177),X178)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X177),X179)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_le__imp__power__dvd) ).
thf(f5636,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3820]) ).
thf(f3820,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2334]) ).
thf(f2334,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2333]) ).
thf(f2333,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ),
inference(rectify,[],[f1002]) ).
thf(f1002,axiom,
! [X18: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_add__le__mono1) ).
thf(f5635,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3819]) ).
thf(f3819,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2332]) ).
thf(f2332,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f2331]) ).
thf(f2331,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ),
inference(rectify,[],[f944]) ).
thf(f944,axiom,
! [X38: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X38),X191)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X38),X192)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_diff__le__mono2) ).
thf(f5634,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3818]) ).
thf(f3818,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2330]) ).
thf(f2330,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2329]) ).
thf(f2329,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) ),
inference(rectify,[],[f945]) ).
thf(f945,axiom,
! [X38: nat,X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X38)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_diff__le__mono) ).
thf(f5633,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3817]) ).
thf(f3817,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2328]) ).
thf(f2328,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(fool_elimination,[],[f2327]) ).
thf(f2327,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ),
inference(rectify,[],[f317]) ).
thf(f317,axiom,
! [X177: nat,X178: nat,X179: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X178),X179)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X177),X178)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X177),X179)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_le__imp__power__dvd) ).
thf(f5632,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3816]) ).
thf(f3816,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2326]) ).
thf(f2326,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1)) ) ),
inference(fool_elimination,[],[f2325]) ).
thf(f2325,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1)) ),
inference(rectify,[],[f1009]) ).
thf(f1009,axiom,
! [X192: nat,X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),X192)),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_le__add__diff) ).
thf(f5631,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3815]) ).
thf(f3815,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2324]) ).
thf(f2324,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ) ),
inference(fool_elimination,[],[f2323]) ).
thf(f2323,plain,
! [X0: real,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ),
inference(rectify,[],[f315]) ).
thf(f315,axiom,
! [X177: real,X178: nat,X179: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X178),X179)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X177),X178)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X177),X179)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd) ).
thf(f5630,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3814]) ).
thf(f3814,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2322]) ).
thf(f2322,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
inference(fool_elimination,[],[f2321]) ).
thf(f2321,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(rectify,[],[f1001]) ).
thf(f1001,axiom,
! [X192: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_trans__le__add2) ).
thf(f5629,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3813]) ).
thf(f3813,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2320]) ).
thf(f2320,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2319]) ).
thf(f2319,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ),
inference(rectify,[],[f1000]) ).
thf(f1000,axiom,
! [X192: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X192)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_trans__le__add1) ).
thf(f7012,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(binary_proxy_clausification,[],[f5628]) ).
thf(f5628,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3812]) ).
thf(f3812,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2318]) ).
thf(f2318,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(fool_elimination,[],[f2317]) ).
thf(f2317,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(rectify,[],[f1012]) ).
thf(f1012,axiom,
! [X19: nat,X18: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X18))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_le__diff__conv2) ).
thf(f7011,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(binary_proxy_clausification,[],[f5628]) ).
thf(f5625,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3810]) ).
thf(f3810,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3809]) ).
thf(f3809,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2314]) ).
thf(f2314,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) ) ),
inference(fool_elimination,[],[f2313]) ).
thf(f2313,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) ),
inference(rectify,[],[f941]) ).
thf(f941,axiom,
! [X18: nat,X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),X18)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940_le__trans) ).
thf(f7014,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f5624]) ).
thf(f5624,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3808]) ).
thf(f3808,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3807]) ).
thf(f3807,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2312]) ).
thf(f2312,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2311]) ).
thf(f2311,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ) ),
inference(rectify,[],[f991]) ).
thf(f991,axiom,
! [X191: nat,X18: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X18))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_less__diff__iff) ).
thf(f7013,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f5624]) ).
thf(f7016,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f5623]) ).
thf(f5623,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3806]) ).
thf(f3806,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3805]) ).
thf(f3805,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2310]) ).
thf(f2310,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2309]) ).
thf(f2309,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ) ),
inference(rectify,[],[f949]) ).
thf(f949,axiom,
! [X191: nat,X18: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X18))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_le__diff__iff) ).
thf(f7015,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f5623]) ).
thf(f5621,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f4306]) ).
thf(f4306,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(nnf_transformation,[],[f3804]) ).
thf(f3804,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) )
<=> ( X0 = X2 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3803]) ).
thf(f3803,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) )
<=> ( X0 = X2 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2308]) ).
thf(f2308,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) )
<=> ( X0 = X2 ) ) ) ),
inference(fool_elimination,[],[f2307]) ).
thf(f2307,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1) )
<=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f947]) ).
thf(f947,axiom,
! [X191: nat,X18: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X18) )
<=> ( X191 = X192 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_eq__diff__iff) ).
thf(f5620,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3802]) ).
thf(f3802,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3801]) ).
thf(f3801,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2306]) ).
thf(f2306,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2305]) ).
thf(f2305,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ) ),
inference(rectify,[],[f948]) ).
thf(f948,axiom,
! [X191: nat,X18: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_Nat_Odiff__diff__eq) ).
thf(f7925,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(forward_demodulation,[],[f6652,f4464]) ).
thf(f6652,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5619,f5971]) ).
thf(f5619,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3800]) ).
thf(f3800,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3799]) ).
thf(f3799,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2304]) ).
thf(f2304,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),one_one_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f2303]) ).
thf(f2303,plain,
! [X0: int,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),one_one_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ) ),
inference(rectify,[],[f378]) ).
thf(f378,axiom,
! [X222: int,X223: nat,X224: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X223),X224)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X222)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X222),one_one_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X222),X224)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X222),X223)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_power__decreasing) ).
thf(f7924,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(forward_demodulation,[],[f6651,f4464]) ).
thf(f6651,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5618,f5971]) ).
thf(f5618,plain,
! [X2: nat,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3798]) ).
thf(f3798,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3797]) ).
thf(f3797,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2302]) ).
thf(f2302,plain,
! [X0: int,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2301]) ).
thf(f2301,plain,
! [X0: int,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ) ),
inference(rectify,[],[f491]) ).
thf(f491,axiom,
! [X288: int,X289: nat,X290: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X289),X290)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X288)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X288),X289)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X288),X290)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_power__increasing) ).
thf(f7923,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(subsumption_resolution,[],[f6649,f6249]) ).
thf(f6649,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5616,f5969]) ).
thf(f5616,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3794]) ).
thf(f3794,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3793]) ).
thf(f3793,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2298]) ).
thf(f2298,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2297]) ).
thf(f2297,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(rectify,[],[f790]) ).
thf(f790,axiom,
! [X423: nat,X424: nat,X425: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X424),X425)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X423)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X423),X424)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X423),X425)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_mult__left__mono) ).
thf(f7922,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(subsumption_resolution,[],[f6648,f6249]) ).
thf(f6648,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5615,f5969]) ).
thf(f5615,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3792]) ).
thf(f3792,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3791]) ).
thf(f3791,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2296]) ).
thf(f2296,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2295]) ).
thf(f2295,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ),
inference(rectify,[],[f793]) ).
thf(f793,axiom,
! [X426: nat,X427: nat,X428: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X427),X428)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X426)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X427),X426)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X428),X426)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_mult__right__mono) ).
thf(f7921,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(subsumption_resolution,[],[f6647,f6249]) ).
thf(f6647,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5614,f5969]) ).
thf(f5614,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3790]) ).
thf(f3790,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3789]) ).
thf(f3789,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2294]) ).
thf(f2294,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2293]) ).
thf(f2293,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) ) ),
inference(rectify,[],[f367]) ).
thf(f367,axiom,
! [X211: nat,X212: nat,X213: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X212),X213)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X212)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X212),X211)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X213),X211)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_power__mono) ).
thf(f7920,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(subsumption_resolution,[],[f6646,f6249]) ).
thf(f6646,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5613,f5972,f5969]) ).
thf(f5613,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3788]) ).
thf(f3788,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3787]) ).
thf(f3787,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2292]) ).
thf(f2292,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),one_one_nat) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f2291]) ).
thf(f2291,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),one_one_nat)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ),
inference(rectify,[],[f379]) ).
thf(f379,axiom,
! [X222: nat,X223: nat,X224: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X223),X224)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X222)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X222),one_one_nat)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X222),X224)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X222),X223)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_power__decreasing) ).
thf(f6645,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5612,f5972]) ).
thf(f5612,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3786]) ).
thf(f3786,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3785]) ).
thf(f3785,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2290]) ).
thf(f2290,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2289]) ).
thf(f2289,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ) ),
inference(rectify,[],[f490]) ).
thf(f490,axiom,
! [X288: nat,X289: nat,X290: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X289),X290)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X288)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X288),X289)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X288),X290)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_power__increasing) ).
thf(f6644,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5611,f5973,f5970]) ).
thf(f5611,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),one_one_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3784]) ).
thf(f3784,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),one_one_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3783]) ).
thf(f3783,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),one_one_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2288]) ).
thf(f2288,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),one_one_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f2287]) ).
thf(f2287,plain,
! [X0: real,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),one_one_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ) ),
inference(rectify,[],[f380]) ).
thf(f380,axiom,
! [X222: real,X223: nat,X224: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X223),X224)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X222)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X222),one_one_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X222),X224)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X222),X223)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_power__decreasing) ).
thf(f6643,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(definition_unfolding,[],[f5610,f5973]) ).
thf(f5610,plain,
! [X2: nat,X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3782]) ).
thf(f3782,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(flattening,[],[f3781]) ).
thf(f3781,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2286]) ).
thf(f2286,plain,
! [X0: real,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2285]) ).
thf(f2285,plain,
! [X0: real,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ) ),
inference(rectify,[],[f489]) ).
thf(f489,axiom,
! [X288: real,X289: nat,X290: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X289),X290)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X288)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X288),X289)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X288),X290)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_power__increasing) ).
thf(f5608,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3779]) ).
thf(f3779,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2282]) ).
thf(f2282,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1) ) ),
inference(fool_elimination,[],[f2281]) ).
thf(f2281,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),X1) ) ),
inference(rectify,[],[f1017]) ).
thf(f1017,axiom,
! [X19: nat,X18: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X20)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X18)),X19) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X19)),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_diff__add__assoc2) ).
thf(f5606,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3777]) ).
thf(f3777,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2278]) ).
thf(f2278,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ) ),
inference(fool_elimination,[],[f2277]) ).
thf(f2277,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ) ),
inference(rectify,[],[f1015]) ).
thf(f1015,axiom,
! [X19: nat,X18: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X20)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X18)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X20)),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_diff__add__assoc) ).
thf(f5605,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3776]) ).
thf(f3776,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2276]) ).
thf(f2276,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(fool_elimination,[],[f2275]) ).
thf(f2275,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
inference(rectify,[],[f1007]) ).
thf(f1007,axiom,
! [X19: nat,X18: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X20)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X20),X18)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X18)),X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_diff__diff__right) ).
thf(f5604,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3775]) ).
thf(f3775,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2274]) ).
thf(f2274,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2273]) ).
thf(f2273,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ),
inference(rectify,[],[f766]) ).
thf(f766,axiom,
! [X216: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X216)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X3),X216)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_divides__mul__r) ).
thf(f5603,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3774]) ).
thf(f3774,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2272]) ).
thf(f2272,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(fool_elimination,[],[f2271]) ).
thf(f2271,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f765]) ).
thf(f765,axiom,
! [X216: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X216),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X216),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_divides__mul__l) ).
thf(f5601,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3772]) ).
thf(f3772,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2268]) ).
thf(f2268,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2267]) ).
thf(f2267,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)) ),
inference(rectify,[],[f770]) ).
thf(f770,axiom,
! [X191: nat,X16: nat,X17: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X17)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),X191)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X17),X191)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_divides__exp) ).
thf(f5600,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3771]) ).
thf(f3771,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2266]) ).
thf(f2266,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ) ),
inference(fool_elimination,[],[f2265]) ).
thf(f2265,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f743]) ).
thf(f743,axiom,
! [X385: nat,X386: nat,X387: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X386),X387)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X386),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X385),X387)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_dvd__mult) ).
thf(f5599,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3770]) ).
thf(f3770,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2264]) ).
thf(f2264,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ) ),
inference(fool_elimination,[],[f2263]) ).
thf(f2263,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)) ),
inference(rectify,[],[f746]) ).
thf(f746,axiom,
! [X388: nat,X389: nat,X390: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X389),X390)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X389),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X390),X388)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_dvd__mult2) ).
thf(f5598,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3769]) ).
thf(f3769,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3768]) ).
thf(f3768,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2262]) ).
thf(f2262,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ),
inference(fool_elimination,[],[f2261]) ).
thf(f2261,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ),
inference(rectify,[],[f764]) ).
thf(f764,axiom,
! [X3: nat,X218: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X218),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X218),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X218),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_divides__add__revr) ).
thf(f5597,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3767]) ).
thf(f3767,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3766]) ).
thf(f3766,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2260]) ).
thf(f2260,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2259]) ).
thf(f2259,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)) ) ),
inference(rectify,[],[f755]) ).
thf(f755,axiom,
! [X395: nat,X396: nat,X397: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X396),X397)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X396),X395)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X396),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X397),X395)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_dvd__add) ).
thf(f5596,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3765]) ).
thf(f3765,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3764]) ).
thf(f3764,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2258]) ).
thf(f2258,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2257]) ).
thf(f2257,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X0)) ) ),
inference(rectify,[],[f927]) ).
thf(f927,axiom,
! [X191: nat,X18: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_dvd__diff__nat) ).
thf(f5594,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3761]) ).
thf(f3761,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3760]) ).
thf(f3760,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f2254]) ).
thf(f2254,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ),
inference(fool_elimination,[],[f2253]) ).
thf(f2253,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ),
inference(rectify,[],[f683]) ).
thf(f683,axiom,
! [X347: nat,X348: nat,X349: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X348),X349)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X349),X347)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X348),X347) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_dvd__trans) ).
thf(f5592,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3759]) ).
thf(f3759,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3758]) ).
thf(f3758,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f3156]) ).
thf(f3156,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ) ),
inference(flattening,[],[f2252]) ).
thf(f2252,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ) ),
inference(fool_elimination,[],[f2251]) ).
thf(f2251,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2)
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ),
inference(rectify,[],[f910]) ).
thf(f910,axiom,
! [X15: nat,X16: nat,X17: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X17)
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X15),X17)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X17),X15) )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X15),X16)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_dvd_Ole__less__trans) ).
thf(f6642,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5590,f5970]) ).
thf(f5590,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3755]) ).
thf(f3755,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(flattening,[],[f3754]) ).
thf(f3754,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2248]) ).
thf(f2248,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ) ),
inference(fool_elimination,[],[f2247]) ).
thf(f2247,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ),
inference(rectify,[],[f817]) ).
thf(f817,axiom,
! [X447: real,X448: real,X449: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X448),X449)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X447),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X449),X447)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X448),X447)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_mult__strict__right__mono__neg) ).
thf(f6641,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5589,f5970]) ).
thf(f5589,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3753]) ).
thf(f3753,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(flattening,[],[f3752]) ).
thf(f3752,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2246]) ).
thf(f2246,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2245]) ).
thf(f2245,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(rectify,[],[f815]) ).
thf(f815,axiom,
! [X444: real,X445: real,X446: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X445),X446)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X444),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X444),X446)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X444),X445)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_mult__strict__left__mono__neg) ).
thf(f6639,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5587,f5970]) ).
thf(f5587,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3749]) ).
thf(f3749,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(flattening,[],[f3748]) ).
thf(f3748,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2242]) ).
thf(f2242,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2241]) ).
thf(f2241,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) ) ),
inference(rectify,[],[f825]) ).
thf(f825,axiom,
! [X456: real,X457: real,X458: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X457),X458)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X456)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X457),X456)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X458),X456)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_mult__strict__right__mono) ).
thf(f6637,plain,
! [X2: real,X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5585,f5969,f5970]) ).
thf(f5585,plain,
! [X2: real,X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3745]) ).
thf(f3745,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(flattening,[],[f3744]) ).
thf(f3744,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2238]) ).
thf(f2238,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) ) ) ) ),
inference(fool_elimination,[],[f2237]) ).
thf(f2237,plain,
! [X0: nat,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) ) ) ),
inference(rectify,[],[f341]) ).
thf(f341,axiom,
! [X199: nat,X200: real,X201: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X200),X201)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X200)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X199)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X200),X199)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X201),X199)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_power__strict__mono) ).
thf(f5584,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3743]) ).
thf(f3743,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2236]) ).
thf(f2236,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
inference(fool_elimination,[],[f2235]) ).
thf(f2235,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(rectify,[],[f692]) ).
thf(f692,axiom,
! [X15: real,X16: real,X17: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X16),X17)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X16)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_real__add__left__mono) ).
thf(f5583,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3742]) ).
thf(f3742,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(flattening,[],[f3741]) ).
thf(f3741,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2234]) ).
thf(f2234,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) ) ) ),
inference(fool_elimination,[],[f2233]) ).
thf(f2233,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X2),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) ) ),
inference(rectify,[],[f883]) ).
thf(f883,axiom,
! [X18: real,X19: real,X20: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X19),X20)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X20),X18)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X19),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_real__le__trans) ).
thf(f6636,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5582,f5970]) ).
thf(f5582,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3740]) ).
thf(f3740,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(flattening,[],[f3739]) ).
thf(f3739,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2232]) ).
thf(f2232,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ) ),
inference(fool_elimination,[],[f2231]) ).
thf(f2231,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ),
inference(rectify,[],[f784]) ).
thf(f784,axiom,
! [X417: real,X418: real,X419: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X418),X419)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X417),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X419),X417)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X418),X417)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_mult__right__mono__neg) ).
thf(f6635,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5581,f5970]) ).
thf(f5581,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3738]) ).
thf(f3738,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(flattening,[],[f3737]) ).
thf(f3737,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2230]) ).
thf(f2230,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ) ),
inference(fool_elimination,[],[f2229]) ).
thf(f2229,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(rectify,[],[f782]) ).
thf(f782,axiom,
! [X414: real,X415: real,X416: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X415),X416)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X414),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X414),X416)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X414),X415)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_mult__left__mono__neg) ).
thf(f6634,plain,
! [X2: real,X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5580,f5970]) ).
thf(f5580,plain,
! [X2: real,X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3736]) ).
thf(f3736,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(flattening,[],[f3735]) ).
thf(f3735,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2228]) ).
thf(f2228,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2227]) ).
thf(f2227,plain,
! [X0: nat,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) ) ),
inference(rectify,[],[f368]) ).
thf(f368,axiom,
! [X211: nat,X212: real,X213: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X212),X213)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X212)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X212),X211)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X213),X211)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_power__mono) ).
thf(f6632,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5578,f5970]) ).
thf(f5578,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3732]) ).
thf(f3732,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(flattening,[],[f3731]) ).
thf(f3731,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2224]) ).
thf(f2224,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2223]) ).
thf(f2223,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) ) ),
inference(rectify,[],[f792]) ).
thf(f792,axiom,
! [X426: real,X427: real,X428: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X427),X428)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X426)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X427),X426)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X428),X426)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_mult__right__mono) ).
thf(f6631,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(definition_unfolding,[],[f5577,f5970]) ).
thf(f5577,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3730]) ).
thf(f3730,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(flattening,[],[f3729]) ).
thf(f3729,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2222]) ).
thf(f2222,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ) ),
inference(fool_elimination,[],[f2221]) ).
thf(f2221,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(rectify,[],[f789]) ).
thf(f789,axiom,
! [X423: real,X424: real,X425: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X424),X425)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X423)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X423),X424)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X423),X425)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_mult__left__mono) ).
thf(f5576,plain,
! [X2: real,X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3728]) ).
thf(f3728,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2220]) ).
thf(f2220,plain,
! [X0: nat,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) ) ),
inference(fool_elimination,[],[f2219]) ).
thf(f2219,plain,
! [X0: nat,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)) ),
inference(rectify,[],[f330]) ).
thf(f330,axiom,
! [X193: nat,X194: real,X195: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X194),X195)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X194),X193)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X195),X193)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_dvd__power__same) ).
thf(f5575,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3727]) ).
thf(f3727,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2218]) ).
thf(f2218,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ) ),
inference(fool_elimination,[],[f2217]) ).
thf(f2217,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ),
inference(rectify,[],[f742]) ).
thf(f742,axiom,
! [X385: real,X386: real,X387: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X386),X387)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X386),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X385),X387)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_dvd__mult) ).
thf(f5574,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3726]) ).
thf(f3726,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2216]) ).
thf(f2216,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) ) ),
inference(fool_elimination,[],[f2215]) ).
thf(f2215,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)) ),
inference(rectify,[],[f745]) ).
thf(f745,axiom,
! [X388: real,X389: real,X390: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X389),X390)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X389),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X390),X388)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_dvd__mult2) ).
thf(f5573,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3725]) ).
thf(f3725,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(flattening,[],[f3724]) ).
thf(f3724,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2214]) ).
thf(f2214,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2213]) ).
thf(f2213,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) ) ),
inference(rectify,[],[f754]) ).
thf(f754,axiom,
! [X395: real,X396: real,X397: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X396),X397)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X396),X395)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X396),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X397),X395)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_dvd__add) ).
thf(f5572,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3723]) ).
thf(f3723,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(flattening,[],[f3722]) ).
thf(f3722,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2212]) ).
thf(f2212,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ) ) ),
inference(fool_elimination,[],[f2211]) ).
thf(f2211,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ) ),
inference(rectify,[],[f760]) ).
thf(f760,axiom,
! [X399: real,X400: real,X401: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X400),X401)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X400),X399)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X400),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X401),X399)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_dvd__diff) ).
thf(f5571,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(cnf_transformation,[],[f3721]) ).
thf(f3721,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(flattening,[],[f3720]) ).
thf(f3720,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) ) ),
inference(ennf_transformation,[],[f2210]) ).
thf(f2210,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) ) ) ),
inference(fool_elimination,[],[f2209]) ).
thf(f2209,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X2),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X1),X0) ) ),
inference(rectify,[],[f682]) ).
thf(f682,axiom,
! [X347: real,X348: real,X349: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X348),X349)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X349),X347)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X348),X347) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_dvd__trans) ).
thf(f7019,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5570]) ).
thf(f5570,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3719]) ).
thf(f3719,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ),
inference(ennf_transformation,[],[f2208]) ).
thf(f2208,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(fool_elimination,[],[f2207]) ).
thf(f2207,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) ) ),
inference(rectify,[],[f834]) ).
thf(f834,axiom,
! [X463: int,X464: int,X465: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X465),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X465),X463)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X465),X464))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X464),X463) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_mult__less__cancel__left__neg) ).
thf(f7018,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5570]) ).
thf(f7021,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5569]) ).
thf(f5569,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3718]) ).
thf(f3718,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2206]) ).
thf(f2206,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(fool_elimination,[],[f2205]) ).
thf(f2205,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(rectify,[],[f851]) ).
thf(f851,axiom,
! [X476: int,X477: int,X478: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X478)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X478),X476)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X478),X477))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X476),X477) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_mult__less__cancel__left__pos) ).
thf(f7020,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5569]) ).
thf(f5567,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4305]) ).
thf(f4305,plain,
! [X0: int,X1: int,X2: int] :
( ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2) ) )
& ( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(nnf_transformation,[],[f3717]) ).
thf(f3717,plain,
! [X0: int,X1: int,X2: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2204]) ).
thf(f2204,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2) ) ) ),
inference(fool_elimination,[],[f2203]) ).
thf(f2203,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2)
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2) ) ) ),
inference(rectify,[],[f1158]) ).
thf(f1158,axiom,
! [X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192)
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X3),X192) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_zcong__zmod__eq) ).
thf(f5565,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4304]) ).
thf(f4304,plain,
! [X0: int,X1: int,X2: int] :
( ( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) ) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(nnf_transformation,[],[f3716]) ).
thf(f3716,plain,
! [X0: int,X1: int,X2: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) )
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2202]) ).
thf(f2202,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) )
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ) ),
inference(fool_elimination,[],[f2201]) ).
thf(f2201,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) ) ),
inference(rectify,[],[f1198]) ).
thf(f1198,axiom,
! [X508: int,X509: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X508) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X509) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X508),X509),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_StandardRes__prop2) ).
thf(f5566,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X2),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),X2) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4304]) ).
thf(f5564,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3715]) ).
thf(f3715,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3714]) ).
thf(f3714,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2200]) ).
thf(f2200,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ) ),
inference(fool_elimination,[],[f2199]) ).
thf(f2199,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ),
inference(rectify,[],[f859]) ).
thf(f859,axiom,
! [X486: int,X487: int,X488: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X488)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X486),X487)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X486),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X488),X487)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_pos__add__strict) ).
thf(f5563,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3713]) ).
thf(f3713,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3712]) ).
thf(f3712,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f3155]) ).
thf(f3155,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) ) ) ) ) ),
inference(flattening,[],[f2198]) ).
thf(f2198,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) ) ) ) ) ),
inference(fool_elimination,[],[f2197]) ).
thf(f2197,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X0),X1) ) ) ) ),
inference(rectify,[],[f589]) ).
thf(f589,axiom,
! [X3: int,X192: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),X192) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_zcong__not) ).
thf(f5562,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3711]) ).
thf(f3711,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3710]) ).
thf(f3710,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2196]) ).
thf(f2196,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2) ) ) ),
inference(fool_elimination,[],[f2195]) ).
thf(f2195,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2) ) ) ),
inference(rectify,[],[f1157]) ).
thf(f1157,axiom,
! [X2: int,X3: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X192),X3)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3)),X192) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_zmod__zdvd__zmod) ).
thf(f7918,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(forward_demodulation,[],[f6630,f4464]) ).
thf(f6630,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(definition_unfolding,[],[f5556,f5971]) ).
thf(f5556,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3703]) ).
thf(f3703,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3702]) ).
thf(f3702,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2188]) ).
thf(f2188,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) = X2 )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) ) ) ) ),
inference(fool_elimination,[],[f2187]) ).
thf(f2187,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) = X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) ) ) ),
inference(rectify,[],[f511]) ).
thf(f511,axiom,
! [X306: int,X307: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X306),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X307)) = X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X306),X2)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X307) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_self__quotient__aux1) ).
thf(f7917,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),vAPP(int,int,bit1,zero_zero_int)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(forward_demodulation,[],[f6629,f4464]) ).
thf(f6629,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(definition_unfolding,[],[f5555,f5971]) ).
thf(f5555,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3701]) ).
thf(f3701,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(flattening,[],[f3700]) ).
thf(f3700,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) != X2 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2186]) ).
thf(f2186,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2) = $true )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) = X2 )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),one_one_int) ) ) ) ),
inference(fool_elimination,[],[f2185]) ).
thf(f2185,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) = X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),one_one_int) ) ) ),
inference(rectify,[],[f510]) ).
thf(f510,axiom,
! [X306: int,X307: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X306),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X307)) = X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X306)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X307),one_one_int) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_self__quotient__aux2) ).
thf(f7916,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(forward_demodulation,[],[f7023,f4464]) ).
thf(f7023,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6628]) ).
thf(f6628,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5554,f5971]) ).
thf(f5554,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3699]) ).
thf(f3699,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2184]) ).
thf(f2184,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(fool_elimination,[],[f2183]) ).
thf(f2183,plain,
! [X0: nat,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f497]) ).
thf(f497,axiom,
! [X294: nat,X295: nat,X296: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X296)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X296),X294)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X296),X295))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X294),X295) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_power__strict__increasing__iff) ).
thf(f7915,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(forward_demodulation,[],[f7022,f4464]) ).
thf(f7022,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6628]) ).
thf(f7914,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(forward_demodulation,[],[f7025,f4464]) ).
thf(f7025,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6627]) ).
thf(f6627,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5553,f5971]) ).
thf(f5553,plain,
! [X2: int,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3698]) ).
thf(f3698,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2182]) ).
thf(f2182,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(fool_elimination,[],[f2181]) ).
thf(f2181,plain,
! [X0: nat,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f304]) ).
thf(f304,axiom,
! [X171: nat,X172: nat,X173: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X173)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X173),X171)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X173),X172))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X171),X172) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_power__increasing__iff) ).
thf(f7913,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(forward_demodulation,[],[f7024,f4464]) ).
thf(f7024,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6627]) ).
thf(f7912,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( X0 = X1 )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) ) ),
inference(forward_demodulation,[],[f6626,f4464]) ).
thf(f6626,plain,
! [X2: int,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5551,f5971]) ).
thf(f5551,plain,
! [X2: int,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f4297]) ).
thf(f4297,plain,
! [X0: nat,X1: nat,X2: int] :
( ( ( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) ) ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(nnf_transformation,[],[f3697]) ).
thf(f3697,plain,
! [X0: nat,X1: nat,X2: int] :
( ( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) )
<=> ( X0 = X1 ) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2180]) ).
thf(f2180,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) )
<=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f2179]) ).
thf(f2179,plain,
! [X0: nat,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0) )
<=> ( X0 = X1 ) ) ),
inference(rectify,[],[f494]) ).
thf(f494,axiom,
! [X291: nat,X292: nat,X293: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X293)
=> ( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X293),X291) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X293),X292) )
<=> ( X291 = X292 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_power__inject__exp) ).
thf(f7911,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))),X1)) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) ) ),
inference(forward_demodulation,[],[f7910,f4464]) ).
thf(f7910,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))),X1)) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(forward_demodulation,[],[f6624,f4464]) ).
thf(f6624,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5550,f5971,f5971]) ).
thf(f5550,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3696]) ).
thf(f3696,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(flattening,[],[f3695]) ).
thf(f3695,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2178]) ).
thf(f2178,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
=> ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) ) ) ),
inference(fool_elimination,[],[f2177]) ).
thf(f2177,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1))
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) ) ),
inference(rectify,[],[f1100]) ).
thf(f1100,axiom,
! [X3: int,X163: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X163))
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_wset__subset) ).
thf(f7909,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(forward_demodulation,[],[f6623,f4464]) ).
thf(f6623,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5549,f5971]) ).
thf(f5549,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3694]) ).
thf(f3694,plain,
! [X0: nat,X1: nat,X2: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(flattening,[],[f3693]) ).
thf(f3693,plain,
! [X0: nat,X1: nat,X2: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2176]) ).
thf(f2176,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2175]) ).
thf(f2175,plain,
! [X0: nat,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f500]) ).
thf(f500,axiom,
! [X297: nat,X298: nat,X299: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X299)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X299),X297)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X299),X298))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X297),X298) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_power__less__imp__less__exp) ).
thf(f7908,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) ) ),
inference(forward_demodulation,[],[f6622,f4464]) ).
thf(f6622,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5548,f5971]) ).
thf(f5548,plain,
! [X2: int,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3692]) ).
thf(f3692,plain,
! [X0: nat,X1: nat,X2: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(flattening,[],[f3691]) ).
thf(f3691,plain,
! [X0: nat,X1: nat,X2: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f2174]) ).
thf(f2174,plain,
! [X0: nat,X1: nat,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2173]) ).
thf(f2173,plain,
! [X0: nat,X1: nat,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f301]) ).
thf(f301,axiom,
! [X168: nat,X169: nat,X170: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X170)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X170),X168)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X170),X169))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X168),X169) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_power__le__imp__le__exp) ).
thf(f7907,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X2) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))),X1)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) ) ),
inference(forward_demodulation,[],[f7906,f4464]) ).
thf(f7906,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))),X1)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(forward_demodulation,[],[f6621,f4464]) ).
thf(f6621,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5547,f5971,f5971]) ).
thf(f5547,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(cnf_transformation,[],[f3690]) ).
thf(f3690,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(flattening,[],[f3689]) ).
thf(f3689,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) != $true ) ),
inference(ennf_transformation,[],[f3154]) ).
thf(f3154,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 ) ) ) ) ),
inference(flattening,[],[f2172]) ).
thf(f2172,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2) = $true )
=> ( ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1)) )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1)) )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f2171]) ).
thf(f2171,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( ~ vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X1))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X1))
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X2) = X0 )
| ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f1103]) ).
thf(f1103,axiom,
! [X3: int,X163: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( ~ vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)),X163))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163))
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2) = X3 )
| ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_wset__mem__imp__or) ).
thf(f7027,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6620]) ).
thf(f6620,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5544,f5969]) ).
thf(f5544,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3684]) ).
thf(f3684,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2166]) ).
thf(f2166,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(fool_elimination,[],[f2165]) ).
thf(f2165,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f1049]) ).
thf(f1049,axiom,
! [X192: nat,X191: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_nat__mult__less__cancel1) ).
thf(f7026,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6620]) ).
thf(f7029,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6619]) ).
thf(f6619,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5543,f5969]) ).
thf(f5543,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3683]) ).
thf(f3683,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2164]) ).
thf(f2164,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(fool_elimination,[],[f2163]) ).
thf(f2163,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f1052]) ).
thf(f1052,axiom,
! [X192: nat,X191: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_nat__mult__le__cancel1) ).
thf(f7028,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6619]) ).
thf(f7031,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6618]) ).
thf(f6618,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5542,f5969]) ).
thf(f5542,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3682]) ).
thf(f3682,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2162]) ).
thf(f2162,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(fool_elimination,[],[f2161]) ).
thf(f2161,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(rectify,[],[f1051]) ).
thf(f1051,axiom,
! [X192: nat,X191: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_nat__mult__dvd__cancel1) ).
thf(f7030,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6618]) ).
thf(f6615,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5539,f5969]) ).
thf(f5539,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3680]) ).
thf(f3680,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(flattening,[],[f3679]) ).
thf(f3679,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2158]) ).
thf(f2158,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2157]) ).
thf(f2157,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f518]) ).
thf(f518,axiom,
! [X192: nat,X191: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X19)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X19),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X19),X191))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_nat__power__less__imp__less) ).
thf(f6614,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5538,f5969]) ).
thf(f5538,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3678]) ).
thf(f3678,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(flattening,[],[f3677]) ).
thf(f3677,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2156]) ).
thf(f2156,plain,
! [X0: int,X1: int,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ) ),
inference(fool_elimination,[],[f2155]) ).
thf(f2155,plain,
! [X0: int,X1: int,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ),
inference(rectify,[],[f660]) ).
thf(f660,axiom,
! [X163: int,X17: int,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X17)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X17),X191)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_zpower__zdvd__prop1) ).
thf(f6613,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5537,f5969]) ).
thf(f5537,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3676]) ).
thf(f3676,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(flattening,[],[f3675]) ).
thf(f3675,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2154]) ).
thf(f2154,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ) ),
inference(fool_elimination,[],[f2153]) ).
thf(f2153,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
inference(rectify,[],[f858]) ).
thf(f858,axiom,
! [X486: nat,X487: nat,X488: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X488)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X486),X487)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X486),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X488),X487)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_pos__add__strict) ).
thf(f6612,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5536,f5969]) ).
thf(f5536,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(cnf_transformation,[],[f3674]) ).
thf(f3674,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(flattening,[],[f3673]) ).
thf(f3673,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(ennf_transformation,[],[f2152]) ).
thf(f2152,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f2151]) ).
thf(f2151,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X0) )
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f1133]) ).
thf(f1133,axiom,
! [X191: nat,X192: nat,X18: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X18)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191) )
=> ( X191 = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1132_mult__left__cancel) ).
thf(f7033,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6611]) ).
thf(f6611,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5535,f5972]) ).
thf(f5535,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(cnf_transformation,[],[f3672]) ).
thf(f3672,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(ennf_transformation,[],[f2150]) ).
thf(f2150,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(fool_elimination,[],[f2149]) ).
thf(f2149,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f496]) ).
thf(f496,axiom,
! [X294: nat,X295: nat,X296: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X296)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X296),X294)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X296),X295))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X294),X295) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_power__strict__increasing__iff) ).
thf(f7032,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6611]) ).
thf(f7035,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6610]) ).
thf(f6610,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5534,f5972]) ).
thf(f5534,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(cnf_transformation,[],[f3671]) ).
thf(f3671,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(ennf_transformation,[],[f2148]) ).
thf(f2148,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(fool_elimination,[],[f2147]) ).
thf(f2147,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f305]) ).
thf(f305,axiom,
! [X171: nat,X172: nat,X173: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X173)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X173),X171)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X173),X172))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X171),X172) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_power__increasing__iff) ).
thf(f7034,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6610]) ).
thf(f6609,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5532,f5972]) ).
thf(f5532,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(cnf_transformation,[],[f4295]) ).
thf(f4295,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(nnf_transformation,[],[f3670]) ).
thf(f3670,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
<=> ( X0 = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(ennf_transformation,[],[f2146]) ).
thf(f2146,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
<=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f2145]) ).
thf(f2145,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0) )
<=> ( X0 = X1 ) ) ),
inference(rectify,[],[f493]) ).
thf(f493,axiom,
! [X291: nat,X292: nat,X293: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X293)
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X293),X291) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X293),X292) )
<=> ( X291 = X292 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_power__inject__exp) ).
thf(f6607,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5531,f5972]) ).
thf(f5531,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(cnf_transformation,[],[f3669]) ).
thf(f3669,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(flattening,[],[f3668]) ).
thf(f3668,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(ennf_transformation,[],[f2144]) ).
thf(f2144,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2143]) ).
thf(f2143,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f499]) ).
thf(f499,axiom,
! [X297: nat,X298: nat,X299: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X299)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X299),X297)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X299),X298))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X297),X298) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_power__less__imp__less__exp) ).
thf(f6606,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5530,f5972]) ).
thf(f5530,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(cnf_transformation,[],[f3667]) ).
thf(f3667,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(flattening,[],[f3666]) ).
thf(f3666,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) ) ),
inference(ennf_transformation,[],[f2142]) ).
thf(f2142,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2141]) ).
thf(f2141,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f302]) ).
thf(f302,axiom,
! [X168: nat,X169: nat,X170: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X170)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X170),X168)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X170),X169))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X168),X169) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_power__le__imp__le__exp) ).
thf(f7037,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6605]) ).
thf(f6605,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5529,f5970]) ).
thf(f5529,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) ) ),
inference(cnf_transformation,[],[f3665]) ).
thf(f3665,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) ) ),
inference(ennf_transformation,[],[f2140]) ).
thf(f2140,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(fool_elimination,[],[f2139]) ).
thf(f2139,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ),
inference(rectify,[],[f833]) ).
thf(f833,axiom,
! [X463: real,X464: real,X465: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X465),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X465),X463)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X465),X464))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X464),X463) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_mult__less__cancel__left__neg) ).
thf(f7036,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6605]) ).
thf(f7039,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6604]) ).
thf(f6604,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5528,f5970]) ).
thf(f5528,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(cnf_transformation,[],[f3664]) ).
thf(f3664,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(ennf_transformation,[],[f2138]) ).
thf(f2138,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(fool_elimination,[],[f2137]) ).
thf(f2137,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(rectify,[],[f850]) ).
thf(f850,axiom,
! [X476: real,X477: real,X478: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X478)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X478),X476)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X478),X477))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X476),X477) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_mult__less__cancel__left__pos) ).
thf(f7038,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6604]) ).
thf(f7041,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6603]) ).
thf(f6603,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5527,f5970]) ).
thf(f5527,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(cnf_transformation,[],[f3663]) ).
thf(f3663,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(ennf_transformation,[],[f2136]) ).
thf(f2136,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ) ),
inference(fool_elimination,[],[f2135]) ).
thf(f2135,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(rectify,[],[f862]) ).
thf(f862,axiom,
! [X16: real,X17: real,X15: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X15)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X16),X15)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X17),X15))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X16),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_real__mult__less__iff1) ).
thf(f7040,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6603]) ).
thf(f7043,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6602]) ).
thf(f6602,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5526,f5970]) ).
thf(f5526,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(cnf_transformation,[],[f3662]) ).
thf(f3662,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(ennf_transformation,[],[f2134]) ).
thf(f2134,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ) ),
inference(fool_elimination,[],[f2133]) ).
thf(f2133,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(rectify,[],[f863]) ).
thf(f863,axiom,
! [X16: real,X17: real,X15: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X15)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X16),X15)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X17),X15))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X16),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_real__mult__le__cancel__iff1) ).
thf(f7042,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6602]) ).
thf(f7045,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6601]) ).
thf(f6601,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5525,f5970]) ).
thf(f5525,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(cnf_transformation,[],[f3661]) ).
thf(f3661,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(ennf_transformation,[],[f2132]) ).
thf(f2132,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(fool_elimination,[],[f2131]) ).
thf(f2131,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(rectify,[],[f864]) ).
thf(f864,axiom,
! [X16: real,X17: real,X15: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X15)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X15),X16)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X15),X17))
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X16),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_real__mult__le__cancel__iff2) ).
thf(f7044,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6601]) ).
thf(f6600,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) ) ),
inference(definition_unfolding,[],[f5524,f5970]) ).
thf(f5524,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(cnf_transformation,[],[f3660]) ).
thf(f3660,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(flattening,[],[f3659]) ).
thf(f3659,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) != $true ) ),
inference(ennf_transformation,[],[f2130]) ).
thf(f2130,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ) ),
inference(fool_elimination,[],[f2129]) ).
thf(f2129,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ) ),
inference(rectify,[],[f866]) ).
thf(f866,axiom,
! [X16: real,X17: real,X15: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X15)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X16),X17)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X15),X16)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X15),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_real__mult__less__mono2) ).
thf(f7047,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6599]) ).
thf(f6599,plain,
! [X2: real,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5523,f5973]) ).
thf(f5523,plain,
! [X2: real,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(cnf_transformation,[],[f3658]) ).
thf(f3658,plain,
! [X0: nat,X1: nat,X2: real] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(ennf_transformation,[],[f2128]) ).
thf(f2128,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(fool_elimination,[],[f2127]) ).
thf(f2127,plain,
! [X0: nat,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f495]) ).
thf(f495,axiom,
! [X294: nat,X295: nat,X296: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X296)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X296),X294)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X296),X295))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X294),X295) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_power__strict__increasing__iff) ).
thf(f7046,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6599]) ).
thf(f7049,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6598]) ).
thf(f6598,plain,
! [X2: real,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5522,f5973]) ).
thf(f5522,plain,
! [X2: real,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(cnf_transformation,[],[f3657]) ).
thf(f3657,plain,
! [X0: nat,X1: nat,X2: real] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(ennf_transformation,[],[f2126]) ).
thf(f2126,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(fool_elimination,[],[f2125]) ).
thf(f2125,plain,
! [X0: nat,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f306]) ).
thf(f306,axiom,
! [X171: nat,X172: nat,X173: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X173)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X173),X171)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X173),X172))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X171),X172) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_power__increasing__iff) ).
thf(f7048,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f6598]) ).
thf(f6597,plain,
! [X2: real,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5520,f5973]) ).
thf(f5520,plain,
! [X2: real,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(cnf_transformation,[],[f4294]) ).
thf(f4294,plain,
! [X0: nat,X1: nat,X2: real] :
( ( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) ) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(nnf_transformation,[],[f3656]) ).
thf(f3656,plain,
! [X0: nat,X1: nat,X2: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) )
<=> ( X0 = X1 ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(ennf_transformation,[],[f2124]) ).
thf(f2124,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) )
=> ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) )
<=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f2123]) ).
thf(f2123,plain,
! [X0: nat,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2)
=> ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0) )
<=> ( X0 = X1 ) ) ),
inference(rectify,[],[f492]) ).
thf(f492,axiom,
! [X291: nat,X292: nat,X293: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X293)
=> ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X293),X291) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X293),X292) )
<=> ( X291 = X292 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_power__inject__exp) ).
thf(f6595,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5519,f5973]) ).
thf(f5519,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(cnf_transformation,[],[f3655]) ).
thf(f3655,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(flattening,[],[f3654]) ).
thf(f3654,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(ennf_transformation,[],[f2122]) ).
thf(f2122,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2121]) ).
thf(f2121,plain,
! [X0: nat,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f498]) ).
thf(f498,axiom,
! [X297: nat,X298: nat,X299: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X299)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X299),X297)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X299),X298))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X297),X298) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp) ).
thf(f6594,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X2) ) ),
inference(definition_unfolding,[],[f5518,f5973]) ).
thf(f5518,plain,
! [X2: real,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(cnf_transformation,[],[f3653]) ).
thf(f3653,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(flattening,[],[f3652]) ).
thf(f3652,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) ) ),
inference(ennf_transformation,[],[f2120]) ).
thf(f2120,plain,
! [X0: nat,X1: nat,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1)) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2119]) ).
thf(f2119,plain,
! [X0: nat,X1: nat,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X2)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X0)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f303]) ).
thf(f303,axiom,
! [X168: nat,X169: nat,X170: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X170)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X170),X168)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X170),X169))
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X168),X169) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_power__le__imp__le__exp) ).
thf(f7905,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7904,f4464]) ).
thf(f7904,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6593,f4464]) ).
thf(f6593,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5517,f5971,f4404]) ).
thf(f5517,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3651]) ).
thf(f3651,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3650]) ).
thf(f3650,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2118]) ).
thf(f2118,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
=> ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f2117]) ).
thf(f2117,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2))
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) ) ) ) ),
inference(rectify,[],[f1097]) ).
thf(f1097,axiom,
! [X3: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163))
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X3)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_wset__mem__inv__mem) ).
thf(f7903,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7902,f4464]) ).
thf(f7902,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7901,f4464]) ).
thf(f7901,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7900,f4464]) ).
thf(f7900,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6592,f4464]) ).
thf(f6592,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5516,f5971,f5971,f5971,f4404]) ).
thf(f5516,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3649]) ).
thf(f3649,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3648]) ).
thf(f3648,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2116]) ).
thf(f2116,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
=> ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f2115]) ).
thf(f2115,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X2),X0)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2))
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) ) ) ) ) ) ),
inference(rectify,[],[f1098]) ).
thf(f1098,axiom,
! [X3: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X3)),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163))
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_wset__inv__mem__mem) ).
thf(f7899,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6591,f4464]) ).
thf(f6591,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5515,f4404]) ).
thf(f5515,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3647]) ).
thf(f3647,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3646]) ).
thf(f3646,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f3153]) ).
thf(f3153,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) ) ) ) ) ) ),
inference(flattening,[],[f2114]) ).
thf(f2114,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) ) ) ) ) ) ),
inference(fool_elimination,[],[f2113]) ).
thf(f2113,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X2),X1)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X2),X0))),X2) ) ) ) ) ),
inference(rectify,[],[f1074]) ).
thf(f1074,axiom,
! [X20: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X163),X2)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X20),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X20))),X163) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_MultInvPair__distinct) ).
thf(f5514,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3645]) ).
thf(f3645,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3644]) ).
thf(f3644,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2112]) ).
thf(f2112,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f2111]) ).
thf(f2111,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X1)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ),
inference(rectify,[],[f658]) ).
thf(f658,axiom,
! [X192: int,X191: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X192),X191))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X191)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X192) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_zprime__zdvd__zmult__better) ).
thf(f5513,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3643]) ).
thf(f3643,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3642]) ).
thf(f3642,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2110]) ).
thf(f2110,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ),
inference(fool_elimination,[],[f2109]) ).
thf(f2109,plain,
! [X0: int,X1: nat,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ),
inference(rectify,[],[f391]) ).
thf(f391,axiom,
! [X2: int,X191: nat,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X191))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_zprime__zdvd__power) ).
thf(f6590,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5512,f5969]) ).
thf(f5512,plain,
! [X2: int,X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3641]) ).
thf(f3641,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3640]) ).
thf(f3640,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2108]) ).
thf(f2108,plain,
! [X0: int,X1: nat,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f2107]) ).
thf(f2107,plain,
! [X0: int,X1: nat,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ),
inference(rectify,[],[f665]) ).
thf(f665,axiom,
! [X17: int,X191: nat,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X17),X191))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_zpower__zdvd__prop2) ).
thf(f7898,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7897,f4464]) ).
thf(f7897,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6589,f4464]) ).
thf(f6589,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5511,f5971,f5971]) ).
thf(f5511,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3639]) ).
thf(f3639,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3638]) ).
thf(f3638,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2106]) ).
thf(f2106,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) ) ) ) ),
inference(fool_elimination,[],[f2105]) ).
thf(f2105,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) ) ) ),
inference(rectify,[],[f1101]) ).
thf(f1101,axiom,
! [X3: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_wset__less) ).
thf(f7896,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7895,f4464]) ).
thf(f7895,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6588,f4464]) ).
thf(f6588,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5510,f5971,f5971]) ).
thf(f5510,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3637]) ).
thf(f3637,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3636]) ).
thf(f3636,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2104]) ).
thf(f2104,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ) ) ),
inference(fool_elimination,[],[f2103]) ).
thf(f2103,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ) ),
inference(rectify,[],[f1102]) ).
thf(f1102,axiom,
! [X3: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_wset__g__1) ).
thf(f7894,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f7893,f4464]) ).
thf(f7893,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(forward_demodulation,[],[f6587,f4464]) ).
thf(f6587,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(definition_unfolding,[],[f5509,f5971,f5971]) ).
thf(f5509,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3635]) ).
thf(f3635,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3634]) ).
thf(f3634,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f2102]) ).
thf(f2102,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f2101]) ).
thf(f2101,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X2)) ) ) ) ),
inference(rectify,[],[f1104]) ).
thf(f1104,axiom,
! [X3: int,X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2)
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_wset__mem) ).
thf(f5506,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(cnf_transformation,[],[f3629]) ).
thf(f3629,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(flattening,[],[f3628]) ).
thf(f3628,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
| ( $true != vAPP(int,$o,zprime,X2) ) ),
inference(ennf_transformation,[],[f3151]) ).
thf(f3151,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int),X2) ) ) ) ),
inference(flattening,[],[f2096]) ).
thf(f2096,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,zprime,X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int),X2) ) ) ) ),
inference(fool_elimination,[],[f2095]) ).
thf(f2095,plain,
! [X0: int,X1: int,X2: int] :
( vAPP(int,$o,zprime,X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X2)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int),X2) ) ) ),
inference(rectify,[],[f662]) ).
thf(f662,axiom,
! [X17: int,X16: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X17),zero_zero_int),X163)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X16),X17)),zero_zero_int),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_zcong__zmult__prop3) ).
thf(f5504,plain,
! [X2: nat > nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X2,X0)),X1)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK26,X2)),vAPP(sTfun(nat,nat),nat,sK27,X2)) ) ),
inference(cnf_transformation,[],[f4293]) ).
thf(f4293,plain,
! [X0: nat,X1: nat,X2: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X2,X0)),X1)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK26,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK27,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK26,X2)),vAPP(sTfun(nat,nat),nat,sK27,X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f3627,f4292]) ).
thf(f4292,plain,
! [X2: nat > nat] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X3)),vAPP(nat,nat,X2,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK26,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK27,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK26,X2)),vAPP(sTfun(nat,nat),nat,sK27,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3627,plain,
! [X0: nat,X1: nat,X2: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X2,X0)),X1)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X3)),vAPP(nat,nat,X2,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) ) ),
inference(ennf_transformation,[],[f2094]) ).
thf(f2094,plain,
! [X0: nat,X1: nat,X2: nat > nat] :
( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X3)),vAPP(nat,nat,X2,X4)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X2,X0)),X1)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
inference(fool_elimination,[],[f2093]) ).
thf(f2093,plain,
! [X0: nat,X1: nat,X2: nat > nat] :
( ! [X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X3)),vAPP(nat,nat,X2,X4)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X2,X0)),X1)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ),
inference(rectify,[],[f1110]) ).
thf(f1110,axiom,
! [X192: nat,X18: nat,X499: nat > nat] :
( ! [X305: nat,X500: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X305),X500)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X499,X305)),vAPP(nat,nat,X499,X500)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X499,X192)),X18)),vAPP(nat,nat,X499,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_mono__nat__linear__lb) ).
thf(f5505,plain,
! [X2: nat > nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X2,X0)),X1)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK26,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK27,X2))) ) ),
inference(cnf_transformation,[],[f4293]) ).
thf(f6586,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) ) ),
inference(definition_unfolding,[],[f5503,f4404]) ).
thf(f5503,plain,
! [X2: int,X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) ) ),
inference(cnf_transformation,[],[f3626]) ).
thf(f3626,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) ) ),
inference(flattening,[],[f3625]) ).
thf(f3625,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) ) ),
inference(ennf_transformation,[],[f3150]) ).
thf(f3150,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X2) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ),
inference(flattening,[],[f2092]) ).
thf(f2092,plain,
! [X0: int,X1: int,X2: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X2) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ) ),
inference(fool_elimination,[],[f2091]) ).
thf(f2091,plain,
! [X0: int,X1: int,X2: int] :
( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X2)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) ) ),
inference(rectify,[],[f505]) ).
thf(f505,axiom,
! [X17: int,X16: int,X163: int] :
( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X17),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X16),X163)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_Euler_Oaux____1) ).
thf(f5477,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3620]) ).
thf(f3620,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3619]) ).
thf(f3619,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f3149]) ).
thf(f3149,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ) ),
inference(flattening,[],[f2084]) ).
thf(f2084,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ) ),
inference(fool_elimination,[],[f2083]) ).
thf(f2083,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0)
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ),
inference(rectify,[],[f901]) ).
thf(f901,axiom,
! [X15: nat,X16: nat,X17: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X17),X16)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X17) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X17),X15)
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X15),X16)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_dvd_Oless__le__trans) ).
thf(f5478,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3620]) ).
thf(f5474,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3616]) ).
thf(f3616,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(flattening,[],[f3615]) ).
thf(f3615,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(ennf_transformation,[],[f3147]) ).
thf(f3147,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ) ),
inference(flattening,[],[f2080]) ).
thf(f2080,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ) ),
inference(fool_elimination,[],[f2079]) ).
thf(f2079,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) )
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) ) ) ),
inference(rectify,[],[f899]) ).
thf(f899,axiom,
! [X15: nat,X16: nat,X17: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X17),X16)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X17) )
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X15),X17)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X17),X15) )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X15),X16)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_dvd_Oless__trans) ).
thf(f5475,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X2) ) ),
inference(cnf_transformation,[],[f3616]) ).
thf(f5471,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) ) ),
inference(cnf_transformation,[],[f3612]) ).
thf(f3612,plain,
! [X0: int,X1: int,X2: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) ) ),
inference(ennf_transformation,[],[f2076]) ).
thf(f2076,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) ) ),
inference(fool_elimination,[],[f2075]) ).
thf(f2075,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X1) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X2),X1) ),
inference(rectify,[],[f1144]) ).
thf(f1144,axiom,
! [X16: int,X192: int,X17: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X17),X192) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),X17),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_Residues_Oaux) ).
thf(f7892,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(subsumption_resolution,[],[f7891,f6249]) ).
thf(f7891,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(subsumption_resolution,[],[f6584,f6249]) ).
thf(f6584,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(definition_unfolding,[],[f5469,f5969,f5969,f5969]) ).
thf(f5469,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(cnf_transformation,[],[f3609]) ).
thf(f3609,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(flattening,[],[f3608]) ).
thf(f3608,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) ) ),
inference(ennf_transformation,[],[f2072]) ).
thf(f2072,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f2071]) ).
thf(f2071,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X1) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f325]) ).
thf(f325,axiom,
! [X188: nat,X189: nat,X190: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X188),X189) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X190),X189) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X188)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X190)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X189)
=> ( X188 = X190 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_power__eq__imp__eq__base) ).
thf(f6583,plain,
! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(definition_unfolding,[],[f5468,f5969,f5970,f5970]) ).
thf(f5468,plain,
! [X2: real,X0: real,X1: nat] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(cnf_transformation,[],[f3607]) ).
thf(f3607,plain,
! [X0: real,X1: nat,X2: real] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(flattening,[],[f3606]) ).
thf(f3606,plain,
! [X0: real,X1: nat,X2: real] :
( ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) ) ),
inference(ennf_transformation,[],[f2070]) ).
thf(f2070,plain,
! [X0: real,X1: nat,X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f2069]) ).
thf(f2069,plain,
! [X0: real,X1: nat,X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[],[f326]) ).
thf(f326,axiom,
! [X188: real,X189: nat,X190: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X188),X189) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X190),X189) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X188)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X190)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X189)
=> ( X188 = X190 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_power__eq__imp__eq__base) ).
thf(f6906,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X1) = X0 ),
inference(equality_resolution,[],[f5466]) ).
thf(f5466,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f3604]) ).
thf(f3604,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f3145]) ).
thf(f3145,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = X2 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = X0 ) ),
inference(rectify,[],[f612]) ).
thf(f612,axiom,
! [X2: int,X3: int,X216: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = X216 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X216),X3) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_Int2_Oaux1) ).
thf(f7059,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( zero_zero_int = X2 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5460]) ).
thf(f5460,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( zero_zero_int = X2 ) ),
inference(cnf_transformation,[],[f3597]) ).
thf(f3597,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) )
| ( zero_zero_int = X2 ) ),
inference(ennf_transformation,[],[f2058]) ).
thf(f2058,plain,
! [X0: int,X1: int,X2: int] :
( ( zero_zero_int != X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(fool_elimination,[],[f2057]) ).
thf(f2057,plain,
! [X0: int,X1: int,X2: int] :
( ( zero_zero_int != X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(rectify,[],[f1064]) ).
thf(f1064,axiom,
! [X192: int,X217: int,X18: int] :
( ( zero_zero_int != X18 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X192),X217)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X192)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X217)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_zdvd__mono) ).
thf(f7058,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( zero_zero_int = X2 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ) ),
inference(binary_proxy_clausification,[],[f5460]) ).
thf(f7061,plain,
! [X2: nat,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6582]) ).
thf(f6582,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5459,f5969]) ).
thf(f5459,plain,
! [X2: nat,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( zero_zero_nat = X2 ) ),
inference(cnf_transformation,[],[f3596]) ).
thf(f3596,plain,
! [X0: int,X1: int,X2: nat] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) )
| ( zero_zero_nat = X2 ) ),
inference(ennf_transformation,[],[f2056]) ).
thf(f2056,plain,
! [X0: int,X1: int,X2: nat] :
( ( zero_zero_nat != X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ),
inference(fool_elimination,[],[f2055]) ).
thf(f2055,plain,
! [X0: int,X1: int,X2: nat] :
( ( zero_zero_nat != X2 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(rectify,[],[f1118]) ).
thf(f1118,axiom,
! [X2: int,X3: int,X191: nat] :
( ( zero_zero_nat != X191 )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),X191)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),X191))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_pow__divides__eq__int) ).
thf(f7060,plain,
! [X2: nat,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6582]) ).
thf(f7063,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6581]) ).
thf(f6581,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5458,f5969]) ).
thf(f5458,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( zero_zero_nat = X2 ) ),
inference(cnf_transformation,[],[f3595]) ).
thf(f3595,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) )
| ( zero_zero_nat = X2 ) ),
inference(ennf_transformation,[],[f2054]) ).
thf(f2054,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( zero_zero_nat != X2 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ),
inference(fool_elimination,[],[f2053]) ).
thf(f2053,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( zero_zero_nat != X2 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(rectify,[],[f1130]) ).
thf(f1130,axiom,
! [X2: nat,X3: nat,X191: nat] :
( ( zero_zero_nat != X191 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X2),X191)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X3),X191))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1129_pow__divides__eq__nat) ).
thf(f7062,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f6581]) ).
thf(f6580,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5457,f5969]) ).
thf(f5457,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),X1) )
| ( zero_zero_nat = X2 ) ),
inference(cnf_transformation,[],[f3594]) ).
thf(f3594,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),X1) )
| ( zero_zero_nat = X2 ) ),
inference(flattening,[],[f3593]) ).
thf(f3593,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),X1) )
| ( zero_zero_nat = X2 ) ),
inference(ennf_transformation,[],[f2052]) ).
thf(f2052,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( zero_zero_nat != X2 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f2051]) ).
thf(f2051,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( zero_zero_nat != X2 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(rectify,[],[f868]) ).
thf(f868,axiom,
! [X16: nat,X17: nat,X191: nat] :
( ( zero_zero_nat != X191 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),X191)),X17)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X16),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_divides__exp2) ).
thf(f6579,plain,
! [X2: real,X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2) != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5455,f5970]) ).
thf(f5455,plain,
! [X2: real,X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2) != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2) )
| ( zero_zero_real = X2 ) ),
inference(cnf_transformation,[],[f4287]) ).
thf(f4287,plain,
! [X0: real,X1: real,X2: real] :
( ( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2) != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2) ) ) )
| ( zero_zero_real = X2 ) ),
inference(nnf_transformation,[],[f3592]) ).
thf(f3592,plain,
! [X0: real,X1: real,X2: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2) )
<=> ( X0 = X1 ) )
| ( zero_zero_real = X2 ) ),
inference(ennf_transformation,[],[f3143]) ).
thf(f3143,plain,
! [X0: real,X1: real,X2: real] :
( ( zero_zero_real != X2 )
=> ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2) )
<=> ( X0 = X1 ) ) ),
inference(rectify,[],[f762]) ).
thf(f762,axiom,
! [X2: real,X3: real,X216: real] :
( ( zero_zero_real != X216 )
=> ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X216) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X3),X216) )
<=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_real__mult__right__cancel) ).
thf(f6577,plain,
! [X2: real,X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0) != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X2 ) ),
inference(definition_unfolding,[],[f5453,f5970]) ).
thf(f5453,plain,
! [X2: real,X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0) != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1) )
| ( zero_zero_real = X2 ) ),
inference(cnf_transformation,[],[f4286]) ).
thf(f4286,plain,
! [X0: real,X1: real,X2: real] :
( ( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0) != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1) ) ) )
| ( zero_zero_real = X2 ) ),
inference(nnf_transformation,[],[f3591]) ).
thf(f3591,plain,
! [X0: real,X1: real,X2: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1) )
<=> ( X0 = X1 ) )
| ( zero_zero_real = X2 ) ),
inference(ennf_transformation,[],[f3142]) ).
thf(f3142,plain,
! [X0: real,X1: real,X2: real] :
( ( zero_zero_real != X2 )
=> ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1) )
<=> ( X0 = X1 ) ) ),
inference(rectify,[],[f763]) ).
thf(f763,axiom,
! [X2: real,X3: real,X216: real] :
( ( zero_zero_real != X216 )
=> ( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X216),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X216),X3) )
<=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_real__mult__left__cancel) ).
thf(f6575,plain,
! [X2: int,X0: int,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5451,f5969,f4404]) ).
thf(f5451,plain,
! [X2: int,X0: int,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) ) ),
inference(cnf_transformation,[],[f3590]) ).
thf(f3590,plain,
! [X0: int,X1: nat,X2: int] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) ) )
& ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) ) ) ),
inference(ennf_transformation,[],[f3141]) ).
thf(f3141,plain,
! [X0: int,X1: nat,X2: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),X1) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) ) ) ),
inference(flattening,[],[f2050]) ).
thf(f2050,plain,
! [X0: int,X1: nat,X2: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),X1) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) ) ) ),
inference(fool_elimination,[],[f2049]) ).
thf(f2049,plain,
! [X0: int,X1: nat,X2: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),X1) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) ) ) ),
inference(rectify,[],[f567]) ).
thf(f567,axiom,
! [X39: int,X18: nat,X40: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),pls)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X39)),X18)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X40),X39))),X18) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),pls)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X39)),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_nat__number__of__mult__left) ).
thf(f6574,plain,
! [X2: int,X0: int,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5452,f4404]) ).
thf(f5452,plain,
! [X2: int,X0: int,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X0)),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X0))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),pls) ) ),
inference(cnf_transformation,[],[f3590]) ).
thf(f5443,plain,
! [X2: int,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,real,number267125858f_real,X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,X2))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(int,real,number267125858f_real,X2))) ),
inference(cnf_transformation,[],[f3133]) ).
thf(f3133,plain,
! [X0: real,X1: real,X2: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,real,number267125858f_real,X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,X2))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(int,real,number267125858f_real,X2))) ),
inference(rectify,[],[f623]) ).
thf(f623,axiom,
! [X330: real,X331: real,X332: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X330),X331)),vAPP(int,real,number267125858f_real,X332)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X330),vAPP(int,real,number267125858f_real,X332))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X331),vAPP(int,real,number267125858f_real,X332))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_left__diff__distrib__number__of) ).
thf(f5441,plain,
! [X2: real,X0: int,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),X2)) ),
inference(cnf_transformation,[],[f3131]) ).
thf(f3131,plain,
! [X0: int,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),X2)) ),
inference(rectify,[],[f621]) ).
thf(f621,axiom,
! [X327: int,X328: real,X329: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X327)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X328),X329)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X327)),X328)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X327)),X329)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_right__diff__distrib__number__of) ).
thf(f7884,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ),
inference(forward_demodulation,[],[f7883,f4464]) ).
thf(f7883,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ),
inference(forward_demodulation,[],[f7882,f4464]) ).
thf(f7882,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
inference(forward_demodulation,[],[f5438,f4464]) ).
thf(f5438,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) ),
inference(cnf_transformation,[],[f3128]) ).
thf(f3128,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) ),
inference(rectify,[],[f632]) ).
thf(f632,axiom,
! [X333: int,X334: int,X335: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X333)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,X334)),X335)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X333),X334))),X335) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_add__number__of__diff1) ).
thf(f5437,plain,
! [X2: real,X0: int,X1: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X1)),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))),X2) ),
inference(cnf_transformation,[],[f3127]) ).
thf(f3127,plain,
! [X0: int,X1: int,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X1)),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))),X2) ),
inference(rectify,[],[f241]) ).
thf(f241,axiom,
! [X140: int,X141: int,X142: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X140)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X141)),X142)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X140),X141))),X142) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__number__of__left) ).
thf(f5436,plain,
! [X2: real,X0: int,X1: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X1)),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) ),
inference(cnf_transformation,[],[f3126]) ).
thf(f3126,plain,
! [X0: int,X1: int,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X1)),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) ),
inference(rectify,[],[f247]) ).
thf(f247,axiom,
! [X147: int,X148: int,X149: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X147)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X148)),X149)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X147),X148))),X149) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__number__of__left) ).
thf(f5435,plain,
! [X2: real,X0: int,X1: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,X1)),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) ),
inference(cnf_transformation,[],[f3125]) ).
thf(f3125,plain,
! [X0: int,X1: int,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,X1)),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) ),
inference(rectify,[],[f631]) ).
thf(f631,axiom,
! [X333: int,X334: int,X335: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X333)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,X334)),X335)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X333),X334))),X335) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_add__number__of__diff1) ).
thf(f5434,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3124]) ).
thf(f3124,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) ),
inference(rectify,[],[f1154]) ).
thf(f1154,axiom,
! [X16: int,X17: int,X192: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X16),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X17),X192))),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X16),X17)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_zdiff__zmod__right) ).
thf(f5433,plain,
! [X2: nat,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3123]) ).
thf(f3123,plain,
! [X0: int,X1: int,X2: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),X1) ),
inference(rectify,[],[f1149]) ).
thf(f1149,axiom,
! [X16: int,X192: int,X17: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X192)),X17)),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),X17)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_zpower__zmod) ).
thf(f5424,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) ),
inference(cnf_transformation,[],[f3114]) ).
thf(f3114,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) ),
inference(rectify,[],[f177]) ).
thf(f177,axiom,
! [X108: int,X109: int,X110: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X108),X109)),X110) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X108),X110)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X109),X110)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(f5423,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) ),
inference(cnf_transformation,[],[f3113]) ).
thf(f3113,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) ),
inference(rectify,[],[f618]) ).
thf(f618,axiom,
! [X92: int,X93: int,X14: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X92),X93)),X14) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X92),X14)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X93),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_zdiff__zmult__distrib) ).
thf(f5421,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2))),X2) ),
inference(cnf_transformation,[],[f3111]) ).
thf(f3111,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X2))),X2) ),
inference(rectify,[],[f1151]) ).
thf(f1151,axiom,
! [X2: int,X3: int,X216: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3)),X216) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X3),X216))),X216) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_zmod__simps_I3_J) ).
thf(f5420,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2)),X1) ),
inference(cnf_transformation,[],[f3110]) ).
thf(f3110,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X2)),X1) ),
inference(rectify,[],[f1155]) ).
thf(f1155,axiom,
! [X16: int,X192: int,X17: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X16),X17)),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X192)),X17)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_zdiff__zmod__left) ).
thf(f7881,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(backward_demodulation,[],[f7877,f5418]) ).
thf(f5418,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(cnf_transformation,[],[f3108]) ).
thf(f3108,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(rectify,[],[f183]) ).
thf(f183,axiom,
! [X115: int,X116: int,X117: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X115),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X116),X117)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X115),X116)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X115),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(f5417,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(cnf_transformation,[],[f3107]) ).
thf(f3107,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(rectify,[],[f617]) ).
thf(f617,axiom,
! [X14: int,X92: int,X93: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X14),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X92),X93)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X14),X92)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X14),X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_zdiff__zmult__distrib2) ).
thf(f5415,plain,
! [X2: nat,X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ),
inference(cnf_transformation,[],[f3105]) ).
thf(f3105,plain,
! [X0: int,X1: int,X2: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X2)) ),
inference(rectify,[],[f463]) ).
thf(f463,axiom,
! [X264: int,X265: int,X266: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X264),X265)),X266) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X264),X266)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X265),X266)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_power__mult__distrib) ).
thf(f5413,plain,
! [X2: nat,X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ),
inference(cnf_transformation,[],[f3103]) ).
thf(f3103,plain,
! [X0: int,X1: nat,X2: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X2)) ),
inference(rectify,[],[f60]) ).
thf(f60,axiom,
! [X16: int,X17: nat,X15: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X17),X15)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),X17)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_zpower__zadd__distrib) ).
thf(f5410,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3100]) ).
thf(f3100,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ),
inference(rectify,[],[f1018]) ).
thf(f1018,axiom,
! [X192: nat,X191: nat,X18: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191)),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_add__mult__distrib) ).
thf(f5409,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3099]) ).
thf(f3099,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ),
inference(rectify,[],[f952]) ).
thf(f952,axiom,
! [X192: nat,X191: nat,X18: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_diff__mult__distrib) ).
thf(f5408,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3098]) ).
thf(f3098,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) ),
inference(rectify,[],[f1186]) ).
thf(f1186,axiom,
! [X192: nat,X191: nat,X18: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191)),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_mod__mult__distrib) ).
thf(f5406,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3096]) ).
thf(f3096,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X2)) ),
inference(rectify,[],[f461]) ).
thf(f461,axiom,
! [X264: nat,X265: nat,X266: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X264),X265)),X266) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X264),X266)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X265),X266)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_power__mult__distrib) ).
thf(f5404,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3094]) ).
thf(f3094,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f1019]) ).
thf(f1019,axiom,
! [X18: nat,X192: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_add__mult__distrib2) ).
thf(f5403,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3093]) ).
thf(f3093,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f953]) ).
thf(f953,axiom,
! [X18: nat,X192: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_diff__mult__distrib2) ).
thf(f5402,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3092]) ).
thf(f3092,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f1187]) ).
thf(f1187,axiom,
! [X18: nat,X192: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_mod__mult__distrib2) ).
thf(f5401,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3091]) ).
thf(f3091,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X2)) ),
inference(rectify,[],[f464]) ).
thf(f464,axiom,
! [X267: nat,X268: nat,X269: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X267),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X268),X269)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X267),X268)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X267),X269)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_power__add) ).
thf(f5399,plain,
! [X2: nat,X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ),
inference(cnf_transformation,[],[f3089]) ).
thf(f3089,plain,
! [X0: real,X1: real,X2: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X2)) ),
inference(rectify,[],[f193]) ).
thf(f193,axiom,
! [X120: real,X121: real,X122: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X120),X121)),X122) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X120),X122)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X121),X122)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(f5398,plain,
! [X2: nat,X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ),
inference(cnf_transformation,[],[f3088]) ).
thf(f3088,plain,
! [X0: real,X1: nat,X2: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X2)) ),
inference(rectify,[],[f465]) ).
thf(f465,axiom,
! [X267: real,X268: nat,X269: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X267),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X268),X269)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X267),X268)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X267),X269)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_power__add) ).
thf(f5395,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ),
inference(cnf_transformation,[],[f3085]) ).
thf(f3085,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) ),
inference(rectify,[],[f179]) ).
thf(f179,axiom,
! [X108: real,X109: real,X110: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X108),X109)),X110) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X108),X110)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X109),X110)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(f5394,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ),
inference(cnf_transformation,[],[f3084]) ).
thf(f3084,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ),
inference(rectify,[],[f185]) ).
thf(f185,axiom,
! [X115: real,X116: real,X117: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X115),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X116),X117)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X115),X116)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X115),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(f7880,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X1)) ),
inference(forward_demodulation,[],[f5393,f5387]) ).
thf(f5393,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3083]) ).
thf(f3083,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)),X1) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X53: int,X54: int,X55: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X53),X54)),X55) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X53),X55)),X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(f7879,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ),
inference(forward_demodulation,[],[f5390,f5385]) ).
thf(f5390,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3080]) ).
thf(f3080,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ),
inference(rectify,[],[f121]) ).
thf(f121,axiom,
! [X74: int,X75: int,X76: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X74),X75)),X76) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X74),X76)),X75) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(f7874,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))))),X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(backward_demodulation,[],[f7730,f5387]) ).
thf(f7873,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(backward_demodulation,[],[f7731,f5387]) ).
thf(f7878,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7872,f5387]) ).
thf(f7872,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(backward_demodulation,[],[f7623,f5387]) ).
thf(f7877,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7876,f4757]) ).
thf(f7876,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7875,f5387]) ).
thf(f7875,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7871,f4757]) ).
thf(f7871,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(backward_demodulation,[],[f7870,f5387]) ).
thf(f5387,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3077]) ).
thf(f3077,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X2) ),
inference(rectify,[],[f107]) ).
thf(f107,axiom,
! [X59: int,X60: int,X61: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X59),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X60),X61)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X59),X60)),X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(f5386,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(cnf_transformation,[],[f3076]) ).
thf(f3076,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X2)) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X62: int,X63: int,X64: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X62),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X63),X64)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X63),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X62),X64)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(f5385,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3075]) ).
thf(f3075,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
inference(rectify,[],[f127]) ).
thf(f127,axiom,
! [X80: int,X81: int,X82: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X80),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X81),X82)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X80),X81)),X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(f7870,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(backward_demodulation,[],[f7625,f5383]) ).
thf(f5383,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ),
inference(cnf_transformation,[],[f3073]) ).
thf(f3073,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ),
inference(rectify,[],[f130]) ).
thf(f130,axiom,
! [X83: int,X84: int,X85: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X83),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X84),X85)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X84),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X83),X85)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(f5380,plain,
! [X2: nat,X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3070]) ).
thf(f3070,plain,
! [X0: int,X1: nat,X2: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),X2) ),
inference(rectify,[],[f472]) ).
thf(f472,axiom,
! [X271: int,X272: nat,X273: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X271),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X272),X273)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X271),X272)),X273) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_power__mult) ).
thf(f7869,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X2),X1)) ),
inference(forward_demodulation,[],[f5379,f5370]) ).
thf(f5379,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3069]) ).
thf(f3069,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)),X1) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X53: nat,X54: nat,X55: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X53),X54)),X55) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X53),X55)),X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(f7868,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(forward_demodulation,[],[f5376,f5368]) ).
thf(f5376,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3066]) ).
thf(f3066,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),X1) ),
inference(rectify,[],[f122]) ).
thf(f122,axiom,
! [X74: nat,X75: nat,X76: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X74),X75)),X76) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X74),X76)),X75) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(f7867,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(forward_demodulation,[],[f5372,f5371]) ).
thf(f5372,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3062]) ).
thf(f3062,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) ),
inference(rectify,[],[f880]) ).
thf(f880,axiom,
! [X19: nat,X20: nat,X18: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),X20)),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),X18)),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_diff__commute) ).
thf(f5371,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3061]) ).
thf(f3061,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(rectify,[],[f935]) ).
thf(f935,axiom,
! [X19: nat,X20: nat,X18: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),X20)),X18) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X19),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_diff__diff__left) ).
thf(f7866,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1))) ),
inference(backward_demodulation,[],[f6278,f5370]) ).
thf(f5370,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3060]) ).
thf(f3060,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2) ),
inference(rectify,[],[f108]) ).
thf(f108,axiom,
! [X59: nat,X60: nat,X61: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X59),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X60),X61)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X59),X60)),X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(f5369,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3059]) ).
thf(f3059,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X2)) ),
inference(rectify,[],[f111]) ).
thf(f111,axiom,
! [X62: nat,X63: nat,X64: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X62),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X63),X64)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X63),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X62),X64)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(f5368,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3058]) ).
thf(f3058,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X80: nat,X81: nat,X82: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X80),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X81),X82)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X80),X81)),X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(f5366,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3056]) ).
thf(f3056,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(rectify,[],[f929]) ).
thf(f929,axiom,
! [X16: nat,X17: nat,X15: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X16),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X17),X15)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X17),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_nat__add__left__commute) ).
thf(f5365,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3055]) ).
thf(f3055,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),X2) ),
inference(rectify,[],[f470]) ).
thf(f470,axiom,
! [X271: nat,X272: nat,X273: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X271),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X272),X273)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X271),X272)),X273) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_power__mult) ).
thf(f5363,plain,
! [X2: nat,X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3053]) ).
thf(f3053,plain,
! [X0: real,X1: nat,X2: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),X2) ),
inference(rectify,[],[f471]) ).
thf(f471,axiom,
! [X271: real,X272: nat,X273: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X271),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X272),X273)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X271),X272)),X273) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_power__mult) ).
thf(f7865,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X2),X1)) ),
inference(forward_demodulation,[],[f5362,f5357]) ).
thf(f5362,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3052]) ).
thf(f3052,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)),X1) ),
inference(rectify,[],[f103]) ).
thf(f103,axiom,
! [X53: real,X54: real,X55: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X53),X54)),X55) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X53),X55)),X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(f7864,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ),
inference(forward_demodulation,[],[f5359,f5355]) ).
thf(f5359,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1) ),
inference(cnf_transformation,[],[f3049]) ).
thf(f3049,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1) ),
inference(rectify,[],[f123]) ).
thf(f123,axiom,
! [X74: real,X75: real,X76: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X74),X75)),X76) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X74),X76)),X75) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(f7863,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1))) ),
inference(backward_demodulation,[],[f6275,f5357]) ).
thf(f7862,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1))) ),
inference(backward_demodulation,[],[f6276,f5357]) ).
thf(f5357,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3047]) ).
thf(f3047,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X2) ),
inference(rectify,[],[f109]) ).
thf(f109,axiom,
! [X59: real,X60: real,X61: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X59),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X60),X61)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X59),X60)),X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(f5356,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ),
inference(cnf_transformation,[],[f3046]) ).
thf(f3046,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X2)) ),
inference(rectify,[],[f112]) ).
thf(f112,axiom,
! [X62: real,X63: real,X64: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X62),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X63),X64)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X63),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X62),X64)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(f5355,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) ),
inference(cnf_transformation,[],[f3045]) ).
thf(f3045,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) ),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X80: real,X81: real,X82: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X80),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X81),X82)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X80),X81)),X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(f5354,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(cnf_transformation,[],[f3044]) ).
thf(f3044,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(rectify,[],[f132]) ).
thf(f132,axiom,
! [X83: real,X84: real,X85: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X83),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X84),X85)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X84),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X83),X85)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(f5353,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(cnf_transformation,[],[f3043]) ).
thf(f3043,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(rectify,[],[f936]) ).
thf(f936,axiom,
! [X18: nat,X192: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X192)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X18),X191)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_Nat_Odiff__cancel) ).
thf(f5352,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(cnf_transformation,[],[f3042]) ).
thf(f3042,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
inference(rectify,[],[f937]) ).
thf(f937,axiom,
! [X192: nat,X18: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X18)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_diff__cancel2) ).
thf(f5351,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2)),X1) ),
inference(cnf_transformation,[],[f3041]) ).
thf(f3041,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X2)),X1) ),
inference(rectify,[],[f1183]) ).
thf(f1183,axiom,
! [X18: nat,X191: nat,X192: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X18),X191)),X192)),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_mod__mult__self3) ).
thf(f6573,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ),
inference(definition_unfolding,[],[f5350,f4404,f4404]) ).
thf(f5350,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ),
inference(cnf_transformation,[],[f2048]) ).
thf(f2048,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ),
inference(fool_elimination,[],[f2047]) ).
thf(f2047,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),
inference(rectify,[],[f477]) ).
thf(f477,axiom,
! [X276: int,X277: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X276),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X277),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_sum__power2__ge__zero) ).
thf(f6572,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ),
inference(definition_unfolding,[],[f5349,f5970,f4404,f4404]) ).
thf(f5349,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ),
inference(cnf_transformation,[],[f2046]) ).
thf(f2046,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ),
inference(fool_elimination,[],[f2045]) ).
thf(f2045,plain,
! [X0: real,X1: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),
inference(rectify,[],[f476]) ).
thf(f476,axiom,
! [X276: real,X277: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X276),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X277),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_sum__power2__ge__zero) ).
thf(f6571,plain,
! [X0: int,X1: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1))) ),
inference(definition_unfolding,[],[f5348,f4404]) ).
thf(f5348,plain,
! [X0: int,X1: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))) ),
inference(cnf_transformation,[],[f2044]) ).
thf(f2044,plain,
! [X0: int,X1: nat] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))) ),
inference(fool_elimination,[],[f2043]) ).
thf(f2043,plain,
! [X0: int,X1: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),
inference(rectify,[],[f485]) ).
thf(f485,axiom,
! [X284: int,X285: nat] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X284),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X285))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_zero__le__even__power_H) ).
thf(f6570,plain,
! [X0: real,X1: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1))) ),
inference(definition_unfolding,[],[f5347,f5970,f4404]) ).
thf(f5347,plain,
! [X0: real,X1: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))) ),
inference(cnf_transformation,[],[f2042]) ).
thf(f2042,plain,
! [X0: real,X1: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))) ),
inference(fool_elimination,[],[f2041]) ).
thf(f2041,plain,
! [X0: real,X1: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),
inference(rectify,[],[f484]) ).
thf(f484,axiom,
! [X284: real,X285: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X284),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X285))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_zero__le__even__power_H) ).
thf(f6569,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) ),
inference(definition_unfolding,[],[f5345,f5970]) ).
thf(f5345,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) ),
inference(cnf_transformation,[],[f2038]) ).
thf(f2038,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) ),
inference(fool_elimination,[],[f2037]) ).
thf(f2037,plain,
! [X0: real,X1: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),
inference(rectify,[],[f413]) ).
thf(f413,axiom,
! [X238: real,X239: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X238),X238)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X239),X239))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_sum__squares__ge__zero) ).
thf(f5344,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1) ),
inference(cnf_transformation,[],[f2036]) ).
thf(f2036,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1) ),
inference(fool_elimination,[],[f2035]) ).
thf(f2035,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1),
inference(rectify,[],[f1145]) ).
thf(f1145,axiom,
! [X16: int,X192: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X192)),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_mod__mod__is__mod) ).
thf(f5343,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1) ),
inference(cnf_transformation,[],[f2034]) ).
thf(f2034,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1) ),
inference(fool_elimination,[],[f2033]) ).
thf(f2033,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1),
inference(rectify,[],[f1192]) ).
thf(f1192,axiom,
! [X16: int,X192: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X16)),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_StandardRes__prop1) ).
thf(f5342,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ),
inference(cnf_transformation,[],[f2032]) ).
thf(f2032,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ),
inference(fool_elimination,[],[f2031]) ).
thf(f2031,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),
inference(rectify,[],[f753]) ).
thf(f753,axiom,
! [X393: int,X394: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X393),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X393),X394)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_dvd__triv__left) ).
thf(f5341,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ),
inference(cnf_transformation,[],[f2030]) ).
thf(f2030,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ),
inference(fool_elimination,[],[f2029]) ).
thf(f2029,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),
inference(rectify,[],[f750]) ).
thf(f750,axiom,
! [X391: int,X392: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X391),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X392),X391)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_dvd__triv__right) ).
thf(f5340,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f2028]) ).
thf(f2028,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f2027]) ).
thf(f2027,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0),
inference(rectify,[],[f943]) ).
thf(f943,axiom,
! [X192: nat,X191: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_Nat_Odiff__le__self) ).
thf(f5339,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f2026]) ).
thf(f2026,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f2025]) ).
thf(f2025,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X0),
inference(rectify,[],[f1189]) ).
thf(f1189,axiom,
! [X192: nat,X191: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191)),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_mod__less__eq__dividend) ).
thf(f5337,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ),
inference(cnf_transformation,[],[f2022]) ).
thf(f2022,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ),
inference(fool_elimination,[],[f2021]) ).
thf(f2021,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),
inference(rectify,[],[f996]) ).
thf(f996,axiom,
! [X191: nat,X192: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_le__add2) ).
thf(f5336,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ),
inference(cnf_transformation,[],[f2020]) ).
thf(f2020,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ),
inference(fool_elimination,[],[f2019]) ).
thf(f2019,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),
inference(rectify,[],[f749]) ).
thf(f749,axiom,
! [X391: nat,X392: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X391),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X392),X391)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_dvd__triv__right) ).
thf(f5335,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2018]) ).
thf(f2018,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ),
inference(fool_elimination,[],[f2017]) ).
thf(f2017,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),
inference(rectify,[],[f752]) ).
thf(f752,axiom,
! [X393: nat,X394: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X393),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X393),X394)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_dvd__triv__left) ).
thf(f5334,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ),
inference(cnf_transformation,[],[f2016]) ).
thf(f2016,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ),
inference(fool_elimination,[],[f2015]) ).
thf(f2015,plain,
! [X0: real,X1: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),
inference(rectify,[],[f748]) ).
thf(f748,axiom,
! [X391: real,X392: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X391),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X392),X391)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_dvd__triv__right) ).
thf(f5333,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ),
inference(cnf_transformation,[],[f2014]) ).
thf(f2014,plain,
! [X0: real,X1: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ),
inference(fool_elimination,[],[f2013]) ).
thf(f2013,plain,
! [X0: real,X1: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),
inference(rectify,[],[f751]) ).
thf(f751,axiom,
! [X393: real,X394: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X393),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X393),X394)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_dvd__triv__left) ).
thf(f5332,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X0),X1) ),
inference(cnf_transformation,[],[f2012]) ).
thf(f2012,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X0),X1) ),
inference(fool_elimination,[],[f2011]) ).
thf(f2011,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X0),X1),
inference(rectify,[],[f564]) ).
thf(f564,axiom,
! [X18: int,X192: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X18),X18),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_zcong__refl) ).
thf(f7861,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),vAPP(int,int,bit1,zero_zero_int)) ),
inference(forward_demodulation,[],[f6568,f4464]) ).
thf(f6568,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) ),
inference(definition_unfolding,[],[f5331,f5971]) ).
thf(f5331,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),one_one_int) ),
inference(cnf_transformation,[],[f2010]) ).
thf(f2010,plain,
! [X0: int,X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),one_one_int) ),
inference(fool_elimination,[],[f2009]) ).
thf(f2009,plain,
! [X0: int,X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),one_one_int),
inference(rectify,[],[f575]) ).
thf(f575,axiom,
! [X2: int,X3: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_zcong__1) ).
thf(f6567,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int) ),
inference(definition_unfolding,[],[f5330,f4404,f4404]) ).
thf(f5330,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ),
inference(cnf_transformation,[],[f3040]) ).
thf(f3040,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ),
inference(flattening,[],[f2008]) ).
thf(f2008,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ),
inference(fool_elimination,[],[f2007]) ).
thf(f2007,plain,
! [X0: int,X1: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int),
inference(rectify,[],[f481]) ).
thf(f481,axiom,
! [X280: int,X281: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X280),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X281),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_not__sum__power2__lt__zero) ).
thf(f6566,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f5329,f4404,f4404,f5970]) ).
thf(f5329,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ),
inference(cnf_transformation,[],[f3039]) ).
thf(f3039,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ),
inference(flattening,[],[f2006]) ).
thf(f2006,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ),
inference(fool_elimination,[],[f2005]) ).
thf(f2005,plain,
! [X0: real,X1: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real),
inference(rectify,[],[f480]) ).
thf(f480,axiom,
! [X280: real,X281: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X280),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X281),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_not__sum__power2__lt__zero) ).
thf(f5328,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ),
inference(cnf_transformation,[],[f3038]) ).
thf(f3038,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ),
inference(flattening,[],[f2004]) ).
thf(f2004,plain,
! [X0: int,X1: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ),
inference(fool_elimination,[],[f2003]) ).
thf(f2003,plain,
! [X0: int,X1: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int),
inference(rectify,[],[f417]) ).
thf(f417,axiom,
! [X242: int,X243: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X242),X242)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X243),X243))),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_not__sum__squares__lt__zero) ).
thf(f6565,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f5327,f5970]) ).
thf(f5327,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ),
inference(cnf_transformation,[],[f3037]) ).
thf(f3037,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ),
inference(flattening,[],[f2002]) ).
thf(f2002,plain,
! [X0: real,X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ),
inference(fool_elimination,[],[f2001]) ).
thf(f2001,plain,
! [X0: real,X1: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real),
inference(rectify,[],[f418]) ).
thf(f418,axiom,
! [X242: real,X243: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X242),X242)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X243),X243))),zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_not__sum__squares__lt__zero) ).
thf(f5326,plain,
! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f3036]) ).
thf(f3036,plain,
! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
inference(flattening,[],[f2000]) ).
thf(f2000,plain,
! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f1999]) ).
thf(f1999,plain,
! [X0: nat,X1: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0),
inference(rectify,[],[f975]) ).
thf(f975,axiom,
! [X19: nat,X20: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X20)),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_not__add__less1) ).
thf(f5325,plain,
! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
inference(cnf_transformation,[],[f3035]) ).
thf(f3035,plain,
! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
inference(flattening,[],[f1998]) ).
thf(f1998,plain,
! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
inference(fool_elimination,[],[f1997]) ).
thf(f1997,plain,
! [X0: nat,X1: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1),
inference(rectify,[],[f976]) ).
thf(f976,axiom,
! [X20: nat,X19: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X20),X19)),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_not__add__less2) ).
thf(f6564,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5322,f4404,f4404]) ).
thf(f5322,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4285]) ).
thf(f4285,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ) ) ),
inference(flattening,[],[f4284]) ).
thf(f4284,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ) ) ),
inference(nnf_transformation,[],[f1996]) ).
thf(f1996,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) )
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(fool_elimination,[],[f1995]) ).
thf(f1995,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int)
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f479]) ).
thf(f479,axiom,
! [X278: int,X279: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X278),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X279),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int)
<=> ( ( zero_zero_int = X279 )
& ( zero_zero_int = X278 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_sum__power2__le__zero__iff) ).
thf(f6563,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5323,f4404,f4404]) ).
thf(f5323,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4285]) ).
thf(f7859,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,zero_zero_int)),zero_zero_int),
inference(forward_demodulation,[],[f7858,f6054]) ).
thf(f7858,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),zero_zero_int),
inference(forward_demodulation,[],[f7857,f6100]) ).
thf(f7857,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int),
inference(forward_demodulation,[],[f6898,f4526]) ).
thf(f6898,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int),
inference(equality_resolution,[],[f6897]) ).
thf(f6897,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int) )
| ( zero_zero_int != X0 ) ),
inference(equality_resolution,[],[f6562]) ).
thf(f6562,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ),
inference(definition_unfolding,[],[f5324,f4404,f4404]) ).
thf(f5324,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f4285]) ).
thf(f7855,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,zero_zero_int)),
inference(forward_demodulation,[],[f7854,f6054]) ).
thf(f7854,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),
inference(forward_demodulation,[],[f7853,f6100]) ).
thf(f7853,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(forward_demodulation,[],[f6896,f4526]) ).
thf(f6896,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),
inference(equality_resolution,[],[f6895]) ).
thf(f6895,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
inference(equality_resolution,[],[f6561]) ).
thf(f6561,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
inference(definition_unfolding,[],[f5319,f4404,f4404]) ).
thf(f5319,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ) ),
inference(cnf_transformation,[],[f4283]) ).
thf(f4283,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) )
& ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ) ) ),
inference(flattening,[],[f4282]) ).
thf(f4282,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) )
& ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ) ) ),
inference(nnf_transformation,[],[f1994]) ).
thf(f1994,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
<=> ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ) ),
inference(fool_elimination,[],[f1993]) ).
thf(f1993,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))
<=> ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ) ),
inference(rectify,[],[f483]) ).
thf(f483,axiom,
! [X282: int,X283: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X282),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X283),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))
<=> ( ( zero_zero_int != X283 )
| ( zero_zero_int != X282 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_sum__power2__gt__zero__iff) ).
thf(f6560,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( zero_zero_int = X0 ) ),
inference(definition_unfolding,[],[f5320,f4404,f4404]) ).
thf(f5320,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f4283]) ).
thf(f6559,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( zero_zero_int = X1 ) ),
inference(definition_unfolding,[],[f5321,f4404,f4404]) ).
thf(f5321,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f4283]) ).
thf(f6558,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5316,f5970,f4404,f4404,f5970]) ).
thf(f5316,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ) ),
inference(cnf_transformation,[],[f4281]) ).
thf(f4281,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ) ) ),
inference(flattening,[],[f4280]) ).
thf(f4280,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ) ) ),
inference(nnf_transformation,[],[f1992]) ).
thf(f1992,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) )
<=> ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) ),
inference(fool_elimination,[],[f1991]) ).
thf(f1991,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real)
<=> ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) ),
inference(rectify,[],[f478]) ).
thf(f478,axiom,
! [X278: real,X279: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X278),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X279),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real)
<=> ( ( zero_zero_real = X279 )
& ( zero_zero_real = X278 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_sum__power2__le__zero__iff) ).
thf(f6557,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5317,f5970,f4404,f4404,f5970]) ).
thf(f5317,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),zero_zero_real) ) ),
inference(cnf_transformation,[],[f4281]) ).
thf(f6554,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f5314,f5970,f4404,f4404,f5970]) ).
thf(f5314,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( zero_zero_real = X0 ) ),
inference(cnf_transformation,[],[f4279]) ).
thf(f4279,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) )
& ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ) ) ),
inference(flattening,[],[f4278]) ).
thf(f4278,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) )
& ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) ) ) ),
inference(nnf_transformation,[],[f1990]) ).
thf(f1990,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
<=> ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) ) ),
inference(fool_elimination,[],[f1989]) ).
thf(f1989,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))
<=> ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) ) ),
inference(rectify,[],[f482]) ).
thf(f482,axiom,
! [X282: real,X283: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X282),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X283),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))
<=> ( ( zero_zero_real != X283 )
| ( zero_zero_real != X282 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_sum__power2__gt__zero__iff) ).
thf(f6553,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f5315,f5970,f4404,f4404,f5970]) ).
thf(f5315,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))) )
| ( zero_zero_real = X1 ) ),
inference(cnf_transformation,[],[f4279]) ).
thf(f5310,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4277]) ).
thf(f4277,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ) ) ),
inference(flattening,[],[f4276]) ).
thf(f4276,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ) ) ),
inference(nnf_transformation,[],[f1988]) ).
thf(f1988,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) )
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(fool_elimination,[],[f1987]) ).
thf(f1987,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int)
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f414]) ).
thf(f414,axiom,
! [X240: int,X241: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X240),X240)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X241),X241))),zero_zero_int)
<=> ( ( zero_zero_int = X241 )
& ( zero_zero_int = X240 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_sum__squares__le__zero__iff) ).
thf(f5311,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4277]) ).
thf(f7837,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,zero_zero_int)),zero_zero_int),
inference(forward_demodulation,[],[f7836,f6054]) ).
thf(f7836,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),zero_zero_int),
inference(forward_demodulation,[],[f6890,f4526]) ).
thf(f6890,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),zero_zero_int),
inference(equality_resolution,[],[f6889]) ).
thf(f6889,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),zero_zero_int) )
| ( zero_zero_int != X0 ) ),
inference(equality_resolution,[],[f5312]) ).
thf(f5312,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))),zero_zero_int) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f4277]) ).
thf(f7830,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,zero_zero_int)),
inference(forward_demodulation,[],[f7829,f6054]) ).
thf(f7829,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),
inference(forward_demodulation,[],[f6888,f4526]) ).
thf(f6888,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))),
inference(equality_resolution,[],[f6887]) ).
thf(f6887,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int))) ) ),
inference(equality_resolution,[],[f5307]) ).
thf(f5307,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) ) ),
inference(cnf_transformation,[],[f4275]) ).
thf(f4275,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) )
| ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) )
& ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) ) ) ),
inference(flattening,[],[f4274]) ).
thf(f4274,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) )
| ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) )
& ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) ) ) ),
inference(nnf_transformation,[],[f1986]) ).
thf(f1986,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) )
<=> ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ) ),
inference(fool_elimination,[],[f1985]) ).
thf(f1985,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)))
<=> ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ) ),
inference(rectify,[],[f419]) ).
thf(f419,axiom,
! [X244: int,X245: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X244),X244)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X245),X245)))
<=> ( ( zero_zero_int != X245 )
| ( zero_zero_int != X244 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_sum__squares__gt__zero__iff) ).
thf(f5308,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) )
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f4275]) ).
thf(f5309,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1))) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f4275]) ).
thf(f6552,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5304,f5970,f5970]) ).
thf(f5304,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ) ),
inference(cnf_transformation,[],[f4273]) ).
thf(f4273,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ) ) ),
inference(flattening,[],[f4272]) ).
thf(f4272,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ) ) ),
inference(nnf_transformation,[],[f1984]) ).
thf(f1984,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) )
<=> ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) ),
inference(fool_elimination,[],[f1983]) ).
thf(f1983,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real)
<=> ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) ),
inference(rectify,[],[f415]) ).
thf(f415,axiom,
! [X240: real,X241: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X240),X240)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X241),X241))),zero_zero_real)
<=> ( ( zero_zero_real = X241 )
& ( zero_zero_real = X240 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_sum__squares__le__zero__iff) ).
thf(f6551,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5305,f5970,f5970]) ).
thf(f5305,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))),zero_zero_real) ) ),
inference(cnf_transformation,[],[f4273]) ).
thf(f6548,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f5302,f5970,f5970]) ).
thf(f5302,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
| ( zero_zero_real = X0 ) ),
inference(cnf_transformation,[],[f4271]) ).
thf(f4271,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
| ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) )
& ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) ) ) ),
inference(flattening,[],[f4270]) ).
thf(f4270,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
| ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) )
& ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) ) ) ),
inference(nnf_transformation,[],[f1982]) ).
thf(f1982,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
<=> ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) ) ),
inference(fool_elimination,[],[f1981]) ).
thf(f1981,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)))
<=> ( ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) ) ),
inference(rectify,[],[f420]) ).
thf(f420,axiom,
! [X244: real,X245: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X244),X244)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X245),X245)))
<=> ( ( zero_zero_real != X245 )
| ( zero_zero_real != X244 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_sum__squares__gt__zero__iff) ).
thf(f6547,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f5303,f5970,f5970]) ).
thf(f5303,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1))) )
| ( zero_zero_real = X1 ) ),
inference(cnf_transformation,[],[f4271]) ).
thf(f7820,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f7819,f4464]) ).
thf(f7819,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f7065,f4464]) ).
thf(f7065,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(binary_proxy_clausification,[],[f6546]) ).
thf(f6546,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ),
inference(definition_unfolding,[],[f5300,f5971,f5971,f5971]) ).
thf(f5300,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))),one_one_int),X1) ),
inference(cnf_transformation,[],[f1980]) ).
thf(f1980,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))),one_one_int),X1) ),
inference(fool_elimination,[],[f1979]) ).
thf(f1979,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))),one_one_int),X1)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) ),
inference(rectify,[],[f638]) ).
thf(f638,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))),one_one_int),X163)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int)),X163) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_inv__not__p__minus__1__aux) ).
thf(f7818,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f7817,f4464]) ).
thf(f7817,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f7064,f4464]) ).
thf(f7064,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(binary_proxy_clausification,[],[f6546]) ).
thf(f6544,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) )
| ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5298,f5969,f5969]) ).
thf(f5298,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) ) ),
inference(cnf_transformation,[],[f4269]) ).
thf(f4269,plain,
! [X0: nat,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
& ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) ) ) ),
inference(flattening,[],[f4268]) ).
thf(f4268,plain,
! [X0: nat,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
& ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) ) ) ),
inference(nnf_transformation,[],[f1978]) ).
thf(f1978,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1))) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) ) ) ),
inference(fool_elimination,[],[f1977]) ).
thf(f1977,plain,
! [X0: nat,X1: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) ) ) ),
inference(rectify,[],[f517]) ).
thf(f517,axiom,
! [X16: nat,X14: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),vAPP(int,nat,number_number_of_nat,X14)))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X16)
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_zero__less__power__nat__eq__number__of) ).
thf(f7067,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f5296]) ).
thf(f5296,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ),
inference(cnf_transformation,[],[f1976]) ).
thf(f1976,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ),
inference(fool_elimination,[],[f1975]) ).
thf(f1975,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ),
inference(rectify,[],[f993]) ).
thf(f993,axiom,
! [X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),X18))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_dvd__reduce) ).
thf(f7066,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f5296]) ).
thf(f5291,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) ) ),
inference(cnf_transformation,[],[f4267]) ).
thf(f7816,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7069,f4464]) ).
thf(f7069,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(binary_proxy_clausification,[],[f6542]) ).
thf(f6542,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) ),
inference(definition_unfolding,[],[f5289,f5971]) ).
thf(f5289,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) ),
inference(cnf_transformation,[],[f1972]) ).
thf(f1972,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) ),
inference(fool_elimination,[],[f1971]) ).
thf(f1971,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f88]) ).
thf(f88,axiom,
! [X14: int,X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X14),one_one_int)),X15)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X14),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add1__zle__eq) ).
thf(f7815,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7068,f4464]) ).
thf(f7068,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(binary_proxy_clausification,[],[f6542]) ).
thf(f7814,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7071,f4464]) ).
thf(f7071,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(binary_proxy_clausification,[],[f6541]) ).
thf(f6541,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f5288,f5971]) ).
thf(f5288,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ),
inference(cnf_transformation,[],[f1970]) ).
thf(f1970,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ),
inference(fool_elimination,[],[f1969]) ).
thf(f1969,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f89]) ).
thf(f89,axiom,
! [X14: int,X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X14),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X15),one_one_int))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X14),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le) ).
thf(f7813,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7070,f4464]) ).
thf(f7070,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(binary_proxy_clausification,[],[f6541]) ).
thf(f7812,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f6540,f4464]) ).
thf(f6540,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f5285,f5971]) ).
thf(f5285,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ) ),
inference(cnf_transformation,[],[f4265]) ).
thf(f4265,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( ( X0 != X1 )
& ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) )
& ( ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ) ) ),
inference(flattening,[],[f4264]) ).
thf(f4264,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( ( X0 != X1 )
& ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) )
& ( ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ) ) ),
inference(nnf_transformation,[],[f1968]) ).
thf(f1968,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
<=> ( ( X0 = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1967]) ).
thf(f1967,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int))
<=> ( ( X0 = X1 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(rectify,[],[f159]) ).
thf(f159,axiom,
! [X14: int,X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X14),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X15),one_one_int))
<=> ( ( X14 = X15 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X14),X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_zless__add1__eq) ).
thf(f7811,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f6539,f4464]) ).
thf(f6539,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(definition_unfolding,[],[f5286,f5971]) ).
thf(f5286,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4265]) ).
thf(f7810,plain,
! [X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))) ),
inference(forward_demodulation,[],[f6882,f4464]) ).
thf(f6882,plain,
! [X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(equality_resolution,[],[f6538]) ).
thf(f6538,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( X0 != X1 ) ),
inference(definition_unfolding,[],[f5287,f5971]) ).
thf(f5287,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f4265]) ).
thf(f7809,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7073,f4464]) ).
thf(f7073,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(binary_proxy_clausification,[],[f6537]) ).
thf(f6537,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f5284,f5971]) ).
thf(f5284,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) ),
inference(cnf_transformation,[],[f1966]) ).
thf(f1966,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) ),
inference(fool_elimination,[],[f1965]) ).
thf(f1965,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f634]) ).
thf(f634,axiom,
! [X14: int,X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X14),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X15),one_one_int))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X14),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_zle__diff1__eq) ).
thf(f7808,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7072,f4464]) ).
thf(f7072,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(binary_proxy_clausification,[],[f6537]) ).
thf(f7807,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(subsumption_resolution,[],[f6417,f6535]) ).
thf(f6535,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(definition_unfolding,[],[f5276,f5969,f5969]) ).
thf(f5276,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f4261]) ).
thf(f4261,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
& ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ) ),
inference(flattening,[],[f4260]) ).
thf(f4260,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
& ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1962]) ).
thf(f1962,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(fool_elimination,[],[f1961]) ).
thf(f1961,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f1038]) ).
thf(f1038,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_nat__0__less__mult__iff) ).
thf(f6533,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ) ),
inference(definition_unfolding,[],[f5272,f5969,f5969,f5969]) ).
thf(f5272,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f4259]) ).
thf(f4259,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ) ) ),
inference(flattening,[],[f4258]) ).
thf(f4258,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1960]) ).
thf(f1960,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(fool_elimination,[],[f1959]) ).
thf(f1959,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f1031]) ).
thf(f1031,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_add__gr__0) ).
thf(f6532,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(definition_unfolding,[],[f5273,f5969,f5969]) ).
thf(f5273,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(cnf_transformation,[],[f4259]) ).
thf(f6531,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f5274,f5969,f5969]) ).
thf(f5274,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4259]) ).
thf(f7805,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(forward_demodulation,[],[f6881,f6037]) ).
thf(f6881,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int))) ),
inference(equality_resolution,[],[f6528]) ).
thf(f6528,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X1 ) ),
inference(definition_unfolding,[],[f5271,f5969,f5969]) ).
thf(f5271,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( zero_zero_nat != X1 ) ),
inference(cnf_transformation,[],[f4257]) ).
thf(f4257,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( ( zero_zero_nat != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) )
& ( ( zero_zero_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ),
inference(flattening,[],[f4256]) ).
thf(f4256,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( ( zero_zero_nat != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) )
& ( ( zero_zero_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1958]) ).
thf(f1958,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
<=> ( ( zero_zero_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(fool_elimination,[],[f1957]) ).
thf(f1957,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1))
<=> ( ( zero_zero_nat = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f515]) ).
thf(f515,axiom,
! [X16: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),X191))
<=> ( ( zero_zero_nat = X191 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_nat__zero__less__power__iff) ).
thf(f6527,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
inference(definition_unfolding,[],[f5266,f5969,f5969,f5969]) ).
thf(f5266,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f4255]) ).
thf(f4255,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
& ( zero_zero_nat != X1 ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ),
inference(flattening,[],[f4254]) ).
thf(f4254,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
& ( zero_zero_nat != X1 ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1956]) ).
thf(f1956,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
<=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X1 ) ) ),
inference(fool_elimination,[],[f1955]) ).
thf(f1955,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
| ( zero_zero_nat = X1 ) ) ),
inference(rectify,[],[f516]) ).
thf(f516,axiom,
! [X16: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),X191))
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X16)
| ( zero_zero_nat = X191 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_zero__less__power__nat__eq) ).
thf(f7799,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(forward_demodulation,[],[f6880,f6037]) ).
thf(f6880,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int))) ),
inference(equality_resolution,[],[f6526]) ).
thf(f6526,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X1 ) ),
inference(definition_unfolding,[],[f5267,f5969,f5969]) ).
thf(f5267,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( zero_zero_nat != X1 ) ),
inference(cnf_transformation,[],[f4255]) ).
thf(f7075,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f6524]) ).
thf(f6524,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ),
inference(definition_unfolding,[],[f5265,f5969]) ).
thf(f5265,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1954]) ).
thf(f1954,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ),
inference(fool_elimination,[],[f1953]) ).
thf(f1953,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
inference(rectify,[],[f960]) ).
thf(f960,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X192))
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_zero__less__diff) ).
thf(f7074,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f6524]) ).
thf(f6522,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5260,f5970,f5970,f5970]) ).
thf(f5260,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) ) ),
inference(cnf_transformation,[],[f4253]) ).
thf(f4253,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) ) ) ),
inference(flattening,[],[f4252]) ).
thf(f4252,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) ) ) ),
inference(nnf_transformation,[],[f1952]) ).
thf(f1952,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) )
<=> ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ) ),
inference(fool_elimination,[],[f1951]) ).
thf(f1951,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real)
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ),
inference(rectify,[],[f809]) ).
thf(f809,axiom,
! [X439: real,X440: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X439),X440)),zero_zero_real)
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X440)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X439),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X440),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X439) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_mult__le__0__iff) ).
thf(f6521,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5261,f5970,f5970,f5970]) ).
thf(f5261,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) ) ),
inference(cnf_transformation,[],[f4253]) ).
thf(f6516,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(definition_unfolding,[],[f5254,f5970,f5970,f5970]) ).
thf(f5254,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(cnf_transformation,[],[f4251]) ).
thf(f4251,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ) ),
inference(flattening,[],[f4250]) ).
thf(f4250,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ) )
& ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1950]) ).
thf(f1950,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
<=> ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ) ),
inference(fool_elimination,[],[f1949]) ).
thf(f1949,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1))
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) ) ) ),
inference(rectify,[],[f811]) ).
thf(f811,axiom,
! [X441: real,X442: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X441),X442))
<=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X442),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X441),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X442)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X441) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_zero__le__mult__iff) ).
thf(f6515,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(definition_unfolding,[],[f5255,f5970,f5970,f5970]) ).
thf(f5255,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(cnf_transformation,[],[f4251]) ).
thf(f5251,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f4249]) ).
thf(f4249,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) ) ) ),
inference(nnf_transformation,[],[f1948]) ).
thf(f1948,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) )
<=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f1947]) ).
thf(f1947,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int)
<=> ( X0 = X1 ) ),
inference(rectify,[],[f574]) ).
thf(f574,axiom,
! [X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),X3),zero_zero_int)
<=> ( X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_IntPrimes_Ozcong__zero) ).
thf(f6879,plain,
! [X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),X1),zero_zero_int) ),
inference(equality_resolution,[],[f5252]) ).
thf(f5252,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),X1),zero_zero_int) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f4249]) ).
thf(f7079,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(binary_proxy_clausification,[],[f5249]) ).
thf(f5249,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ),
inference(cnf_transformation,[],[f1944]) ).
thf(f1944,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ),
inference(fool_elimination,[],[f1943]) ).
thf(f1943,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) ),
inference(rectify,[],[f656]) ).
thf(f656,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X163),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_zcong__eq__zdvd__prop) ).
thf(f7078,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(binary_proxy_clausification,[],[f5249]) ).
thf(f7083,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5247]) ).
thf(f5247,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f1940]) ).
thf(f1940,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ),
inference(fool_elimination,[],[f1939]) ).
thf(f1939,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X18: int,X38: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X18)),vAPP(int,int,bit1,X38))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J) ).
thf(f7082,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5247]) ).
thf(f7087,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5245]) ).
thf(f5245,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f1936]) ).
thf(f1936,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(fool_elimination,[],[f1935]) ).
thf(f1935,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f150]) ).
thf(f150,axiom,
! [X36: int,X37: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X36)),vAPP(int,int,bit0,X37))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X36),X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__int__code_I15_J) ).
thf(f7086,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5245]) ).
thf(f7091,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5243]) ).
thf(f5243,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f1932]) ).
thf(f1932,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(fool_elimination,[],[f1931]) ).
thf(f1931,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f85]) ).
thf(f85,axiom,
! [X36: int,X37: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X36)),vAPP(int,int,bit1,X37))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X36),X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__int__code_I14_J) ).
thf(f7090,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5243]) ).
thf(f7095,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5241]) ).
thf(f5241,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f1928]) ).
thf(f1928,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(fool_elimination,[],[f1927]) ).
thf(f1927,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X18: int,X38: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X18)),vAPP(int,int,bit0,X38))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J) ).
thf(f7094,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5241]) ).
thf(f7103,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5237]) ).
thf(f5237,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f1920]) ).
thf(f1920,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ),
inference(fool_elimination,[],[f1919]) ).
thf(f1919,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X18: int,X38: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X18)),vAPP(int,int,bit1,X38))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J) ).
thf(f7102,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5237]) ).
thf(f7107,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5235]) ).
thf(f5235,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f1916]) ).
thf(f1916,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(fool_elimination,[],[f1915]) ).
thf(f1915,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f84]) ).
thf(f84,axiom,
! [X18: int,X38: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X18)),vAPP(int,int,bit0,X38))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J) ).
thf(f7106,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5235]) ).
thf(f7111,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5233]) ).
thf(f5233,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f1912]) ).
thf(f1912,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(fool_elimination,[],[f1911]) ).
thf(f1911,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f155]) ).
thf(f155,axiom,
! [X36: int,X37: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X36)),vAPP(int,int,bit1,X37))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X36),X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_less__eq__int__code_I14_J) ).
thf(f7110,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ) ),
inference(binary_proxy_clausification,[],[f5233]) ).
thf(f7115,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5231]) ).
thf(f5231,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f1908]) ).
thf(f1908,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(fool_elimination,[],[f1907]) ).
thf(f1907,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X18: int,X38: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X18)),vAPP(int,int,bit0,X38))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J) ).
thf(f7114,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(binary_proxy_clausification,[],[f5231]) ).
thf(f7774,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) ) ),
inference(forward_demodulation,[],[f7773,f4464]) ).
thf(f7773,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),X1) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) ) ),
inference(forward_demodulation,[],[f7772,f4464]) ).
thf(f7772,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7771,f4464]) ).
thf(f7771,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f5225,f4464]) ).
thf(f5225,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(cnf_transformation,[],[f4247]) ).
thf(f4247,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) )
& ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ) ),
inference(nnf_transformation,[],[f1900]) ).
thf(f1900,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
<=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(fool_elimination,[],[f1899]) ).
thf(f1899,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1))
<=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(rectify,[],[f1137]) ).
thf(f1137,axiom,
! [X16: int,X17: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X16)),vAPP(int,int,number_number_of_int,X17))
<=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X17)),vAPP(int,int,number_number_of_int,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_zdvd__iff__zmod__eq__0__number__of) ).
thf(f7770,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7769,f4464]) ).
thf(f7769,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(forward_demodulation,[],[f7768,f4464]) ).
thf(f7768,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(forward_demodulation,[],[f7767,f4464]) ).
thf(f7767,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),X1) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(forward_demodulation,[],[f5226,f4464]) ).
thf(f5226,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X1)),vAPP(int,int,number_number_of_int,X0)) ) ),
inference(cnf_transformation,[],[f4247]) ).
thf(f7766,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(subsumption_resolution,[],[f6511,f5222]) ).
thf(f6511,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(definition_unfolding,[],[f5221,f4404]) ).
thf(f5221,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4246]) ).
thf(f4246,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f4245]) ).
thf(f4245,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) )
& ( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f3589]) ).
thf(f3589,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ) ),
inference(ennf_transformation,[],[f1898]) ).
thf(f1898,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) ) ) ) ),
inference(fool_elimination,[],[f1897]) ).
thf(f1897,plain,
! [X0: int,X1: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1))
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) ) ) ),
inference(rectify,[],[f416]) ).
thf(f416,axiom,
! [X40: int,X39: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39))
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),X39)
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X40),X39)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_less__nat__number__of) ).
thf(f5222,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4246]) ).
thf(f6510,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(definition_unfolding,[],[f5224,f4404]) ).
thf(f5224,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X1) ) ),
inference(cnf_transformation,[],[f4246]) ).
thf(f5219,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4244]) ).
thf(f4244,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f3033]) ).
thf(f3033,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ),
inference(flattening,[],[f1896]) ).
thf(f1896,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ),
inference(fool_elimination,[],[f1895]) ).
thf(f1895,plain,
! [X0: int,X1: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1))
<=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ),
inference(rectify,[],[f50]) ).
thf(f50,axiom,
! [X25: int,X26: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X25)),vAPP(int,nat,number_number_of_nat,X26))
<=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X26)),vAPP(int,nat,number_number_of_nat,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
thf(f5220,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) ) ),
inference(cnf_transformation,[],[f4244]) ).
thf(f6509,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(definition_unfolding,[],[f5216,f4404]) ).
thf(f5216,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4243]) ).
thf(f4243,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
& ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f4242]) ).
thf(f4242,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
& ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f3588]) ).
thf(f3588,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) ),
inference(ennf_transformation,[],[f3032]) ).
thf(f3032,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) ) ),
inference(flattening,[],[f1894]) ).
thf(f1894,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) ) ),
inference(fool_elimination,[],[f1893]) ).
thf(f1893,plain,
! [X0: int,X1: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1))
<=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) ),
inference(rectify,[],[f421]) ).
thf(f421,axiom,
! [X40: int,X39: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X40)),vAPP(int,nat,number_number_of_nat,X39))
<=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X40),X39)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X40),pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_le__nat__number__of) ).
thf(f5217,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4243]) ).
thf(f6508,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5218,f4404]) ).
thf(f5218,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,X0)),vAPP(int,nat,number_number_of_nat,X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ) ),
inference(cnf_transformation,[],[f4243]) ).
thf(f7121,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f5215]) ).
thf(f5215,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(cnf_transformation,[],[f1892]) ).
thf(f1892,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(fool_elimination,[],[f1891]) ).
thf(f1891,plain,
! [X0: int,X1: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X27: int,X28: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X27)),vAPP(int,real,number267125858f_real,X28))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X27),X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__number__of) ).
thf(f7120,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f5215]) ).
thf(f7123,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f5214]) ).
thf(f5214,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(cnf_transformation,[],[f1890]) ).
thf(f1890,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(fool_elimination,[],[f1889]) ).
thf(f1889,plain,
! [X0: int,X1: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
! [X29: int,X30: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X29)),vAPP(int,real,number267125858f_real,X30))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X29),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__number__of) ).
thf(f7122,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ) ),
inference(binary_proxy_clausification,[],[f5214]) ).
thf(f5212,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ) ),
inference(cnf_transformation,[],[f4241]) ).
thf(f4241,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ) ) ),
inference(nnf_transformation,[],[f3031]) ).
thf(f3031,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) )
<=> ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(flattening,[],[f1888]) ).
thf(f1888,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) )
<=> ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(fool_elimination,[],[f1887]) ).
thf(f1887,plain,
! [X0: int,X1: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1))
<=> ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) ),
inference(rectify,[],[f51]) ).
thf(f51,axiom,
! [X25: int,X26: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X25)),vAPP(int,real,number267125858f_real,X26))
<=> ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X26)),vAPP(int,real,number267125858f_real,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(f5213,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X1)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(cnf_transformation,[],[f4241]) ).
thf(f7125,plain,
! [X0: int,X1: int > $o] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),X1) )
| ( $false = vAPP(int,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f5211]) ).
thf(f5211,plain,
! [X0: int,X1: int > $o] : ( vAPP(int,$o,X1,X0) = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),X1) ),
inference(cnf_transformation,[],[f1886]) ).
thf(f1886,plain,
! [X0: int,X1: int > $o] : ( vAPP(int,$o,X1,X0) = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),X1) ),
inference(fool_elimination,[],[f1885]) ).
thf(f1885,plain,
! [X0: int,X1: int > $o] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),X1)
<=> vAPP(int,$o,X1,X0) ),
inference(rectify,[],[f119]) ).
thf(f119,axiom,
! [X71: int,X72: int > $o] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X71),X72)
<=> vAPP(int,$o,X72,X71) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_mem__def) ).
thf(f7124,plain,
! [X0: int,X1: int > $o] :
( ( $false = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),X1) )
| ( $true = vAPP(int,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f5211]) ).
thf(f7127,plain,
! [X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f5210]) ).
thf(f5210,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),zero_zero_int) ),
inference(cnf_transformation,[],[f1884]) ).
thf(f1884,plain,
! [X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),zero_zero_int) ),
inference(fool_elimination,[],[f1883]) ).
thf(f1883,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),zero_zero_int) ),
inference(rectify,[],[f628]) ).
thf(f628,axiom,
! [X18: int,X38: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),X38)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X18),X38)),zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_less__bin__lemma) ).
thf(f7126,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f5210]) ).
thf(f6507,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK25,X1),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) ) ),
inference(definition_unfolding,[],[f5205,f4404]) ).
thf(f5205,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK25,X1),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) ) ),
inference(cnf_transformation,[],[f4238]) ).
thf(f4238,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) )
| ! [X2: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK25,X1),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f4236,f4237]) ).
thf(f4237,plain,
! [X0: int,X1: int] :
( ? [X3: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK25,X1),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ) ),
introduced(choice_axiom,[]) ).
thf(f4236,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) )
| ! [X2: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ) )
& ( ? [X3: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) ) ) ),
inference(rectify,[],[f4235]) ).
thf(f4235,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) )
| ! [X2: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ) )
& ( ? [X2: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1880]) ).
thf(f1880,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) )
<=> ? [X2: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ) ),
inference(fool_elimination,[],[f1879]) ).
thf(f1879,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1)
<=> ? [X2: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ),
inference(rectify,[],[f669]) ).
thf(f669,axiom,
! [X192: int,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X192),X16)
<=> ? [X1: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X16),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_QuadRes__def) ).
thf(f6506,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1),X0) ) ),
inference(definition_unfolding,[],[f5206,f4404]) ).
thf(f5206,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1),X0) ) ),
inference(cnf_transformation,[],[f4238]) ).
thf(f5200,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK24,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4232]) ).
thf(f4232,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) )
& ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK24,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f4230,f4231]) ).
thf(f4231,plain,
! [X0: nat,X1: nat] :
( ? [X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) = X1 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK24,X1),X0)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f4230,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) )
& ( ? [X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(rectify,[],[f4229]) ).
thf(f4229,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) )
& ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1876]) ).
thf(f1876,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
<=> ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 ) ),
inference(fool_elimination,[],[f1875]) ).
thf(f1875,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
<=> ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 ) ),
inference(rectify,[],[f998]) ).
thf(f998,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191)
<=> ? [X320: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X320) = X191 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_le__iff__add) ).
thf(f6876,plain,
! [X2: nat,X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
inference(equality_resolution,[],[f5201]) ).
thf(f5201,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) ),
inference(cnf_transformation,[],[f4232]) ).
thf(f6873,plain,
! [X1: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X1) ),
inference(equality_resolution,[],[f5191]) ).
thf(f5191,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f4224]) ).
thf(f4224,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) )
& ( ( ( X0 != X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
inference(flattening,[],[f4223]) ).
thf(f4223,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) )
& ( ( ( X0 != X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1870]) ).
thf(f1870,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
<=> ( ( X0 != X1 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
inference(fool_elimination,[],[f1869]) ).
thf(f1869,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
<=> ( ( X0 != X1 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(rectify,[],[f687]) ).
thf(f687,axiom,
! [X16: real,X17: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X16),X17)
<=> ( ( X16 != X17 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X16),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_real__less__def) ).
thf(f7129,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6505]) ).
thf(f6505,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f5189,f5970]) ).
thf(f5189,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),zero_zero_real) ),
inference(cnf_transformation,[],[f1868]) ).
thf(f1868,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),zero_zero_real) ),
inference(fool_elimination,[],[f1867]) ).
thf(f1867,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),zero_zero_real) ),
inference(rectify,[],[f676]) ).
thf(f676,axiom,
! [X16: real,X17: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X16),X17)
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X16),X17)),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_real__le__eq__diff) ).
thf(f7128,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6505]) ).
thf(f5187,plain,
! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f4222]) ).
thf(f4222,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( ( X0 != X1 )
& ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) )
& ( ( X0 = X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
inference(flattening,[],[f4221]) ).
thf(f4221,plain,
! [X0: real,X1: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( ( X0 != X1 )
& ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) )
& ( ( X0 = X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1866]) ).
thf(f1866,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
<=> ( ( X0 = X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
inference(fool_elimination,[],[f1865]) ).
thf(f1865,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
<=> ( ( X0 = X1 )
| vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(rectify,[],[f686]) ).
thf(f686,axiom,
! [X16: real,X17: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X16),X17)
<=> ( ( X16 = X17 )
| vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X16),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_less__eq__real__def) ).
thf(f6501,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5167,f4404,f4404]) ).
thf(f5167,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) != zero_zero_int ) ),
inference(cnf_transformation,[],[f4211]) ).
thf(f4211,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = zero_zero_int )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) != zero_zero_int ) ) ),
inference(flattening,[],[f4210]) ).
thf(f4210,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = zero_zero_int )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) != zero_zero_int ) ) ),
inference(nnf_transformation,[],[f3025]) ).
thf(f3025,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = zero_zero_int )
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f457]) ).
thf(f457,axiom,
! [X260: int,X261: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X260),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X261),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
<=> ( ( zero_zero_int = X261 )
& ( zero_zero_int = X260 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_sum__power2__eq__zero__iff) ).
thf(f6500,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5168,f4404,f4404]) ).
thf(f5168,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) != zero_zero_int ) ),
inference(cnf_transformation,[],[f4211]) ).
thf(f6498,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5164,f5970,f5970,f4404,f4404]) ).
thf(f5164,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f4209]) ).
thf(f4209,plain,
! [X0: real,X1: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ) ),
inference(flattening,[],[f4208]) ).
thf(f4208,plain,
! [X0: real,X1: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ) ),
inference(nnf_transformation,[],[f3024]) ).
thf(f3024,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
<=> ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) ),
inference(rectify,[],[f456]) ).
thf(f456,axiom,
! [X260: real,X261: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X260),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X261),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
<=> ( ( zero_zero_real = X261 )
& ( zero_zero_real = X260 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_sum__power2__eq__zero__iff) ).
thf(f6497,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5165,f5970,f5970,f4404,f4404]) ).
thf(f5165,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f4209]) ).
thf(f5161,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) ) ),
inference(cnf_transformation,[],[f4207]) ).
thf(f4207,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) ) ) ),
inference(flattening,[],[f4206]) ).
thf(f4206,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) ) ) ),
inference(nnf_transformation,[],[f3023]) ).
thf(f3023,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) )
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f386]) ).
thf(f386,axiom,
! [X229: int,X230: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X229),X229)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X230),X230)) )
<=> ( ( zero_zero_int = X230 )
& ( zero_zero_int = X229 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_sum__squares__eq__zero__iff) ).
thf(f5162,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X1)) ) ),
inference(cnf_transformation,[],[f4207]) ).
thf(f6492,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) != vAPP(int,real,number267125858f_real,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5155,f5970,f5970]) ).
thf(f5155,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) ) ),
inference(cnf_transformation,[],[f4203]) ).
thf(f4203,plain,
! [X0: real,X1: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) ) ) ),
inference(flattening,[],[f4202]) ).
thf(f4202,plain,
! [X0: real,X1: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) )
| ( zero_zero_real != X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) ) ) ),
inference(nnf_transformation,[],[f3021]) ).
thf(f3021,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) )
<=> ( ( zero_zero_real = X1 )
& ( zero_zero_real = X0 ) ) ),
inference(rectify,[],[f867]) ).
thf(f867,axiom,
! [X16: real,X17: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X16),X16)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X17),X17)) )
<=> ( ( zero_zero_real = X17 )
& ( zero_zero_real = X16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_real__two__squares__add__zero__iff) ).
thf(f6491,plain,
! [X0: real,X1: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) != vAPP(int,real,number267125858f_real,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5156,f5970,f5970]) ).
thf(f5156,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X1)) ) ),
inference(cnf_transformation,[],[f4203]) ).
thf(f6489,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(definition_unfolding,[],[f5153,f5969]) ).
thf(f5153,plain,
! [X0: int,X1: int] :
( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4201]) ).
thf(f4201,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f4200]) ).
thf(f4200,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f3020]) ).
thf(f3020,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f585]) ).
thf(f585,axiom,
! [X318: int,X319: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X318),vAPP(int,nat,number_number_of_nat,X319)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X319) )
& ( zero_zero_int = X318 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_power__eq__0__iff__number__of) ).
thf(f6486,plain,
! [X0: nat,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5150,f5969,f5969]) ).
thf(f5150,plain,
! [X0: nat,X1: int] :
( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4199]) ).
thf(f4199,plain,
! [X0: nat,X1: int] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f4198]) ).
thf(f4198,plain,
! [X0: nat,X1: int] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f3019]) ).
thf(f3019,plain,
! [X0: nat,X1: int] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_nat = X0 ) ) ),
inference(rectify,[],[f584]) ).
thf(f584,axiom,
! [X318: nat,X319: int] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X318),vAPP(int,nat,number_number_of_nat,X319)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X319) )
& ( zero_zero_nat = X318 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_power__eq__0__iff__number__of) ).
thf(f6483,plain,
! [X0: real,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) != vAPP(int,real,number267125858f_real,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5147,f5969,f5970]) ).
thf(f5147,plain,
! [X0: real,X1: int] :
( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f4197]) ).
thf(f4197,plain,
! [X0: real,X1: int] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f4196]) ).
thf(f4196,plain,
! [X0: real,X1: int] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f3018]) ).
thf(f3018,plain,
! [X0: real,X1: int] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_real = X0 ) ) ),
inference(rectify,[],[f583]) ).
thf(f583,axiom,
! [X318: real,X319: int] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X318),vAPP(int,nat,number_number_of_nat,X319)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X319) )
& ( zero_zero_real = X318 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_power__eq__0__iff__number__of) ).
thf(f5144,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != X0 )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f4195]) ).
thf(f4195,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = X0 )
| ( zero_zero_int != X1 ) )
& ( ( zero_zero_int = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != X0 ) ) ),
inference(nnf_transformation,[],[f3017]) ).
thf(f3017,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = X0 )
<=> ( zero_zero_int = X1 ) ),
inference(rectify,[],[f354]) ).
thf(f354,axiom,
! [X206: int,X207: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X206),X207) = X206 )
<=> ( zero_zero_int = X207 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add__0__iff) ).
thf(f6851,plain,
! [X0: real] : ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(equality_resolution,[],[f6478]) ).
thf(f6478,plain,
! [X0: real,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X1 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) != vAPP(int,real,number267125858f_real,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5140,f5969,f5970]) ).
thf(f5140,plain,
! [X0: real,X1: nat] :
( ( zero_zero_nat != X1 )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) ) ),
inference(cnf_transformation,[],[f4193]) ).
thf(f4193,plain,
! [X0: real,X1: nat] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_nat != X1 )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) ) ) ),
inference(flattening,[],[f4192]) ).
thf(f4192,plain,
! [X0: real,X1: nat] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_real != X0 ) )
& ( ( ( zero_zero_nat != X1 )
& ( zero_zero_real = X0 ) )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3015]) ).
thf(f3015,plain,
! [X0: real,X1: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) )
<=> ( ( zero_zero_nat != X1 )
& ( zero_zero_real = X0 ) ) ),
inference(rectify,[],[f314]) ).
thf(f314,axiom,
! [X175: real,X176: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X175),X176) = zero_zero_real )
<=> ( ( zero_zero_nat != X176 )
& ( zero_zero_real = X175 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_power__eq__0__iff) ).
thf(f6476,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != X0 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f5137,f5970]) ).
thf(f5137,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f4191]) ).
thf(f4191,plain,
! [X0: real,X1: real] :
( ( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = X0 )
| ( zero_zero_real != X1 ) )
& ( ( zero_zero_real = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != X0 ) ) ),
inference(nnf_transformation,[],[f3014]) ).
thf(f3014,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = X0 )
<=> ( zero_zero_real = X1 ) ),
inference(rectify,[],[f356]) ).
thf(f356,axiom,
! [X206: real,X207: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X206),X207) = X206 )
<=> ( zero_zero_real = X207 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
thf(f5132,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),sK23,X1),X0)) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4188]) ).
thf(f4188,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) )
| ! [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) != X0 ) )
& ( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),sK23,X1),X0)) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f4186,f4187]) ).
thf(f4187,plain,
! [X0: int,X1: int] :
( ? [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3) = X0 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),sK23,X1),X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f4186,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) )
| ! [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) != X0 ) )
& ( ? [X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X3) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ) ),
inference(rectify,[],[f4185]) ).
thf(f4185,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) )
| ! [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) != X0 ) )
& ( ? [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3012]) ).
thf(f3012,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) )
<=> ? [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) = X0 ) ),
inference(rectify,[],[f1142]) ).
thf(f1142,axiom,
! [X192: int,X218: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X192),X218) )
<=> ? [X501: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X218),X501) = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_zmod__eq__0__iff) ).
thf(f6846,plain,
! [X2: int,X1: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2)),X1) ),
inference(equality_resolution,[],[f5133]) ).
thf(f5133,plain,
! [X2: int,X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) != X0 ) ),
inference(cnf_transformation,[],[f4188]) ).
thf(f5130,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) ) ),
inference(cnf_transformation,[],[f4184]) ).
thf(f4184,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1856]) ).
thf(f1856,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) )
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ) ),
inference(fool_elimination,[],[f1855]) ).
thf(f1855,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ),
inference(rectify,[],[f1190]) ).
thf(f1190,axiom,
! [X192: int,X16: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X16) )
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_StandardRes__eq__zcong) ).
thf(f5131,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ) ),
inference(cnf_transformation,[],[f4184]) ).
thf(f6845,plain,
! [X0: int] : ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(equality_resolution,[],[f6474]) ).
thf(f6474,plain,
! [X0: int,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X1 )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) ) ),
inference(definition_unfolding,[],[f5128,f5969]) ).
thf(f5128,plain,
! [X0: int,X1: nat] :
( ( zero_zero_nat != X1 )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4183]) ).
thf(f4183,plain,
! [X0: int,X1: nat] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_nat != X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) ) ) ),
inference(flattening,[],[f4182]) ).
thf(f4182,plain,
! [X0: int,X1: nat] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) )
| ( zero_zero_nat = X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_nat != X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3011]) ).
thf(f3011,plain,
! [X0: int,X1: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) )
<=> ( ( zero_zero_nat != X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f312]) ).
thf(f312,axiom,
! [X175: int,X176: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X175),X176) )
<=> ( ( zero_zero_nat != X176 )
& ( zero_zero_int = X175 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_power__eq__0__iff) ).
thf(f6469,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f5121,f5969,f5969]) ).
thf(f5121,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4179]) ).
thf(f4179,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( zero_zero_nat != X1 )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) ) ) ),
inference(flattening,[],[f4178]) ).
thf(f4178,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( zero_zero_nat != X1 )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3009]) ).
thf(f3009,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
<=> ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) ) ),
inference(rectify,[],[f962]) ).
thf(f962,axiom,
! [X192: nat,X191: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191) )
<=> ( ( zero_zero_nat = X191 )
& ( zero_zero_nat = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_add__is__0) ).
thf(f6468,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f5122,f5969,f5969]) ).
thf(f5122,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4179]) ).
thf(f6837,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(equality_resolution,[],[f6463]) ).
thf(f6463,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5115,f5969,f5969]) ).
thf(f5115,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4175]) ).
thf(f4175,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat != X0 )
| ( zero_zero_nat = X1 ) )
& ( ( ( zero_zero_nat = X0 )
& ( zero_zero_nat != X1 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ) ),
inference(flattening,[],[f4174]) ).
thf(f4174,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat != X0 )
| ( zero_zero_nat = X1 ) )
& ( ( ( zero_zero_nat = X0 )
& ( zero_zero_nat != X1 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3007]) ).
thf(f3007,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
<=> ( ( zero_zero_nat = X0 )
& ( zero_zero_nat != X1 ) ) ),
inference(rectify,[],[f769]) ).
thf(f769,axiom,
! [X192: nat,X191: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X192),X191) )
<=> ( ( zero_zero_nat = X192 )
& ( zero_zero_nat != X191 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_nat__power__eq__0__iff) ).
thf(f6462,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f5116,f5969,f5969]) ).
thf(f5116,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4175]) ).
thf(f6460,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5113,f5969]) ).
thf(f5113,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4173]) ).
thf(f4173,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f1854]) ).
thf(f1854,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) )
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f1853]) ).
thf(f1853,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) )
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f969]) ).
thf(f969,axiom,
! [X192: nat,X191: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191) )
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_diff__is__0__eq) ).
thf(f6458,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f5111,f5969]) ).
thf(f5111,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4172]) ).
thf(f4172,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) )
| ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) != X0 ) )
& ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f4170,f4171]) ).
thf(f4171,plain,
! [X0: nat,X1: nat] :
( ? [X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3) = X0 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK22,X1),X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f4170,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) )
| ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) != X0 ) )
& ( ? [X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X3) = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) ) ) ),
inference(rectify,[],[f4169]) ).
thf(f4169,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) )
| ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) != X0 ) )
& ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3006]) ).
thf(f3006,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) )
<=> ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) = X0 ) ),
inference(rectify,[],[f1180]) ).
thf(f1180,axiom,
! [X192: nat,X218: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X218) )
<=> ? [X501: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X218),X501) = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_mod__eq__0__iff) ).
thf(f6835,plain,
! [X2: nat,X1: nat] : ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2)),X1) ),
inference(equality_resolution,[],[f6457]) ).
thf(f6457,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) != X0 ) ),
inference(definition_unfolding,[],[f5112,f5969]) ).
thf(f5112,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X2) != X0 ) ),
inference(cnf_transformation,[],[f4172]) ).
thf(f7753,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,int,bit1,zero_zero_int) = X1 )
| ( min = X0 ) ),
inference(forward_demodulation,[],[f7752,f4464]) ).
thf(f7752,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X1 )
| ( min = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f7751,f4464]) ).
thf(f7751,plain,
! [X0: int,X1: int] :
( ( min = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f6452,f4464]) ).
thf(f6452,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5103,f5971,f5971]) ).
thf(f5103,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( one_one_int = X1 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4166]) ).
thf(f4166,plain,
! [X0: int,X1: int] :
( ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) )
| ( ( ( vAPP(int,int,number_number_of_int,min) != X1 )
| ( vAPP(int,int,number_number_of_int,min) != X0 ) )
& ( ( one_one_int != X1 )
| ( one_one_int != X0 ) ) ) )
& ( ( ( vAPP(int,int,number_number_of_int,min) = X1 )
& ( vAPP(int,int,number_number_of_int,min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ) ),
inference(flattening,[],[f4165]) ).
thf(f4165,plain,
! [X0: int,X1: int] :
( ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) )
| ( ( ( vAPP(int,int,number_number_of_int,min) != X1 )
| ( vAPP(int,int,number_number_of_int,min) != X0 ) )
& ( ( one_one_int != X1 )
| ( one_one_int != X0 ) ) ) )
& ( ( ( vAPP(int,int,number_number_of_int,min) = X1 )
& ( vAPP(int,int,number_number_of_int,min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3004]) ).
thf(f3004,plain,
! [X0: int,X1: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) )
<=> ( ( ( vAPP(int,int,number_number_of_int,min) = X1 )
& ( vAPP(int,int,number_number_of_int,min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) ) ) ),
inference(rectify,[],[f553]) ).
thf(f553,axiom,
! [X192: int,X191: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X192),X191) )
<=> ( ( ( vAPP(int,int,number_number_of_int,min) = X191 )
& ( vAPP(int,int,number_number_of_int,min) = X192 ) )
| ( ( one_one_int = X191 )
& ( one_one_int = X192 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_zmult__eq__1__iff) ).
thf(f7750,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( min = X1 ) ),
inference(forward_demodulation,[],[f7749,f4464]) ).
thf(f7749,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( min = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f7748,f4464]) ).
thf(f7748,plain,
! [X0: int,X1: int] :
( ( min = X1 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f6451,f4464]) ).
thf(f6451,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X1 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5104,f5971,f5971]) ).
thf(f5104,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X1 )
| ( one_one_int = X0 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4166]) ).
thf(f7747,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,int,bit1,zero_zero_int) = X1 )
| ( min = X1 ) ),
inference(forward_demodulation,[],[f7746,f4464]) ).
thf(f7746,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X1 )
| ( min = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f7745,f4464]) ).
thf(f7745,plain,
! [X0: int,X1: int] :
( ( min = X1 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f6450,f4464]) ).
thf(f6450,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X1 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5105,f5971,f5971]) ).
thf(f5105,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X1 )
| ( one_one_int = X1 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4166]) ).
thf(f7738,plain,
vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min),
inference(forward_demodulation,[],[f7737,f4464]) ).
thf(f7737,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min),
inference(forward_demodulation,[],[f6830,f4464]) ).
thf(f6830,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,number_number_of_int,min)),
inference(equality_resolution,[],[f6829]) ).
thf(f6829,plain,
! [X0: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,number_number_of_int,min)) )
| ( vAPP(int,int,number_number_of_int,min) != X0 ) ),
inference(equality_resolution,[],[f6448]) ).
thf(f6448,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( vAPP(int,int,number_number_of_int,min) != X1 )
| ( vAPP(int,int,number_number_of_int,min) != X0 ) ),
inference(definition_unfolding,[],[f5107,f5971]) ).
thf(f5107,plain,
! [X0: int,X1: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) )
| ( vAPP(int,int,number_number_of_int,min) != X1 )
| ( vAPP(int,int,number_number_of_int,min) != X0 ) ),
inference(cnf_transformation,[],[f4166]) ).
thf(f6441,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5093,f5972,f5972]) ).
thf(f5093,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = X0 )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4160]) ).
thf(f4160,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( one_one_nat != X1 )
| ( one_one_nat != X0 ) )
& ( ( ( one_one_nat = X1 )
& ( one_one_nat = X0 ) )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) ) ) ),
inference(flattening,[],[f4159]) ).
thf(f4159,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
| ( one_one_nat != X1 )
| ( one_one_nat != X0 ) )
& ( ( ( one_one_nat = X1 )
& ( one_one_nat = X0 ) )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3001]) ).
thf(f3001,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) )
<=> ( ( one_one_nat = X1 )
& ( one_one_nat = X0 ) ) ),
inference(rectify,[],[f1028]) ).
thf(f1028,axiom,
! [X192: nat,X191: nat] :
( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191) )
<=> ( ( one_one_nat = X191 )
& ( one_one_nat = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_nat__1__eq__mult__iff) ).
thf(f6440,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5094,f5972,f5972]) ).
thf(f5094,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = X1 )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4160]) ).
thf(f6438,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5090,f5969,f5972,f5972]) ).
thf(f5090,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( one_one_nat = X0 )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4158]) ).
thf(f4158,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( ( zero_zero_nat != X1 )
& ( one_one_nat != X0 ) ) )
& ( ( zero_zero_nat = X1 )
| ( one_one_nat = X0 )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ) ),
inference(flattening,[],[f4157]) ).
thf(f4157,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( ( zero_zero_nat != X1 )
& ( one_one_nat != X0 ) ) )
& ( ( zero_zero_nat = X1 )
| ( one_one_nat = X0 )
| ( one_one_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ) ),
inference(nnf_transformation,[],[f3000]) ).
thf(f3000,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
<=> ( ( zero_zero_nat = X1 )
| ( one_one_nat = X0 ) ) ),
inference(rectify,[],[f870]) ).
thf(f870,axiom,
! [X16: nat,X191: nat] :
( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),X191) )
<=> ( ( zero_zero_nat = X191 )
| ( one_one_nat = X16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_exp__eq__1) ).
thf(f5088,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit1,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f4156]) ).
thf(f4156,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,bit1,X0) = vAPP(int,int,bit1,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit1,X1) ) ) ),
inference(nnf_transformation,[],[f2999]) ).
thf(f2999,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,X0) = vAPP(int,int,bit1,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
! [X18: int,X38: int] :
( ( vAPP(int,int,bit1,X18) = vAPP(int,int,bit1,X38) )
<=> ( X18 = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_rel__simps_I51_J) ).
thf(f5086,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit0,X0) != vAPP(int,int,bit0,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f4155]) ).
thf(f4155,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,bit0,X0) = vAPP(int,int,bit0,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,int,bit0,X0) != vAPP(int,int,bit0,X1) ) ) ),
inference(nnf_transformation,[],[f2998]) ).
thf(f2998,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit0,X0) = vAPP(int,int,bit0,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f142]) ).
thf(f142,axiom,
! [X18: int,X38: int] :
( ( vAPP(int,int,bit0,X18) = vAPP(int,int,bit0,X38) )
<=> ( X18 = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_rel__simps_I48_J) ).
thf(f5084,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,X0) != vAPP(int,int,number_number_of_int,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f4154]) ).
thf(f4154,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,number_number_of_int,X0) = vAPP(int,int,number_number_of_int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,int,number_number_of_int,X0) != vAPP(int,int,number_number_of_int,X1) ) ) ),
inference(nnf_transformation,[],[f2997]) ).
thf(f2997,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,X0) = vAPP(int,int,number_number_of_int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f136]) ).
thf(f136,axiom,
! [X88: int,X89: int] :
( ( vAPP(int,int,number_number_of_int,X88) = vAPP(int,int,number_number_of_int,X89) )
<=> ( X88 = X89 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_eq__number__of) ).
thf(f5082,plain,
! [X0: int,X1: int] :
( ( vAPP(int,real,number267125858f_real,X0) != vAPP(int,real,number267125858f_real,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f4153]) ).
thf(f4153,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,real,number267125858f_real,X0) = vAPP(int,real,number267125858f_real,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,real,number267125858f_real,X0) != vAPP(int,real,number267125858f_real,X1) ) ) ),
inference(nnf_transformation,[],[f2996]) ).
thf(f2996,plain,
! [X0: int,X1: int] :
( ( vAPP(int,real,number267125858f_real,X0) = vAPP(int,real,number267125858f_real,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f137]) ).
thf(f137,axiom,
! [X88: int,X89: int] :
( ( vAPP(int,real,number267125858f_real,X88) = vAPP(int,real,number267125858f_real,X89) )
<=> ( X88 = X89 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_eq__number__of) ).
thf(f6435,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5069,f4404,f4404]) ).
thf(f5069,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f3587]) ).
thf(f3587,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(flattening,[],[f3586]) ).
thf(f3586,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(ennf_transformation,[],[f1848]) ).
thf(f1848,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1847]) ).
thf(f1847,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(rectify,[],[f475]) ).
thf(f475,axiom,
! [X274: int,X275: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X274),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X275),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X275)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X274),X275) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_power2__less__imp__less) ).
thf(f6434,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5068,f4404,f4404]) ).
thf(f5068,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f3585]) ).
thf(f3585,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(flattening,[],[f3584]) ).
thf(f3584,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(ennf_transformation,[],[f1846]) ).
thf(f1846,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1845]) ).
thf(f1845,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(rectify,[],[f448]) ).
thf(f448,axiom,
! [X254: int,X255: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X254),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X255),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X255)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X254),X255) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_power2__le__imp__le) ).
thf(f7736,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(subsumption_resolution,[],[f6433,f6249]) ).
thf(f6433,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5067,f5969,f4404,f4404]) ).
thf(f5067,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f3583]) ).
thf(f3583,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(flattening,[],[f3582]) ).
thf(f3582,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(ennf_transformation,[],[f1844]) ).
thf(f1844,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f1843]) ).
thf(f1843,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f474]) ).
thf(f474,axiom,
! [X274: nat,X275: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X274),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X275),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X275)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X274),X275) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_power2__less__imp__less) ).
thf(f7735,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(subsumption_resolution,[],[f6432,f6249]) ).
thf(f6432,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5066,f5969,f4404,f4404]) ).
thf(f5066,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f3581]) ).
thf(f3581,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(flattening,[],[f3580]) ).
thf(f3580,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(ennf_transformation,[],[f1842]) ).
thf(f1842,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f1841]) ).
thf(f1841,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f447]) ).
thf(f447,axiom,
! [X254: nat,X255: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X254),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X255),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X255)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X254),X255) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_power2__le__imp__le) ).
thf(f6431,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5065,f5970,f4404,f4404]) ).
thf(f5065,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f3579]) ).
thf(f3579,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(flattening,[],[f3578]) ).
thf(f3578,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(ennf_transformation,[],[f1840]) ).
thf(f1840,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
inference(fool_elimination,[],[f1839]) ).
thf(f1839,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(rectify,[],[f473]) ).
thf(f473,axiom,
! [X274: real,X275: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X274),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X275),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X275)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X274),X275) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_power2__less__imp__less) ).
thf(f6430,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f5064,f5970,f4404,f4404]) ).
thf(f5064,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f3577]) ).
thf(f3577,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(flattening,[],[f3576]) ).
thf(f3576,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(ennf_transformation,[],[f1838]) ).
thf(f1838,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ) ),
inference(fool_elimination,[],[f1837]) ).
thf(f1837,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(rectify,[],[f446]) ).
thf(f446,axiom,
! [X254: real,X255: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X254),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X255),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X255)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X254),X255) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_power2__le__imp__le) ).
thf(f6429,plain,
! [X0: int,X1: nat] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1))),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5063,f4404]) ).
thf(f5063,plain,
! [X0: int,X1: nat] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3575]) ).
thf(f3575,plain,
! [X0: int,X1: nat] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_int) ) ),
inference(ennf_transformation,[],[f1836]) ).
thf(f1836,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_int) )
=> ( zero_zero_int = X0 ) ),
inference(fool_elimination,[],[f1835]) ).
thf(f1835,plain,
! [X0: int,X1: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_int)
=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f508]) ).
thf(f508,axiom,
! [X303: int,X304: nat] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X303),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X304))),zero_zero_int)
=> ( zero_zero_int = X303 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_even__power__le__0__imp__0) ).
thf(f6428,plain,
! [X0: real,X1: nat] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1))),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f5062,f5970,f4404,f5970]) ).
thf(f5062,plain,
! [X0: real,X1: nat] :
( ( zero_zero_real = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_real) ) ),
inference(cnf_transformation,[],[f3574]) ).
thf(f3574,plain,
! [X0: real,X1: nat] :
( ( zero_zero_real = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_real) ) ),
inference(ennf_transformation,[],[f1834]) ).
thf(f1834,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_real) )
=> ( zero_zero_real = X0 ) ),
inference(fool_elimination,[],[f1833]) ).
thf(f1833,plain,
! [X0: real,X1: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1))),zero_zero_real)
=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f507]) ).
thf(f507,axiom,
! [X303: real,X304: nat] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X303),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X304))),zero_zero_real)
=> ( zero_zero_real = X303 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_even__power__le__0__imp__0) ).
thf(f7734,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),min),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,bit1,zero_zero_int)),X1) ) ),
inference(forward_demodulation,[],[f7733,f4464]) ).
thf(f7733,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),min),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(forward_demodulation,[],[f7732,f4464]) ).
thf(f7732,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(forward_demodulation,[],[f6427,f4464]) ).
thf(f6427,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(definition_unfolding,[],[f5061,f5971,f4404]) ).
thf(f5061,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(cnf_transformation,[],[f3573]) ).
thf(f3573,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(flattening,[],[f3572]) ).
thf(f3572,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(ennf_transformation,[],[f2992]) ).
thf(f2992,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) ) ) ),
inference(flattening,[],[f1832]) ).
thf(f1832,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) ) ) ),
inference(fool_elimination,[],[f1831]) ).
thf(f1831,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,min)),X1)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) ) ),
inference(rectify,[],[f608]) ).
thf(f608,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),vAPP(int,int,number_number_of_int,min)),X163)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),one_one_int),X163) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_zcong__neg__1__impl__ne__1) ).
thf(f7731,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6426,f4464]) ).
thf(f6426,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(definition_unfolding,[],[f5060,f4404]) ).
thf(f5060,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(cnf_transformation,[],[f3571]) ).
thf(f3571,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(flattening,[],[f3570]) ).
thf(f3570,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(ennf_transformation,[],[f2991]) ).
thf(f2991,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) ) ) ) ),
inference(flattening,[],[f1830]) ).
thf(f1830,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) ) ) ) ),
inference(fool_elimination,[],[f1829]) ).
thf(f1829,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)
=> ( vAPP(int,$o,zprime,X1)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X1) ) ) ),
inference(rectify,[],[f1094]) ).
thf(f1094,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X16),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16)))),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_Int2_Oaux____1) ).
thf(f7730,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6425,f4464]) ).
thf(f6425,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(definition_unfolding,[],[f5059,f4404]) ).
thf(f5059,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(cnf_transformation,[],[f3569]) ).
thf(f3569,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(flattening,[],[f3568]) ).
thf(f3568,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(ennf_transformation,[],[f2990]) ).
thf(f2990,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) ) ) ) ),
inference(flattening,[],[f1828]) ).
thf(f1828,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) ) ) ) ),
inference(fool_elimination,[],[f1827]) ).
thf(f1827,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)
=> ( vAPP(int,$o,zprime,X1)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)))),X0),X1) ) ) ),
inference(rectify,[],[f1093]) ).
thf(f1093,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X16),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16))),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16)))),X16),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_Int2_Oaux____2) ).
thf(f7729,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6424,f4464]) ).
thf(f6424,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(definition_unfolding,[],[f5058,f4404]) ).
thf(f5058,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(cnf_transformation,[],[f3567]) ).
thf(f3567,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(flattening,[],[f3566]) ).
thf(f3566,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(ennf_transformation,[],[f2989]) ).
thf(f2989,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) ) ) ) ),
inference(flattening,[],[f1826]) ).
thf(f1826,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) ) ) ) ),
inference(fool_elimination,[],[f1825]) ).
thf(f1825,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)
=> ( vAPP(int,$o,zprime,X1)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),X0),X1) ) ) ),
inference(rectify,[],[f1086]) ).
thf(f1086,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16))),X16),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_MultInv__prop4) ).
thf(f7725,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7724,f4464]) ).
thf(f7724,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(forward_demodulation,[],[f6422,f4464]) ).
thf(f6422,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(definition_unfolding,[],[f5056,f5971,f4404]) ).
thf(f5056,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),one_one_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(cnf_transformation,[],[f3563]) ).
thf(f3563,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),one_one_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(flattening,[],[f3562]) ).
thf(f3562,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),one_one_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(ennf_transformation,[],[f2987]) ).
thf(f2987,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),one_one_int),X1) ) ) ) ),
inference(flattening,[],[f1822]) ).
thf(f1822,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),one_one_int),X1) ) ) ) ),
inference(fool_elimination,[],[f1821]) ).
thf(f1821,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)
=> ( vAPP(int,$o,zprime,X1)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0))),one_one_int),X1) ) ) ),
inference(rectify,[],[f1096]) ).
thf(f1096,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X16),vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16))),one_one_int),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_MultInv__prop2) ).
thf(f7723,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6421,f4464]) ).
thf(f6421,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) ) ),
inference(definition_unfolding,[],[f5055,f4404]) ).
thf(f5055,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(cnf_transformation,[],[f3561]) ).
thf(f3561,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(flattening,[],[f3560]) ).
thf(f3560,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
| ( $true != vAPP(int,$o,zprime,X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) ) ),
inference(ennf_transformation,[],[f2986]) ).
thf(f2986,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) ) ) ) ),
inference(flattening,[],[f1820]) ).
thf(f1820,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1) )
=> ( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) ) ) ) ),
inference(fool_elimination,[],[f1819]) ).
thf(f1819,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)
=> ( vAPP(int,$o,zprime,X1)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X1),X0)),zero_zero_int),X1) ) ) ),
inference(rectify,[],[f1087]) ).
thf(f1087,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X163)
=> ( vAPP(int,$o,zprime,X163)
=> ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X163)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),multInv,X163),X16)),zero_zero_int),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_MultInv__prop3) ).
thf(f5054,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) ) ),
inference(cnf_transformation,[],[f3559]) ).
thf(f3559,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) ) ),
inference(ennf_transformation,[],[f1818]) ).
thf(f1818,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(fool_elimination,[],[f1817]) ).
thf(f1817,plain,
! [X0: int,X1: int] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ),
inference(rectify,[],[f1113]) ).
thf(f1113,axiom,
! [X3: int,X2: int] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),d22set,X2))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_d22set__le) ).
thf(f7722,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) ) ),
inference(forward_demodulation,[],[f6420,f4464]) ).
thf(f6420,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) ) ),
inference(definition_unfolding,[],[f5053,f5971]) ).
thf(f5053,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) ) ),
inference(cnf_transformation,[],[f3558]) ).
thf(f3558,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) ) ),
inference(ennf_transformation,[],[f1816]) ).
thf(f1816,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(fool_elimination,[],[f1815]) ).
thf(f1815,plain,
! [X0: int,X1: int] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),d22set,X1))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ),
inference(rectify,[],[f1115]) ).
thf(f1115,axiom,
! [X3: int,X2: int] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),d22set,X2))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_d22set__g__1) ).
thf(f5052,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0) = X0 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),sr,X1)) ) ),
inference(cnf_transformation,[],[f3557]) ).
thf(f3557,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0) = X0 )
| ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),sr,X1)) ) ),
inference(ennf_transformation,[],[f1814]) ).
thf(f1814,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),sr,X1)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0) = X0 ) ),
inference(fool_elimination,[],[f1813]) ).
thf(f1813,plain,
! [X0: int,X1: int] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X0),vAPP(int,sTfun(int,$o),sr,X1))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0) = X0 ) ),
inference(rectify,[],[f1194]) ).
thf(f1194,axiom,
! [X16: int,X163: int] :
( vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X16),vAPP(int,sTfun(int,$o),sr,X163))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X163),X16) = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1193_StandardRes__SR__prop) ).
thf(f7721,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f6419,f4464]) ).
thf(f6419,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f5051,f5971]) ).
thf(f5051,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) ) ),
inference(cnf_transformation,[],[f3556]) ).
thf(f3556,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) ) ),
inference(ennf_transformation,[],[f1812]) ).
thf(f1812,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(fool_elimination,[],[f1811]) ).
thf(f1811,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f1070]) ).
thf(f1070,axiom,
! [X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_norR__mem__unique__aux) ).
thf(f5049,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(cnf_transformation,[],[f3553]) ).
thf(f3553,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(flattening,[],[f3552]) ).
thf(f3552,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ) ),
inference(ennf_transformation,[],[f1808]) ).
thf(f1808,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ) ),
inference(fool_elimination,[],[f1807]) ).
thf(f1807,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(rectify,[],[f837]) ).
thf(f837,axiom,
! [X466: int,X467: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X466),X467))
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X467)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X466) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_zero__less__mult__pos2) ).
thf(f6418,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(definition_unfolding,[],[f5048,f5969,f5969,f5969]) ).
thf(f5048,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f3551]) ).
thf(f3551,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(flattening,[],[f3550]) ).
thf(f3550,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(ennf_transformation,[],[f1806]) ).
thf(f1806,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) ),
inference(fool_elimination,[],[f1805]) ).
thf(f1805,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(rectify,[],[f839]) ).
thf(f839,axiom,
! [X468: nat,X469: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X468),X469))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X468)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X469) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_zero__less__mult__pos) ).
thf(f6417,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(definition_unfolding,[],[f5047,f5969,f5969,f5969]) ).
thf(f5047,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(cnf_transformation,[],[f3549]) ).
thf(f3549,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(flattening,[],[f3548]) ).
thf(f3548,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) ) ),
inference(ennf_transformation,[],[f1804]) ).
thf(f1804,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(fool_elimination,[],[f1803]) ).
thf(f1803,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f836]) ).
thf(f836,axiom,
! [X466: nat,X467: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X466),X467))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X467)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X466) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_zero__less__mult__pos2) ).
thf(f6416,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(definition_unfolding,[],[f5046,f5970,f5970,f5970]) ).
thf(f5046,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(cnf_transformation,[],[f3547]) ).
thf(f3547,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(flattening,[],[f3546]) ).
thf(f3546,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(ennf_transformation,[],[f1802]) ).
thf(f1802,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true ) ) ),
inference(fool_elimination,[],[f1801]) ).
thf(f1801,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) ),
inference(rectify,[],[f838]) ).
thf(f838,axiom,
! [X468: real,X469: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X468),X469))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X468)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X469) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_zero__less__mult__pos) ).
thf(f6415,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(definition_unfolding,[],[f5045,f5970,f5970,f5970]) ).
thf(f5045,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(cnf_transformation,[],[f3545]) ).
thf(f3545,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(flattening,[],[f3544]) ).
thf(f3544,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) ) ),
inference(ennf_transformation,[],[f1800]) ).
thf(f1800,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true ) ) ),
inference(fool_elimination,[],[f1799]) ).
thf(f1799,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ),
inference(rectify,[],[f835]) ).
thf(f835,axiom,
! [X466: real,X467: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X466),X467))
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X467)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X466) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_zero__less__mult__pos2) ).
thf(f7720,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(forward_demodulation,[],[f6414,f4464]) ).
thf(f6414,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(definition_unfolding,[],[f5044,f5971]) ).
thf(f5044,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3543]) ).
thf(f3543,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(ennf_transformation,[],[f1798]) ).
thf(f1798,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) ) ),
inference(fool_elimination,[],[f1797]) ).
thf(f1797,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) ),
inference(rectify,[],[f87]) ).
thf(f87,axiom,
! [X14: int,X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X14),X15)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X14),one_one_int)),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zless__imp__add1__zle) ).
thf(f5043,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3542]) ).
thf(f3542,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(ennf_transformation,[],[f2985]) ).
thf(f2985,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) ) ),
inference(flattening,[],[f1796]) ).
thf(f1796,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true != vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) ) ),
inference(fool_elimination,[],[f1795]) ).
thf(f1795,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ~ vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) ),
inference(rectify,[],[f1114]) ).
thf(f1114,axiom,
! [X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X3)
=> ~ vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),d22set,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1113_d22set__le__swap) ).
thf(f5042,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3541]) ).
thf(f3541,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(flattening,[],[f3540]) ).
thf(f3540,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(ennf_transformation,[],[f1794]) ).
thf(f1794,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f1793]) ).
thf(f1793,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f41]) ).
thf(f41,axiom,
! [X15: int,X14: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X15),X14)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X14),X15)
=> ( X14 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zle__antisym) ).
thf(f5041,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3539]) ).
thf(f3539,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(flattening,[],[f3538]) ).
thf(f3538,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(ennf_transformation,[],[f1792]) ).
thf(f1792,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
=> ( ( X0 != X1 )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1791]) ).
thf(f1791,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
=> ( ( X0 != X1 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(rectify,[],[f571]) ).
thf(f571,axiom,
! [X315: int,X316: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X315),X316)
=> ( ( X315 != X316 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X315),X316) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_order__le__neq__implies__less) ).
thf(f5040,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3537]) ).
thf(f3537,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(flattening,[],[f3536]) ).
thf(f3536,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(ennf_transformation,[],[f1790]) ).
thf(f1790,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1789]) ).
thf(f1789,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) ) ),
inference(rectify,[],[f338]) ).
thf(f338,axiom,
! [X15: int,X191: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X15),X191)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X191)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X15),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_zdvd__imp__le) ).
thf(f5039,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3535]) ).
thf(f3535,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(flattening,[],[f3534]) ).
thf(f3534,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(ennf_transformation,[],[f1788]) ).
thf(f1788,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ) ),
inference(fool_elimination,[],[f1787]) ).
thf(f1787,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X1)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(rectify,[],[f655]) ).
thf(f655,axiom,
! [X191: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X191),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X191),X192)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X192),zero_zero_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_zdvd__bounds) ).
thf(f6413,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f5036,f5969]) ).
thf(f5036,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4145]) ).
thf(f4145,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f3532,f4144]) ).
thf(f4144,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3532,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1784]) ).
thf(f1784,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ? [X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ) ),
inference(fool_elimination,[],[f1783]) ).
thf(f1783,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ? [X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X2) ) ),
inference(rectify,[],[f1117]) ).
thf(f1117,axiom,
! [X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
=> ? [X320: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X19),X320) = X20 )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X320) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_less__imp__add__positive) ).
thf(f5037,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK21,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f4145]) ).
thf(f5031,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3527]) ).
thf(f3527,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f3526]) ).
thf(f3526,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1774]) ).
thf(f1774,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f1773]) ).
thf(f1773,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f942]) ).
thf(f942,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
=> ( X191 = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_le__antisym) ).
thf(f5029,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3523]) ).
thf(f3523,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f3522]) ).
thf(f3522,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1770]) ).
thf(f1770,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( X0 != X1 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f1769]) ).
thf(f1769,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ( X0 != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f570]) ).
thf(f570,axiom,
! [X315: nat,X316: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X315),X316)
=> ( ( X315 != X316 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X315),X316) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_order__le__neq__implies__less) ).
thf(f5028,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3521]) ).
thf(f3521,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1768]) ).
thf(f1768,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) ) ),
inference(fool_elimination,[],[f1767]) ).
thf(f1767,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) ) ),
inference(rectify,[],[f1184]) ).
thf(f1184,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_le__mod__geq) ).
thf(f5027,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3520]) ).
thf(f3520,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1766]) ).
thf(f1766,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) = X1 ) ),
inference(fool_elimination,[],[f1765]) ).
thf(f1765,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)),X0) = X1 ) ),
inference(rectify,[],[f1013]) ).
thf(f1013,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)),X191) = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_le__add__diff__inverse2) ).
thf(f5026,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3519]) ).
thf(f3519,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1764]) ).
thf(f1764,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X1 ) ),
inference(fool_elimination,[],[f1763]) ).
thf(f1763,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X1 ) ),
inference(rectify,[],[f1010]) ).
thf(f1010,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)) = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_le__add__diff__inverse) ).
thf(f5025,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3518]) ).
thf(f3518,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1762]) ).
thf(f1762,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X0 ) ),
inference(fool_elimination,[],[f1761]) ).
thf(f1761,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0)) = X0 ) ),
inference(rectify,[],[f946]) ).
thf(f946,axiom,
! [X19: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X191)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X19)) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_diff__diff__cancel) ).
thf(f6411,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f5024,f5969]) ).
thf(f5024,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3517]) ).
thf(f3517,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1760]) ).
thf(f1760,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ),
inference(fool_elimination,[],[f1759]) ).
thf(f1759,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ),
inference(rectify,[],[f968]) ).
thf(f968,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191)
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_diff__is__0__eq_H) ).
thf(f6410,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f5019,f5969]) ).
thf(f5019,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3511]) ).
thf(f3511,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(flattening,[],[f3510]) ).
thf(f3510,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1752]) ).
thf(f1752,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f1751]) ).
thf(f1751,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(rectify,[],[f1040]) ).
thf(f1040,axiom,
! [X18: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X18),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X18),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_dvd__imp__le) ).
thf(f6408,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f5013,f5969]) ).
thf(f5013,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3503]) ).
thf(f3503,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(flattening,[],[f3502]) ).
thf(f3502,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1744]) ).
thf(f1744,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( zero_zero_nat = X1 ) ) ),
inference(fool_elimination,[],[f1743]) ).
thf(f1743,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
| ( zero_zero_nat = X1 ) ) ),
inference(rectify,[],[f860]) ).
thf(f860,axiom,
! [X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
| ( zero_zero_nat = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_divides__ge) ).
thf(f6407,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1) )
| ( X0 = X1 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(definition_unfolding,[],[f5012,f4404,f5969]) ).
thf(f5012,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1) )
| ( X0 = X1 )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3501]) ).
thf(f3501,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1) )
| ( X0 = X1 )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(flattening,[],[f3500]) ).
thf(f3500,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1) )
| ( X0 = X1 )
| ( zero_zero_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f1742]) ).
thf(f1742,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1) )
| ( X0 = X1 )
| ( zero_zero_nat = X1 ) ) ),
inference(fool_elimination,[],[f1741]) ).
thf(f1741,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)
| ( X0 = X1 )
| ( zero_zero_nat = X1 ) ) ),
inference(rectify,[],[f668]) ).
thf(f668,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X191),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X191)),X192)
| ( X191 = X192 )
| ( zero_zero_nat = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_divides__cases) ).
thf(f5011,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f3499]) ).
thf(f3499,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(flattening,[],[f3498]) ).
thf(f3498,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(ennf_transformation,[],[f1740]) ).
thf(f1740,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f1739]) ).
thf(f1739,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f884]) ).
thf(f884,axiom,
! [X15: real,X14: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X15),X14)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X14),X15)
=> ( X14 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_real__le__antisym) ).
thf(f5010,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f3497]) ).
thf(f3497,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(flattening,[],[f3496]) ).
thf(f3496,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(ennf_transformation,[],[f1738]) ).
thf(f1738,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) )
=> ( ( X0 != X1 )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
inference(fool_elimination,[],[f1737]) ).
thf(f1737,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1)
=> ( ( X0 != X1 )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(rectify,[],[f569]) ).
thf(f569,axiom,
! [X315: real,X316: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X315),X316)
=> ( ( X315 != X316 )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X315),X316) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_order__le__neq__implies__less) ).
thf(f5007,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3493]) ).
thf(f3493,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(flattening,[],[f3492]) ).
thf(f3492,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(ennf_transformation,[],[f1732]) ).
thf(f1732,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1731]) ).
thf(f1731,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ),
inference(rectify,[],[f829]) ).
thf(f829,axiom,
! [X459: int,X460: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X460),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X459),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X460),X459)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_mult__neg__neg) ).
thf(f5004,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3489]) ).
thf(f3489,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),zero_zero_int) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(ennf_transformation,[],[f1728]) ).
thf(f1728,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),zero_zero_int) ) ) ),
inference(fool_elimination,[],[f1727]) ).
thf(f1727,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),zero_zero_int) ) ),
inference(rectify,[],[f1163]) ).
thf(f1163,axiom,
! [X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3)),zero_zero_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_neg__mod__conj) ).
thf(f5005,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3489]) ).
thf(f5003,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3488]) ).
thf(f3488,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(flattening,[],[f3487]) ).
thf(f3487,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(ennf_transformation,[],[f1726]) ).
thf(f1726,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 ) ) ),
inference(fool_elimination,[],[f1725]) ).
thf(f1725,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = X1 ) ) ),
inference(rectify,[],[f1164]) ).
thf(f1164,axiom,
! [X3: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X3),X2)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_mod__neg__neg__trivial) ).
thf(f7719,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f7718,f6075]) ).
thf(f7718,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X0))),vAPP(int,int,bit0,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f7717,f4779]) ).
thf(f7717,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,X0))),vAPP(int,int,bit0,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f7716,f7427]) ).
thf(f7716,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,bit0,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f7715,f7427]) ).
thf(f7715,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f7714,f7427]) ).
thf(f7714,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f7713,f4464]) ).
thf(f7713,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(forward_demodulation,[],[f6406,f4464]) ).
thf(f6406,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(definition_unfolding,[],[f5000,f5971,f4404,f4404,f4404,f5971,f5971]) ).
thf(f5000,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1))),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3482]) ).
thf(f3482,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1))),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) ) ),
inference(ennf_transformation,[],[f1720]) ).
thf(f1720,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1))),one_one_int) ) ),
inference(fool_elimination,[],[f1719]) ).
thf(f1719,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),zero_zero_int)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1))),one_one_int) ) ),
inference(rectify,[],[f1135]) ).
thf(f1135,axiom,
! [X3: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X2),zero_zero_int)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),one_one_int)),X2))),one_one_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1134_neg__zmod__mult__2) ).
thf(f4998,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3480]) ).
thf(f3480,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1716]) ).
thf(f1716,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1) ) ),
inference(fool_elimination,[],[f1715]) ).
thf(f1715,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X1),X0)),X1) ),
inference(rectify,[],[f1193]) ).
thf(f1193,axiom,
! [X16: int,X163: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X163),X16)),X163) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_StandardRes__ubound) ).
thf(f4997,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3479]) ).
thf(f3479,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1714]) ).
thf(f1714,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ),
inference(fool_elimination,[],[f1713]) ).
thf(f1713,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ),
inference(rectify,[],[f369]) ).
thf(f369,axiom,
! [X214: nat,X215: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X215)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X215),X214)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_zero__less__power) ).
thf(f4992,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f4142]) ).
thf(f4993,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),sK20,X1),X0)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f4142]) ).
thf(f7712,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,int,bit1,zero_zero_int) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f7711,f4464]) ).
thf(f7711,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f6405,f4464]) ).
thf(f6405,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(definition_unfolding,[],[f4988,f5971,f5971]) ).
thf(f4988,plain,
! [X0: int,X1: int] :
( ( one_one_int = X1 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f4140]) ).
thf(f4140,plain,
! [X0: int,X1: int] :
( ( ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( one_one_int != X0 )
| ( one_one_int != X1 ) )
& ( ( ( one_one_int = X0 )
& ( one_one_int = X1 ) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) ) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f4139]) ).
thf(f4139,plain,
! [X0: int,X1: int] :
( ( ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( one_one_int != X0 )
| ( one_one_int != X1 ) )
& ( ( ( one_one_int = X0 )
& ( one_one_int = X1 ) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) ) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(nnf_transformation,[],[f3474]) ).
thf(f3474,plain,
! [X0: int,X1: int] :
( ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
<=> ( ( one_one_int = X0 )
& ( one_one_int = X1 ) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1706]) ).
thf(f1706,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
<=> ( ( one_one_int = X0 )
& ( one_one_int = X1 ) ) ) ),
inference(fool_elimination,[],[f1705]) ).
thf(f1705,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
<=> ( ( one_one_int = X0 )
& ( one_one_int = X1 ) ) ) ),
inference(rectify,[],[f428]) ).
thf(f428,axiom,
! [X191: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X192),X191) )
<=> ( ( one_one_int = X191 )
& ( one_one_int = X192 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_pos__zmult__eq__1__iff) ).
thf(f7710,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f7709,f4464]) ).
thf(f7709,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f6404,f4464]) ).
thf(f6404,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(definition_unfolding,[],[f4989,f5971,f5971]) ).
thf(f4989,plain,
! [X0: int,X1: int] :
( ( one_one_int = X0 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f4140]) ).
thf(f4987,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3473]) ).
thf(f3473,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3472]) ).
thf(f3472,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1704]) ).
thf(f1704,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),zero_zero_int) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) ) ) ),
inference(fool_elimination,[],[f1703]) ).
thf(f1703,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)),zero_zero_int)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) ) ) ),
inference(rectify,[],[f1165]) ).
thf(f1165,axiom,
! [X3: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)),zero_zero_int)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_mod__pos__neg__trivial) ).
thf(f4986,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3471]) ).
thf(f3471,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3470]) ).
thf(f3470,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1702]) ).
thf(f1702,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ) ),
inference(fool_elimination,[],[f1701]) ).
thf(f1701,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(rectify,[],[f404]) ).
thf(f404,axiom,
! [X3: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X3))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_pos__zmult__pos) ).
thf(f4985,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3469]) ).
thf(f3469,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3468]) ).
thf(f3468,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f2982]) ).
thf(f2982,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ) ) ),
inference(flattening,[],[f1700]) ).
thf(f1700,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ) ) ),
inference(fool_elimination,[],[f1699]) ).
thf(f1699,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X1),zero_zero_int),X0) ) ),
inference(rectify,[],[f654]) ).
thf(f654,axiom,
! [X192: int,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),X192)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X16),zero_zero_int),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_zcong__not__zero) ).
thf(f4984,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3467]) ).
thf(f3467,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3466]) ).
thf(f3466,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f2981]) ).
thf(f2981,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ) ),
inference(flattening,[],[f1698]) ).
thf(f1698,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ) ),
inference(fool_elimination,[],[f1697]) ).
thf(f1697,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X1) ) ),
inference(rectify,[],[f327]) ).
thf(f327,axiom,
! [X191: int,X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X192)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X192),X191)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X191),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_zdvd__not__zless) ).
thf(f7707,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f7706,f4464]) ).
thf(f7706,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f6402,f4464]) ).
thf(f6402,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(definition_unfolding,[],[f4983,f5971,f5971]) ).
thf(f4983,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3465]) ).
thf(f3465,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3464]) ).
thf(f3464,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = X1 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1696]) ).
thf(f1696,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) != X1 )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int)) ) ) ) ),
inference(fool_elimination,[],[f1695]) ).
thf(f1695,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) != X1 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int)) ) ) ),
inference(rectify,[],[f633]) ).
thf(f633,axiom,
! [X2: int,X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),X2)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int) != X16 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),one_one_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_Euler_Oaux1) ).
thf(f4982,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3463]) ).
thf(f3463,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3462]) ).
thf(f3462,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1694]) ).
thf(f1694,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) ) ) ),
inference(fool_elimination,[],[f1693]) ).
thf(f1693,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)),zero_zero_int) ) ),
inference(rectify,[],[f846]) ).
thf(f846,axiom,
! [X472: int,X473: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X473)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X472),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X473),X472)),zero_zero_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_mult__pos__neg) ).
thf(f4981,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3461]) ).
thf(f3461,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3460]) ).
thf(f3460,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1692]) ).
thf(f1692,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) ) ) ),
inference(fool_elimination,[],[f1691]) ).
thf(f1691,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),zero_zero_int) ) ),
inference(rectify,[],[f843]) ).
thf(f843,axiom,
! [X470: int,X471: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X471)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X470),zero_zero_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X470),X471)),zero_zero_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_mult__pos__neg2) ).
thf(f7705,plain,
! [X0: nat,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f6401,f4464]) ).
thf(f6401,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(definition_unfolding,[],[f4980,f5971]) ).
thf(f4980,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3459]) ).
thf(f3459,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3458]) ).
thf(f3458,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),one_one_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1690]) ).
thf(f1690,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),one_one_int) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1689]) ).
thf(f1689,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),one_one_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ),
inference(rectify,[],[f407]) ).
thf(f407,axiom,
! [X236: nat,X237: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X237)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X237),one_one_int)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X237),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X237),X236))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X237),X236)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_power__Suc__less) ).
thf(f4979,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3457]) ).
thf(f3457,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(flattening,[],[f3456]) ).
thf(f3456,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(ennf_transformation,[],[f1688]) ).
thf(f1688,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1687]) ).
thf(f1687,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ),
inference(rectify,[],[f849]) ).
thf(f849,axiom,
! [X474: int,X475: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X475)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X474)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X475),X474)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_mult__pos__pos) ).
thf(f4978,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3455]) ).
thf(f7704,plain,
! [X0: nat,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) ) ),
inference(forward_demodulation,[],[f6400,f4464]) ).
thf(f6400,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4976,f5971]) ).
thf(f4976,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(cnf_transformation,[],[f3454]) ).
thf(f3454,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(ennf_transformation,[],[f1684]) ).
thf(f1684,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) ) ),
inference(fool_elimination,[],[f1683]) ).
thf(f1683,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) ),
inference(rectify,[],[f295]) ).
thf(f295,axiom,
! [X164: nat,X165: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X165)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X165),X164)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X165),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X165),X164))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_power__less__power__Suc) ).
thf(f7703,plain,
! [X0: nat,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) ) ),
inference(forward_demodulation,[],[f7702,f4464]) ).
thf(f7702,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f6399,f4464]) ).
thf(f6399,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4975,f5971,f5971]) ).
thf(f4975,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(cnf_transformation,[],[f3453]) ).
thf(f3453,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(ennf_transformation,[],[f1682]) ).
thf(f1682,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) ) ),
inference(fool_elimination,[],[f1681]) ).
thf(f1681,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0))) ),
inference(rectify,[],[f298]) ).
thf(f298,axiom,
! [X166: nat,X167: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X167)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X167),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X167),X166))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_power__gt1__lemma) ).
thf(f7701,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X0)) ) ),
inference(forward_demodulation,[],[f6398,f4464]) ).
thf(f6398,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4974,f5971]) ).
thf(f4974,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(cnf_transformation,[],[f3452]) ).
thf(f3452,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(ennf_transformation,[],[f1680]) ).
thf(f1680,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) )
=> ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X0)) ) ),
inference(fool_elimination,[],[f1679]) ).
thf(f1679,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1)
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X1),X0)) ),
inference(rectify,[],[f1099]) ).
thf(f1099,axiom,
! [X163: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X2),vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,X2),X163)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_wset__mem__mem) ).
thf(f7700,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) ) ),
inference(forward_demodulation,[],[f6397,f4464]) ).
thf(f6397,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4973,f5971]) ).
thf(f4973,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(cnf_transformation,[],[f3451]) ).
thf(f3451,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(flattening,[],[f3450]) ).
thf(f3450,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(ennf_transformation,[],[f1678]) ).
thf(f1678,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0) )
=> ( $true = vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) ) ) ),
inference(fool_elimination,[],[f1677]) ).
thf(f1677,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X1),X0)
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X1),vAPP(int,sTfun(int,$o),d22set,X0)) ) ),
inference(rectify,[],[f1116]) ).
thf(f1116,axiom,
! [X2: int,X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X3)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X3),X2)
=> vAPP(sTfun(int,$o),$o,vAPP(int,sTfun(sTfun(int,$o),$o),member_int,X3),vAPP(int,sTfun(int,$o),d22set,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_d22set__mem) ).
thf(f7699,plain,
! [X0: nat,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(forward_demodulation,[],[f7698,f4464]) ).
thf(f7698,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f6396,f4464]) ).
thf(f6396,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4972,f5971,f5969,f5971]) ).
thf(f4972,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(cnf_transformation,[],[f3449]) ).
thf(f3449,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(flattening,[],[f3448]) ).
thf(f3448,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) ) ),
inference(ennf_transformation,[],[f1676]) ).
thf(f1676,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1675]) ).
thf(f1675,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ),
inference(rectify,[],[f556]) ).
thf(f556,axiom,
! [X311: nat,X312: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X312)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X311)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X312),X311)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_one__less__power) ).
thf(f7697,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7696,f6075]) ).
thf(f7696,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X0))),vAPP(int,int,bit0,X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7695,f4779]) ).
thf(f7695,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,X0))),vAPP(int,int,bit0,X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7694,f7427]) ).
thf(f7694,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,bit0,X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7693,f7427]) ).
thf(f7693,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7692,f4464]) ).
thf(f7692,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f7691,f7427]) ).
thf(f7691,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(forward_demodulation,[],[f6395,f4464]) ).
thf(f6395,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(definition_unfolding,[],[f4958,f5971,f4404,f4404,f5971,f4404]) ).
thf(f4958,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(cnf_transformation,[],[f3424]) ).
thf(f3424,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true ) ),
inference(ennf_transformation,[],[f1648]) ).
thf(f1648,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) ) ),
inference(fool_elimination,[],[f1647]) ).
thf(f1647,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1))) ) ),
inference(rectify,[],[f1175]) ).
thf(f1175,axiom,
! [X3: int,X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X3))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X3),X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_pos__zmod__mult__2) ).
thf(f7686,plain,
! [X0: nat,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ),
inference(forward_demodulation,[],[f7685,f4464]) ).
thf(f7685,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(forward_demodulation,[],[f6388,f4464]) ).
thf(f6388,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4951,f5971,f5971]) ).
thf(f4951,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) ) ),
inference(cnf_transformation,[],[f3411]) ).
thf(f3411,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) ) ),
inference(ennf_transformation,[],[f1634]) ).
thf(f1634,plain,
! [X0: nat,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ) ),
inference(fool_elimination,[],[f1633]) ).
thf(f1633,plain,
! [X0: nat,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0)) ),
inference(rectify,[],[f488]) ).
thf(f488,axiom,
! [X286: nat,X287: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X287)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X287),X286)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_one__le__power) ).
thf(f6385,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4948,f5969]) ).
thf(f4948,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3406]) ).
thf(f3406,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1628]) ).
thf(f1628,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) ) ),
inference(fool_elimination,[],[f1627]) ).
thf(f1627,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) ),
inference(rectify,[],[f1179]) ).
thf(f1179,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191)),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_mod__less__divisor) ).
thf(f6384,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4947,f5969]) ).
thf(f4947,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3405]) ).
thf(f3405,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1626]) ).
thf(f1626,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) ) ),
inference(fool_elimination,[],[f1625]) ).
thf(f1625,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1)),X1) ),
inference(rectify,[],[f1178]) ).
thf(f1178,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191)),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_mod__le__divisor) ).
thf(f6383,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4946,f5969,f5969]) ).
thf(f4946,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3404]) ).
thf(f3404,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1624]) ).
thf(f1624,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ) ),
inference(fool_elimination,[],[f1623]) ).
thf(f1623,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ),
inference(rectify,[],[f370]) ).
thf(f370,axiom,
! [X214: nat,X215: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X215)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X215),X214)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_zero__less__power) ).
thf(f6382,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4944,f5972,f5969]) ).
thf(f4944,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4138]) ).
thf(f4138,plain,
! [X0: nat,X1: nat] :
( ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) )
| ( one_one_nat != X0 ) )
& ( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(nnf_transformation,[],[f3403]) ).
thf(f3403,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) )
<=> ( one_one_nat = X0 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1622]) ).
thf(f1622,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) )
<=> ( one_one_nat = X0 ) ) ),
inference(fool_elimination,[],[f1621]) ).
thf(f1621,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1)
<=> ( one_one_nat = X0 ) ) ),
inference(rectify,[],[f875]) ).
thf(f875,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X192)),X192)
<=> ( one_one_nat = X191 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_dvd__mult__cancel2) ).
thf(f6380,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4942,f5972,f5969]) ).
thf(f4942,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4137]) ).
thf(f4137,plain,
! [X0: nat,X1: nat] :
( ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1) )
| ( one_one_nat != X0 ) )
& ( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(nnf_transformation,[],[f3402]) ).
thf(f3402,plain,
! [X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1) )
<=> ( one_one_nat = X0 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1620]) ).
thf(f1620,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1) )
<=> ( one_one_nat = X0 ) ) ),
inference(fool_elimination,[],[f1619]) ).
thf(f1619,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),X1)
<=> ( one_one_nat = X0 ) ) ),
inference(rectify,[],[f876]) ).
thf(f876,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191)),X192)
<=> ( one_one_nat = X191 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_dvd__mult__cancel1) ).
thf(f6378,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4941,f5969]) ).
thf(f4941,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3401]) ).
thf(f3401,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3400]) ).
thf(f3400,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f2980]) ).
thf(f2980,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ),
inference(flattening,[],[f1618]) ).
thf(f1618,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f1617]) ).
thf(f1617,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ),
inference(rectify,[],[f1030]) ).
thf(f1030,axiom,
! [X191: nat,X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X191),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_nat__dvd__not__less) ).
thf(f6377,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4940,f5969,f5969]) ).
thf(f4940,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3399]) ).
thf(f3399,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3398]) ).
thf(f3398,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1616]) ).
thf(f1616,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ) ),
inference(fool_elimination,[],[f1615]) ).
thf(f1615,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(rectify,[],[f1129]) ).
thf(f1129,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X192),X191)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_dvd__pos__nat) ).
thf(f6374,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4937,f5972,f5969]) ).
thf(f4937,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3393]) ).
thf(f3393,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3392]) ).
thf(f3392,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1610]) ).
thf(f1610,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),one_one_nat) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1609]) ).
thf(f1609,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),one_one_nat)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ) ),
inference(rectify,[],[f408]) ).
thf(f408,axiom,
! [X236: nat,X237: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X237)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X237),one_one_nat)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X237),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X237),X236))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X237),X236)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_power__Suc__less) ).
thf(f6373,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4936,f5969,f5969]) ).
thf(f4936,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3391]) ).
thf(f3391,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3390]) ).
thf(f3390,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1608]) ).
thf(f1608,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) ) ) ),
inference(fool_elimination,[],[f1607]) ).
thf(f1607,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X0) ) ),
inference(rectify,[],[f959]) ).
thf(f959,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X192)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)),X192) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_diff__less) ).
thf(f6372,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4935,f5969,f5969,f5969]) ).
thf(f4935,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3389]) ).
thf(f3389,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3388]) ).
thf(f3388,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1606]) ).
thf(f1606,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1605]) ).
thf(f1605,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) ) ),
inference(rectify,[],[f848]) ).
thf(f848,axiom,
! [X474: nat,X475: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X475)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X474)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X475),X474)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_mult__pos__pos) ).
thf(f6371,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4932,f5970,f5970,f5969]) ).
thf(f4932,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4136]) ).
thf(f4136,plain,
! [X0: real,X1: nat] :
( ( ! [X3: real] :
( ( vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)),X1) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)) ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f3387,f4135]) ).
thf(f4135,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ! [X3: real] :
( ( X2 = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
=> ( ! [X3: real] :
( ( vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)),X1) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3387,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ! [X3: real] :
( ( X2 = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3386]) ).
thf(f3386,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ! [X3: real] :
( ( X2 = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1604]) ).
thf(f1604,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ? [X2: real] :
( ! [X3: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) ) )
=> ( X2 = X3 ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) ) ) ),
inference(fool_elimination,[],[f1603]) ).
thf(f1603,plain,
! [X0: real,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ? [X2: real] :
( ! [X3: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) = X0 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
=> ( X2 = X3 ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) ) ) ),
inference(rectify,[],[f874]) ).
thf(f874,axiom,
! [X2: real,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ? [X0: real] :
( ! [X1: real] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X191) = X2 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
=> ( X0 = X1 ) )
& ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X191) = X2 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_realpow__pos__nth__unique) ).
thf(f6370,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)),X1) = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4933,f5970,f5969]) ).
thf(f4933,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0)),X1) = X0 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4136]) ).
thf(f7682,plain,
! [X3: real,X1: nat] :
( ( vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) = X3 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(subsumption_resolution,[],[f6798,f6351]) ).
thf(f6798,plain,
! [X3: real,X1: nat] :
( ( vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) = X3 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(equality_resolution,[],[f6369]) ).
thf(f6369,plain,
! [X3: real,X0: real,X1: nat] :
( ( vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4934,f5970,f5970,f5969]) ).
thf(f4934,plain,
! [X3: real,X0: real,X1: nat] :
( ( vAPP(real,real,vAPP(nat,sTfun(real,real),sK19,X1),X0) = X3 )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X3),X1) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X3) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4136]) ).
thf(f6368,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4930,f5970,f5970,f5969]) ).
thf(f4930,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4134]) ).
thf(f4134,plain,
! [X0: real,X1: nat] :
( ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)),X1) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)) ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f3385,f4133]) ).
thf(f4133,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
=> ( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)),X1) = X0 )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3385,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(flattening,[],[f3384]) ).
thf(f3384,plain,
! [X0: real,X1: nat] :
( ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1602]) ).
thf(f1602,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) = $true ) ) ) ),
inference(fool_elimination,[],[f1601]) ).
thf(f1601,plain,
! [X0: real,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ? [X2: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X2),X1) = X0 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2) ) ) ),
inference(rectify,[],[f873]) ).
thf(f873,axiom,
! [X2: real,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X2)
=> ? [X489: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X489),X191) = X2 )
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X489) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_realpow__pos__nth) ).
thf(f6367,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)),X1) = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4931,f5970,f5969]) ).
thf(f4931,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(nat,sTfun(real,real),sK18,X1),X0)),X1) = X0 )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f4134]) ).
thf(f6366,plain,
! [X0: int,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4929,f5972,f5969]) ).
thf(f4929,plain,
! [X0: int,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3383]) ).
thf(f3383,plain,
! [X0: int,X1: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1600]) ).
thf(f1600,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) ) ),
inference(fool_elimination,[],[f1599]) ).
thf(f1599,plain,
! [X0: int,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) ) ),
inference(rectify,[],[f695]) ).
thf(f695,axiom,
! [X350: int,X351: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X351)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X350),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X351),one_one_nat))),X350) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X350),X351) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_realpow__minus__mult) ).
thf(f6365,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4928,f5972,f5969]) ).
thf(f4928,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3382]) ).
thf(f3382,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1598]) ).
thf(f1598,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) ) ),
inference(fool_elimination,[],[f1597]) ).
thf(f1597,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) ) ),
inference(rectify,[],[f693]) ).
thf(f693,axiom,
! [X350: nat,X351: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X351)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X350),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X351),one_one_nat))),X350) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X350),X351) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_realpow__minus__mult) ).
thf(f6364,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4927,f5972,f5969]) ).
thf(f4927,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3381]) ).
thf(f3381,plain,
! [X0: real,X1: nat] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(ennf_transformation,[],[f1596]) ).
thf(f1596,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) ) ),
inference(fool_elimination,[],[f1595]) ).
thf(f1595,plain,
! [X0: real,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1)
=> ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))),X0) ) ),
inference(rectify,[],[f694]) ).
thf(f694,axiom,
! [X350: real,X351: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X351)
=> ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X350),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X351),one_one_nat))),X350) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X350),X351) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_realpow__minus__mult) ).
thf(f6363,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4926,f5972]) ).
thf(f4926,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(cnf_transformation,[],[f3380]) ).
thf(f3380,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(ennf_transformation,[],[f1594]) ).
thf(f1594,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) ) ),
inference(fool_elimination,[],[f1593]) ).
thf(f1593,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) ),
inference(rectify,[],[f296]) ).
thf(f296,axiom,
! [X164: nat,X165: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X165)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X165),X164)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X165),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X165),X164))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_power__less__power__Suc) ).
thf(f6362,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4925,f5972,f5972]) ).
thf(f4925,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(cnf_transformation,[],[f3379]) ).
thf(f3379,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(ennf_transformation,[],[f1592]) ).
thf(f1592,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) ) ),
inference(fool_elimination,[],[f1591]) ).
thf(f1591,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0))) ),
inference(rectify,[],[f299]) ).
thf(f299,axiom,
! [X166: nat,X167: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X167)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X167),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X167),X166))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_power__gt1__lemma) ).
thf(f6361,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4924,f5972,f5969,f5972]) ).
thf(f4924,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(cnf_transformation,[],[f3378]) ).
thf(f3378,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(flattening,[],[f3377]) ).
thf(f3377,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) ) ),
inference(ennf_transformation,[],[f1590]) ).
thf(f1590,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1589]) ).
thf(f1589,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ) ),
inference(rectify,[],[f555]) ).
thf(f555,axiom,
! [X311: nat,X312: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),X312)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X311)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X312),X311)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_one__less__power) ).
thf(f6356,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4919,f5972,f5972]) ).
thf(f4919,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X1) ) ),
inference(cnf_transformation,[],[f3369]) ).
thf(f3369,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X1) ) ),
inference(ennf_transformation,[],[f1580]) ).
thf(f1580,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ) ),
inference(fool_elimination,[],[f1579]) ).
thf(f1579,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),X0)) ),
inference(rectify,[],[f487]) ).
thf(f487,axiom,
! [X286: nat,X287: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),X287)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,one_one_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X287),X286)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_one__le__power) ).
thf(f6355,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4918,f5970,f5970,f5970]) ).
thf(f4918,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) ),
inference(cnf_transformation,[],[f3368]) ).
thf(f3368,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) ),
inference(flattening,[],[f3367]) ).
thf(f3367,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) ),
inference(ennf_transformation,[],[f1578]) ).
thf(f1578,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1577]) ).
thf(f1577,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ),
inference(rectify,[],[f828]) ).
thf(f828,axiom,
! [X459: real,X460: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X460),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X459),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X460),X459)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_mult__neg__neg) ).
thf(f6351,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4914,f5970,f5970]) ).
thf(f4914,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(cnf_transformation,[],[f3360]) ).
thf(f3360,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(ennf_transformation,[],[f1570]) ).
thf(f1570,plain,
! [X0: nat,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ),
inference(fool_elimination,[],[f1569]) ).
thf(f1569,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ),
inference(rectify,[],[f371]) ).
thf(f371,axiom,
! [X214: nat,X215: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X215)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X215),X214)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_zero__less__power) ).
thf(f6350,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4913,f5970,f5970,f5970]) ).
thf(f4913,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(cnf_transformation,[],[f3359]) ).
thf(f3359,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(flattening,[],[f3358]) ).
thf(f3358,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(ennf_transformation,[],[f1568]) ).
thf(f1568,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f1567]) ).
thf(f1567,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f841]) ).
thf(f841,axiom,
! [X470: real,X471: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X471)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X470),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X470),X471)),zero_zero_real) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_mult__pos__neg2) ).
thf(f6349,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4912,f5970,f5970,f5970]) ).
thf(f4912,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(cnf_transformation,[],[f3357]) ).
thf(f3357,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(flattening,[],[f3356]) ).
thf(f3356,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(ennf_transformation,[],[f1566]) ).
thf(f1566,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f1565]) ).
thf(f1565,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) ) ),
inference(rectify,[],[f844]) ).
thf(f844,axiom,
! [X472: real,X473: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X473)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X472),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X473),X472)),zero_zero_real) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_mult__pos__neg) ).
thf(f6348,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4911,f5973,f5970]) ).
thf(f4911,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),one_one_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(cnf_transformation,[],[f3355]) ).
thf(f3355,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),one_one_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(flattening,[],[f3354]) ).
thf(f3354,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),one_one_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(ennf_transformation,[],[f1564]) ).
thf(f1564,plain,
! [X0: nat,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),one_one_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1563]) ).
thf(f1563,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),one_one_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ),
inference(rectify,[],[f409]) ).
thf(f409,axiom,
! [X236: nat,X237: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X237)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X237),one_one_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X237),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X237),X236))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X237),X236)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_power__Suc__less) ).
thf(f6346,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4909,f5970,f5970,f5970]) ).
thf(f4909,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(cnf_transformation,[],[f3351]) ).
thf(f3351,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(flattening,[],[f3350]) ).
thf(f3350,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) != $true )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) != $true ) ),
inference(ennf_transformation,[],[f1560]) ).
thf(f1560,plain,
! [X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = $true )
=> ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = $true )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1559]) ).
thf(f1559,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ),
inference(rectify,[],[f847]) ).
thf(f847,axiom,
! [X474: real,X475: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X475)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X474)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X475),X474)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_mult__pos__pos) ).
thf(f6345,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4908,f5973]) ).
thf(f4908,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(cnf_transformation,[],[f3349]) ).
thf(f3349,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(ennf_transformation,[],[f1558]) ).
thf(f1558,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) ) ),
inference(fool_elimination,[],[f1557]) ).
thf(f1557,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) ),
inference(rectify,[],[f297]) ).
thf(f297,axiom,
! [X164: nat,X165: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X165)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X165),X164)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X165),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X165),X164))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_power__less__power__Suc) ).
thf(f6344,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4907,f5973,f5973]) ).
thf(f4907,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(cnf_transformation,[],[f3348]) ).
thf(f3348,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(ennf_transformation,[],[f1556]) ).
thf(f1556,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) ) ),
inference(fool_elimination,[],[f1555]) ).
thf(f1555,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0))) ),
inference(rectify,[],[f300]) ).
thf(f300,axiom,
! [X166: nat,X167: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X167)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X167),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X167),X166))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_power__gt1__lemma) ).
thf(f6343,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4906,f5973,f5969,f5973]) ).
thf(f4906,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(cnf_transformation,[],[f3347]) ).
thf(f3347,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(flattening,[],[f3346]) ).
thf(f3346,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) ) ),
inference(ennf_transformation,[],[f1554]) ).
thf(f1554,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1553]) ).
thf(f1553,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ),
inference(rectify,[],[f554]) ).
thf(f554,axiom,
! [X311: nat,X312: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),X312)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X311)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X312),X311)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_one__less__power) ).
thf(f6342,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4905,f5970,f5970]) ).
thf(f4905,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ),
inference(cnf_transformation,[],[f3345]) ).
thf(f3345,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ),
inference(ennf_transformation,[],[f1552]) ).
thf(f1552,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ),
inference(fool_elimination,[],[f1551]) ).
thf(f1551,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ),
inference(rectify,[],[f365]) ).
thf(f365,axiom,
! [X209: nat,X210: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X210)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X210),X209)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_zero__le__power) ).
thf(f6338,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X1) ) ),
inference(definition_unfolding,[],[f4901,f5973,f5973]) ).
thf(f4901,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X1) ) ),
inference(cnf_transformation,[],[f3338]) ).
thf(f3338,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X1) ) ),
inference(ennf_transformation,[],[f1544]) ).
thf(f1544,plain,
! [X0: nat,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ) ),
inference(fool_elimination,[],[f1543]) ).
thf(f1543,plain,
! [X0: nat,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0)) ),
inference(rectify,[],[f486]) ).
thf(f486,axiom,
! [X286: nat,X287: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),X287)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X287),X286)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_one__le__power) ).
thf(f7681,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6337,f4464]) ).
thf(f6337,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4900,f4404]) ).
thf(f4900,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3337]) ).
thf(f3337,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3336]) ).
thf(f3336,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1542]) ).
thf(f1542,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 ) ) ) ) ),
inference(fool_elimination,[],[f1541]) ).
thf(f1541,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) = X0 ) ) ) ) ),
inference(rectify,[],[f1073]) ).
thf(f1073,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X163)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2)) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_inv__inv) ).
thf(f7680,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7679,f4464]) ).
thf(f7679,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7678,f4464]) ).
thf(f7678,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6336,f4464]) ).
thf(f6336,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4899,f5971,f5971,f5971]) ).
thf(f4899,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3335]) ).
thf(f3335,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3334]) ).
thf(f3334,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1540]) ).
thf(f1540,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) ) ) ) ) ),
inference(fool_elimination,[],[f1539]) ).
thf(f1539,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)),X1)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),one_one_int),X1) ) ) ) ),
inference(rectify,[],[f641]) ).
thf(f641,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X2)),one_one_int),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int)),X163)
| vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),one_one_int),X163) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_zcong__square) ).
thf(f7677,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6335,f4464]) ).
thf(f6335,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4898,f5971]) ).
thf(f4898,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3333]) ).
thf(f3333,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3332]) ).
thf(f3332,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1538]) ).
thf(f1538,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),one_one_int),X1) ) ) ) ),
inference(fool_elimination,[],[f1537]) ).
thf(f1537,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0))),one_one_int),X1) ) ) ),
inference(rectify,[],[f1088]) ).
thf(f1088,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2))),one_one_int),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_inv__is__inv) ).
thf(f7676,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,bit1,zero_zero_int)),X1) )
| ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7675,f4464]) ).
thf(f7675,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7674,f4464]) ).
thf(f7674,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6334,f4464]) ).
thf(f6334,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4897,f5971,f5971,f5971]) ).
thf(f4897,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) = X0 )
| ( one_one_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3331]) ).
thf(f3331,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) = X0 )
| ( one_one_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3330]) ).
thf(f3330,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) = X0 )
| ( one_one_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1536]) ).
thf(f1536,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1) )
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) = X0 )
| ( one_one_int = X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f1535]) ).
thf(f1535,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),one_one_int),X1)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) = X0 )
| ( one_one_int = X0 ) ) ) ) ) ),
inference(rectify,[],[f642]) ).
thf(f642,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),X2)),one_one_int),X163)
=> ( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int) = X2 )
| ( one_one_int = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_zcong__square__zless) ).
thf(f7673,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7672,f4464]) ).
thf(f7672,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7671,f4464]) ).
thf(f7671,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6333,f4464]) ).
thf(f6333,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4896,f5971,f5971,f5971]) ).
thf(f4896,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3329]) ).
thf(f3329,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3328]) ).
thf(f3328,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1534]) ).
thf(f1534,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) ) ) ) ),
inference(fool_elimination,[],[f1533]) ).
thf(f1533,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) ) ) ),
inference(rectify,[],[f1081]) ).
thf(f1081,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_inv__less__p__minus__1) ).
thf(f7670,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7669,f4464]) ).
thf(f7669,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7668,f4464]) ).
thf(f7668,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6332,f4464]) ).
thf(f6332,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4895,f5971,f5971,f5971]) ).
thf(f4895,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3327]) ).
thf(f3327,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3326]) ).
thf(f3326,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1532]) ).
thf(f1532,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) ) ) ) ),
inference(fool_elimination,[],[f1531]) ).
thf(f1531,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0)) ) ) ),
inference(rectify,[],[f1080]) ).
thf(f1080,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_inv__g__1) ).
thf(f7667,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7666,f4464]) ).
thf(f7666,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7665,f4464]) ).
thf(f7665,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6331,f4464]) ).
thf(f6331,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4894,f5971,f5971,f5971]) ).
thf(f4894,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3325]) ).
thf(f3325,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3324]) ).
thf(f3324,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1530]) ).
thf(f1530,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) ) ) ) ),
inference(fool_elimination,[],[f1529]) ).
thf(f1529,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) ) ) ) ),
inference(rectify,[],[f1079]) ).
thf(f1079,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_inv__not__p__minus__1) ).
thf(f7664,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7663,f4464]) ).
thf(f7663,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6330,f4464]) ).
thf(f6330,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4893,f5971,f5971]) ).
thf(f4893,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3323]) ).
thf(f3323,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3322]) ).
thf(f3322,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1528]) ).
thf(f1528,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 ) ) ) ),
inference(fool_elimination,[],[f1527]) ).
thf(f1527,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != X0 ) ) ) ),
inference(rectify,[],[f1077]) ).
thf(f1077,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2) != X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_inv__distinct) ).
thf(f7662,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7661,f4464]) ).
thf(f7661,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6329,f4464]) ).
thf(f6329,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4892,f5971,f5971]) ).
thf(f4892,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3321]) ).
thf(f3321,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3320]) ).
thf(f3320,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1526]) ).
thf(f1526,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) ) ) ) ),
inference(fool_elimination,[],[f1525]) ).
thf(f1525,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) ) ) ) ),
inference(rectify,[],[f1083]) ).
thf(f1083,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_inv__not__0) ).
thf(f7660,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7659,f4464]) ).
thf(f7659,plain,
! [X0: int,X1: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f7658,f4464]) ).
thf(f7658,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(forward_demodulation,[],[f6328,f4464]) ).
thf(f6328,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(definition_unfolding,[],[f4891,f5971,f5971,f5971]) ).
thf(f4891,plain,
! [X0: int,X1: int] :
( ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(cnf_transformation,[],[f3319]) ).
thf(f3319,plain,
! [X0: int,X1: int] :
( ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(flattening,[],[f3318]) ).
thf(f3318,plain,
! [X0: int,X1: int] :
( ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
| ( $true != vAPP(int,$o,zprime,X1) ) ),
inference(ennf_transformation,[],[f1524]) ).
thf(f1524,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,zprime,X1) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int)) )
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) ) ) ) ),
inference(fool_elimination,[],[f1523]) ).
thf(f1523,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,zprime,X1)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),one_one_int))
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X1),X0) ) ) ) ),
inference(rectify,[],[f1078]) ).
thf(f1078,axiom,
! [X2: int,X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),inv,X163),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_inv__not__1) ).
thf(f4890,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X1) ) ),
inference(cnf_transformation,[],[f3317]) ).
thf(f3317,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X1) ) ),
inference(flattening,[],[f3316]) ).
thf(f3316,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X1) ) ),
inference(ennf_transformation,[],[f1522]) ).
thf(f1522,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X1) )
=> ( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X0) )
=> ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ) ),
inference(fool_elimination,[],[f1521]) ).
thf(f1521,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,twoSqu919416604sum2sq,X1)
=> ( vAPP(int,$o,twoSqu919416604sum2sq,X0)
=> vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) ) ),
inference(rectify,[],[f91]) ).
thf(f91,axiom,
! [X17: int,X16: int] :
( vAPP(int,$o,twoSqu919416604sum2sq,X16)
=> ( vAPP(int,$o,twoSqu919416604sum2sq,X17)
=> vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X16),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq) ).
thf(f7657,plain,
! [X0: int,X1: int > $o] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(sTfun(int,$o),int,sK17,X1)) )
| ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,sK17,X1)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X1,X0) ) ),
inference(forward_demodulation,[],[f7656,f4464]) ).
thf(f7656,plain,
! [X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,sK17,X1)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,X1,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,X1)) ) ),
inference(forward_demodulation,[],[f6327,f4464]) ).
thf(f6327,plain,
! [X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,X0) )
| ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,sK17,X1)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(sTfun(int,$o),int,sK17,X1)) ) ),
inference(definition_unfolding,[],[f4888,f5971,f5971]) ).
thf(f4888,plain,
! [X0: int,X1: int > $o] :
( ( $true = vAPP(int,$o,X1,X0) )
| ( $true = vAPP(int,$o,X1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(sTfun(int,$o),int,sK17,X1)),one_one_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),vAPP(sTfun(int,$o),int,sK17,X1)) ) ),
inference(cnf_transformation,[],[f4132]) ).
thf(f4886,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3313]) ).
thf(f3313,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f2978]) ).
thf(f2978,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) = X0 ) ),
inference(flattening,[],[f1516]) ).
thf(f1516,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) = X0 ) ),
inference(fool_elimination,[],[f1515]) ).
thf(f1515,plain,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) = X0 ) ),
inference(rectify,[],[f984]) ).
thf(f984,axiom,
! [X192: nat,X191: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)) = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_add__diff__inverse) ).
thf(f6326,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),X0) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4883,f5969]) ).
thf(f4883,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),X0) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4130]) ).
thf(f4130,plain,
! [X0: nat,X1: nat > $o] :
( ( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),one_one_nat)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),X0) ) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f3312,f4129]) ).
thf(f4129,plain,
! [X0: nat,X1: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),one_one_nat)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) )
=> ( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),one_one_nat)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3312,plain,
! [X0: nat,X1: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),one_one_nat)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(flattening,[],[f3311]) ).
thf(f3311,plain,
! [X0: nat,X1: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),one_one_nat)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f2977]) ).
thf(f2977,plain,
! [X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
=> ( ( $true = vAPP(nat,$o,X1,X0) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),one_one_nat)) )
& ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
=> ( $true != vAPP(nat,$o,X1,X3) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ) ) ),
inference(flattening,[],[f1514]) ).
thf(f1514,plain,
! [X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
=> ( ( $true = vAPP(nat,$o,X1,X0) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),one_one_nat)) )
& ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
=> ( $true != vAPP(nat,$o,X1,X3) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f1513]) ).
thf(f1513,plain,
! [X0: nat,X1: nat > $o] :
( ~ vAPP(nat,$o,X1,zero_zero_nat)
=> ( vAPP(nat,$o,X1,X0)
=> ? [X2: nat] :
( vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),one_one_nat))
& ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2)
=> ~ vAPP(nat,$o,X1,X3) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ) ),
inference(rectify,[],[f1044]) ).
thf(f1044,axiom,
! [X191: nat,X490: nat > $o] :
( ~ vAPP(nat,$o,X490,zero_zero_nat)
=> ( vAPP(nat,$o,X490,X191)
=> ? [X320: nat] :
( vAPP(nat,$o,X490,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X320),one_one_nat))
& ! [X493: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X493),X320)
=> ~ vAPP(nat,$o,X490,X493) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X320),X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_ex__least__nat__less) ).
thf(f6325,plain,
! [X3: nat,X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4884,f5969]) ).
thf(f4884,plain,
! [X3: nat,X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4130]) ).
thf(f7655,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0))) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f6324,f4752]) ).
thf(f6324,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4885,f5972,f5969]) ).
thf(f4885,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK16,X1),X0)),one_one_nat)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4130]) ).
thf(f6323,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)),X0) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4880,f5969]) ).
thf(f4880,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)),X0) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4128]) ).
thf(f4128,plain,
! [X0: nat,X1: nat > $o] :
( ( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)),X0) ) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f3310,f4127]) ).
thf(f4127,plain,
! [X0: nat,X1: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,X2) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
=> ( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3310,plain,
! [X0: nat,X1: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,X2) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(flattening,[],[f3309]) ).
thf(f3309,plain,
! [X0: nat,X1: nat > $o] :
( ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,X2) )
& ! [X3: nat] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f2976]) ).
thf(f2976,plain,
! [X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
=> ( ( $true = vAPP(nat,$o,X1,X0) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,X2) )
& ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
=> ( $true != vAPP(nat,$o,X1,X3) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ) ) ),
inference(flattening,[],[f1512]) ).
thf(f1512,plain,
! [X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,zero_zero_nat) )
=> ( ( $true = vAPP(nat,$o,X1,X0) )
=> ? [X2: nat] :
( ( $true = vAPP(nat,$o,X1,X2) )
& ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
=> ( $true != vAPP(nat,$o,X1,X3) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f1511]) ).
thf(f1511,plain,
! [X0: nat,X1: nat > $o] :
( ~ vAPP(nat,$o,X1,zero_zero_nat)
=> ( vAPP(nat,$o,X1,X0)
=> ? [X2: nat] :
( vAPP(nat,$o,X1,X2)
& ! [X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2)
=> ~ vAPP(nat,$o,X1,X3) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ) ),
inference(rectify,[],[f1112]) ).
thf(f1112,axiom,
! [X191: nat,X490: nat > $o] :
( ~ vAPP(nat,$o,X490,zero_zero_nat)
=> ( vAPP(nat,$o,X490,X191)
=> ? [X320: nat] :
( vAPP(nat,$o,X490,X320)
& ! [X493: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X493),X320)
=> ~ vAPP(nat,$o,X490,X493) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X320),X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1111_ex__least__nat__le) ).
thf(f6322,plain,
! [X3: nat,X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4881,f5969]) ).
thf(f4881,plain,
! [X3: nat,X0: nat,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4128]) ).
thf(f6321,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4882,f5969]) ).
thf(f4882,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK15,X1),X0)) )
| ( $true != vAPP(nat,$o,X1,X0) )
| ( $true = vAPP(nat,$o,X1,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4128]) ).
thf(f4878,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3308]) ).
thf(f3308,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(ennf_transformation,[],[f1510]) ).
thf(f1510,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f1509]) ).
thf(f1509,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f990]) ).
thf(f990,axiom,
! [X192: nat,X191: nat] :
( ( ( X191 = X192 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_less__or__eq__imp__le) ).
thf(f6320,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4876,f5969]) ).
thf(f4876,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3307]) ).
thf(f3307,plain,
! [X0: int,X1: nat] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) )
| ( ( one_one_int != X0 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) ),
inference(ennf_transformation,[],[f1508]) ).
thf(f1508,plain,
! [X0: int,X1: nat] :
( ( ( one_one_int = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ) ),
inference(fool_elimination,[],[f1507]) ).
thf(f1507,plain,
! [X0: int,X1: nat] :
( ( ( one_one_int = X0 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(rectify,[],[f559]) ).
thf(f559,axiom,
! [X313: int,X314: nat] :
( ( ( one_one_int = X313 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X314) )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X313),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X313),X314)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_dvd__power) ).
thf(f6318,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4874,f5969]) ).
thf(f4874,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3306]) ).
thf(f3306,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) )
| ( ( one_one_nat != X0 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) ),
inference(ennf_transformation,[],[f1506]) ).
thf(f1506,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_nat = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f1505]) ).
thf(f1505,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_nat = X0 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(rectify,[],[f558]) ).
thf(f558,axiom,
! [X313: nat,X314: nat] :
( ( ( one_one_nat = X313 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X314) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X313),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X313),X314)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_dvd__power) ).
thf(f6316,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4872,f5969]) ).
thf(f4872,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3305]) ).
thf(f3305,plain,
! [X0: real,X1: nat] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) )
| ( ( one_one_real != X0 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) ) ),
inference(ennf_transformation,[],[f1504]) ).
thf(f1504,plain,
! [X0: real,X1: nat] :
( ( ( one_one_real = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) ) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ) ),
inference(fool_elimination,[],[f1503]) ).
thf(f1503,plain,
! [X0: real,X1: nat] :
( ( ( one_one_real = X0 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X1) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ),
inference(rectify,[],[f557]) ).
thf(f557,axiom,
! [X313: real,X314: nat] :
( ( ( one_one_real = X313 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X314) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X313),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X313),X314)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_dvd__power) ).
thf(f7653,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(subsumption_resolution,[],[f6314,f6249]) ).
thf(f6314,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4866,f5969,f5969,f5969]) ).
thf(f4866,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) ) ),
inference(cnf_transformation,[],[f3302]) ).
thf(f3302,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) )
| ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) ) ) ) ),
inference(ennf_transformation,[],[f1498]) ).
thf(f1498,plain,
! [X0: nat,X1: nat] :
( ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) ) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) ) ),
inference(fool_elimination,[],[f1497]) ).
thf(f1497,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) ),
inference(rectify,[],[f772]) ).
thf(f772,axiom,
! [X402: nat,X403: nat] :
( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X402)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X403),zero_zero_nat) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X402),zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X403) ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X403),X402)),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_split__mult__neg__le) ).
thf(f7652,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(subsumption_resolution,[],[f6313,f6249]) ).
thf(f6313,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4867,f5969,f5969,f5969]) ).
thf(f4867,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f3302]) ).
thf(f6312,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4864,f5970,f5970,f5970]) ).
thf(f4864,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ),
inference(cnf_transformation,[],[f3301]) ).
thf(f3301,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ) ) ),
inference(ennf_transformation,[],[f1496]) ).
thf(f1496,plain,
! [X0: real,X1: real] :
( ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) ) ),
inference(fool_elimination,[],[f1495]) ).
thf(f1495,plain,
! [X0: real,X1: real] :
( ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) ),
inference(rectify,[],[f771]) ).
thf(f771,axiom,
! [X402: real,X403: real] :
( ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X402)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X403),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X402),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X403) ) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X403),X402)),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_split__mult__neg__le) ).
thf(f6311,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4865,f5970,f5970,f5970]) ).
thf(f4865,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) ) ),
inference(cnf_transformation,[],[f3301]) ).
thf(f6310,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) ) ),
inference(definition_unfolding,[],[f4862,f5970,f5970,f5970]) ).
thf(f4862,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ),
inference(cnf_transformation,[],[f3300]) ).
thf(f3300,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) ) )
& ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ) ) ),
inference(ennf_transformation,[],[f1494]) ).
thf(f1494,plain,
! [X0: real,X1: real] :
( ( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) ) )
| ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) ) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ) ),
inference(fool_elimination,[],[f1493]) ).
thf(f1493,plain,
! [X0: real,X1: real] :
( ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) ) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) ),
inference(rectify,[],[f774]) ).
thf(f774,axiom,
! [X404: real,X405: real] :
( ( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X404),zero_zero_real)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X405),zero_zero_real) )
| ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X404)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X405) ) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X405),X404)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_split__mult__pos__le) ).
thf(f6309,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4863,f5970,f5970,f5970]) ).
thf(f4863,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),zero_zero_real) ) ),
inference(cnf_transformation,[],[f3300]) ).
thf(f6308,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4853,f4404,f4404]) ).
thf(f4853,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(cnf_transformation,[],[f3283]) ).
thf(f3283,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(flattening,[],[f3282]) ).
thf(f3282,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) != $true )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(ennf_transformation,[],[f1476]) ).
thf(f1476,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f1475]) ).
thf(f1475,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f451]) ).
thf(f451,axiom,
! [X256: int,X257: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X256),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X257),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X256)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X257)
=> ( X256 = X257 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_power2__eq__imp__eq) ).
thf(f7651,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(subsumption_resolution,[],[f7650,f6249]) ).
thf(f7650,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(subsumption_resolution,[],[f6307,f6249]) ).
thf(f6307,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4852,f5969,f5969,f4404,f4404]) ).
thf(f4852,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(cnf_transformation,[],[f3281]) ).
thf(f3281,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(flattening,[],[f3280]) ).
thf(f3280,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(ennf_transformation,[],[f1474]) ).
thf(f1474,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f1473]) ).
thf(f1473,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X1)
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f450]) ).
thf(f450,axiom,
! [X256: nat,X257: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X256),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X257),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X256)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X257)
=> ( X256 = X257 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_power2__eq__imp__eq) ).
thf(f6306,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4851,f5970,f5970,f4404,f4404]) ).
thf(f4851,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(cnf_transformation,[],[f3279]) ).
thf(f3279,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(flattening,[],[f3278]) ).
thf(f3278,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
| ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(ennf_transformation,[],[f1472]) ).
thf(f1472,plain,
! [X0: real,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f1471]) ).
thf(f1471,plain,
! [X0: real,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X1)
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f449]) ).
thf(f449,axiom,
! [X256: real,X257: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X256),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X257),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X256)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),X257)
=> ( X256 = X257 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq) ).
thf(f6305,plain,
! [X0: nat,X1: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != X0 ) ),
inference(definition_unfolding,[],[f4850,f5969,f5972]) ).
thf(f4850,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( one_one_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f3277]) ).
thf(f3277,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( one_one_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != X0 ) ),
inference(flattening,[],[f3276]) ).
thf(f3276,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( one_one_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f2967]) ).
thf(f2967,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) = X0 )
=> ( ( zero_zero_nat = X0 )
| ( one_one_nat = X1 ) ) ),
inference(rectify,[],[f1039]) ).
thf(f1039,axiom,
! [X192: nat,X191: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191) = X192 )
=> ( ( zero_zero_nat = X192 )
| ( one_one_nat = X191 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_mult__eq__self__implies__10) ).
thf(f6304,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != X0 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f4849,f5969]) ).
thf(f4849,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f3275]) ).
thf(f3275,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f2966]) ).
thf(f2966,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 )
=> ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f961]) ).
thf(f961,axiom,
! [X192: nat,X191: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191) = X192 )
=> ( zero_zero_nat = X191 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_add__eq__self__zero) ).
thf(f4847,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),sK14,X1),X0)) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ),
inference(cnf_transformation,[],[f4126]) ).
thf(f4126,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),sK14,X1),X0)) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f3272,f4125]) ).
thf(f4125,plain,
! [X0: int,X1: int] :
( ? [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) = X0 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),sK14,X1),X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f3272,plain,
! [X0: int,X1: int] :
( ? [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) ) ),
inference(ennf_transformation,[],[f2964]) ).
thf(f2964,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1) )
=> ? [X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X2) = X0 ) ),
inference(rectify,[],[f1176]) ).
thf(f1176,axiom,
! [X506: int,X507: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X506),X507) )
=> ? [X501: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X507),X501) = X506 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_zmod__eq__0D) ).
thf(f6302,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f4845,f5969,f5969]) ).
thf(f4845,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3269]) ).
thf(f3269,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ),
inference(flattening,[],[f3268]) ).
thf(f3268,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f2962]) ).
thf(f2962,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) )
=> ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f888]) ).
thf(f888,axiom,
! [X192: nat,X191: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191) )
=> ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),X192) )
=> ( X191 = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_diffs0__imp__equal) ).
thf(f7649,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( min = X0 ) ),
inference(forward_demodulation,[],[f7648,f4464]) ).
thf(f7648,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( min = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f7647,f4464]) ).
thf(f7647,plain,
! [X0: int,X1: int] :
( ( min = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f6300,f4464]) ).
thf(f6300,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4843,f5971,f5971]) ).
thf(f4843,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( one_one_int = X0 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ),
inference(cnf_transformation,[],[f3265]) ).
thf(f3265,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( one_one_int = X0 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ),
inference(flattening,[],[f3264]) ).
thf(f3264,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( one_one_int = X0 )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ) ),
inference(ennf_transformation,[],[f2960]) ).
thf(f2960,plain,
! [X0: int,X1: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) )
=> ( ( vAPP(int,int,number_number_of_int,min) = X0 )
| ( one_one_int = X0 ) ) ),
inference(rectify,[],[f552]) ).
thf(f552,axiom,
! [X192: int,X191: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X192),X191) )
=> ( ( vAPP(int,int,number_number_of_int,min) = X192 )
| ( one_one_int = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_pos__zmult__eq__1__iff__lemma) ).
thf(f4840,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( zero_zero_int = X0 )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f3261]) ).
thf(f3261,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( zero_zero_int = X0 )
| ( zero_zero_int = X1 ) ),
inference(flattening,[],[f3260]) ).
thf(f3260,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) )
| ( zero_zero_int = X0 )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[],[f2959]) ).
thf(f2959,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
=> ( ( zero_zero_int != X0 )
=> ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) ) ) ),
inference(rectify,[],[f704]) ).
thf(f704,axiom,
! [X354: int,X355: int] :
( ( zero_zero_int != X355 )
=> ( ( zero_zero_int != X354 )
=> ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X355),X354) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_no__zero__divisors) ).
thf(f4839,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f3259]) ).
thf(f3259,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[],[f2958]) ).
thf(f2958,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != X1 )
=> ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),X0) ) ),
inference(rectify,[],[f333]) ).
thf(f333,axiom,
! [X196: nat,X197: int] :
( ( zero_zero_int != X197 )
=> ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X197),X196) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_field__power__not__zero) ).
thf(f6299,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f4838,f5969,f5969,f5969]) ).
thf(f4838,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) )
| ( zero_zero_nat = X0 )
| ( zero_zero_nat = X1 ) ),
inference(cnf_transformation,[],[f3258]) ).
thf(f3258,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) )
| ( zero_zero_nat = X0 )
| ( zero_zero_nat = X1 ) ),
inference(flattening,[],[f3257]) ).
thf(f3257,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) )
| ( zero_zero_nat = X0 )
| ( zero_zero_nat = X1 ) ),
inference(ennf_transformation,[],[f2957]) ).
thf(f2957,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
=> ( ( zero_zero_nat != X0 )
=> ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) ) ) ),
inference(rectify,[],[f703]) ).
thf(f703,axiom,
! [X354: nat,X355: nat] :
( ( zero_zero_nat != X355 )
=> ( ( zero_zero_nat != X354 )
=> ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X355),X354) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_no__zero__divisors) ).
thf(f6298,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) != vAPP(int,real,number267125858f_real,zero_zero_int) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f4837,f5970,f5970,f5970]) ).
thf(f4837,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) )
| ( zero_zero_real = X0 )
| ( zero_zero_real = X1 ) ),
inference(cnf_transformation,[],[f3256]) ).
thf(f3256,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) )
| ( zero_zero_real = X0 )
| ( zero_zero_real = X1 ) ),
inference(flattening,[],[f3255]) ).
thf(f3255,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) )
| ( zero_zero_real = X0 )
| ( zero_zero_real = X1 ) ),
inference(ennf_transformation,[],[f2956]) ).
thf(f2956,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
=> ( ( zero_zero_real != X0 )
=> ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) ) ) ),
inference(rectify,[],[f702]) ).
thf(f702,axiom,
! [X354: real,X355: real] :
( ( zero_zero_real != X355 )
=> ( ( zero_zero_real != X354 )
=> ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X355),X354) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_no__zero__divisors) ).
thf(f6297,plain,
! [X0: nat,X1: real] :
( ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0) != vAPP(int,real,number267125858f_real,zero_zero_int) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f4836,f5970,f5970]) ).
thf(f4836,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0) )
| ( zero_zero_real = X1 ) ),
inference(cnf_transformation,[],[f3254]) ).
thf(f3254,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0) )
| ( zero_zero_real = X1 ) ),
inference(ennf_transformation,[],[f2955]) ).
thf(f2955,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != X1 )
=> ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),X0) ) ),
inference(rectify,[],[f334]) ).
thf(f334,axiom,
! [X196: nat,X197: real] :
( ( zero_zero_real != X197 )
=> ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X197),X196) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_field__power__not__zero) ).
thf(f4835,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3253]) ).
thf(f3253,plain,
! [X0: nat,X1: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( X0 = X1 ) ),
inference(flattening,[],[f3252]) ).
thf(f3252,plain,
! [X0: nat,X1: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f2954]) ).
thf(f2954,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ) ),
inference(flattening,[],[f1466]) ).
thf(f1466,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ) ),
inference(fool_elimination,[],[f1465]) ).
thf(f1465,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1)
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X1),X0)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X1) ) ) ),
inference(rectify,[],[f921]) ).
thf(f921,axiom,
! [X2: nat,X3: nat] :
( ( X2 != X3 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3)
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X3),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_dvd_Oneq__le__trans) ).
thf(f4832,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3249]) ).
thf(f3249,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 ) ),
inference(flattening,[],[f3248]) ).
thf(f3248,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f2952]) ).
thf(f2952,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ) ) ),
inference(flattening,[],[f1462]) ).
thf(f1462,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ) ) ),
inference(fool_elimination,[],[f1461]) ).
thf(f1461,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ) ),
inference(rectify,[],[f893]) ).
thf(f893,axiom,
! [X16: nat,X17: nat] :
( ( X16 != X17 )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X16),X17)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X17),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_linorder__neqE__nat) ).
thf(f4831,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3247]) ).
thf(f3247,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ),
inference(flattening,[],[f3246]) ).
thf(f3246,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f2951]) ).
thf(f2951,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
=> ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
inference(flattening,[],[f1460]) ).
thf(f1460,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
=> ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
inference(fool_elimination,[],[f1459]) ).
thf(f1459,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
=> ( ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ),
inference(rectify,[],[f677]) ).
thf(f677,axiom,
! [X344: real,X345: real] :
( ( X344 != X345 )
=> ( ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X344),X345)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X345),X344) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_linorder__neqE__linordered__idom) ).
thf(f4828,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1454]) ).
thf(f1454,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f1453]) ).
thf(f1453,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f939]) ).
thf(f939,axiom,
! [X192: nat,X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X192)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_nat__le__linear) ).
thf(f4827,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1452]) ).
thf(f1452,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ) ),
inference(fool_elimination,[],[f1451]) ).
thf(f1451,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X1),X0)
| vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X1) ),
inference(rectify,[],[f882]) ).
thf(f882,axiom,
! [X15: real,X14: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X14),X15)
| vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X15),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_real__le__linear) ).
thf(f4824,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3245]) ).
thf(f3245,plain,
! [X0: int,X1: int] :
( ( ( ( ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) ) )
& ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) ) ) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) )
& ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ) ),
inference(ennf_transformation,[],[f2950]) ).
thf(f2950,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
=> ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) ) ),
inference(flattening,[],[f1450]) ).
thf(f1450,plain,
! [X0: int,X1: int] :
( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( ( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
=> ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) ) ) )
& ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) )
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) ) ),
inference(fool_elimination,[],[f1449]) ).
thf(f1449,plain,
! [X0: int,X1: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> ( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0)
=> ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0)
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) ) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1)
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) ) ) ),
inference(rectify,[],[f667]) ).
thf(f667,axiom,
! [X2: int,X163: int] :
( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X163)
=> ( ( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X163),X2)
=> ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X2),X163) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X163),X2)
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X2),X163) ) ) ) )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X2),zero_zero_int),X163)
=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X2),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_Legendre__def) ).
thf(f7646,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) = vAPP(int,int,bit1,zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f6296,f4464]) ).
thf(f6296,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(definition_unfolding,[],[f4825,f5971]) ).
thf(f4825,plain,
! [X0: int,X1: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3245]) ).
thf(f7645,plain,
! [X0: int,X1: int] :
( ( min = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(forward_demodulation,[],[f4826,f4464]) ).
thf(f4826,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,X1),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X1) ) ),
inference(cnf_transformation,[],[f3245]) ).
thf(f7634,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1) = $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ) ),
inference(forward_demodulation,[],[f7633,f4464]) ).
thf(f7633,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7632,f4464]) ).
thf(f7632,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,bit0,X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7631,f4464]) ).
thf(f7631,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7630,f7427]) ).
thf(f7630,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7629,f4464]) ).
thf(f7629,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7628,f4464]) ).
thf(f7628,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,number_number_of_int,X0))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7627,f4757]) ).
thf(f7627,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,bit1,zero_zero_int))),X1))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f7626,f4464]) ).
thf(f7626,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,number_number_of_int,X1)))),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(forward_demodulation,[],[f6294,f4464]) ).
thf(f6294,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,number_number_of_int,X1)))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(definition_unfolding,[],[f4823,f4404,f5971,f5971]) ).
thf(f4823,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),one_one_int)),vAPP(int,int,number_number_of_int,X1)))),one_one_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,number_number_of_int,X1)) ) ),
inference(cnf_transformation,[],[f3244]) ).
thf(f4820,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 ) ),
inference(cnf_transformation,[],[f3243]) ).
thf(f3243,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) )
& ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(ennf_transformation,[],[f2948]) ).
thf(f2948,plain,
! [X0: nat,X1: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X1) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 ) ) ),
inference(flattening,[],[f1446]) ).
thf(f1446,plain,
! [X0: nat,X1: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X1) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 ) ) ),
inference(fool_elimination,[],[f1445]) ).
thf(f1445,plain,
! [X0: nat,X1: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X1) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = X0 ) ) ),
inference(rectify,[],[f1182]) ).
thf(f1182,axiom,
! [X192: nat,X191: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X191)),X191) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X192),X191)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X192),X191) = X192 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_mod__if) ).
thf(f4821,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),div_mod_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f3243]) ).
thf(f6293,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4817,f4404]) ).
thf(f4817,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ),
inference(cnf_transformation,[],[f3242]) ).
thf(f6292,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4818,f4404,f4404]) ).
thf(f4818,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ),
inference(cnf_transformation,[],[f3242]) ).
thf(f6290,plain,
! [X0: int,X1: int] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4815,f5969,f4404]) ).
thf(f4815,plain,
! [X0: int,X1: int] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,X1)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),pls) ) ),
inference(cnf_transformation,[],[f3241]) ).
thf(f6287,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),X0)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f4814,f5972,f5969]) ).
thf(f4814,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat)),X0)) )
| ( zero_zero_nat = X1 ) ),
inference(cnf_transformation,[],[f3240]) ).
thf(f3240,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat)),X0)) )
| ( zero_zero_nat = X1 ) )
& ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) )
| ( zero_zero_nat != X1 ) ) ),
inference(ennf_transformation,[],[f2945]) ).
thf(f2945,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat != X1 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat)),X0)) ) )
& ( ( zero_zero_nat = X1 )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) ) ) ),
inference(rectify,[],[f696]) ).
thf(f696,axiom,
! [X191: nat,X192: nat] :
( ( ( zero_zero_nat != X192 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),one_one_nat)),X191)) ) )
& ( ( zero_zero_nat = X192 )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_mult__eq__if) ).
thf(f6285,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))))) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X1 ) ),
inference(definition_unfolding,[],[f4812,f5972,f5969]) ).
thf(f4812,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))) )
| ( zero_zero_nat = X1 ) ),
inference(cnf_transformation,[],[f3239]) ).
thf(f3239,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))) )
| ( zero_zero_nat = X1 ) )
& ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) )
| ( zero_zero_nat != X1 ) ) ),
inference(ennf_transformation,[],[f2944]) ).
thf(f2944,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat != X1 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),one_one_nat))) ) )
& ( ( zero_zero_nat = X1 )
=> ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1) ) ) ),
inference(rectify,[],[f697]) ).
thf(f697,axiom,
! [X163: nat,X192: nat] :
( ( ( zero_zero_nat != X192 )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X163),X192) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X163),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X163),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),one_one_nat))) ) )
& ( ( zero_zero_nat = X192 )
=> ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X163),X192) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_power__eq__if) ).
thf(f7625,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7624,f4464]) ).
thf(f7624,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f6284,f4757]) ).
thf(f6284,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4810,f4404,f4404,f4404,f4404,f4404,f4404,f4404]) ).
thf(f4810,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2943]) ).
thf(f2943,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X2: int,X3: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),X3))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(f7623,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7622,f4464]) ).
thf(f7622,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f6283,f4757]) ).
thf(f6283,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4809,f4404,f4404,f4404,f4404,f4404,f4404,f4404]) ).
thf(f4809,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2942]) ).
thf(f2942,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),X0)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f652]) ).
thf(f652,axiom,
! [X2: int,X3: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),X3))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))),X2)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_zdiff__power3) ).
thf(f7621,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7620,f4763]) ).
thf(f7620,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7619,f7427]) ).
thf(f7619,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f6282,f4464]) ).
thf(f6282,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4808,f4404,f4404,f4404,f4404]) ).
thf(f4808,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2941]) ).
thf(f2941,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X2: int,X3: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)),X3))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(f7618,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))) ),
inference(forward_demodulation,[],[f7617,f4763]) ).
thf(f7617,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X0)),X1)) ),
inference(forward_demodulation,[],[f7616,f7427]) ).
thf(f7616,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0)),X1)) ),
inference(forward_demodulation,[],[f6281,f4464]) ).
thf(f6281,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1)) ),
inference(definition_unfolding,[],[f4807,f4404,f4404,f4404,f4404]) ).
thf(f4807,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(cnf_transformation,[],[f2940]) ).
thf(f2940,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X4: int,X5: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X4),X5)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X4),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X5),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X4)),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(f7615,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7614,f4763]) ).
thf(f7614,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f7613,f7427]) ).
thf(f7613,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(forward_demodulation,[],[f6280,f4464]) ).
thf(f6280,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4806,f4404,f4404,f4404,f4404]) ).
thf(f4806,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2939]) ).
thf(f2939,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f651]) ).
thf(f651,axiom,
! [X2: int,X3: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X2)),X3))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_zdiff__power2) ).
thf(f7612,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))) ),
inference(forward_demodulation,[],[f7611,f4763]) ).
thf(f7611,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X0)),X1)) ),
inference(forward_demodulation,[],[f7610,f7427]) ).
thf(f7610,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0)),X1)) ),
inference(forward_demodulation,[],[f6279,f4464]) ).
thf(f6279,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1)) ),
inference(definition_unfolding,[],[f4805,f4404,f4404,f4404,f4404]) ).
thf(f4805,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(cnf_transformation,[],[f2938]) ).
thf(f2938,plain,
! [X0: int,X1: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(rectify,[],[f650]) ).
thf(f650,axiom,
! [X336: int,X337: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X336),X337)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X336),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X337),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X336)),X337)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_power2__diff) ).
thf(f6278,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1)) ),
inference(definition_unfolding,[],[f4804,f4404,f4404,f4404,f4404]) ).
thf(f4804,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(cnf_transformation,[],[f2937]) ).
thf(f2937,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X4: nat,X5: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X4),X5)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X4),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X5),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X4)),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(f6276,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1)) ),
inference(definition_unfolding,[],[f4802,f4404,f4404,f4404,f4404]) ).
thf(f4802,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(cnf_transformation,[],[f2935]) ).
thf(f2935,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(rectify,[],[f293]) ).
thf(f293,axiom,
! [X16: real,X17: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X16),X17)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X16),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X17),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X16)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_real__sum__squared__expand) ).
thf(f6275,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),X1)) ),
inference(definition_unfolding,[],[f4801,f4404,f4404,f4404,f4404]) ).
thf(f4801,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(cnf_transformation,[],[f2934]) ).
thf(f2934,plain,
! [X0: real,X1: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),X1)) ),
inference(rectify,[],[f649]) ).
thf(f649,axiom,
! [X336: real,X337: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X336),X337)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X336),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X337),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X336)),X337)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_power2__diff) ).
thf(f6274,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4800,f4404,f4404]) ).
thf(f4800,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2933]) ).
thf(f2933,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) ),
inference(rectify,[],[f698]) ).
thf(f698,axiom,
! [X16: nat,X17: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X16),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X17),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X16),X17)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X16),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_diff__square) ).
thf(f6273,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4799,f4404,f4404]) ).
thf(f4799,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2932]) ).
thf(f2932,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f643]) ).
thf(f643,axiom,
! [X2: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_zspecial__product) ).
thf(f7609,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(forward_demodulation,[],[f7608,f4464]) ).
thf(f7608,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,bit0,X1)) ),
inference(forward_demodulation,[],[f7607,f4464]) ).
thf(f7607,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ),
inference(forward_demodulation,[],[f7606,f7427]) ).
thf(f7606,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ),
inference(forward_demodulation,[],[f7605,f4464]) ).
thf(f7605,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X1)) ),
inference(forward_demodulation,[],[f7604,f4464]) ).
thf(f7604,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),X1)) ),
inference(forward_demodulation,[],[f6272,f4464]) ).
thf(f6272,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1))) ),
inference(definition_unfolding,[],[f4798,f4404]) ).
thf(f4798,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) ),
inference(cnf_transformation,[],[f2931]) ).
thf(f2931,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X0))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X1))) ),
inference(rectify,[],[f1166]) ).
thf(f1166,axiom,
! [X40: int,X14: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,X40)),vAPP(int,int,number_number_of_int,X14))) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X40))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_zmod__number__of__Bit0) ).
thf(f6271,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4797,f4404,f4404]) ).
thf(f4797,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2930]) ).
thf(f2930,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X95: int,X96: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X95),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X96)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X95),X96)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_power__even__eq) ).
thf(f6270,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4796,f4404,f4404]) ).
thf(f4796,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2929]) ).
thf(f2929,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f162]) ).
thf(f162,axiom,
! [X95: nat,X96: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X95),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X96)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X95),X96)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_power__even__eq) ).
thf(f6269,plain,
! [X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4795,f4404,f4404]) ).
thf(f4795,plain,
! [X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2928]) ).
thf(f2928,plain,
! [X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f161]) ).
thf(f161,axiom,
! [X95: real,X96: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X95),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X96)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X95),X96)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_power__even__eq) ).
thf(f6268,plain,
! [X0: int,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) ),
inference(definition_unfolding,[],[f4794,f4404]) ).
thf(f4794,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(cnf_transformation,[],[f2927]) ).
thf(f2927,plain,
! [X0: int,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),X1)) ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X9: int,X10: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X10)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X9),X10)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X9),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(f6267,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) ),
inference(definition_unfolding,[],[f4793,f4404]) ).
thf(f4793,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2926]) ).
thf(f2926,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X9: nat,X10: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X10)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X9),X10)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X9),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(f6266,plain,
! [X0: real,X1: nat] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X1)) ),
inference(definition_unfolding,[],[f4792,f4404]) ).
thf(f4792,plain,
! [X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ),
inference(cnf_transformation,[],[f2925]) ).
thf(f2925,plain,
! [X0: real,X1: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),X1)) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X9: real,X10: nat] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X10)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X9),X10)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X9),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(f7603,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))),X1) ),
inference(forward_demodulation,[],[f6265,f4464]) ).
thf(f6265,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X1) ),
inference(definition_unfolding,[],[f4790,f5971]) ).
thf(f4790,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) ),
inference(cnf_transformation,[],[f2923]) ).
thf(f2923,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),one_one_int)),X1) ),
inference(rectify,[],[f227]) ).
thf(f227,axiom,
! [X133: int,X134: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X133),X134)),X134) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X133),one_one_int)),X134) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(f7602,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(forward_demodulation,[],[f6264,f4464]) ).
thf(f6264,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4789,f5971]) ).
thf(f4789,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)),X0) ),
inference(cnf_transformation,[],[f2922]) ).
thf(f2922,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)),X0) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X135: int,X136: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X135),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X136),X135)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X136),one_one_int)),X135) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(f6263,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),X1) ),
inference(definition_unfolding,[],[f4787,f5972]) ).
thf(f4787,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),one_one_nat)),X1) ),
inference(cnf_transformation,[],[f2920]) ).
thf(f2920,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),one_one_nat)),X1) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X133: nat,X134: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X133),X134)),X134) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X133),one_one_nat)),X134) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(f6262,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4786,f5972]) ).
thf(f4786,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),one_one_nat)),X0) ),
inference(cnf_transformation,[],[f2919]) ).
thf(f2919,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),one_one_nat)),X0) ),
inference(rectify,[],[f231]) ).
thf(f231,axiom,
! [X135: nat,X136: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X135),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X136),X135)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X136),one_one_nat)),X135) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(f6261,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)))),X1) ),
inference(definition_unfolding,[],[f4784,f5973]) ).
thf(f4784,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),one_one_real)),X1) ),
inference(cnf_transformation,[],[f2917]) ).
thf(f2917,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),one_one_real)),X1) ),
inference(rectify,[],[f229]) ).
thf(f229,axiom,
! [X133: real,X134: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X133),X134)),X134) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X133),one_one_real)),X134) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(f6260,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4783,f5973]) ).
thf(f4783,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),one_one_real)),X0) ),
inference(cnf_transformation,[],[f2916]) ).
thf(f2916,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),one_one_real)),X0) ),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X135: real,X136: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X135),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X136),X135)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X136),one_one_real)),X135) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(f4782,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))),X1) ),
inference(cnf_transformation,[],[f2915]) ).
thf(f2915,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1))),X1) ),
inference(rectify,[],[f269]) ).
thf(f269,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,X18)),X38) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X38))),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_mult__Bit1) ).
thf(f7597,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,bit1,vAPP(int,int,bit0,X0))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,bit1,vAPP(int,int,bit0,X0))) ) ),
inference(forward_demodulation,[],[f7596,f6075]) ).
thf(f7596,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),vAPP(int,int,bit0,X0)))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,bit1,vAPP(int,int,bit0,X0))) ) ),
inference(forward_demodulation,[],[f7595,f4779]) ).
thf(f7595,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,bit1,vAPP(int,int,bit0,X0))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,bit0,X0)))) ) ),
inference(forward_demodulation,[],[f7594,f6075]) ).
thf(f7594,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),vAPP(int,int,bit0,X0)))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,bit0,X0)))) ) ),
inference(backward_demodulation,[],[f7583,f4779]) ).
thf(f4779,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f2912]) ).
thf(f2912,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(rectify,[],[f252]) ).
thf(f252,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X18)),vAPP(int,int,bit0,X38)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__Bit1__Bit0) ).
thf(f4778,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ),
inference(cnf_transformation,[],[f2911]) ).
thf(f2911,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ),
inference(rectify,[],[f206]) ).
thf(f206,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X18)),vAPP(int,int,bit0,X38)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__Bit0__Bit0) ).
thf(f4775,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ),
inference(cnf_transformation,[],[f2908]) ).
thf(f2908,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ),
inference(rectify,[],[f625]) ).
thf(f625,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit1,X18)),vAPP(int,int,bit0,X38)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X18),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_diff__bin__simps_I9_J) ).
thf(f4774,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f2907]) ).
thf(f2907,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) ),
inference(rectify,[],[f616]) ).
thf(f616,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit0,X18)),vAPP(int,int,bit0,X38)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X18),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_diff__bin__simps_I7_J) ).
thf(f4771,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f2904]) ).
thf(f2904,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(rectify,[],[f253]) ).
thf(f253,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),X38)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X18)),vAPP(int,int,bit1,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__Bit0__Bit1) ).
thf(f4770,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f2903]) ).
thf(f2903,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit1,X1)) ),
inference(rectify,[],[f626]) ).
thf(f626,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X18),X38)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,bit1,X18)),vAPP(int,int,bit1,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_diff__bin__simps_I10_J) ).
thf(f4766,plain,
! [X0: int,X1: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(cnf_transformation,[],[f2899]) ).
thf(f2899,plain,
! [X0: int,X1: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(rectify,[],[f245]) ).
thf(f245,axiom,
! [X145: int,X146: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X145),X146)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,X145)),vAPP(int,real,number267125858f_real,X146)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_number__of__mult) ).
thf(f4765,plain,
! [X0: int,X1: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(cnf_transformation,[],[f2898]) ).
thf(f2898,plain,
! [X0: int,X1: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(rectify,[],[f251]) ).
thf(f251,axiom,
! [X152: int,X153: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X152),X153)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X152)),vAPP(int,real,number267125858f_real,X153)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_number__of__add) ).
thf(f4764,plain,
! [X0: int,X1: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(cnf_transformation,[],[f2897]) ).
thf(f2897,plain,
! [X0: int,X1: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X1)) ),
inference(rectify,[],[f613]) ).
thf(f613,axiom,
! [X325: int,X326: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X325),X326)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(int,real,number267125858f_real,X325)),vAPP(int,real,number267125858f_real,X326)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_number__of__diff) ).
thf(f7583,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,bit0,X0)))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,bit0,X0)))) ) ),
inference(forward_demodulation,[],[f7582,f7427]) ).
thf(f7582,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0)))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,bit0,X0)))) ) ),
inference(forward_demodulation,[],[f7581,f4763]) ).
thf(f7581,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,bit0,X0)))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))) ) ),
inference(forward_demodulation,[],[f7580,f7427]) ).
thf(f7580,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0)))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))) ) ),
inference(backward_demodulation,[],[f7578,f4763]) ).
thf(f4763,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X0)),X1) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ),
inference(cnf_transformation,[],[f2896]) ).
thf(f2896,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X0)),X1) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1)) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,X18)),X38) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X18),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mult__Bit0) ).
thf(f4762,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f2895]) ).
thf(f2895,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) = X0 ),
inference(rectify,[],[f933]) ).
thf(f933,axiom,
! [X192: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X192),X191)),X191) = X192 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_diff__add__inverse2) ).
thf(f4761,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) = X1 ),
inference(cnf_transformation,[],[f2894]) ).
thf(f2894,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) = X1 ),
inference(rectify,[],[f934]) ).
thf(f934,axiom,
! [X191: nat,X192: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),X192)),X191) = X192 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_diff__add__inverse) ).
thf(f7579,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(backward_demodulation,[],[f7576,f4759]) ).
thf(f4759,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ),
inference(cnf_transformation,[],[f2892]) ).
thf(f2892,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X1) ),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X15: int,X14: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X15),X14) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X14),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_zmult__commute) ).
thf(f7578,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))) ) ),
inference(forward_demodulation,[],[f7577,f4757]) ).
thf(f7577,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(backward_demodulation,[],[f7489,f4757]) ).
thf(f7576,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),m)) ),
inference(backward_demodulation,[],[f7410,f4757]) ).
thf(f4757,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) ),
inference(cnf_transformation,[],[f2890]) ).
thf(f2890,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X86: int,X87: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X86),X87) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X87),X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(f4756,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) ),
inference(cnf_transformation,[],[f2889]) ).
thf(f2889,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X0),X1) ),
inference(rectify,[],[f1185]) ).
thf(f1185,axiom,
! [X192: int,X16: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),X192) = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,X192),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_StandardRes__def) ).
thf(f4754,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) ),
inference(cnf_transformation,[],[f2887]) ).
thf(f2887,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X1) ),
inference(rectify,[],[f951]) ).
thf(f951,axiom,
! [X192: nat,X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X191) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X191),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_nat__mult__commute) ).
thf(f4752,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) ),
inference(cnf_transformation,[],[f2885]) ).
thf(f2885,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X86: nat,X87: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X86),X87) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X87),X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(f4750,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1) ),
inference(cnf_transformation,[],[f2883]) ).
thf(f2883,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X1) ),
inference(rectify,[],[f690]) ).
thf(f690,axiom,
! [X15: real,X14: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X15),X14) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X14),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_real__mult__commute) ).
thf(f4749,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) ),
inference(cnf_transformation,[],[f2882]) ).
thf(f2882,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) ),
inference(rectify,[],[f135]) ).
thf(f135,axiom,
! [X86: real,X87: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X86),X87) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X87),X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(f6259,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ),
inference(definition_unfolding,[],[f4748,f5969]) ).
thf(f4748,plain,
! [X0: nat,X1: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2881]) ).
thf(f2881,plain,
! [X0: nat,X1: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ),
inference(rectify,[],[f965]) ).
thf(f965,axiom,
! [X191: nat,X192: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X191),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X191),X192)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_diff__add__0) ).
thf(f4746,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit0,X1) ),
inference(cnf_transformation,[],[f2879]) ).
thf(f2879,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit0,X1) ),
inference(rectify,[],[f197]) ).
thf(f197,axiom,
! [X18: int,X38: int] : ( vAPP(int,int,bit1,X18) != vAPP(int,int,bit0,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rel__simps_I50_J) ).
thf(f6258,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4745,f4404]) ).
thf(f4745,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f1440]) ).
thf(f1440,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(fool_elimination,[],[f1439]) ).
thf(f1439,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),
inference(rectify,[],[f220]) ).
thf(f220,axiom,
! [X16: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X16),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_power2__ge__self) ).
thf(f6257,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4744,f4404]) ).
thf(f4744,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f1438]) ).
thf(f1438,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(fool_elimination,[],[f1437]) ).
thf(f1437,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),
inference(rectify,[],[f445]) ).
thf(f445,axiom,
! [X253: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X253),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_zero__le__power2) ).
thf(f6256,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4743,f5970,f4404]) ).
thf(f4743,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f1436]) ).
thf(f1436,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(fool_elimination,[],[f1435]) ).
thf(f1435,plain,
! [X0: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),
inference(rectify,[],[f444]) ).
thf(f444,axiom,
! [X253: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X253),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_zero__le__power2) ).
thf(f6255,plain,
! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)) ),
inference(definition_unfolding,[],[f4742,f5973,f4404]) ).
thf(f4742,plain,
! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)) ),
inference(cnf_transformation,[],[f1434]) ).
thf(f1434,plain,
! [X0: nat] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)) ),
inference(fool_elimination,[],[f1433]) ).
thf(f1433,plain,
! [X0: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),
inference(rectify,[],[f872]) ).
thf(f872,axiom,
! [X191: nat] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X191)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_two__realpow__ge__one) ).
thf(f4741,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0))) ),
inference(cnf_transformation,[],[f1432]) ).
thf(f1432,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0))) ),
inference(fool_elimination,[],[f1431]) ).
thf(f1431,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0))),
inference(rectify,[],[f1024]) ).
thf(f1024,axiom,
! [X192: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X192))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_le__cube) ).
thf(f4740,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0)) ),
inference(cnf_transformation,[],[f1430]) ).
thf(f1430,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0)) ),
inference(fool_elimination,[],[f1429]) ).
thf(f1429,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0)),
inference(rectify,[],[f1025]) ).
thf(f1025,axiom,
! [X192: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X192),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),X192)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_le__square) ).
thf(f4737,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X0) ),
inference(cnf_transformation,[],[f1424]) ).
thf(f1424,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X0) ),
inference(fool_elimination,[],[f1423]) ).
thf(f1423,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X0),zero_zero_int),X0),
inference(rectify,[],[f644]) ).
thf(f644,axiom,
! [X192: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,X192),zero_zero_int),X192),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_zcong__id) ).
thf(f4736,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X0) ),
inference(cnf_transformation,[],[f1422]) ).
thf(f1422,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X0) ),
inference(fool_elimination,[],[f1421]) ).
thf(f1421,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),X0),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X14: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zle__refl) ).
thf(f4735,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X0) ),
inference(cnf_transformation,[],[f1420]) ).
thf(f1420,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X0) ),
inference(fool_elimination,[],[f1419]) ).
thf(f1419,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),X0),
inference(rectify,[],[f681]) ).
thf(f681,axiom,
! [X346: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X346),X346),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_dvd__refl) ).
thf(f4734,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
inference(cnf_transformation,[],[f1418]) ).
thf(f1418,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
inference(fool_elimination,[],[f1417]) ).
thf(f1417,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0),
inference(rectify,[],[f938]) ).
thf(f938,axiom,
! [X191: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),X191),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_le__refl) ).
thf(f4732,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X0) ),
inference(cnf_transformation,[],[f1414]) ).
thf(f1414,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X0) ),
inference(fool_elimination,[],[f1413]) ).
thf(f1413,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),X0),
inference(rectify,[],[f680]) ).
thf(f680,axiom,
! [X346: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X346),X346),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_dvd__refl) ).
thf(f4731,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X0) ),
inference(cnf_transformation,[],[f1412]) ).
thf(f1412,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X0) ),
inference(fool_elimination,[],[f1411]) ).
thf(f1411,plain,
! [X0: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X0),X0),
inference(rectify,[],[f881]) ).
thf(f881,axiom,
! [X14: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_real__le__refl) ).
thf(f4730,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X0) ),
inference(cnf_transformation,[],[f1410]) ).
thf(f1410,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X0) ),
inference(fool_elimination,[],[f1409]) ).
thf(f1409,plain,
! [X0: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),X0),
inference(rectify,[],[f679]) ).
thf(f679,axiom,
! [X346: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X346),X346),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_dvd__refl) ).
thf(f4729,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),zero_zero_int) ),
inference(cnf_transformation,[],[f1408]) ).
thf(f1408,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),zero_zero_int) ),
inference(fool_elimination,[],[f1407]) ).
thf(f1407,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X0),zero_zero_int),
inference(rectify,[],[f675]) ).
thf(f675,axiom,
! [X343: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X343),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_dvd__0__right) ).
thf(f7575,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,bit1,zero_zero_int)),X0) ),
inference(forward_demodulation,[],[f6253,f4464]) ).
thf(f6253,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4728,f5971]) ).
thf(f4728,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,one_one_int),X0) ),
inference(cnf_transformation,[],[f1406]) ).
thf(f1406,plain,
! [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,one_one_int),X0) ),
inference(fool_elimination,[],[f1405]) ).
thf(f1405,plain,
! [X0: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,one_one_int),X0),
inference(rectify,[],[f759]) ).
thf(f759,axiom,
! [X398: int] : vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,one_one_int),X398),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_one__dvd) ).
thf(f6251,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(definition_unfolding,[],[f4726,f5969]) ).
thf(f4726,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f1402]) ).
thf(f1402,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ),
inference(fool_elimination,[],[f1401]) ).
thf(f1401,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat),
inference(rectify,[],[f674]) ).
thf(f674,axiom,
! [X343: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X343),zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_dvd__0__right) ).
thf(f6249,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ),
inference(definition_unfolding,[],[f4724,f5969]) ).
thf(f4724,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f1398]) ).
thf(f1398,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0) ),
inference(fool_elimination,[],[f1397]) ).
thf(f1397,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X0),
inference(rectify,[],[f967]) ).
thf(f967,axiom,
! [X191: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,zero_zero_nat),X191),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_less__eq__nat_Osimps_I1_J) ).
thf(f6247,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4722,f5972]) ).
thf(f4722,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ),
inference(cnf_transformation,[],[f1394]) ).
thf(f1394,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ),
inference(fool_elimination,[],[f1393]) ).
thf(f1393,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0),
inference(rectify,[],[f1125]) ).
thf(f1125,axiom,
! [X2: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(f6246,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4721,f5970]) ).
thf(f4721,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),zero_zero_real) ),
inference(cnf_transformation,[],[f1392]) ).
thf(f1392,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),zero_zero_real) ),
inference(fool_elimination,[],[f1391]) ).
thf(f1391,plain,
! [X0: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X0),zero_zero_real),
inference(rectify,[],[f673]) ).
thf(f673,axiom,
! [X343: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,X343),zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_dvd__0__right) ).
thf(f6245,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4720,f5973]) ).
thf(f4720,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,one_one_real),X0) ),
inference(cnf_transformation,[],[f1390]) ).
thf(f1390,plain,
! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,one_one_real),X0) ),
inference(fool_elimination,[],[f1389]) ).
thf(f1389,plain,
! [X0: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,one_one_real),X0),
inference(rectify,[],[f757]) ).
thf(f757,axiom,
! [X398: real] : vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,one_one_real),X398),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_one__dvd) ).
thf(f6244,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),zero_zero_int) ),
inference(definition_unfolding,[],[f4719,f4404]) ).
thf(f4719,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int) ),
inference(cnf_transformation,[],[f2878]) ).
thf(f2878,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int) ),
inference(flattening,[],[f1388]) ).
thf(f1388,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int) ),
inference(fool_elimination,[],[f1387]) ).
thf(f1387,plain,
! [X0: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int),
inference(rectify,[],[f453]) ).
thf(f453,axiom,
! [X258: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X258),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_power2__less__0) ).
thf(f6243,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4718,f4404,f5970]) ).
thf(f4718,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_real) ),
inference(cnf_transformation,[],[f2877]) ).
thf(f2877,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_real) ),
inference(flattening,[],[f1386]) ).
thf(f1386,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_real) ),
inference(fool_elimination,[],[f1385]) ).
thf(f1385,plain,
! [X0: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_real),
inference(rectify,[],[f452]) ).
thf(f452,axiom,
! [X258: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X258),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_power2__less__0) ).
thf(f4714,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(cnf_transformation,[],[f2873]) ).
thf(f2873,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(flattening,[],[f1378]) ).
thf(f1378,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
inference(fool_elimination,[],[f1377]) ).
thf(f1377,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0),
inference(rectify,[],[f892]) ).
thf(f892,axiom,
! [X191: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X191),X191),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_less__irrefl__nat) ).
thf(f6239,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(definition_unfolding,[],[f4711,f5969]) ).
thf(f4711,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f2870]) ).
thf(f2870,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) ),
inference(flattening,[],[f1372]) ).
thf(f1372,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat) ),
inference(fool_elimination,[],[f1371]) ).
thf(f1371,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),zero_zero_nat),
inference(rectify,[],[f879]) ).
thf(f879,axiom,
! [X191: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X191),zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_878_less__zeroE) ).
thf(f6238,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(definition_unfolding,[],[f4709,f5972,f5972]) ).
thf(f4709,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ),
inference(cnf_transformation,[],[f3237]) ).
thf(f3237,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ),
inference(ennf_transformation,[],[f2868]) ).
thf(f2868,plain,
! [X0: nat] :
~ ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ),
inference(flattening,[],[f1368]) ).
thf(f1368,plain,
! [X0: nat] :
~ ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ),
inference(fool_elimination,[],[f1367]) ).
thf(f1367,plain,
! [X0: nat] :
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ),
inference(rectify,[],[f1124]) ).
thf(f1124,axiom,
! [X2: nat] :
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),one_one_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot) ).
thf(f6237,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(definition_unfolding,[],[f4708,f5969,f5969]) ).
thf(f4708,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ),
inference(cnf_transformation,[],[f3236]) ).
thf(f3236,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ),
inference(ennf_transformation,[],[f2867]) ).
thf(f2867,plain,
! [X0: nat] :
~ ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ),
inference(flattening,[],[f1366]) ).
thf(f1366,plain,
! [X0: nat] :
~ ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ),
inference(fool_elimination,[],[f1365]) ).
thf(f1365,plain,
! [X0: nat] :
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f1123]) ).
thf(f1123,axiom,
! [X2: nat] :
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),zero_zero_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less) ).
thf(f7573,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int),
inference(forward_demodulation,[],[f7572,f6054]) ).
thf(f7572,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),zero_zero_int)),
inference(forward_demodulation,[],[f6786,f6100]) ).
thf(f6786,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),
inference(equality_resolution,[],[f6236]) ).
thf(f6236,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f4706,f4404]) ).
thf(f4706,plain,
! [X0: int] :
( ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f4124]) ).
thf(f4124,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( zero_zero_int = X0 ) )
& ( ( zero_zero_int != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ) ),
inference(nnf_transformation,[],[f1364]) ).
thf(f1364,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
<=> ( zero_zero_int != X0 ) ),
inference(fool_elimination,[],[f1363]) ).
thf(f1363,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
<=> ( zero_zero_int != X0 ) ),
inference(rectify,[],[f455]) ).
thf(f455,axiom,
! [X259: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X259),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
<=> ( zero_zero_int != X259 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_zero__less__power2) ).
thf(f6235,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) )
| ( zero_zero_int = X0 ) ),
inference(definition_unfolding,[],[f4707,f4404]) ).
thf(f4707,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f4124]) ).
thf(f7570,plain,
$true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,zero_zero_int)),
inference(forward_demodulation,[],[f7569,f6042]) ).
thf(f7569,plain,
$true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,zero_zero_int))),
inference(forward_demodulation,[],[f6785,f6097]) ).
thf(f6785,plain,
$true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),
inference(equality_resolution,[],[f6234]) ).
thf(f6234,plain,
! [X0: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f4704,f5970,f5970,f4404]) ).
thf(f4704,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
inference(cnf_transformation,[],[f4123]) ).
thf(f4123,plain,
! [X0: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( zero_zero_real = X0 ) )
& ( ( zero_zero_real != X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ) ),
inference(nnf_transformation,[],[f1362]) ).
thf(f1362,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
<=> ( zero_zero_real != X0 ) ),
inference(fool_elimination,[],[f1361]) ).
thf(f1361,plain,
! [X0: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
<=> ( zero_zero_real != X0 ) ),
inference(rectify,[],[f454]) ).
thf(f454,axiom,
! [X259: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X259),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))))
<=> ( zero_zero_real != X259 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_zero__less__power2) ).
thf(f6233,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4705,f5970,f4404,f5970]) ).
thf(f4705,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( zero_zero_real = X0 ) ),
inference(cnf_transformation,[],[f4123]) ).
thf(f7135,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6231]) ).
thf(f6231,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4701,f5970,f5970]) ).
thf(f4701,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ),
inference(cnf_transformation,[],[f1356]) ).
thf(f1356,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ),
inference(fool_elimination,[],[f1355]) ).
thf(f1355,plain,
! [X0: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real)
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ),
inference(rectify,[],[f385]) ).
thf(f385,axiom,
! [X228: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X228),X228)),zero_zero_real)
<=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X228),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_even__less__0__iff) ).
thf(f7134,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6231]) ).
thf(f7139,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6230]) ).
thf(f6230,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),zero_zero_int) ),
inference(definition_unfolding,[],[f4699,f4404,f4404]) ).
thf(f4699,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),pls) ),
inference(cnf_transformation,[],[f1352]) ).
thf(f1352,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),pls) ),
inference(fool_elimination,[],[f1351]) ).
thf(f1351,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X18)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rel__simps_I12_J) ).
thf(f7138,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6230]) ).
thf(f7141,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),min) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),min) ) ),
inference(binary_proxy_clausification,[],[f4698]) ).
thf(f4698,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),min) ),
inference(cnf_transformation,[],[f1350]) ).
thf(f1350,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),min) ),
inference(fool_elimination,[],[f1349]) ).
thf(f1349,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),min) ),
inference(rectify,[],[f529]) ).
thf(f529,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X18)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),min) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_rel__simps_I13_J) ).
thf(f7140,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,X0)),min) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),min) ) ),
inference(binary_proxy_clausification,[],[f4698]) ).
thf(f7145,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6229]) ).
thf(f6229,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ),
inference(definition_unfolding,[],[f4696,f4404,f4404]) ).
thf(f4696,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),pls) ),
inference(cnf_transformation,[],[f1346]) ).
thf(f1346,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),pls) ),
inference(fool_elimination,[],[f1345]) ).
thf(f1345,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ),
inference(rectify,[],[f152]) ).
thf(f152,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X18)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rel__simps_I10_J) ).
thf(f7144,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6229]) ).
thf(f7147,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),min) ) ),
inference(binary_proxy_clausification,[],[f4695]) ).
thf(f4695,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),min) ),
inference(cnf_transformation,[],[f1344]) ).
thf(f1344,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),min) ),
inference(fool_elimination,[],[f1343]) ).
thf(f1343,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ),
inference(rectify,[],[f551]) ).
thf(f551,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X18)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),min) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_rel__simps_I11_J) ).
thf(f7146,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,X0)),min) ) ),
inference(binary_proxy_clausification,[],[f4695]) ).
thf(f7153,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6226]) ).
thf(f6226,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),zero_zero_int) ),
inference(definition_unfolding,[],[f4692,f4404,f4404]) ).
thf(f4692,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),pls) ),
inference(cnf_transformation,[],[f1338]) ).
thf(f1338,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),pls) ),
inference(fool_elimination,[],[f1337]) ).
thf(f1337,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X18)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X18),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J) ).
thf(f7152,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6226]) ).
thf(f7155,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),min) ) ),
inference(binary_proxy_clausification,[],[f4691]) ).
thf(f4691,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),min) ),
inference(cnf_transformation,[],[f1336]) ).
thf(f1336,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),min) ),
inference(fool_elimination,[],[f1335]) ).
thf(f1335,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ),
inference(rectify,[],[f535]) ).
thf(f535,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X18)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),min) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_rel__simps_I30_J) ).
thf(f7154,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,X0)),min) ) ),
inference(binary_proxy_clausification,[],[f4691]) ).
thf(f7157,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6225]) ).
thf(f6225,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),zero_zero_int) ),
inference(definition_unfolding,[],[f4690,f4404,f4404]) ).
thf(f4690,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),pls) ),
inference(cnf_transformation,[],[f1334]) ).
thf(f1334,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),pls) ),
inference(fool_elimination,[],[f1333]) ).
thf(f1333,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ),
inference(rectify,[],[f157]) ).
thf(f157,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X18)),pls)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rel__simps_I27_J) ).
thf(f7156,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),zero_zero_int) ) ),
inference(binary_proxy_clausification,[],[f6225]) ).
thf(f7159,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),min) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ) ),
inference(binary_proxy_clausification,[],[f4689]) ).
thf(f4689,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ),
inference(cnf_transformation,[],[f1332]) ).
thf(f1332,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),min) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ),
inference(fool_elimination,[],[f1331]) ).
thf(f1331,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ),
inference(rectify,[],[f539]) ).
thf(f539,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X18)),min)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X18),min) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_rel__simps_I28_J) ).
thf(f7158,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,X0)),min) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),min) ) ),
inference(binary_proxy_clausification,[],[f4689]) ).
thf(f7169,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,X0)) ) ),
inference(binary_proxy_clausification,[],[f6220]) ).
thf(f6220,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,X0)) ),
inference(definition_unfolding,[],[f4684,f4404,f4404]) ).
thf(f4684,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit0,X0)) ),
inference(cnf_transformation,[],[f1322]) ).
thf(f1322,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit0,X0)) ),
inference(fool_elimination,[],[f1321]) ).
thf(f1321,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit0,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),vAPP(int,int,bit0,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rel__simps_I4_J) ).
thf(f7168,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,X0)) ) ),
inference(binary_proxy_clausification,[],[f6220]) ).
thf(f7173,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit1,X0)) ) ),
inference(binary_proxy_clausification,[],[f4682]) ).
thf(f4682,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit1,X0)) ),
inference(cnf_transformation,[],[f1318]) ).
thf(f1318,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit1,X0)) ),
inference(fool_elimination,[],[f1317]) ).
thf(f1317,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit1,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ),
inference(rectify,[],[f530]) ).
thf(f530,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit1,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_rel__simps_I9_J) ).
thf(f7172,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit1,X0)) ) ),
inference(binary_proxy_clausification,[],[f4682]) ).
thf(f7175,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit0,X0)) ) ),
inference(binary_proxy_clausification,[],[f4681]) ).
thf(f4681,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit0,X0)) ),
inference(cnf_transformation,[],[f1316]) ).
thf(f1316,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit0,X0)) ),
inference(fool_elimination,[],[f1315]) ).
thf(f1315,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit0,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ),
inference(rectify,[],[f533]) ).
thf(f533,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit0,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_rel__simps_I8_J) ).
thf(f7174,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),vAPP(int,int,bit0,X0)) ) ),
inference(binary_proxy_clausification,[],[f4681]) ).
thf(f7185,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit1,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),X0) ) ),
inference(binary_proxy_clausification,[],[f4676]) ).
thf(f4676,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit1,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),X0) ),
inference(cnf_transformation,[],[f1306]) ).
thf(f1306,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit1,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),X0) ),
inference(fool_elimination,[],[f1305]) ).
thf(f1305,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit1,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),X0) ),
inference(rectify,[],[f536]) ).
thf(f536,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit1,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_rel__simps_I26_J) ).
thf(f7184,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit1,X0)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),X0) ) ),
inference(binary_proxy_clausification,[],[f4676]) ).
thf(f7187,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit0,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ) ),
inference(binary_proxy_clausification,[],[f4675]) ).
thf(f4675,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit0,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ),
inference(cnf_transformation,[],[f1304]) ).
thf(f1304,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit0,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ),
inference(fool_elimination,[],[f1303]) ).
thf(f1303,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit0,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ),
inference(rectify,[],[f550]) ).
thf(f550,axiom,
! [X18: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit0,X18))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_rel__simps_I25_J) ).
thf(f7186,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),vAPP(int,int,bit0,X0)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),X0) ) ),
inference(binary_proxy_clausification,[],[f4675]) ).
thf(f7189,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,X0)) ) ),
inference(binary_proxy_clausification,[],[f6214]) ).
thf(f6214,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,X0)) ),
inference(definition_unfolding,[],[f4674,f4404,f5969]) ).
thf(f4674,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) ),
inference(cnf_transformation,[],[f1302]) ).
thf(f1302,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) ),
inference(fool_elimination,[],[f1301]) ).
thf(f1301,plain,
! [X0: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) ),
inference(rectify,[],[f560]) ).
thf(f560,axiom,
! [X40: int] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X40))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_less__0__number__of) ).
thf(f7188,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,X0)) ) ),
inference(binary_proxy_clausification,[],[f6214]) ).
thf(f7191,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6213]) ).
thf(f6213,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4673,f5970,f4404]) ).
thf(f4673,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),zero_zero_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ),
inference(cnf_transformation,[],[f1300]) ).
thf(f1300,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),zero_zero_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ),
inference(fool_elimination,[],[f1299]) ).
thf(f1299,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),zero_zero_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),pls) ),
inference(rectify,[],[f433]) ).
thf(f433,axiom,
! [X249: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X249)),zero_zero_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X249),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_less__special_I3_J) ).
thf(f7190,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),zero_zero_int) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6213]) ).
thf(f7193,plain,
! [X0: int] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6212]) ).
thf(f6212,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,zero_zero_int)) ),
inference(definition_unfolding,[],[f4672,f5973,f4404]) ).
thf(f4672,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),one_one_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,pls)) ),
inference(cnf_transformation,[],[f1298]) ).
thf(f1298,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),one_one_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,pls)) ),
inference(fool_elimination,[],[f1297]) ).
thf(f1297,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),one_one_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,pls)) ),
inference(rectify,[],[f164]) ).
thf(f164,axiom,
! [X97: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X97)),one_one_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X97),vAPP(int,int,bit1,pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_less__special_I4_J) ).
thf(f7192,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6212]) ).
thf(f7195,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6211]) ).
thf(f6211,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4671,f4404,f5970]) ).
thf(f4671,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f1296]) ).
thf(f1296,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),zero_zero_real) ),
inference(fool_elimination,[],[f1295]) ).
thf(f1295,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),zero_zero_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) ),
inference(rectify,[],[f436]) ).
thf(f436,axiom,
! [X251: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X251)),zero_zero_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X251),pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_le__special_I3_J) ).
thf(f7194,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6211]) ).
thf(f7197,plain,
! [X0: int] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6210]) ).
thf(f6210,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,zero_zero_int)) ),
inference(definition_unfolding,[],[f4670,f5973,f4404]) ).
thf(f4670,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),one_one_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,pls)) ),
inference(cnf_transformation,[],[f1294]) ).
thf(f1294,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),one_one_real) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,pls)) ),
inference(fool_elimination,[],[f1293]) ).
thf(f1293,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),one_one_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,pls)) ),
inference(rectify,[],[f168]) ).
thf(f168,axiom,
! [X99: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X99)),one_one_real)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X99),vAPP(int,int,bit1,pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_le__special_I4_J) ).
thf(f7196,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(binary_proxy_clausification,[],[f6210]) ).
thf(f7199,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f6209]) ).
thf(f6209,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0)) ),
inference(definition_unfolding,[],[f4669,f5970,f4404]) ).
thf(f4669,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) ),
inference(cnf_transformation,[],[f1292]) ).
thf(f1292,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) ),
inference(fool_elimination,[],[f1291]) ).
thf(f1291,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X0) ),
inference(rectify,[],[f431]) ).
thf(f431,axiom,
! [X248: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(int,real,number267125858f_real,X248))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),X248) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_less__special_I1_J) ).
thf(f7198,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f6209]) ).
thf(f7201,plain,
! [X0: int] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) ) ),
inference(binary_proxy_clausification,[],[f6208]) ).
thf(f6208,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) ),
inference(definition_unfolding,[],[f4668,f5973,f4404]) ).
thf(f4668,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,pls)),X0) ),
inference(cnf_transformation,[],[f1290]) ).
thf(f1290,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,pls)),X0) ),
inference(fool_elimination,[],[f1289]) ).
thf(f1289,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(int,real,number267125858f_real,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,pls)),X0) ),
inference(rectify,[],[f166]) ).
thf(f166,axiom,
! [X98: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,one_one_real),vAPP(int,real,number267125858f_real,X98))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,pls)),X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_less__special_I2_J) ).
thf(f7200,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) ) ),
inference(binary_proxy_clausification,[],[f6208]) ).
thf(f7203,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $false )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f6207]) ).
thf(f6207,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0)) ),
inference(definition_unfolding,[],[f4667,f5970,f4404]) ).
thf(f4667,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) ),
inference(cnf_transformation,[],[f1288]) ).
thf(f1288,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) ),
inference(fool_elimination,[],[f1287]) ).
thf(f1287,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X0) ),
inference(rectify,[],[f434]) ).
thf(f434,axiom,
! [X250: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,zero_zero_real),vAPP(int,real,number267125858f_real,X250))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),X250) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_le__special_I1_J) ).
thf(f7202,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f6207]) ).
thf(f7205,plain,
! [X0: int] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X0) ) ),
inference(binary_proxy_clausification,[],[f6206]) ).
thf(f6206,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X0) ),
inference(definition_unfolding,[],[f4666,f5973,f4404]) ).
thf(f4666,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,pls)),X0) ),
inference(cnf_transformation,[],[f1286]) ).
thf(f1286,plain,
! [X0: int] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,pls)),X0) ),
inference(fool_elimination,[],[f1285]) ).
thf(f1285,plain,
! [X0: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(int,real,number267125858f_real,X0))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,pls)),X0) ),
inference(rectify,[],[f170]) ).
thf(f170,axiom,
! [X100: int] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,one_one_real),vAPP(int,real,number267125858f_real,X100))
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,pls)),X100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_le__special_I2_J) ).
thf(f7204,plain,
! [X0: int] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_eq_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X0) ) ),
inference(binary_proxy_clausification,[],[f6206]) ).
thf(f7538,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(forward_demodulation,[],[f7207,f4464]) ).
thf(f7207,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(binary_proxy_clausification,[],[f6205]) ).
thf(f6205,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4665,f5971]) ).
thf(f4665,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0) ),
inference(cnf_transformation,[],[f1284]) ).
thf(f1284,plain,
! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0) ),
inference(fool_elimination,[],[f1283]) ).
thf(f1283,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X0)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ),
inference(rectify,[],[f427]) ).
thf(f427,axiom,
! [X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,one_one_int),X15)
<=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_int__one__le__iff__zero__less) ).
thf(f7537,plain,
! [X0: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(forward_demodulation,[],[f7206,f4464]) ).
thf(f7206,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(binary_proxy_clausification,[],[f6205]) ).
thf(f6204,plain,
! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4663,f5969,f5969]) ).
thf(f4663,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f4122]) ).
thf(f4122,plain,
! [X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
| ( zero_zero_nat != X0 ) )
& ( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) ) ) ),
inference(nnf_transformation,[],[f1282]) ).
thf(f1282,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
<=> ( zero_zero_nat = X0 ) ),
inference(fool_elimination,[],[f1281]) ).
thf(f1281,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat)
<=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f966]) ).
thf(f966,axiom,
! [X191: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X191),zero_zero_nat)
<=> ( zero_zero_nat = X191 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_le__0__eq) ).
thf(f6784,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,zero_zero_int)),
inference(equality_resolution,[],[f6203]) ).
thf(f6203,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X0 ) ),
inference(definition_unfolding,[],[f4664,f5969,f5969]) ).
thf(f4664,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),zero_zero_nat) )
| ( zero_zero_nat != X0 ) ),
inference(cnf_transformation,[],[f4122]) ).
thf(f6783,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(equality_resolution,[],[f6201]) ).
thf(f6201,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) != X0 ) ),
inference(definition_unfolding,[],[f4662,f5972,f5972]) ).
thf(f4662,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
| ( one_one_nat != X0 ) ),
inference(cnf_transformation,[],[f4121]) ).
thf(f4121,plain,
! [X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
| ( one_one_nat != X0 ) )
& ( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ) ),
inference(nnf_transformation,[],[f1280]) ).
thf(f1280,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
<=> ( one_one_nat = X0 ) ),
inference(fool_elimination,[],[f1279]) ).
thf(f1279,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat)
<=> ( one_one_nat = X0 ) ),
inference(rectify,[],[f1020]) ).
thf(f1020,axiom,
! [X192: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X192),one_one_nat)
<=> ( one_one_nat = X192 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_nat__dvd__1__iff__1) ).
thf(f6782,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(equality_resolution,[],[f6199]) ).
thf(f6199,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) != X0 ) ),
inference(definition_unfolding,[],[f4660,f5972,f5972]) ).
thf(f4660,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
| ( one_one_nat != X0 ) ),
inference(cnf_transformation,[],[f4120]) ).
thf(f4120,plain,
! [X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
| ( one_one_nat != X0 ) )
& ( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ) ),
inference(nnf_transformation,[],[f1278]) ).
thf(f1278,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
<=> ( one_one_nat = X0 ) ),
inference(fool_elimination,[],[f1277]) ).
thf(f1277,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat)
<=> ( one_one_nat = X0 ) ),
inference(rectify,[],[f1127]) ).
thf(f1127,axiom,
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),one_one_nat)
<=> ( one_one_nat = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique) ).
thf(f6781,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,zero_zero_int)),
inference(equality_resolution,[],[f6197]) ).
thf(f6197,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X0 ) ),
inference(definition_unfolding,[],[f4658,f5969,f5969]) ).
thf(f4658,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
| ( zero_zero_nat != X0 ) ),
inference(cnf_transformation,[],[f4119]) ).
thf(f4119,plain,
! [X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
| ( zero_zero_nat != X0 ) )
& ( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ) ),
inference(nnf_transformation,[],[f1276]) ).
thf(f1276,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
<=> ( zero_zero_nat = X0 ) ),
inference(fool_elimination,[],[f1275]) ).
thf(f1275,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0)
<=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f1120]) ).
thf(f1120,axiom,
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X2)
<=> ( zero_zero_nat = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique) ).
thf(f7519,plain,
! [X2: int,X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X2 )
| ( X0 = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f6195,f4464]) ).
thf(f6195,plain,
! [X2: int,X0: int] :
( ( X0 = X2 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(definition_unfolding,[],[f4652,f5971]) ).
thf(f4652,plain,
! [X2: int,X0: int] :
( ( X0 = X2 )
| ( one_one_int = X2 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X2),X0) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X2) != $true )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(cnf_transformation,[],[f4118]) ).
thf(f7518,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,sK13,X0)) ) ),
inference(forward_demodulation,[],[f6194,f4464]) ).
thf(f6194,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,sK13,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(definition_unfolding,[],[f4653,f5971]) ).
thf(f4653,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,sK13,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(cnf_transformation,[],[f4118]) ).
thf(f7517,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK13,X0)),X0) ) ),
inference(forward_demodulation,[],[f6193,f4464]) ).
thf(f6193,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK13,X0)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(definition_unfolding,[],[f4654,f5971]) ).
thf(f4654,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK13,X0)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(cnf_transformation,[],[f4118]) ).
thf(f7516,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( vAPP(int,int,sK13,X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( $true = vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f7515,f4464]) ).
thf(f7515,plain,
! [X0: int] :
( ( vAPP(int,int,sK13,X0) != vAPP(int,int,bit1,zero_zero_int) )
| ( $true = vAPP(int,$o,zprime,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(forward_demodulation,[],[f6192,f4464]) ).
thf(f6192,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( vAPP(int,int,sK13,X0) != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(definition_unfolding,[],[f4655,f5971,f5971]) ).
thf(f4655,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( one_one_int != vAPP(int,int,sK13,X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(cnf_transformation,[],[f4118]) ).
thf(f7514,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,zprime,X0) )
| ( vAPP(int,int,sK13,X0) != X0 ) ),
inference(forward_demodulation,[],[f6191,f4464]) ).
thf(f6191,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( vAPP(int,int,sK13,X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(definition_unfolding,[],[f4656,f5971]) ).
thf(f4656,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
| ( vAPP(int,int,sK13,X0) != X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(cnf_transformation,[],[f4118]) ).
thf(f4649,plain,
! [X0: int] :
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,vAPP(int,int,sK11,X0)),vAPP(int,int,sK12,X0))) = X0 )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) ) ),
inference(cnf_transformation,[],[f4113]) ).
thf(f4113,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ! [X1: int,X2: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) != X0 ) )
& ( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,vAPP(int,int,sK11,X0)),vAPP(int,int,sK12,X0))) = X0 )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f4111,f4112]) ).
thf(f4112,plain,
! [X0: int] :
( ? [X3: int,X4: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X3),X4)) = X0 )
=> ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,vAPP(int,int,sK11,X0)),vAPP(int,int,sK12,X0))) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f4111,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ! [X1: int,X2: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) != X0 ) )
& ( ? [X3: int,X4: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X3),X4)) = X0 )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) ) ) ),
inference(rectify,[],[f4110]) ).
thf(f4110,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ! [X1: int,X2: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) != X0 ) )
& ( ? [X1: int,X2: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) = X0 )
| ( $true != vAPP(int,$o,twoSqu919416604sum2sq,X0) ) ) ),
inference(nnf_transformation,[],[f1272]) ).
thf(f1272,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X0) )
<=> ? [X1: int,X2: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) = X0 ) ),
inference(fool_elimination,[],[f1271]) ).
thf(f1271,plain,
! [X0: int] :
( vAPP(int,$o,twoSqu919416604sum2sq,X0)
<=> ? [X1: int,X2: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) = X0 ) ),
inference(rectify,[],[f1061]) ).
thf(f1061,axiom,
! [X16: int] :
( vAPP(int,$o,twoSqu919416604sum2sq,X16)
<=> ? [X495: int,X496: int] : ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X495),X496)) = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_is__sum2sq__def) ).
thf(f6780,plain,
! [X2: int,X1: int] : ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2))) ),
inference(equality_resolution,[],[f4650]) ).
thf(f4650,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,X0) )
| ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,X1),X2)) != X0 ) ),
inference(cnf_transformation,[],[f4113]) ).
thf(f6190,plain,
! [X0: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) ) ),
inference(definition_unfolding,[],[f4647,f5970,f5970]) ).
thf(f4647,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) ) ),
inference(cnf_transformation,[],[f4109]) ).
thf(f4109,plain,
! [X0: real] :
( ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) )
| ( zero_zero_real != X0 ) )
& ( ( zero_zero_real = X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) ) ) ),
inference(nnf_transformation,[],[f2866]) ).
thf(f2866,plain,
! [X0: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) )
<=> ( zero_zero_real = X0 ) ),
inference(flattening,[],[f1270]) ).
thf(f1270,plain,
! [X0: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) )
<=> ( zero_zero_real = X0 ) ),
inference(fool_elimination,[],[f1269]) ).
thf(f1269,plain,
! [X0: real] :
( ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0))
<=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f528]) ).
thf(f528,axiom,
! [X16: real] :
( ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X16),X16))
<=> ( zero_zero_real = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_not__real__square__gt__zero) ).
thf(f7508,plain,
$true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,zero_zero_int)),
inference(forward_demodulation,[],[f6779,f6042]) ).
thf(f6779,plain,
$true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,zero_zero_int))),
inference(equality_resolution,[],[f6189]) ).
thf(f6189,plain,
! [X0: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) != X0 ) ),
inference(definition_unfolding,[],[f4648,f5970,f5970]) ).
thf(f4648,plain,
! [X0: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)) )
| ( zero_zero_real != X0 ) ),
inference(cnf_transformation,[],[f4109]) ).
thf(f6188,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4645,f4404]) ).
thf(f4645,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != zero_zero_int ) ),
inference(cnf_transformation,[],[f4108]) ).
thf(f4108,plain,
! [X0: int] :
( ( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = zero_zero_int )
| ( zero_zero_int != X0 ) )
& ( ( zero_zero_int = X0 )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) != zero_zero_int ) ) ),
inference(nnf_transformation,[],[f2865]) ).
thf(f2865,plain,
! [X0: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = zero_zero_int )
<=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f443]) ).
thf(f443,axiom,
! [X252: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X252),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
<=> ( zero_zero_int = X252 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_zero__eq__power2) ).
thf(f6778,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(equality_resolution,[],[f6187]) ).
thf(f6187,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ( zero_zero_int != X0 ) ),
inference(definition_unfolding,[],[f4646,f4404]) ).
thf(f4646,plain,
! [X0: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = zero_zero_int )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f4108]) ).
thf(f6186,plain,
! [X0: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4643,f5970,f5970,f4404]) ).
thf(f4643,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(cnf_transformation,[],[f4107]) ).
thf(f4107,plain,
! [X0: real] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( zero_zero_real != X0 ) )
& ( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ) ),
inference(nnf_transformation,[],[f2864]) ).
thf(f2864,plain,
! [X0: real] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
<=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f442]) ).
thf(f442,axiom,
! [X252: real] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X252),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
<=> ( zero_zero_real = X252 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_zero__eq__power2) ).
thf(f6777,plain,
vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(equality_resolution,[],[f6185]) ).
thf(f6185,plain,
! [X0: real] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) != X0 ) ),
inference(definition_unfolding,[],[f4644,f5970,f4404,f5970]) ).
thf(f4644,plain,
! [X0: real] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( zero_zero_real != X0 ) ),
inference(cnf_transformation,[],[f4107]) ).
thf(f7505,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(forward_demodulation,[],[f7504,f4464]) ).
thf(f7504,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(forward_demodulation,[],[f7503,f4464]) ).
thf(f7503,plain,
! [X0: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(forward_demodulation,[],[f6184,f4464]) ).
thf(f6184,plain,
! [X0: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4641,f5971,f4404,f4404]) ).
thf(f4641,plain,
! [X0: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(cnf_transformation,[],[f4106]) ).
thf(f4106,plain,
! [X0: int] :
( ( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) )
& ( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ) ),
inference(nnf_transformation,[],[f2863]) ).
thf(f2863,plain,
! [X0: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
<=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(rectify,[],[f1173]) ).
thf(f1173,axiom,
! [X16: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
<=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X16),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_neq__one__mod__two) ).
thf(f7501,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(forward_demodulation,[],[f7500,f4464]) ).
thf(f7500,plain,
! [X0: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(forward_demodulation,[],[f7499,f4464]) ).
thf(f7499,plain,
! [X0: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(forward_demodulation,[],[f6183,f4464]) ).
thf(f6183,plain,
! [X0: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4642,f4404,f5971,f4404]) ).
thf(f4642,plain,
! [X0: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(cnf_transformation,[],[f4106]) ).
thf(f4639,plain,
! [X0: int] :
( ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) )
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f4105]) ).
thf(f4105,plain,
! [X0: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) )
| ( zero_zero_int != X0 ) )
& ( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ) ) ),
inference(nnf_transformation,[],[f2862]) ).
thf(f2862,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) )
<=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f357]) ).
thf(f357,axiom,
! [X208: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X208),X208) )
<=> ( zero_zero_int = X208 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_double__eq__0__iff) ).
thf(f6182,plain,
! [X0: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) != vAPP(int,real,number267125858f_real,zero_zero_int) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4637,f5970,f5970]) ).
thf(f4637,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) ) ),
inference(cnf_transformation,[],[f4104]) ).
thf(f4104,plain,
! [X0: real] :
( ( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) )
| ( zero_zero_real != X0 ) )
& ( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) ) ) ),
inference(nnf_transformation,[],[f2861]) ).
thf(f2861,plain,
! [X0: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) )
<=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f358]) ).
thf(f358,axiom,
! [X208: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X208),X208) )
<=> ( zero_zero_real = X208 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_double__eq__0__iff) ).
thf(f6774,plain,
min = vAPP(int,int,bit1,min),
inference(equality_resolution,[],[f4636]) ).
thf(f4636,plain,
! [X0: int] :
( ( min = vAPP(int,int,bit1,X0) )
| ( min != X0 ) ),
inference(cnf_transformation,[],[f4103]) ).
thf(f4103,plain,
! [X0: int] :
( ( ( min = vAPP(int,int,bit1,X0) )
| ( min != X0 ) )
& ( ( min = X0 )
| ( min != vAPP(int,int,bit1,X0) ) ) ),
inference(nnf_transformation,[],[f2860]) ).
thf(f2860,plain,
! [X0: int] :
( ( min = vAPP(int,int,bit1,X0) )
<=> ( min = X0 ) ),
inference(rectify,[],[f519]) ).
thf(f519,axiom,
! [X18: int] :
( ( vAPP(int,int,bit1,X18) = min )
<=> ( min = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_rel__simps_I47_J) ).
thf(f4633,plain,
! [X0: int] :
( ( min != vAPP(int,int,bit1,X0) )
| ( min = X0 ) ),
inference(cnf_transformation,[],[f4102]) ).
thf(f4102,plain,
! [X0: int] :
( ( ( min = vAPP(int,int,bit1,X0) )
| ( min != X0 ) )
& ( ( min = X0 )
| ( min != vAPP(int,int,bit1,X0) ) ) ),
inference(nnf_transformation,[],[f2859]) ).
thf(f2859,plain,
! [X0: int] :
( ( min = vAPP(int,int,bit1,X0) )
<=> ( min = X0 ) ),
inference(rectify,[],[f520]) ).
thf(f520,axiom,
! [X38: int] :
( ( vAPP(int,int,bit1,X38) = min )
<=> ( min = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_rel__simps_I43_J) ).
thf(f6773,plain,
min = vAPP(int,int,bit1,min),
inference(equality_resolution,[],[f4634]) ).
thf(f4634,plain,
! [X0: int] :
( ( min = vAPP(int,int,bit1,X0) )
| ( min != X0 ) ),
inference(cnf_transformation,[],[f4102]) ).
thf(f6178,plain,
! [X0: int] :
( ( vAPP(int,nat,number_number_of_nat,X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4629,f4404,f5969]) ).
thf(f4629,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),pls) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ),
inference(cnf_transformation,[],[f4100]) ).
thf(f6772,plain,
zero_zero_int = vAPP(int,int,bit0,zero_zero_int),
inference(equality_resolution,[],[f6175]) ).
thf(f6175,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(int,int,bit0,X0) )
| ( zero_zero_int != X0 ) ),
inference(definition_unfolding,[],[f4628,f4404,f4404]) ).
thf(f4628,plain,
! [X0: int] :
( ( pls = vAPP(int,int,bit0,X0) )
| ( pls != X0 ) ),
inference(cnf_transformation,[],[f4099]) ).
thf(f4099,plain,
! [X0: int] :
( ( ( pls = vAPP(int,int,bit0,X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != vAPP(int,int,bit0,X0) ) ) ),
inference(nnf_transformation,[],[f2858]) ).
thf(f2858,plain,
! [X0: int] :
( ( pls = vAPP(int,int,bit0,X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X18: int] :
( ( pls = vAPP(int,int,bit0,X18) )
<=> ( pls = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_rel__simps_I44_J) ).
thf(f6174,plain,
! [X0: int] :
( ( zero_zero_int != vAPP(int,int,bit0,X0) )
| ( zero_zero_int = X0 ) ),
inference(definition_unfolding,[],[f4625,f4404,f4404]) ).
thf(f4625,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != vAPP(int,int,bit0,X0) ) ),
inference(cnf_transformation,[],[f4098]) ).
thf(f4098,plain,
! [X0: int] :
( ( ( pls = vAPP(int,int,bit0,X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != vAPP(int,int,bit0,X0) ) ) ),
inference(nnf_transformation,[],[f2857]) ).
thf(f2857,plain,
! [X0: int] :
( ( pls = vAPP(int,int,bit0,X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f200]) ).
thf(f200,axiom,
! [X38: int] :
( ( pls = vAPP(int,int,bit0,X38) )
<=> ( pls = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_rel__simps_I38_J) ).
thf(f6771,plain,
zero_zero_int = vAPP(int,int,bit0,zero_zero_int),
inference(equality_resolution,[],[f6173]) ).
thf(f6173,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(int,int,bit0,X0) )
| ( zero_zero_int != X0 ) ),
inference(definition_unfolding,[],[f4626,f4404,f4404]) ).
thf(f4626,plain,
! [X0: int] :
( ( pls = vAPP(int,int,bit0,X0) )
| ( pls != X0 ) ),
inference(cnf_transformation,[],[f4098]) ).
thf(f6770,plain,
$true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,zero_zero_int)),
inference(equality_resolution,[],[f6171]) ).
thf(f6171,plain,
! [X0: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ) ),
inference(definition_unfolding,[],[f4624,f5969,f5969]) ).
thf(f4624,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(cnf_transformation,[],[f4097]) ).
thf(f4097,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ) ),
inference(nnf_transformation,[],[f1264]) ).
thf(f1264,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(fool_elimination,[],[f1263]) ).
thf(f1263,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f957]) ).
thf(f957,axiom,
! [X191: nat] :
( ( zero_zero_nat != X191 )
<=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_neq0__conv) ).
thf(f6170,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4620,f5969,f5969]) ).
thf(f4620,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f4096]) ).
thf(f4096,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) )
& ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) )
| ( zero_zero_nat = X0 ) ) ),
inference(flattening,[],[f4095]) ).
thf(f4095,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) )
& ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) )
| ( zero_zero_nat = X0 ) ) ),
inference(nnf_transformation,[],[f2856]) ).
thf(f2856,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
<=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) ) ),
inference(flattening,[],[f1262]) ).
thf(f1262,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
<=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) ) ),
inference(fool_elimination,[],[f1261]) ).
thf(f1261,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
<=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),zero_zero_nat) ) ),
inference(rectify,[],[f1121]) ).
thf(f1121,axiom,
! [X2: nat] :
( ( zero_zero_nat != X2 )
<=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),zero_zero_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_gcd__lcm__complete__lattice__nat_Oless__top) ).
thf(f6167,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X0 ) ),
inference(definition_unfolding,[],[f4617,f5972,f5972]) ).
thf(f4617,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) )
| ( one_one_nat = X0 ) ),
inference(cnf_transformation,[],[f4094]) ).
thf(f4094,plain,
! [X0: nat] :
( ( ( one_one_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) )
& ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) )
| ( one_one_nat = X0 ) ) ),
inference(flattening,[],[f4093]) ).
thf(f4093,plain,
! [X0: nat] :
( ( ( one_one_nat != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) )
& ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) )
| ( one_one_nat = X0 ) ) ),
inference(nnf_transformation,[],[f2855]) ).
thf(f2855,plain,
! [X0: nat] :
( ( one_one_nat != X0 )
<=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) ) ),
inference(flattening,[],[f1260]) ).
thf(f1260,plain,
! [X0: nat] :
( ( one_one_nat != X0 )
<=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) ) ),
inference(fool_elimination,[],[f1259]) ).
thf(f1259,plain,
! [X0: nat] :
( ( one_one_nat != X0 )
<=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X0) ) ),
inference(rectify,[],[f1126]) ).
thf(f1126,axiom,
! [X2: nat] :
( ( one_one_nat != X2 )
<=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),one_one_nat)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,one_one_nat),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_gcd__lcm__complete__lattice__nat_Obot__less) ).
thf(f7489,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(forward_demodulation,[],[f7488,f4464]) ).
thf(f7488,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(forward_demodulation,[],[f7487,f4464]) ).
thf(f7487,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(forward_demodulation,[],[f7486,f4464]) ).
thf(f7486,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(forward_demodulation,[],[f7485,f4464]) ).
thf(f7485,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(forward_demodulation,[],[f6164,f4464]) ).
thf(f6164,plain,
! [X0: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
inference(definition_unfolding,[],[f4616,f5971,f4404,f5971,f4404,f5971]) ).
thf(f4616,plain,
! [X0: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) ) ),
inference(cnf_transformation,[],[f3233]) ).
thf(f3233,plain,
! [X0: int] :
( ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) )
| ( $true != vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) ) ),
inference(ennf_transformation,[],[f1258]) ).
thf(f1258,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) )
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) ) ),
inference(fool_elimination,[],[f1257]) ).
thf(f1257,plain,
! [X0: int] :
( vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int))
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0)),one_one_int)) ) ),
inference(rectify,[],[f666]) ).
thf(f666,axiom,
! [X192: int] :
( vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X192)),one_one_int))
=> ( one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X192)),one_one_int)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_Legendre__1mod4) ).
thf(f7484,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,bit1,zero_zero_int)),min),X0) ) ),
inference(forward_demodulation,[],[f7483,f4464]) ).
thf(f7483,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,bit1,zero_zero_int)),min),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) ) ),
inference(forward_demodulation,[],[f7482,f4464]) ).
thf(f7482,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),min),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) ) ),
inference(forward_demodulation,[],[f6163,f4464]) ).
thf(f6163,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) ) ),
inference(definition_unfolding,[],[f4615,f5971,f4404]) ).
thf(f4615,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,one_one_int),vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0) ) ),
inference(cnf_transformation,[],[f3232]) ).
thf(f3232,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,one_one_int),vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0) ) ),
inference(ennf_transformation,[],[f2854]) ).
thf(f2854,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,one_one_int),vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(flattening,[],[f1256]) ).
thf(f1256,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0) )
=> ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,one_one_int),vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(fool_elimination,[],[f1255]) ).
thf(f1255,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,one_one_int),vAPP(int,int,number_number_of_int,min)),X0) ),
inference(rectify,[],[f609]) ).
thf(f609,axiom,
! [X192: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X192)
=> ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,one_one_int),vAPP(int,int,number_number_of_int,min)),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_one__not__neg__one__mod__m) ).
thf(f7477,plain,
! [X0: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,min),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(forward_demodulation,[],[f7476,f4464]) ).
thf(f7476,plain,
! [X0: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(forward_demodulation,[],[f6162,f4464]) ).
thf(f6162,plain,
! [X0: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(definition_unfolding,[],[f4612,f5971]) ).
thf(f4612,plain,
! [X0: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(cnf_transformation,[],[f3230]) ).
thf(f3230,plain,
! [X0: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) ) ),
inference(ennf_transformation,[],[f1252]) ).
thf(f1252,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(fool_elimination,[],[f1251]) ).
thf(f1251,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X0)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(rectify,[],[f1174]) ).
thf(f1174,axiom,
! [X3: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),X3)
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,vAPP(int,int,number_number_of_int,min)),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_zmod__minus1) ).
thf(f7475,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,zprime,vAPP(int,int,sK10,X0)) ) ),
inference(forward_demodulation,[],[f6161,f4464]) ).
thf(f6161,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,sK10,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(definition_unfolding,[],[f4610,f5971]) ).
thf(f4610,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,sK10,X0)) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(cnf_transformation,[],[f4092]) ).
thf(f4092,plain,
! [X0: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK10,X0)),X0) )
& ( $true = vAPP(int,$o,zprime,vAPP(int,int,sK10,X0)) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f3229,f4091]) ).
thf(f4091,plain,
! [X0: int] :
( ? [X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( $true = vAPP(int,$o,zprime,X1) ) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK10,X0)),X0) )
& ( $true = vAPP(int,$o,zprime,vAPP(int,int,sK10,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3229,plain,
! [X0: int] :
( ? [X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( $true = vAPP(int,$o,zprime,X1) ) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(ennf_transformation,[],[f1250]) ).
thf(f1250,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) )
=> ? [X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0) )
& ( $true = vAPP(int,$o,zprime,X1) ) ) ),
inference(fool_elimination,[],[f1249]) ).
thf(f1249,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0)
=> ? [X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X1),X0)
& vAPP(int,$o,zprime,X1) ) ),
inference(rectify,[],[f1068]) ).
thf(f1068,axiom,
! [X2: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X2)
=> ? [X498: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,X498),X2)
& vAPP(int,$o,zprime,X498) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_zprime__factor__exists) ).
thf(f7474,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK10,X0)),X0) ) ),
inference(forward_demodulation,[],[f6160,f4464]) ).
thf(f6160,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK10,X0)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ) ),
inference(definition_unfolding,[],[f4611,f5971]) ).
thf(f4611,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,sK10,X0)),X0) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),X0) ) ),
inference(cnf_transformation,[],[f4092]) ).
thf(f7473,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(forward_demodulation,[],[f6159,f4464]) ).
thf(f6159,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(definition_unfolding,[],[f4609,f5971]) ).
thf(f4609,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f3228]) ).
thf(f3228,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f1248]) ).
thf(f1248,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)) ) ),
inference(fool_elimination,[],[f1247]) ).
thf(f1247,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)) ),
inference(rectify,[],[f438]) ).
thf(f438,axiom,
! [X15: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X15)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_le__imp__0__less) ).
thf(f7472,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( zero_zero_int = X0 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(forward_demodulation,[],[f7471,f4464]) ).
thf(f7471,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,zero_zero_int) = X0 )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(forward_demodulation,[],[f6158,f4464]) ).
thf(f6158,plain,
! [X0: int] :
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(definition_unfolding,[],[f4608,f5971,f4404]) ).
thf(f4608,plain,
! [X0: int] :
( ( one_one_int = X0 )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(cnf_transformation,[],[f3227]) ).
thf(f3227,plain,
! [X0: int] :
( ( one_one_int = X0 )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(flattening,[],[f3226]) ).
thf(f3226,plain,
! [X0: int] :
( ( one_one_int = X0 )
| ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) != $true ) ),
inference(ennf_transformation,[],[f1246]) ).
thf(f1246,plain,
! [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) )
=> ( ( one_one_int = X0 )
| ( zero_zero_int = X0 ) ) ) ),
inference(fool_elimination,[],[f1245]) ).
thf(f1245,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))
=> ( ( one_one_int = X0 )
| ( zero_zero_int = X0 ) ) ) ),
inference(rectify,[],[f506]) ).
thf(f506,axiom,
! [X16: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X16)
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X16),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))
=> ( ( one_one_int = X16 )
| ( zero_zero_int = X16 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_int__pos__lt__two__imp__zero__or__one) ).
thf(f4607,plain,
! [X0: int] :
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0) )
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f3225]) ).
thf(f3225,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0) ) ),
inference(ennf_transformation,[],[f1244]) ).
thf(f1244,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0) )
=> ( zero_zero_int = X0 ) ),
inference(fool_elimination,[],[f1243]) ).
thf(f1243,plain,
! [X0: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X0)
=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f727]) ).
thf(f727,axiom,
! [X367: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),X367)
=> ( zero_zero_int = X367 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_dvd__0__left) ).
thf(f6157,plain,
! [X0: nat] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) ) ),
inference(definition_unfolding,[],[f4606,f5972,f5972]) ).
thf(f4606,plain,
! [X0: nat] :
( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ),
inference(cnf_transformation,[],[f3224]) ).
thf(f3224,plain,
! [X0: nat] :
( ( one_one_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) ) ),
inference(ennf_transformation,[],[f1242]) ).
thf(f1242,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat) )
=> ( one_one_nat = X0 ) ),
inference(fool_elimination,[],[f1241]) ).
thf(f1241,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X0),one_one_nat)
=> ( one_one_nat = X0 ) ),
inference(rectify,[],[f1128]) ).
thf(f1128,axiom,
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,X2),one_one_nat)
=> ( one_one_nat = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot) ).
thf(f6155,plain,
! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4604,f5969,f5969]) ).
thf(f4604,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ),
inference(cnf_transformation,[],[f3222]) ).
thf(f3222,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) ) ),
inference(ennf_transformation,[],[f1238]) ).
thf(f1238,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0) )
=> ( zero_zero_nat = X0 ) ),
inference(fool_elimination,[],[f1237]) ).
thf(f1237,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X0)
=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f1119]) ).
thf(f1119,axiom,
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,zero_zero_nat),X2)
=> ( zero_zero_nat = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_gcd__lcm__complete__lattice__nat_Otop__le) ).
thf(f6154,plain,
! [X0: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( vAPP(int,real,number267125858f_real,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4603,f5970,f5970]) ).
thf(f4603,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,zero_zero_real),X0) ) ),
inference(cnf_transformation,[],[f3221]) ).
thf(f3221,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,zero_zero_real),X0) ) ),
inference(ennf_transformation,[],[f1236]) ).
thf(f1236,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,zero_zero_real),X0) )
=> ( zero_zero_real = X0 ) ),
inference(fool_elimination,[],[f1235]) ).
thf(f1235,plain,
! [X0: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,zero_zero_real),X0)
=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f725]) ).
thf(f725,axiom,
! [X367: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),dvd_dvd_real,zero_zero_real),X367)
=> ( zero_zero_real = X367 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_dvd__0__left) ).
thf(f7470,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int)))),min),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f7469,f4464]) ).
thf(f7469,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),min),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f6153,f4464]) ).
thf(f6153,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(definition_unfolding,[],[f4602,f5971]) ).
thf(f4602,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))),vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(cnf_transformation,[],[f3220]) ).
thf(f3220,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))),vAPP(int,int,number_number_of_int,min)),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(ennf_transformation,[],[f1234]) ).
thf(f1234,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))),vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(fool_elimination,[],[f1233]) ).
thf(f1233,plain,
! [X0: int] :
( vAPP(int,$o,zprime,X0)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))),vAPP(int,int,number_number_of_int,min)),X0) ),
inference(rectify,[],[f1071]) ).
thf(f1071,axiom,
! [X163: int] :
( vAPP(int,$o,zprime,X163)
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),one_one_int))),vAPP(int,int,number_number_of_int,min)),X163) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_Wilson__Russ) ).
thf(f7468,plain,
! [X0: int] :
( ( vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f7467,f4464]) ).
thf(f7467,plain,
! [X0: int] :
( ( vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)) = X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = X0 )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f7466,f4464]) ).
thf(f7466,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = X0 )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f6152,f4464]) ).
thf(f6152,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = X0 )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(definition_unfolding,[],[f4601,f4404,f4404,f4404]) ).
thf(f4601,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = X0 )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(cnf_transformation,[],[f3219]) ).
thf(f3219,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = X0 )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(flattening,[],[f3218]) ).
thf(f3218,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))) = X0 )
| ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = X0 )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(ennf_transformation,[],[f1232]) ).
thf(f1232,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
=> ( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) != X0 )
=> ( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))) != X0 )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) ) ) ) ),
inference(fool_elimination,[],[f1231]) ).
thf(f1231,plain,
! [X0: int] :
( vAPP(int,$o,zprime,X0)
=> ( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) != X0 )
=> ( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))) != X0 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) ) ) ),
inference(rectify,[],[f291]) ).
thf(f291,axiom,
! [X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) != X163 )
=> ( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit1,pls))) != X163 )
=> vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X163) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_prime__g__5) ).
thf(f7465,plain,
! [X0: int] :
( ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(forward_demodulation,[],[f6151,f4464]) ).
thf(f6151,plain,
! [X0: int] :
( ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(definition_unfolding,[],[f4600,f4404,f4404]) ).
thf(f4600,plain,
! [X0: int] :
( ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(cnf_transformation,[],[f3217]) ).
thf(f3217,plain,
! [X0: int] :
( ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) )
| ( $true != vAPP(int,$o,zprime,X0) ) ),
inference(ennf_transformation,[],[f1230]) ).
thf(f1230,plain,
! [X0: int] :
( ( $true = vAPP(int,$o,zprime,X0) )
=> ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) ) ),
inference(fool_elimination,[],[f1229]) ).
thf(f1229,plain,
! [X0: int] :
( vAPP(int,$o,zprime,X0)
=> ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X0) ) ),
inference(rectify,[],[f1111]) ).
thf(f1111,axiom,
! [X163: int] :
( vAPP(int,$o,zprime,X163)
=> ( vAPP(int,sTfun(int,$o),d22set,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),wset,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X163),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),X163) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_d22set__eq__wset) ).
thf(f6150,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4599,f5969,f5969]) ).
thf(f4599,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f3216]) ).
thf(f3216,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f1228]) ).
thf(f1228,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ) ),
inference(fool_elimination,[],[f1227]) ).
thf(f1227,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f954]) ).
thf(f954,axiom,
! [X191: nat] :
( ( zero_zero_nat != X191 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_gr0I) ).
thf(f7464,plain,
! [X0: nat] :
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) )
| ( min = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) ) ),
inference(forward_demodulation,[],[f7463,f4464]) ).
thf(f7463,plain,
! [X0: nat] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(int,int,bit1,zero_zero_int) )
| ( min = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) ) ),
inference(forward_demodulation,[],[f7462,f4464]) ).
thf(f7462,plain,
! [X0: nat] :
( ( min = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),X0) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(forward_demodulation,[],[f6149,f4464]) ).
thf(f6149,plain,
! [X0: nat] :
( ( vAPP(int,int,number_number_of_int,min) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) )
| ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4598,f5971]) ).
thf(f4598,plain,
! [X0: nat] :
( ( vAPP(int,int,number_number_of_int,min) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) )
| ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(cnf_transformation,[],[f2853]) ).
thf(f2853,plain,
! [X0: nat] :
( ( vAPP(int,int,number_number_of_int,min) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) )
| ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X0) ) ),
inference(rectify,[],[f661]) ).
thf(f661,axiom,
! [X191: nat] :
( ( vAPP(int,int,number_number_of_int,min) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X191) )
| ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),X191) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_neg__one__power) ).
thf(f7460,plain,
! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(forward_demodulation,[],[f6147,f4464]) ).
thf(f6147,plain,
! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(definition_unfolding,[],[f4597,f5971]) ).
thf(f4597,plain,
! [X0: int] :
( ( vAPP(int,int,zfact,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,zfact,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),one_one_int))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,X0),zero_zero_int) ) ),
inference(cnf_transformation,[],[f3215]) ).
thf(f7459,plain,
! [X0: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,int,bit1,zero_zero_int) )
| ( vAPP(int,nat,number_number_of_nat,X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(forward_demodulation,[],[f6146,f4464]) ).
thf(f6146,plain,
! [X0: int] :
( ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| ( vAPP(int,nat,number_number_of_nat,X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f4594,f5971,f5969]) ).
thf(f4594,plain,
! [X0: int] :
( ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ),
inference(cnf_transformation,[],[f3214]) ).
thf(f3214,plain,
! [X0: int] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) ) )
& ( ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ) ),
inference(ennf_transformation,[],[f2851]) ).
thf(f2851,plain,
! [X0: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
=> ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f594]) ).
thf(f594,axiom,
! [X321: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X321) )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X321)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X321) )
=> ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X321)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_power__0__left__number__of) ).
thf(f6144,plain,
! [X0: int] :
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( vAPP(int,nat,number_number_of_nat,X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f4592,f5972,f5969,f5969]) ).
thf(f4592,plain,
! [X0: int] :
( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ),
inference(cnf_transformation,[],[f3213]) ).
thf(f3213,plain,
! [X0: int] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) ) )
& ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ) ),
inference(ennf_transformation,[],[f2850]) ).
thf(f2850,plain,
! [X0: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
=> ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f593]) ).
thf(f593,axiom,
! [X321: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X321) )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X321)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X321) )
=> ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,X321)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_power__0__left__number__of) ).
thf(f6142,plain,
! [X0: int] :
( ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,X0)) )
| ( vAPP(int,nat,number_number_of_nat,X0) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f4590,f5973,f5970,f5969]) ).
thf(f4590,plain,
! [X0: int] :
( ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ),
inference(cnf_transformation,[],[f3212]) ).
thf(f3212,plain,
! [X0: int] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) ) )
& ( ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ) ),
inference(ennf_transformation,[],[f2849]) ).
thf(f2849,plain,
! [X0: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) )
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
=> ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f592]) ).
thf(f592,axiom,
! [X321: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X321) )
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X321)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X321) )
=> ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,X321)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_power__0__left__number__of) ).
thf(f6139,plain,
! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4589,f5969]) ).
thf(f4589,plain,
! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f3211]) ).
thf(f3211,plain,
! [X0: nat] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) )
& ( ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f2848]) ).
thf(f2848,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) ) )
& ( ( zero_zero_nat = X0 )
=> ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X0) ) ) ),
inference(rectify,[],[f335]) ).
thf(f335,axiom,
! [X198: nat] :
( ( ( zero_zero_nat != X198 )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X198) ) )
& ( ( zero_zero_nat = X198 )
=> ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),X198) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_power__0__left) ).
thf(f6137,plain,
! [X0: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4587,f5969,f5969,f5969]) ).
thf(f4587,plain,
! [X0: nat] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f3210]) ).
thf(f3210,plain,
! [X0: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) )
& ( ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f2847]) ).
thf(f2847,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) ) )
& ( ( zero_zero_nat = X0 )
=> ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X0) ) ) ),
inference(rectify,[],[f336]) ).
thf(f336,axiom,
! [X198: nat] :
( ( ( zero_zero_nat != X198 )
=> ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X198) ) )
& ( ( zero_zero_nat = X198 )
=> ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),X198) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_power__0__left) ).
thf(f6135,plain,
! [X0: nat] :
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 ) ),
inference(definition_unfolding,[],[f4585,f5970,f5970,f5969]) ).
thf(f4585,plain,
! [X0: nat] :
( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f3209]) ).
thf(f3209,plain,
! [X0: nat] :
( ( ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) )
& ( ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f2846]) ).
thf(f2846,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) ) )
& ( ( zero_zero_nat = X0 )
=> ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X0) ) ) ),
inference(rectify,[],[f337]) ).
thf(f337,axiom,
! [X198: nat] :
( ( ( zero_zero_nat != X198 )
=> ( zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X198) ) )
& ( ( zero_zero_nat = X198 )
=> ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),X198) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_power__0__left) ).
thf(f4583,plain,
! [X0: int] : ( vAPP(int,sTfun(int,$o),sr,X0) = vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,vAPP(sTfun(int,$o),sTfun(int,$o),vAPP(sTfun(int,sTfun($o,$o)),sTfun(sTfun(int,$o),sTfun(int,$o)),sCOMB,vAPP(sTfun(int,$o),sTfun(int,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(int,$o),sTfun(int,sTfun($o,$o))),bCOMB,vAND),vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),vAPP(int,sTfun(int,$o),vAPP(sTfun(int,sTfun(int,$o)),sTfun(int,sTfun(int,$o)),cCOMB,ord_less_int),X0))) ),
inference(cnf_transformation,[],[f1224]) ).
thf(f1224,plain,
! [X0: int] : ( vAPP(int,sTfun(int,$o),sr,X0) = vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,vAPP(sTfun(int,$o),sTfun(int,$o),vAPP(sTfun(int,sTfun($o,$o)),sTfun(sTfun(int,$o),sTfun(int,$o)),sCOMB,vAPP(sTfun(int,$o),sTfun(int,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(int,$o),sTfun(int,sTfun($o,$o))),bCOMB,vAND),vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),vAPP(int,sTfun(int,$o),vAPP(sTfun(int,sTfun(int,$o)),sTfun(int,sTfun(int,$o)),cCOMB,ord_less_int),X0))) ),
inference(fool_elimination,[],[f1223]) ).
thf(f1223,plain,
! [X0: int] :
( vAPP(int,sTfun(int,$o),sr,X0) = vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,
^ [X1: int] : vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X1)),vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0))) ),
inference(rectify,[],[f1134]) ).
thf(f1134,axiom,
! [X163: int] :
( vAPP(int,sTfun(int,$o),sr,X163) = vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,
^ [X0: int] : vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0)),vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X163))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1133_SR__def) ).
thf(f6134,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4582,f4404,f4404,f4404,f4404]) ).
thf(f4582,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2845]) ).
thf(f2845,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f294]) ).
thf(f294,axiom,
! [X16: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X16),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X16)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_four__x__squared) ).
thf(f6133,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4581,f4404,f4404,f4404]) ).
thf(f4581,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2844]) ).
thf(f2844,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
! [X16: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X16),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_quartic__square__square) ).
thf(f6132,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(definition_unfolding,[],[f4580,f4404,f4404]) ).
thf(f4580,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(cnf_transformation,[],[f2843]) ).
thf(f2843,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X2: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X2),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X2),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_cube__square) ).
thf(f6128,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4576,f4404]) ).
thf(f4576,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),X0) ),
inference(cnf_transformation,[],[f2839]) ).
thf(f2839,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0)),X0) ),
inference(rectify,[],[f272]) ).
thf(f272,axiom,
! [X158: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X158),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X158),X158)),X158) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_power3__eq__cube) ).
thf(f6127,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4575,f4404]) ).
thf(f4575,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0)),X0) ),
inference(cnf_transformation,[],[f2838]) ).
thf(f2838,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0)),X0) ),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
! [X158: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X158),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X158),X158)),X158) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_power3__eq__cube) ).
thf(f6126,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4574,f4404]) ).
thf(f4574,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),X0) ),
inference(cnf_transformation,[],[f2837]) ).
thf(f2837,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0)),X0) ),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
! [X158: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X158),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X158),X158)),X158) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_power3__eq__cube) ).
thf(f7451,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(forward_demodulation,[],[f6124,f6101]) ).
thf(f6124,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(definition_unfolding,[],[f4571,f5973]) ).
thf(f4571,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),vAPP(int,real,number267125858f_real,X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(cnf_transformation,[],[f2834]) ).
thf(f2834,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),vAPP(int,real,number267125858f_real,X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(rectify,[],[f256]) ).
thf(f256,axiom,
! [X154: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,X154)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),vAPP(int,real,number267125858f_real,X154))),vAPP(int,real,number267125858f_real,X154)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_number__of__Bit1) ).
thf(f7450,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,X0)) ),
inference(forward_demodulation,[],[f6123,f6055]) ).
thf(f6123,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(definition_unfolding,[],[f4570,f5970]) ).
thf(f4570,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(cnf_transformation,[],[f2833]) ).
thf(f2833,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),vAPP(int,real,number267125858f_real,X0))),vAPP(int,real,number267125858f_real,X0)) ),
inference(rectify,[],[f423]) ).
thf(f423,axiom,
! [X246: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X246)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),vAPP(int,real,number267125858f_real,X246))),vAPP(int,real,number267125858f_real,X246)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_number__of__Bit0) ).
thf(f7449,plain,
! [X0: nat] : ( vAPP(int,int,bit1,zero_zero_int) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)) ),
inference(forward_demodulation,[],[f7448,f4464]) ).
thf(f7448,plain,
! [X0: nat] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,min),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)) ),
inference(forward_demodulation,[],[f6122,f4464]) ).
thf(f6122,plain,
! [X0: nat] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)) ),
inference(definition_unfolding,[],[f4569,f5971,f4404]) ).
thf(f4569,plain,
! [X0: nat] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)) ),
inference(cnf_transformation,[],[f2832]) ).
thf(f2832,plain,
! [X0: nat] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)) ),
inference(rectify,[],[f582]) ).
thf(f582,axiom,
! [X317: nat] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X317)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_power__m1__even) ).
thf(f6121,plain,
! [X0: nat] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0)) ),
inference(definition_unfolding,[],[f4568,f5973,f4404]) ).
thf(f4568,plain,
! [X0: nat] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)) ),
inference(cnf_transformation,[],[f2831]) ).
thf(f2831,plain,
! [X0: nat] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0)) ),
inference(rectify,[],[f581]) ).
thf(f581,axiom,
! [X317: nat] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,min)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X317)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_power__m1__even) ).
thf(f7443,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,real,number267125858f_real,X0)) ),
inference(forward_demodulation,[],[f7442,f4526]) ).
thf(f7442,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,real,number267125858f_real,X0)) ),
inference(forward_demodulation,[],[f6119,f6101]) ).
thf(f6119,plain,
! [X0: int] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,real,number267125858f_real,X0)) ),
inference(definition_unfolding,[],[f4566,f5973,f5973]) ).
thf(f4566,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real)),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) ),
inference(cnf_transformation,[],[f2829]) ).
thf(f2829,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real)),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X0)) ),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
! [X157: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real)),vAPP(int,real,number267125858f_real,X157)) = vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,X157)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0) ).
thf(f7435,plain,
! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ),
inference(forward_demodulation,[],[f7434,f4526]) ).
thf(f7434,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ),
inference(forward_demodulation,[],[f6115,f4464]) ).
thf(f6115,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4562,f4404]) ).
thf(f4562,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2825]) ).
thf(f2825,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
! [X162: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X162),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X162),X162) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_mult__2__right) ).
thf(f6112,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4559,f4404]) ).
thf(f4559,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) ),
inference(cnf_transformation,[],[f2822]) ).
thf(f2822,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) ),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
! [X159: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),X159) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X159),X159) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_semiring__mult__2) ).
thf(f6105,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4552,f4404]) ).
thf(f4552,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2815]) ).
thf(f2815,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f283]) ).
thf(f283,axiom,
! [X161: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X161),vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X161),X161) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_semiring__mult__2__right) ).
thf(f6102,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,zero_zero_int))) ),
inference(definition_unfolding,[],[f4549,f5973,f4404]) ).
thf(f4549,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),one_one_real) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,pls))) ),
inference(cnf_transformation,[],[f2812]) ).
thf(f2812,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X0)),one_one_real) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,bit1,pls))) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X12: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,X12)),one_one_real) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X12),vAPP(int,int,bit1,pls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).
thf(f7429,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(forward_demodulation,[],[f7428,f4526]) ).
thf(f7428,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(backward_demodulation,[],[f6094,f6101]) ).
thf(f6101,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)) ),
inference(definition_unfolding,[],[f4548,f5973,f4404]) ).
thf(f4548,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,pls)),X0)) ),
inference(cnf_transformation,[],[f2811]) ).
thf(f2811,plain,
! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),vAPP(int,real,number267125858f_real,X0)) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,pls)),X0)) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X11: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),vAPP(int,real,number267125858f_real,X11)) = vAPP(int,real,number267125858f_real,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,pls)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).
thf(f6100,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4547,f4404]) ).
thf(f4547,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0) ),
inference(cnf_transformation,[],[f2810]) ).
thf(f2810,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),X0) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X7: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X7),X7) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X7),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(f6099,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4546,f4404]) ).
thf(f4546,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2809]) ).
thf(f2809,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X7: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X7),X7) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X7),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(f6098,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4545,f4404]) ).
thf(f4545,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2808]) ).
thf(f2808,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f62]) ).
thf(f62,axiom,
! [X15: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X15),X15) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X15),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__mult__2__right) ).
thf(f6097,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(definition_unfolding,[],[f4544,f4404]) ).
thf(f4544,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(cnf_transformation,[],[f2807]) ).
thf(f2807,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),X0) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
! [X7: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X7),X7) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X7),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(f6095,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4542,f5972,f5972]) ).
thf(f4542,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat)),X0) ),
inference(cnf_transformation,[],[f2805]) ).
thf(f2805,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat)),X0) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X137: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X137),X137) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat)),X137) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(f6094,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)))),X0) ),
inference(definition_unfolding,[],[f4541,f5973,f5973]) ).
thf(f4541,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real)),X0) ),
inference(cnf_transformation,[],[f2804]) ).
thf(f2804,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real)),X0) ),
inference(rectify,[],[f235]) ).
thf(f235,axiom,
! [X137: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X137),X137) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real)),X137) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(f6093,plain,
! [X0: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,zero_zero_int),vAPP(int,int,bit1,X0)) ),
inference(definition_unfolding,[],[f4540,f4404]) ).
thf(f4540,plain,
! [X0: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),vAPP(int,int,bit1,X0)) ),
inference(cnf_transformation,[],[f2803]) ).
thf(f2803,plain,
! [X0: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),vAPP(int,int,bit1,X0)) ),
inference(rectify,[],[f635]) ).
thf(f635,axiom,
! [X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),vAPP(int,int,bit1,X38)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_diff__bin__simps_I4_J) ).
thf(f6092,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,zero_zero_int),vAPP(int,int,bit0,X0)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,zero_zero_int),X0)) ),
inference(definition_unfolding,[],[f4539,f4404,f4404]) ).
thf(f4539,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),vAPP(int,int,bit0,X0)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),X0)) ),
inference(cnf_transformation,[],[f2802]) ).
thf(f2802,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),vAPP(int,int,bit0,X0)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),X0)) ),
inference(rectify,[],[f627]) ).
thf(f627,axiom,
! [X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),vAPP(int,int,bit0,X38)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,pls),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_diff__bin__simps_I3_J) ).
thf(f4538,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),vAPP(int,int,bit1,X0)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) ),
inference(cnf_transformation,[],[f2801]) ).
thf(f2801,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),vAPP(int,int,bit1,X0)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) ),
inference(rectify,[],[f637]) ).
thf(f637,axiom,
! [X38: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),vAPP(int,int,bit1,X38)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_diff__bin__simps_I6_J) ).
thf(f4537,plain,
! [X0: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),vAPP(int,int,bit0,X0)) ),
inference(cnf_transformation,[],[f2800]) ).
thf(f2800,plain,
! [X0: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),vAPP(int,int,bit0,X0)) ),
inference(rectify,[],[f636]) ).
thf(f636,axiom,
! [X38: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),X38)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,min),vAPP(int,int,bit0,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_diff__bin__simps_I5_J) ).
thf(f7424,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X0) ),
inference(forward_demodulation,[],[f6091,f4464]) ).
thf(f6091,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)),X0) ),
inference(definition_unfolding,[],[f4536,f5971]) ).
thf(f4536,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f2799]) ).
thf(f2799,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
! [X18: int] : ( vAPP(int,int,bit1,X18) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X18)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Bit1__def) ).
thf(f7423,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),X0)),X0) ),
inference(forward_demodulation,[],[f6090,f4464]) ).
thf(f6090,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)),X0) ),
inference(definition_unfolding,[],[f4535,f5971]) ).
thf(f4535,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f2798]) ).
thf(f2798,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(rectify,[],[f406]) ).
thf(f406,axiom,
! [X15: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X15)),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_odd__nonzero) ).
thf(f7418,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),min) ),
inference(forward_demodulation,[],[f4525,f4464]) ).
thf(f4525,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,min)) ),
inference(cnf_transformation,[],[f2788]) ).
thf(f2788,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),vAPP(int,int,number_number_of_int,min)) ),
inference(rectify,[],[f1156]) ).
thf(f1156,axiom,
! [X2: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),vAPP(int,int,number_number_of_int,min)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_zmod__minus1__right) ).
thf(f7416,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,bit1,zero_zero_int)) = X0 ),
inference(forward_demodulation,[],[f6080,f4464]) ).
thf(f6080,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = X0 ),
inference(definition_unfolding,[],[f4523,f5971]) ).
thf(f4523,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),one_one_int) = X0 ),
inference(cnf_transformation,[],[f2786]) ).
thf(f2786,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),one_one_int) = X0 ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X118: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X118),one_one_int) = X118 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(f6079,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),zero_zero_int) = X0 ),
inference(definition_unfolding,[],[f4520,f4404]) ).
thf(f4520,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),pls) = X0 ),
inference(cnf_transformation,[],[f2783]) ).
thf(f2783,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),pls) = X0 ),
inference(rectify,[],[f204]) ).
thf(f204,axiom,
! [X18: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X18),pls) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add__Pls__right) ).
thf(f6078,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),zero_zero_int) = X0 ),
inference(definition_unfolding,[],[f4519,f4404]) ).
thf(f4519,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),pls) = X0 ),
inference(cnf_transformation,[],[f2782]) ).
thf(f2782,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),pls) = X0 ),
inference(rectify,[],[f615]) ).
thf(f615,axiom,
! [X18: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X18),pls) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_diff__bin__simps_I1_J) ).
thf(f7414,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit1,zero_zero_int)),X0) = X0 ),
inference(forward_demodulation,[],[f6076,f4464]) ).
thf(f6076,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) = X0 ),
inference(definition_unfolding,[],[f4517,f5971]) ).
thf(f4517,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,one_one_int),X0) = X0 ),
inference(cnf_transformation,[],[f2780]) ).
thf(f2780,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,one_one_int),X0) = X0 ),
inference(rectify,[],[f209]) ).
thf(f209,axiom,
! [X15: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,one_one_int),X15) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_zmult__1) ).
thf(f6075,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X0) = X0 ),
inference(definition_unfolding,[],[f4514,f4404]) ).
thf(f4514,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,pls),X0) = X0 ),
inference(cnf_transformation,[],[f2777]) ).
thf(f2777,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,pls),X0) = X0 ),
inference(rectify,[],[f205]) ).
thf(f205,axiom,
! [X18: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,pls),X18) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__Pls) ).
thf(f6073,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) = X0 ),
inference(definition_unfolding,[],[f4512,f5972]) ).
thf(f4512,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f2775]) ).
thf(f2775,plain,
! [X0: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),one_one_nat) = X0 ),
inference(rectify,[],[f424]) ).
thf(f424,axiom,
! [X247: int] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X247),one_one_nat) = X247 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_power__one__right) ).
thf(f6071,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) = X0 ),
inference(definition_unfolding,[],[f4510,f5972]) ).
thf(f4510,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f2773]) ).
thf(f2773,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),one_one_nat) = X0 ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X118: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X118),one_one_nat) = X118 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(f6069,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) = X0 ),
inference(definition_unfolding,[],[f4508,f5969]) ).
thf(f4508,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f2771]) ).
thf(f2771,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),zero_zero_nat) = X0 ),
inference(rectify,[],[f352]) ).
thf(f352,axiom,
! [X205: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X205),zero_zero_nat) = X205 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(f6067,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) = X0 ),
inference(definition_unfolding,[],[f4506,f5972]) ).
thf(f4506,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f2769]) ).
thf(f2769,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),one_one_nat) = X0 ),
inference(rectify,[],[f426]) ).
thf(f426,axiom,
! [X247: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X247),one_one_nat) = X247 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_power__one__right) ).
thf(f6066,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) = X0 ),
inference(definition_unfolding,[],[f4505,f5969]) ).
thf(f4505,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f2768]) ).
thf(f2768,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),zero_zero_nat) = X0 ),
inference(rectify,[],[f886]) ).
thf(f886,axiom,
! [X192: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),zero_zero_nat) = X192 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_minus__nat_Odiff__0) ).
thf(f6064,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) = X0 ),
inference(definition_unfolding,[],[f4503,f5972]) ).
thf(f4503,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,one_one_nat),X0) = X0 ),
inference(cnf_transformation,[],[f2766]) ).
thf(f2766,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,one_one_nat),X0) = X0 ),
inference(rectify,[],[f1029]) ).
thf(f1029,axiom,
! [X191: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,one_one_nat),X191) = X191 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_nat__mult__1) ).
thf(f6062,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) = X0 ),
inference(definition_unfolding,[],[f4501,f5969]) ).
thf(f4501,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X0) = X0 ),
inference(cnf_transformation,[],[f2764]) ).
thf(f2764,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X0) = X0 ),
inference(rectify,[],[f349]) ).
thf(f349,axiom,
! [X204: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X204) = X204 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(f6060,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) = X0 ),
inference(definition_unfolding,[],[f4499,f5972]) ).
thf(f4499,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f2762]) ).
thf(f2762,plain,
! [X0: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),one_one_nat) = X0 ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X24: real] : ( vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X24),one_one_nat) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(f6058,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) = X0 ),
inference(definition_unfolding,[],[f4497,f5970]) ).
thf(f4497,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real) = X0 ),
inference(cnf_transformation,[],[f2760]) ).
thf(f2760,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real) = X0 ),
inference(rectify,[],[f353]) ).
thf(f353,axiom,
! [X205: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X205),zero_zero_real) = X205 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(f6055,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) = X0 ),
inference(definition_unfolding,[],[f4494,f5970]) ).
thf(f4494,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0) = X0 ),
inference(cnf_transformation,[],[f2757]) ).
thf(f2757,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0) = X0 ),
inference(rectify,[],[f350]) ).
thf(f350,axiom,
! [X204: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X204) = X204 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(f4493,plain,
! [X0: int > $o] : ( vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,X0) = X0 ),
inference(cnf_transformation,[],[f2756]) ).
thf(f2756,plain,
! [X0: int > $o] : ( vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,X0) = X0 ),
inference(rectify,[],[f120]) ).
thf(f120,axiom,
! [X73: int > $o] : ( vAPP(sTfun(int,$o),sTfun(int,$o),collect_int,X73) = X73 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Collect__def) ).
thf(f4492,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X0) ),
inference(cnf_transformation,[],[f2755]) ).
thf(f2755,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X0),X0) ),
inference(rectify,[],[f1152]) ).
thf(f1152,axiom,
! [X2: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_zmod__self) ).
thf(f4490,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),zero_zero_int) ),
inference(cnf_transformation,[],[f2753]) ).
thf(f2753,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X0),zero_zero_int) ),
inference(rectify,[],[f709]) ).
thf(f709,axiom,
! [X358: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,X358),zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_mult__zero__right) ).
thf(f4487,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,zero_zero_int),X0) ),
inference(cnf_transformation,[],[f2750]) ).
thf(f2750,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,zero_zero_int),X0) ),
inference(rectify,[],[f1153]) ).
thf(f1153,axiom,
! [X3: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),div_mod_int,zero_zero_int),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_zmod__zero) ).
thf(f6054,plain,
! [X0: int] : ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,zero_zero_int),X0) ),
inference(definition_unfolding,[],[f4486,f4404,f4404]) ).
thf(f4486,plain,
! [X0: int] : ( pls = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,pls),X0) ),
inference(cnf_transformation,[],[f2749]) ).
thf(f2749,plain,
! [X0: int] : ( pls = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,pls),X0) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X14: int] : ( pls = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,pls),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_mult__Pls) ).
thf(f6053,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ),
inference(definition_unfolding,[],[f4485,f5969]) ).
thf(f4485,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0) ),
inference(cnf_transformation,[],[f2748]) ).
thf(f2748,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0) ),
inference(rectify,[],[f887]) ).
thf(f887,axiom,
! [X192: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X192),X192) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_diff__self__eq__0) ).
thf(f6050,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(definition_unfolding,[],[f4482,f5969,f5969]) ).
thf(f4482,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f2745]) ).
thf(f2745,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X0),zero_zero_nat) ),
inference(rectify,[],[f971]) ).
thf(f971,axiom,
! [X192: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,X192),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_mult__0__right) ).
thf(f6047,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ),
inference(definition_unfolding,[],[f4479,f5969,f5969]) ).
thf(f4479,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f2742]) ).
thf(f2742,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f970]) ).
thf(f970,axiom,
! [X191: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),times_times_nat,zero_zero_nat),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_mult__0) ).
thf(f6046,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),X0) ),
inference(definition_unfolding,[],[f4478,f5969,f5969]) ).
thf(f4478,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,zero_zero_nat),X0) ),
inference(cnf_transformation,[],[f2741]) ).
thf(f2741,plain,
! [X0: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,zero_zero_nat),X0) ),
inference(rectify,[],[f885]) ).
thf(f885,axiom,
! [X191: nat] : ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,zero_zero_nat),X191) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_diff__0__eq__0) ).
thf(f6044,plain,
! [X0: real] : ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),vAPP(int,real,number267125858f_real,zero_zero_int)) ),
inference(definition_unfolding,[],[f4476,f5970,f5970]) ).
thf(f4476,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),zero_zero_real) ),
inference(cnf_transformation,[],[f2739]) ).
thf(f2739,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X0),zero_zero_real) ),
inference(rectify,[],[f707]) ).
thf(f707,axiom,
! [X358: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,X358),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_mult__zero__right) ).
thf(f6042,plain,
! [X0: real] : ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,vAPP(int,real,number267125858f_real,zero_zero_int)),X0) ),
inference(definition_unfolding,[],[f4474,f5970,f5970]) ).
thf(f4474,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,zero_zero_real),X0) ),
inference(cnf_transformation,[],[f2737]) ).
thf(f2737,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,zero_zero_real),X0) ),
inference(rectify,[],[f710]) ).
thf(f710,axiom,
! [X359: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),times_times_real,zero_zero_real),X359) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_mult__zero__left) ).
thf(f7412,plain,
! [X0: int] : ( vAPP(int,int,bit1,zero_zero_int) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(forward_demodulation,[],[f6040,f4464]) ).
thf(f6040,plain,
! [X0: int] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(definition_unfolding,[],[f4472,f5971,f5969]) ).
thf(f4472,plain,
! [X0: int] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f2735]) ).
thf(f2735,plain,
! [X0: int] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),zero_zero_nat) ),
inference(rectify,[],[f544]) ).
thf(f544,axiom,
! [X309: int] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X309),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(f7411,plain,
! [X0: nat] : ( vAPP(int,int,bit1,zero_zero_int) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,bit1,zero_zero_int)),X0) ),
inference(forward_demodulation,[],[f6039,f4464]) ).
thf(f6039,plain,
! [X0: nat] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4471,f5971,f5971]) ).
thf(f4471,plain,
! [X0: nat] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,one_one_int),X0) ),
inference(cnf_transformation,[],[f2734]) ).
thf(f2734,plain,
! [X0: nat] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,one_one_int),X0) ),
inference(rectify,[],[f469]) ).
thf(f469,axiom,
! [X270: nat] : ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,one_one_int),X270) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_power__one) ).
thf(f6037,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(definition_unfolding,[],[f4469,f5972,f5969]) ).
thf(f4469,plain,
! [X0: nat] : ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f2732]) ).
thf(f2732,plain,
! [X0: nat] : ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),zero_zero_nat) ),
inference(rectify,[],[f546]) ).
thf(f546,axiom,
! [X310: nat] : ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X310),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_power__0) ).
thf(f6036,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4468,f5972,f5972]) ).
thf(f4468,plain,
! [X0: nat] : ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,one_one_nat),X0) ),
inference(cnf_transformation,[],[f2731]) ).
thf(f2731,plain,
! [X0: nat] : ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,one_one_nat),X0) ),
inference(rectify,[],[f468]) ).
thf(f468,axiom,
! [X270: nat] : ( one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,one_one_nat),X270) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_power__one) ).
thf(f6034,plain,
! [X0: real] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ),
inference(definition_unfolding,[],[f4466,f5973,f5969]) ).
thf(f4466,plain,
! [X0: real] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f2729]) ).
thf(f2729,plain,
! [X0: real] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X0),zero_zero_nat) ),
inference(rectify,[],[f545]) ).
thf(f545,axiom,
! [X310: real] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,X310),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_power__0) ).
thf(f6033,plain,
! [X0: nat] : ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),X0) ),
inference(definition_unfolding,[],[f4465,f5973,f5973]) ).
thf(f4465,plain,
! [X0: nat] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,one_one_real),X0) ),
inference(cnf_transformation,[],[f2728]) ).
thf(f2728,plain,
! [X0: nat] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,one_one_real),X0) ),
inference(rectify,[],[f467]) ).
thf(f467,axiom,
! [X270: nat] : ( one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,one_one_real),X270) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_power__one) ).
thf(f7410,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),m)),vAPP(int,int,bit1,zero_zero_int)) ),
inference(forward_demodulation,[],[f7409,f4464]) ).
thf(f7409,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,bit1,zero_zero_int)) ),
inference(backward_demodulation,[],[f5975,f4464]) ).
thf(f4462,plain,
! [X0: int] : ( min != vAPP(int,int,bit0,X0) ),
inference(cnf_transformation,[],[f2725]) ).
thf(f2725,plain,
! [X0: int] : ( min != vAPP(int,int,bit0,X0) ),
inference(rectify,[],[f525]) ).
thf(f525,axiom,
! [X38: int] : ( vAPP(int,int,bit0,X38) != min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_rel__simps_I42_J) ).
thf(f6030,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int),
inference(definition_unfolding,[],[f4459,f4404]) ).
thf(f4459,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int) != $true,
inference(cnf_transformation,[],[f2722]) ).
thf(f2722,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int) != $true,
inference(flattening,[],[f1222]) ).
thf(f1222,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int) != $true,
inference(fool_elimination,[],[f1221]) ).
thf(f1221,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int),
inference(rectify,[],[f400]) ).
thf(f400,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_bin__less__0__simps_I1_J) ).
thf(f6029,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int),
inference(definition_unfolding,[],[f4458,f4404,f4404]) ).
thf(f4458,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),pls) != $true,
inference(cnf_transformation,[],[f2721]) ).
thf(f2721,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),pls) != $true,
inference(flattening,[],[f1220]) ).
thf(f1220,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),pls) != $true,
inference(fool_elimination,[],[f1219]) ).
thf(f1219,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),pls),
inference(rectify,[],[f68]) ).
thf(f68,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J) ).
thf(f6028,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),min),
inference(definition_unfolding,[],[f4457,f4404]) ).
thf(f4457,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),min) != $true,
inference(cnf_transformation,[],[f2720]) ).
thf(f2720,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),min) != $true,
inference(flattening,[],[f1218]) ).
thf(f1218,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),min) != $true,
inference(fool_elimination,[],[f1217]) ).
thf(f1217,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),min),
inference(rectify,[],[f531]) ).
thf(f531,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_rel__simps_I3_J) ).
thf(f4456,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),min) != $true,
inference(cnf_transformation,[],[f2719]) ).
thf(f2719,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),min) != $true,
inference(flattening,[],[f1216]) ).
thf(f1216,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),min) != $true,
inference(fool_elimination,[],[f1215]) ).
thf(f1215,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),min),
inference(rectify,[],[f526]) ).
thf(f526,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_rel__simps_I7_J) ).
thf(f6027,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min),
inference(definition_unfolding,[],[f4455,f4404]) ).
thf(f4455,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),min) != $true,
inference(cnf_transformation,[],[f2718]) ).
thf(f2718,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),min) != $true,
inference(flattening,[],[f1214]) ).
thf(f1214,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),min) != $true,
inference(fool_elimination,[],[f1213]) ).
thf(f1213,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),min),
inference(rectify,[],[f537]) ).
thf(f537,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,pls),min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_rel__simps_I20_J) ).
thf(f6026,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4454,f4404,f4404,f5971]) ).
thf(f4454,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(cnf_transformation,[],[f4090]) ).
thf(f4090,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f3208,f4089]) ).
thf(f4089,plain,
( ? [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ) ),
introduced(choice_axiom,[]) ).
thf(f3208,plain,
? [X0: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ),
inference(ennf_transformation,[],[f2717]) ).
thf(f2717,plain,
~ ! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ),
inference(flattening,[],[f1212]) ).
thf(f1212,plain,
~ ! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ),
inference(fool_elimination,[],[f1211]) ).
thf(f1211,plain,
~ ! [X0: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(rectify,[],[f513]) ).
thf(f513,axiom,
~ ! [X308: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X308),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(f4451,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK8),
inference(cnf_transformation,[],[f4088]) ).
thf(f4088,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK8) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f3207,f4087]) ).
thf(f4087,plain,
( ? [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) )
=> ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
& ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),sK8) ) ) ),
introduced(choice_axiom,[]) ).
thf(f3207,plain,
? [X0: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(ennf_transformation,[],[f1210]) ).
thf(f1210,plain,
~ ! [X0: int] :
~ ( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true ) ),
inference(fool_elimination,[],[f1209]) ).
thf(f1209,plain,
~ ! [X0: int] :
~ ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) ),
inference(rectify,[],[f310]) ).
thf(f310,axiom,
~ ! [X174: int] :
~ ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),X174),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X174),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X174) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) ).
thf(f6025,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4452,f4404,f5971]) ).
thf(f4452,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(cnf_transformation,[],[f4088]) ).
thf(f6024,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4453,f4404,f5971]) ).
thf(f4453,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(cnf_transformation,[],[f4088]) ).
thf(f6023,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),sK7),
inference(definition_unfolding,[],[f4450,f4404,f5971,f4404,f5971]) ).
thf(f4450,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),sK7),
inference(cnf_transformation,[],[f4086]) ).
thf(f4086,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f3206,f4085]) ).
thf(f4085,plain,
( ? [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),X0) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),sK7) ) ),
introduced(choice_axiom,[]) ).
thf(f3206,plain,
? [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),X0) ),
inference(ennf_transformation,[],[f2716]) ).
thf(f2716,plain,
~ ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),X0) ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
~ ! [X13: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) != vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(f7357,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t),
inference(subsumption_resolution,[],[f6022,f5975]) ).
thf(f6022,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK5),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK6),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t) ) ),
inference(definition_unfolding,[],[f4449,f4404,f5971,f4404,f4404,f5971]) ).
thf(f4449,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK5),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK6),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t) != $true ) ),
inference(cnf_transformation,[],[f4084]) ).
thf(f4084,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK5),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK6),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f3205,f4083]) ).
thf(f4083,plain,
( ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK5),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK6),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
introduced(choice_axiom,[]) ).
thf(f3205,plain,
( ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t) != $true ) ),
inference(ennf_transformation,[],[f1208]) ).
thf(f1208,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t) = $true )
=> ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ) ),
inference(fool_elimination,[],[f1207]) ).
thf(f1207,plain,
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t)
=> ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t)
=> ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(f7351,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,number_number_of_int,min)),
inference(global_subsumption,[],[f5974,f1202,f1201,f5975,f5976,f5977,f5978,f5979,f5980,f5981,f5982,f5983,f5984,f5985,f4405,f5988,f5991,f5992,f5993,f5994,f6002,f6003,f6004,f6005,f6006,f6007,f6008,f6009,f6010,f6011,f6012,f6013,f6014,f6015,f6016,f6017,f6018,f6019,f4444,f7345,f6021]) ).
thf(f6021,plain,
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,number_number_of_int,min)) ) ),
inference(definition_unfolding,[],[f4448,f5971,f4404,f5971,f4404,f5971]) ).
thf(f4448,plain,
( ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)) = $true ) ),
inference(cnf_transformation,[],[f3204]) ).
thf(f3204,plain,
( ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)) = $true ) ),
inference(ennf_transformation,[],[f2715]) ).
thf(f2715,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)) != $true )
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ) ),
inference(flattening,[],[f1206]) ).
thf(f1206,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min)) != $true )
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ) ),
inference(fool_elimination,[],[f1205]) ).
thf(f1205,plain,
( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min))
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ) ),
inference(rectify,[],[f611]) ).
thf(f611,axiom,
( ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),vAPP(int,int,number_number_of_int,min))
=> ( one_one_int != vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(f7345,plain,
t != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)),
inference(subsumption_resolution,[],[f6020,f5975]) ).
thf(f6020,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK4),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) )
| ( t != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
inference(definition_unfolding,[],[f4447,f4404,f5971,f4404,f4404,f5971]) ).
thf(f4447,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK4),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( one_one_int != t ) ),
inference(cnf_transformation,[],[f4082]) ).
thf(f4082,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK4),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) )
| ( one_one_int != t ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f3203,f4081]) ).
thf(f4081,plain,
( ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK3),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK4),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) ) ),
introduced(choice_axiom,[]) ).
thf(f3203,plain,
( ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) )
| ( one_one_int != t ) ),
inference(ennf_transformation,[],[f2]) ).
thf(f2,axiom,
( ( one_one_int = t )
=> ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(f4444,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),s) = $true,
inference(cnf_transformation,[],[f1204]) ).
thf(f1204,plain,
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),s) = $true ) ),
inference(fool_elimination,[],[f1203]) ).
thf(f1203,plain,
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),s) ),
inference(rectify,[],[f308]) ).
thf(f308,axiom,
( vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int))
& vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),s) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_s0p) ).
thf(f6019,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4445,f4404,f5971]) ).
thf(f4445,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f1204]) ).
thf(f6018,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4446,f4404,f5971]) ).
thf(f4446,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)) = $true,
inference(cnf_transformation,[],[f1204]) ).
thf(f6017,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4443,f4404,f5971,f4404,f5971]) ).
thf(f4443,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t),
inference(cnf_transformation,[],[f6]) ).
thf(f6,axiom,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_t) ).
thf(f6016,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),
inference(definition_unfolding,[],[f4442,f4404,f5971,f4404]) ).
thf(f4442,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),
inference(cnf_transformation,[],[f610]) ).
thf(f610,axiom,
vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),one_one_int) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(int,int,number_number_of_int,min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(f6015,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4441,f4404,f5971,f5971]) ).
thf(f4441,plain,
vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),one_one_int)),
inference(cnf_transformation,[],[f292]) ).
thf(f292,axiom,
vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
thf(f6014,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4440,f5971,f4404,f5971]) ).
thf(f4440,plain,
one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
inference(cnf_transformation,[],[f514]) ).
thf(f514,axiom,
one_one_int = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(f6013,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4439,f4404,f5971,f5971]) ).
thf(f4439,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int),
inference(cnf_transformation,[],[f33]) ).
thf(f33,axiom,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_one__add__one__is__two) ).
thf(f6012,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4438,f4404,f5971,f5971]) ).
thf(f4438,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int),
inference(cnf_transformation,[],[f286]) ).
thf(f286,axiom,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_semiring__one__add__one__is__two) ).
thf(f6011,plain,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4437,f4404,f5972,f5972]) ).
thf(f4437,plain,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat),
inference(cnf_transformation,[],[f63]) ).
thf(f63,axiom,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nat__1__add__1) ).
thf(f6010,plain,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4436,f4404,f5972,f5972]) ).
thf(f4436,plain,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat),
inference(cnf_transformation,[],[f287]) ).
thf(f287,axiom,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_semiring__one__add__one__is__two) ).
thf(f6009,plain,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4435,f4404,f5973,f5973]) ).
thf(f4435,plain,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real),
inference(cnf_transformation,[],[f288]) ).
thf(f288,axiom,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_semiring__one__add__one__is__two) ).
thf(f6008,plain,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f4434,f4404,f5973,f5973]) ).
thf(f4434,plain,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real),
inference(cnf_transformation,[],[f34]) ).
thf(f34,axiom,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,one_one_real),one_one_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_one__add__one__is__two) ).
thf(f6007,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4433,f4404]) ).
thf(f4433,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f441]) ).
thf(f441,axiom,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_zero__power2) ).
thf(f6006,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4432,f5969,f5969,f4404]) ).
thf(f4432,plain,
zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f440]) ).
thf(f440,axiom,
zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_zero__power2) ).
thf(f6005,plain,
vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4431,f5970,f5970,f4404]) ).
thf(f4431,plain,
zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f439]) ).
thf(f439,axiom,
zero_zero_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,zero_zero_real),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_zero__power2) ).
thf(f6004,plain,
vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4430,f5971,f5971,f4404]) ).
thf(f4430,plain,
one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,one_one_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f17]) ).
thf(f17,axiom,
one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,one_one_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__power2) ).
thf(f6003,plain,
vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4429,f5972,f5972,f4404]) ).
thf(f4429,plain,
one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,one_one_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f18]) ).
thf(f18,axiom,
one_one_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,one_one_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(f6002,plain,
vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f4428,f5973,f5973,f4404]) ).
thf(f4428,plain,
one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,one_one_real),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f19]) ).
thf(f19,axiom,
one_one_real = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,one_one_real),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(f5994,plain,
vAPP(int,int,number_number_of_int,min) != vAPP(int,int,number_number_of_int,zero_zero_int),
inference(definition_unfolding,[],[f4417,f4404]) ).
thf(f4417,plain,
vAPP(int,int,number_number_of_int,pls) != vAPP(int,int,number_number_of_int,min),
inference(cnf_transformation,[],[f540]) ).
thf(f540,axiom,
vAPP(int,int,number_number_of_int,pls) != vAPP(int,int,number_number_of_int,min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_eq__number__of__Pls__Min) ).
thf(f5993,plain,
zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int),
inference(definition_unfolding,[],[f4416,f4404]) ).
thf(f4416,plain,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
inference(cnf_transformation,[],[f392]) ).
thf(f392,axiom,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_semiring__norm_I112_J) ).
thf(f5992,plain,
zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int),
inference(definition_unfolding,[],[f4415,f4404]) ).
thf(f4415,plain,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
inference(cnf_transformation,[],[f394]) ).
thf(f394,axiom,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_number__of__Pls) ).
thf(f5991,plain,
zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int),
inference(definition_unfolding,[],[f4414,f4404]) ).
thf(f4414,plain,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
inference(cnf_transformation,[],[f402]) ).
thf(f402,axiom,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_zero__is__num__zero) ).
thf(f5988,plain,
zero_zero_int = vAPP(int,int,bit0,zero_zero_int),
inference(definition_unfolding,[],[f4409,f4404,f4404]) ).
thf(f4409,plain,
pls = vAPP(int,int,bit0,pls),
inference(cnf_transformation,[],[f201]) ).
thf(f201,axiom,
pls = vAPP(int,int,bit0,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Bit0__Pls) ).
thf(f4405,plain,
min = vAPP(int,int,bit1,min),
inference(cnf_transformation,[],[f521]) ).
thf(f521,axiom,
min = vAPP(int,int,bit1,min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_Bit1__Min) ).
thf(f5985,plain,
zero_zero_int != min,
inference(definition_unfolding,[],[f4403,f4404]) ).
thf(f4403,plain,
pls != min,
inference(cnf_transformation,[],[f522]) ).
thf(f522,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_rel__simps_I37_J) ).
thf(f5984,plain,
zero_zero_int != min,
inference(definition_unfolding,[],[f4402,f4404]) ).
thf(f4402,plain,
pls != min,
inference(cnf_transformation,[],[f523]) ).
thf(f523,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_rel__simps_I40_J) ).
thf(f5983,plain,
zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4401,f5971]) ).
thf(f4401,plain,
one_one_int != zero_zero_int,
inference(cnf_transformation,[],[f715]) ).
thf(f715,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_zero__neq__one) ).
thf(f5982,plain,
zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4400,f5971]) ).
thf(f4400,plain,
one_one_int != zero_zero_int,
inference(cnf_transformation,[],[f718]) ).
thf(f718,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_one__neq__zero) ).
thf(f5981,plain,
zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4399,f5971]) ).
thf(f4399,plain,
one_one_int != zero_zero_int,
inference(cnf_transformation,[],[f360]) ).
thf(f360,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_int__0__neq__1) ).
thf(f5980,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4398,f5972,f5969]) ).
thf(f4398,plain,
one_one_nat != zero_zero_nat,
inference(cnf_transformation,[],[f717]) ).
thf(f717,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_one__neq__zero) ).
thf(f5979,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4397,f5972,f5969]) ).
thf(f4397,plain,
one_one_nat != zero_zero_nat,
inference(cnf_transformation,[],[f714]) ).
thf(f714,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_zero__neq__one) ).
thf(f5978,plain,
vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4396,f5973,f5970]) ).
thf(f4396,plain,
one_one_real != zero_zero_real,
inference(cnf_transformation,[],[f685]) ).
thf(f685,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_real__zero__not__eq__one) ).
thf(f5977,plain,
vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4395,f5973,f5970]) ).
thf(f4395,plain,
one_one_real != zero_zero_real,
inference(cnf_transformation,[],[f716]) ).
thf(f716,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_one__neq__zero) ).
thf(f5976,plain,
vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f4394,f5973,f5970]) ).
thf(f4394,plain,
one_one_real != zero_zero_real,
inference(cnf_transformation,[],[f713]) ).
thf(f713,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_zero__neq__one) ).
thf(f5975,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) ),
inference(definition_unfolding,[],[f4393,f4404,f4404,f4404,f5971]) ).
thf(f4393,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ),
inference(cnf_transformation,[],[f3202]) ).
thf(f3202,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ),
inference(ennf_transformation,[],[f1200]) ).
thf(f1200,negated_conjecture,
~ ? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ),
inference(negated_conjecture,[],[f1199]) ).
thf(f1199,conjecture,
? [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X1),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),m)),one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1201,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f5974,plain,
zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int),
inference(definition_unfolding,[],[f4413,f4404]) ).
thf(f4413,plain,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
inference(cnf_transformation,[],[f396]) ).
thf(f396,axiom,
vAPP(int,int,number_number_of_int,pls) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
thf(f10739,plain,
spl44_190,
inference(avatar_split_clause,[],[f10738,f10731]) ).
thf(f10737,plain,
spl44_190,
inference(avatar_split_clause,[],[f10724,f10731]) ).
thf(f10736,plain,
spl44_190,
inference(avatar_split_clause,[],[f10735,f10731]) ).
thf(f10734,plain,
spl44_190,
inference(avatar_split_clause,[],[f10728,f10731]) ).
thf(f10711,plain,
( spl44_189
| ~ spl44_143 ),
inference(avatar_split_clause,[],[f10690,f9929,f10707]) ).
thf(f10707,plain,
( spl44_189
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,t),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_189])]) ).
thf(f10690,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f10673]) ).
thf(f10673,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143 ),
inference(superposition,[],[f9931,f7778]) ).
thf(f10710,plain,
( spl44_189
| ~ spl44_143 ),
inference(avatar_split_clause,[],[f10700,f9929,f10707]) ).
thf(f10700,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143 ),
inference(trivial_inequality_removal,[],[f10663]) ).
thf(f10663,plain,
( ( $true = $false )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,t),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_143 ),
inference(superposition,[],[f7778,f9931]) ).
thf(f10564,plain,
( spl44_188
| ~ spl44_187 ),
inference(avatar_split_clause,[],[f10559,f10455,f10561]) ).
thf(f10561,plain,
( spl44_188
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_188])]) ).
thf(f10455,plain,
( spl44_187
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_187])]) ).
thf(f10559,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) )
| ~ spl44_187 ),
inference(trivial_inequality_removal,[],[f10558]) ).
thf(f10558,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))),zero_zero_int) )
| ~ spl44_187 ),
inference(superposition,[],[f6178,f10457]) ).
thf(f10457,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_187 ),
inference(avatar_component_clause,[],[f10455]) ).
thf(f10539,plain,
( ~ spl44_86
| ~ spl44_186 ),
inference(avatar_contradiction_clause,[],[f10538]) ).
thf(f10538,plain,
( $false
| ~ spl44_86
| ~ spl44_186 ),
inference(trivial_inequality_removal,[],[f10525]) ).
thf(f10525,plain,
( ( $true = $false )
| ~ spl44_86
| ~ spl44_186 ),
inference(superposition,[],[f10453,f8384]) ).
thf(f8384,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min) )
| ~ spl44_86 ),
inference(avatar_component_clause,[],[f8382]) ).
thf(f8382,plain,
( spl44_86
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_86])]) ).
thf(f10453,plain,
( ! [X0: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),X0) = $true )
| ~ spl44_186 ),
inference(avatar_component_clause,[],[f10452]) ).
thf(f10536,plain,
( ~ spl44_86
| ~ spl44_186 ),
inference(avatar_contradiction_clause,[],[f10535]) ).
thf(f10535,plain,
( $false
| ~ spl44_86
| ~ spl44_186 ),
inference(trivial_inequality_removal,[],[f10530]) ).
thf(f10530,plain,
( ( $true = $false )
| ~ spl44_86
| ~ spl44_186 ),
inference(superposition,[],[f8384,f10453]) ).
thf(f10460,plain,
( spl44_187
| spl44_186 ),
inference(avatar_split_clause,[],[f10446,f10452,f10455]) ).
thf(f10459,plain,
( spl44_187
| spl44_186 ),
inference(avatar_split_clause,[],[f10447,f10452,f10455]) ).
thf(f10458,plain,
( spl44_186
| spl44_187 ),
inference(avatar_split_clause,[],[f10449,f10455,f10452]) ).
thf(f10196,plain,
( ~ spl44_185
| spl44_6
| ~ spl44_96 ),
inference(avatar_split_clause,[],[f10191,f8996,f7239,f10193]) ).
thf(f10193,plain,
( spl44_185
<=> ( min = vAPP(int,int,zfact,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_185])]) ).
thf(f7239,plain,
( spl44_6
<=> ( zero_zero_int = min ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_6])]) ).
thf(f8996,plain,
( spl44_96
<=> ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_96])]) ).
thf(f10191,plain,
( ( min != vAPP(int,int,zfact,zero_zero_int) )
| spl44_6
| ~ spl44_96 ),
inference(subsumption_resolution,[],[f10189,f7241]) ).
thf(f7241,plain,
( ( zero_zero_int != min )
| spl44_6 ),
inference(avatar_component_clause,[],[f7239]) ).
thf(f10189,plain,
( ( min != vAPP(int,int,zfact,zero_zero_int) )
| ( zero_zero_int = min )
| ~ spl44_96 ),
inference(superposition,[],[f4633,f8998]) ).
thf(f8998,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_96 ),
inference(avatar_component_clause,[],[f8996]) ).
thf(f10184,plain,
( ~ spl44_184
| spl44_180 ),
inference(avatar_split_clause,[],[f10179,f10151,f10181]) ).
thf(f10181,plain,
( spl44_184
<=> ( zero_zero_int = vAPP(int,int,zfact,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_184])]) ).
thf(f10151,plain,
( spl44_180
<=> ( zero_zero_int = vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_180])]) ).
thf(f10179,plain,
( ( zero_zero_int != vAPP(int,int,zfact,zero_zero_int) )
| spl44_180 ),
inference(superposition,[],[f10153,f4464]) ).
thf(f10153,plain,
( ( zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_180 ),
inference(avatar_component_clause,[],[f10151]) ).
thf(f10172,plain,
( ~ spl44_183
| spl44_175 ),
inference(avatar_split_clause,[],[f10167,f10121,f10169]) ).
thf(f10121,plain,
( spl44_175
<=> ( t = vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_175])]) ).
thf(f10167,plain,
( ( t != vAPP(int,int,zfact,zero_zero_int) )
| spl44_175 ),
inference(superposition,[],[f10123,f4464]) ).
thf(f10123,plain,
( ( t != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_175 ),
inference(avatar_component_clause,[],[f10121]) ).
thf(f10166,plain,
( ~ spl44_182
| spl44_98
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10161,f9585,f9326,f10163]) ).
thf(f10163,plain,
( spl44_182
<=> ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_182])]) ).
thf(f9326,plain,
( spl44_98
<=> ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_98])]) ).
thf(f10161,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_98
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9328,f9587]) ).
thf(f9328,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,min)) )
| spl44_98 ),
inference(avatar_component_clause,[],[f9326]) ).
thf(f10160,plain,
( ~ spl44_181
| spl44_99
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10155,f9585,f9331,f10157]) ).
thf(f9331,plain,
( spl44_99
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_99])]) ).
thf(f10155,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_99
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9333,f9587]) ).
thf(f9333,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min)) )
| spl44_99 ),
inference(avatar_component_clause,[],[f9331]) ).
thf(f10154,plain,
( ~ spl44_180
| spl44_100
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10149,f9585,f9336,f10151]) ).
thf(f9336,plain,
( spl44_100
<=> ( zero_zero_int = vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_100])]) ).
thf(f10149,plain,
( ( zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_100
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9338,f9587]) ).
thf(f9338,plain,
( ( zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,min)) )
| spl44_100 ),
inference(avatar_component_clause,[],[f9336]) ).
thf(f10148,plain,
( spl44_179
| ~ spl44_101
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10143,f9585,f9341,f10145]) ).
thf(f10145,plain,
( spl44_179
<=> ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_179])]) ).
thf(f9341,plain,
( spl44_101
<=> ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_101])]) ).
thf(f10143,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_101
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9343,f9587]) ).
thf(f9343,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_101 ),
inference(avatar_component_clause,[],[f9341]) ).
thf(f10142,plain,
( spl44_178
| ~ spl44_102
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10137,f9585,f9346,f10139]) ).
thf(f10139,plain,
( spl44_178
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_178])]) ).
thf(f9346,plain,
( spl44_102
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_102])]) ).
thf(f10137,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_102
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9348,f9587]) ).
thf(f9348,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_102 ),
inference(avatar_component_clause,[],[f9346]) ).
thf(f10136,plain,
( spl44_177
| ~ spl44_103
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10131,f9585,f9351,f10133]) ).
thf(f10133,plain,
( spl44_177
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_177])]) ).
thf(f9351,plain,
( spl44_103
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_103])]) ).
thf(f10131,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_103
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9353,f9587]) ).
thf(f9353,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_103 ),
inference(avatar_component_clause,[],[f9351]) ).
thf(f10130,plain,
( spl44_176
| ~ spl44_104
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10125,f9585,f9356,f10127]) ).
thf(f10127,plain,
( spl44_176
<=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_176])]) ).
thf(f9356,plain,
( spl44_104
<=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_104])]) ).
thf(f10125,plain,
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_104
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9358,f9587]) ).
thf(f9358,plain,
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))) )
| ~ spl44_104 ),
inference(avatar_component_clause,[],[f9356]) ).
thf(f10124,plain,
( ~ spl44_175
| spl44_105
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10119,f9585,f9361,f10121]) ).
thf(f9361,plain,
( spl44_105
<=> ( t = vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_105])]) ).
thf(f10119,plain,
( ( t != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,zero_zero_int)) )
| spl44_105
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9363,f9587]) ).
thf(f9363,plain,
( ( t != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,min)) )
| spl44_105 ),
inference(avatar_component_clause,[],[f9361]) ).
thf(f10118,plain,
( spl44_174
| ~ spl44_106
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10113,f9585,f9396,f10115]) ).
thf(f10115,plain,
( spl44_174
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) = vAPP(int,int,zfact,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_174])]) ).
thf(f9396,plain,
( spl44_106
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) = vAPP(int,int,zfact,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_106])]) ).
thf(f10113,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) = vAPP(int,int,zfact,zero_zero_int) )
| ~ spl44_106
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9398,f9587]) ).
thf(f9398,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) = vAPP(int,int,zfact,min) )
| ~ spl44_106 ),
inference(avatar_component_clause,[],[f9396]) ).
thf(f10112,plain,
( spl44_173
| ~ spl44_107
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10107,f9585,f9404,f10109]) ).
thf(f10109,plain,
( spl44_173
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_173])]) ).
thf(f9404,plain,
( spl44_107
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_107])]) ).
thf(f10107,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_107
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9406,f9587]) ).
thf(f9406,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))) )
| ~ spl44_107 ),
inference(avatar_component_clause,[],[f9404]) ).
thf(f10106,plain,
( spl44_172
| ~ spl44_108
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10101,f9585,f9424,f10103]) ).
thf(f10103,plain,
( spl44_172
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_172])]) ).
thf(f9424,plain,
( spl44_108
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_108])]) ).
thf(f10101,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_108
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9426,f9587]) ).
thf(f9426,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_108 ),
inference(avatar_component_clause,[],[f9424]) ).
thf(f10100,plain,
( spl44_171
| ~ spl44_109
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10095,f9585,f9429,f10097]) ).
thf(f10097,plain,
( spl44_171
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_171])]) ).
thf(f9429,plain,
( spl44_109
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_109])]) ).
thf(f10095,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_109
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9431,f9587]) ).
thf(f9431,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_109 ),
inference(avatar_component_clause,[],[f9429]) ).
thf(f10094,plain,
( spl44_170
| ~ spl44_110
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10089,f9585,f9434,f10091]) ).
thf(f9434,plain,
( spl44_110
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,min)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_110])]) ).
thf(f10089,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ~ spl44_110
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9436,f9587]) ).
thf(f9436,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,min)),t) )
| ~ spl44_110 ),
inference(avatar_component_clause,[],[f9434]) ).
thf(f10088,plain,
( spl44_169
| ~ spl44_111
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10083,f9585,f9439,f10085]) ).
thf(f10085,plain,
( spl44_169
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_169])]) ).
thf(f9439,plain,
( spl44_111
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_111])]) ).
thf(f10083,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_111
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9441,f9587]) ).
thf(f9441,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,zfact,min)) )
| ~ spl44_111 ),
inference(avatar_component_clause,[],[f9439]) ).
thf(f10082,plain,
( spl44_168
| ~ spl44_112
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10077,f9585,f9444,f10079]) ).
thf(f9444,plain,
( spl44_112
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_112])]) ).
thf(f10077,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_112
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9446,f9587]) ).
thf(f9446,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,zfact,min)) )
| ~ spl44_112 ),
inference(avatar_component_clause,[],[f9444]) ).
thf(f10076,plain,
( spl44_167
| ~ spl44_113
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10071,f9585,f9449,f10073]) ).
thf(f9449,plain,
( spl44_113
<=> ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,zfact,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_113])]) ).
thf(f10071,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_113
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9451,f9587]) ).
thf(f9451,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,zfact,min))) )
| ~ spl44_113 ),
inference(avatar_component_clause,[],[f9449]) ).
thf(f10070,plain,
( spl44_166
| ~ spl44_114
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10065,f9585,f9454,f10067]) ).
thf(f10067,plain,
( spl44_166
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_166])]) ).
thf(f9454,plain,
( spl44_114
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_114])]) ).
thf(f10065,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_114
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9456,f9587]) ).
thf(f9456,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_114 ),
inference(avatar_component_clause,[],[f9454]) ).
thf(f10064,plain,
( spl44_165
| ~ spl44_115
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10059,f9585,f9459,f10061]) ).
thf(f9459,plain,
( spl44_115
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_115])]) ).
thf(f10059,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_115
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9461,f9587]) ).
thf(f9461,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,min))) )
| ~ spl44_115 ),
inference(avatar_component_clause,[],[f9459]) ).
thf(f10058,plain,
( spl44_164
| ~ spl44_116
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10053,f9585,f9464,f10055]) ).
thf(f9464,plain,
( spl44_116
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_116])]) ).
thf(f10053,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,zero_zero_int))) )
| ~ spl44_116
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9466,f9587]) ).
thf(f9466,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,min))) )
| ~ spl44_116 ),
inference(avatar_component_clause,[],[f9464]) ).
thf(f10052,plain,
( spl44_163
| ~ spl44_117
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10047,f9585,f9469,f10049]) ).
thf(f10049,plain,
( spl44_163
<=> ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_163])]) ).
thf(f9469,plain,
( spl44_117
<=> ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_117])]) ).
thf(f10047,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_117
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9471,f9587]) ).
thf(f9471,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_117 ),
inference(avatar_component_clause,[],[f9469]) ).
thf(f10046,plain,
( spl44_162
| ~ spl44_118
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10041,f9585,f9474,f10043]) ).
thf(f10043,plain,
( spl44_162
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_162])]) ).
thf(f9474,plain,
( spl44_118
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_118])]) ).
thf(f10041,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_118
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9476,f9587]) ).
thf(f9476,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_118 ),
inference(avatar_component_clause,[],[f9474]) ).
thf(f10040,plain,
( spl44_161
| ~ spl44_119
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10035,f9585,f9479,f10037]) ).
thf(f10037,plain,
( spl44_161
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_161])]) ).
thf(f9479,plain,
( spl44_119
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_119])]) ).
thf(f10035,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_119
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9481,f9587]) ).
thf(f9481,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_119 ),
inference(avatar_component_clause,[],[f9479]) ).
thf(f10034,plain,
( spl44_160
| ~ spl44_120
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10029,f9585,f9484,f10031]) ).
thf(f10031,plain,
( spl44_160
<=> ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_160])]) ).
thf(f9484,plain,
( spl44_120
<=> ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_120])]) ).
thf(f10029,plain,
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int))))))) )
| ~ spl44_120
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9486,f9587]) ).
thf(f9486,plain,
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min))))))) )
| ~ spl44_120 ),
inference(avatar_component_clause,[],[f9484]) ).
thf(f10028,plain,
( spl44_159
| ~ spl44_121
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10023,f9585,f9489,f10025]) ).
thf(f10025,plain,
( spl44_159
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_159])]) ).
thf(f9489,plain,
( spl44_121
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_121])]) ).
thf(f10023,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),min) )
| ~ spl44_121
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9491,f9587]) ).
thf(f9491,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),min) )
| ~ spl44_121 ),
inference(avatar_component_clause,[],[f9489]) ).
thf(f10022,plain,
( spl44_158
| ~ spl44_122
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10017,f9585,f9494,f10019]) ).
thf(f10019,plain,
( spl44_158
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_158])]) ).
thf(f9494,plain,
( spl44_122
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_122])]) ).
thf(f10017,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_122
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9496,f9587]) ).
thf(f9496,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_122 ),
inference(avatar_component_clause,[],[f9494]) ).
thf(f10016,plain,
( spl44_157
| ~ spl44_123
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10011,f9585,f9499,f10013]) ).
thf(f10013,plain,
( spl44_157
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_157])]) ).
thf(f9499,plain,
( spl44_123
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_123])]) ).
thf(f10011,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_123
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9501,f9587]) ).
thf(f9501,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_123 ),
inference(avatar_component_clause,[],[f9499]) ).
thf(f10010,plain,
( spl44_156
| ~ spl44_124
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f10005,f9585,f9504,f10007]) ).
thf(f10007,plain,
( spl44_156
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_156])]) ).
thf(f9504,plain,
( spl44_124
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_124])]) ).
thf(f10005,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) )
| ~ spl44_124
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9506,f9587]) ).
thf(f9506,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) )
| ~ spl44_124 ),
inference(avatar_component_clause,[],[f9504]) ).
thf(f10004,plain,
( spl44_155
| ~ spl44_125
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9999,f9585,f9509,f10001]) ).
thf(f10001,plain,
( spl44_155
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_155])]) ).
thf(f9509,plain,
( spl44_125
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_125])]) ).
thf(f9999,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_125
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9511,f9587]) ).
thf(f9511,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_125 ),
inference(avatar_component_clause,[],[f9509]) ).
thf(f9998,plain,
( spl44_154
| ~ spl44_126
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9993,f9585,f9514,f9995]) ).
thf(f9995,plain,
( spl44_154
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_154])]) ).
thf(f9514,plain,
( spl44_126
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_126])]) ).
thf(f9993,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_126
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9516,f9587]) ).
thf(f9516,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_126 ),
inference(avatar_component_clause,[],[f9514]) ).
thf(f9992,plain,
( spl44_153
| ~ spl44_127
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9987,f9585,f9519,f9989]) ).
thf(f9989,plain,
( spl44_153
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_153])]) ).
thf(f9519,plain,
( spl44_127
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_127])]) ).
thf(f9987,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_127
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9521,f9587]) ).
thf(f9521,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_127 ),
inference(avatar_component_clause,[],[f9519]) ).
thf(f9986,plain,
( spl44_152
| ~ spl44_128
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9981,f9585,f9524,f9983]) ).
thf(f9983,plain,
( spl44_152
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_152])]) ).
thf(f9524,plain,
( spl44_128
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_128])]) ).
thf(f9981,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_128
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9526,f9587]) ).
thf(f9526,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_128 ),
inference(avatar_component_clause,[],[f9524]) ).
thf(f9980,plain,
( spl44_151
| ~ spl44_129
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9975,f9585,f9529,f9977]) ).
thf(f9977,plain,
( spl44_151
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_151])]) ).
thf(f9529,plain,
( spl44_129
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_129])]) ).
thf(f9975,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_129
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9531,f9587]) ).
thf(f9531,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_129 ),
inference(avatar_component_clause,[],[f9529]) ).
thf(f9974,plain,
( spl44_150
| ~ spl44_130
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9969,f9585,f9534,f9971]) ).
thf(f9971,plain,
( spl44_150
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_150])]) ).
thf(f9534,plain,
( spl44_130
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_130])]) ).
thf(f9969,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_130
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9536,f9587]) ).
thf(f9536,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_130 ),
inference(avatar_component_clause,[],[f9534]) ).
thf(f9968,plain,
( spl44_149
| ~ spl44_131
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9963,f9585,f9539,f9965]) ).
thf(f9965,plain,
( spl44_149
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_149])]) ).
thf(f9539,plain,
( spl44_131
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_131])]) ).
thf(f9963,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_131
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9541,f9587]) ).
thf(f9541,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,zfact,min)) )
| ~ spl44_131 ),
inference(avatar_component_clause,[],[f9539]) ).
thf(f9962,plain,
( spl44_148
| ~ spl44_132
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9957,f9585,f9544,f9959]) ).
thf(f9959,plain,
( spl44_148
<=> ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_148])]) ).
thf(f9544,plain,
( spl44_132
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_132])]) ).
thf(f9957,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),t) )
| ~ spl44_132
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9546,f9587]) ).
thf(f9546,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) )
| ~ spl44_132 ),
inference(avatar_component_clause,[],[f9544]) ).
thf(f9956,plain,
( spl44_147
| ~ spl44_133
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9951,f9585,f9549,f9953]) ).
thf(f9953,plain,
( spl44_147
<=> ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_147])]) ).
thf(f9549,plain,
( spl44_133
<=> ( vAPP(int,int,zfact,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_133])]) ).
thf(f9951,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))) )
| ~ spl44_133
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9551,f9587]) ).
thf(f9551,plain,
( ( vAPP(int,int,zfact,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_133 ),
inference(avatar_component_clause,[],[f9549]) ).
thf(f9950,plain,
( spl44_146
| ~ spl44_134
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9945,f9585,f9554,f9947]) ).
thf(f9947,plain,
( spl44_146
<=> ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_146])]) ).
thf(f9554,plain,
( spl44_134
<=> ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_134])]) ).
thf(f9945,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) )
| ~ spl44_134
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9556,f9587]) ).
thf(f9556,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) )
| ~ spl44_134 ),
inference(avatar_component_clause,[],[f9554]) ).
thf(f9944,plain,
( spl44_145
| ~ spl44_135
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9939,f9585,f9559,f9941]) ).
thf(f9941,plain,
( spl44_145
<=> ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_145])]) ).
thf(f9559,plain,
( spl44_135
<=> ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_135])]) ).
thf(f9939,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),sK7) )
| ~ spl44_135
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9561,f9587]) ).
thf(f9561,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),sK7) )
| ~ spl44_135 ),
inference(avatar_component_clause,[],[f9559]) ).
thf(f9938,plain,
( spl44_144
| ~ spl44_136
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9933,f9585,f9564,f9935]) ).
thf(f9935,plain,
( spl44_144
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_144])]) ).
thf(f9564,plain,
( spl44_136
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_136])]) ).
thf(f9933,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,zero_zero_int)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,zero_zero_int)))) )
| ~ spl44_136
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9566,f9587]) ).
thf(f9566,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min)))) )
| ~ spl44_136 ),
inference(avatar_component_clause,[],[f9564]) ).
thf(f9932,plain,
( spl44_143
| ~ spl44_137
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9927,f9585,f9569,f9929]) ).
thf(f9569,plain,
( spl44_137
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_137])]) ).
thf(f9927,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),t) )
| ~ spl44_137
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9571,f9587]) ).
thf(f9571,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),t) )
| ~ spl44_137 ),
inference(avatar_component_clause,[],[f9569]) ).
thf(f9926,plain,
( spl44_142
| ~ spl44_138
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9921,f9585,f9574,f9923]) ).
thf(f9574,plain,
( spl44_138
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_138])]) ).
thf(f9921,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,zero_zero_int)),zero_zero_int) )
| ~ spl44_138
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9576,f9587]) ).
thf(f9576,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),zero_zero_int) )
| ~ spl44_138 ),
inference(avatar_component_clause,[],[f9574]) ).
thf(f9920,plain,
( spl44_141
| ~ spl44_139
| ~ spl44_140 ),
inference(avatar_split_clause,[],[f9915,f9585,f9579,f9917]) ).
thf(f9917,plain,
( spl44_141
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,zfact,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_141])]) ).
thf(f9579,plain,
( spl44_139
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,zfact,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_139])]) ).
thf(f9915,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,zfact,zero_zero_int)) )
| ~ spl44_139
| ~ spl44_140 ),
inference(forward_demodulation,[],[f9581,f9587]) ).
thf(f9581,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,zfact,min)) )
| ~ spl44_139 ),
inference(avatar_component_clause,[],[f9579]) ).
thf(f9588,plain,
( spl44_140
| ~ spl44_96
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9583,f9001,f8996,f9585]) ).
thf(f9583,plain,
( ( vAPP(int,int,zfact,zero_zero_int) = vAPP(int,int,zfact,min) )
| ~ spl44_96
| ~ spl44_97 ),
inference(backward_demodulation,[],[f9003,f8998]) ).
thf(f9582,plain,
( spl44_139
| ~ spl44_93
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9310,f9001,f8751,f9579]) ).
thf(f8751,plain,
( spl44_93
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_93])]) ).
thf(f9310,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,zfact,min)) )
| ~ spl44_93
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8753,f9003]) ).
thf(f8753,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,bit1,zero_zero_int)) )
| ~ spl44_93 ),
inference(avatar_component_clause,[],[f8751]) ).
thf(f9577,plain,
( spl44_138
| ~ spl44_92
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9309,f9001,f8553,f9574]) ).
thf(f8553,plain,
( spl44_92
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_92])]) ).
thf(f9309,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),zero_zero_int) )
| ~ spl44_92
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8555,f9003]) ).
thf(f8555,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) )
| ~ spl44_92 ),
inference(avatar_component_clause,[],[f8553]) ).
thf(f9572,plain,
( spl44_137
| ~ spl44_85
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9308,f9001,f8338,f9569]) ).
thf(f8338,plain,
( spl44_85
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_85])]) ).
thf(f9308,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,zfact,min)),t) )
| ~ spl44_85
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8340,f9003]) ).
thf(f8340,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) )
| ~ spl44_85 ),
inference(avatar_component_clause,[],[f8338]) ).
thf(f9567,plain,
( spl44_136
| ~ spl44_83
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9307,f9001,f8297,f9564]) ).
thf(f8297,plain,
( spl44_83
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_83])]) ).
thf(f9307,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min)))) )
| ~ spl44_83
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8299,f9003]) ).
thf(f8299,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_83 ),
inference(avatar_component_clause,[],[f8297]) ).
thf(f9562,plain,
( spl44_135
| ~ spl44_82
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9306,f9001,f8292,f9559]) ).
thf(f8292,plain,
( spl44_82
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_82])]) ).
thf(f9306,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),sK7) )
| ~ spl44_82
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8294,f9003]) ).
thf(f8294,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_82 ),
inference(avatar_component_clause,[],[f8292]) ).
thf(f9557,plain,
( spl44_134
| ~ spl44_81
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9305,f9001,f8285,f9554]) ).
thf(f8285,plain,
( spl44_81
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_81])]) ).
thf(f9305,plain,
( ( vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) )
| ~ spl44_81
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8287,f9003]) ).
thf(f8287,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_81 ),
inference(avatar_component_clause,[],[f8285]) ).
thf(f9552,plain,
( spl44_133
| ~ spl44_79
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9304,f9001,f8267,f9549]) ).
thf(f8267,plain,
( spl44_79
<=> ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_79])]) ).
thf(f9304,plain,
( ( vAPP(int,int,zfact,min) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_79
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8269,f9003]) ).
thf(f8269,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_79 ),
inference(avatar_component_clause,[],[f8267]) ).
thf(f9547,plain,
( spl44_132
| ~ spl44_78
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9303,f9001,f8257,f9544]) ).
thf(f8257,plain,
( spl44_78
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_78])]) ).
thf(f9303,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,zfact,min))) )
| ~ spl44_78
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8259,f9003]) ).
thf(f8259,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_78 ),
inference(avatar_component_clause,[],[f8257]) ).
thf(f9542,plain,
( spl44_131
| ~ spl44_77
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9302,f9001,f8248,f9539]) ).
thf(f8248,plain,
( spl44_77
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_77])]) ).
thf(f9302,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,zfact,min)) )
| ~ spl44_77
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8250,f9003]) ).
thf(f8250,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) )
| ~ spl44_77 ),
inference(avatar_component_clause,[],[f8248]) ).
thf(f9537,plain,
( spl44_130
| ~ spl44_75
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9301,f9001,f8229,f9534]) ).
thf(f8229,plain,
( spl44_75
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_75])]) ).
thf(f9301,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_75
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8231,f9003]) ).
thf(f8231,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_75 ),
inference(avatar_component_clause,[],[f8229]) ).
thf(f9532,plain,
( spl44_129
| ~ spl44_74
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9300,f9001,f8220,f9529]) ).
thf(f8220,plain,
( spl44_74
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_74])]) ).
thf(f9300,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_74
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8222,f9003]) ).
thf(f8222,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_74 ),
inference(avatar_component_clause,[],[f8220]) ).
thf(f9527,plain,
( spl44_128
| ~ spl44_71
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9299,f9001,f8189,f9524]) ).
thf(f8189,plain,
( spl44_71
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_71])]) ).
thf(f9299,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_71
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8191,f9003]) ).
thf(f8191,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_71 ),
inference(avatar_component_clause,[],[f8189]) ).
thf(f9522,plain,
( spl44_127
| ~ spl44_70
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9298,f9001,f8180,f9519]) ).
thf(f8180,plain,
( spl44_70
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_70])]) ).
thf(f9298,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_70
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8182,f9003]) ).
thf(f8182,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_70 ),
inference(avatar_component_clause,[],[f8180]) ).
thf(f9517,plain,
( spl44_126
| ~ spl44_69
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9297,f9001,f8171,f9514]) ).
thf(f8171,plain,
( spl44_69
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_69])]) ).
thf(f9297,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_69
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8173,f9003]) ).
thf(f8173,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_69 ),
inference(avatar_component_clause,[],[f8171]) ).
thf(f9512,plain,
( spl44_125
| ~ spl44_68
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9296,f9001,f8160,f9509]) ).
thf(f8160,plain,
( spl44_68
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_68])]) ).
thf(f9296,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_68
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8162,f9003]) ).
thf(f8162,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_68 ),
inference(avatar_component_clause,[],[f8160]) ).
thf(f9507,plain,
( spl44_124
| ~ spl44_67
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9295,f9001,f8149,f9504]) ).
thf(f8149,plain,
( spl44_67
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_67])]) ).
thf(f9295,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) )
| ~ spl44_67
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8151,f9003]) ).
thf(f8151,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min)) )
| ~ spl44_67 ),
inference(avatar_component_clause,[],[f8149]) ).
thf(f9502,plain,
( spl44_123
| ~ spl44_66
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9294,f9001,f8138,f9499]) ).
thf(f8138,plain,
( spl44_66
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_66])]) ).
thf(f9294,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_66
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8140,f9003]) ).
thf(f8140,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_66 ),
inference(avatar_component_clause,[],[f8138]) ).
thf(f9497,plain,
( spl44_122
| ~ spl44_65
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9293,f9001,f8127,f9494]) ).
thf(f8127,plain,
( spl44_65
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_65])]) ).
thf(f9293,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_65
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8129,f9003]) ).
thf(f8129,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s1),s1)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_65 ),
inference(avatar_component_clause,[],[f8127]) ).
thf(f9492,plain,
( spl44_121
| ~ spl44_63
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9292,f9001,f8105,f9489]) ).
thf(f8105,plain,
( spl44_63
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_63])]) ).
thf(f9292,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))),min) )
| ~ spl44_63
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8107,f9003]) ).
thf(f8107,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),min) )
| ~ spl44_63 ),
inference(avatar_component_clause,[],[f8105]) ).
thf(f9487,plain,
( spl44_120
| ~ spl44_62
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9291,f9001,f8095,f9484]) ).
thf(f8095,plain,
( spl44_62
<=> ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_62])]) ).
thf(f9291,plain,
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min))))))) )
| ~ spl44_62
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8097,f9003]) ).
thf(f8097,plain,
( ( $true = vAPP(int,$o,twoSqu919416604sum2sq,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_62 ),
inference(avatar_component_clause,[],[f8095]) ).
thf(f9482,plain,
( spl44_119
| ~ spl44_61
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9290,f9001,f8085,f9479]) ).
thf(f8085,plain,
( spl44_61
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_61])]) ).
thf(f9290,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_61
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8087,f9003]) ).
thf(f8087,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_61 ),
inference(avatar_component_clause,[],[f8085]) ).
thf(f9477,plain,
( spl44_118
| ~ spl44_60
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9289,f9001,f8076,f9474]) ).
thf(f8076,plain,
( spl44_60
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_60])]) ).
thf(f9289,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_60
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8078,f9003]) ).
thf(f8078,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,t),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_60 ),
inference(avatar_component_clause,[],[f8076]) ).
thf(f9472,plain,
( spl44_117
| ~ spl44_59
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9288,f9001,f8067,f9469]) ).
thf(f8067,plain,
( spl44_59
<=> ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_59])]) ).
thf(f9288,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_59
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8069,f9003]) ).
thf(f8069,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_59 ),
inference(avatar_component_clause,[],[f8067]) ).
thf(f9467,plain,
( spl44_116
| ~ spl44_58
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9287,f9001,f8058,f9464]) ).
thf(f8058,plain,
( spl44_58
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_58])]) ).
thf(f9287,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,zfact,min))) )
| ~ spl44_58
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8060,f9003]) ).
thf(f8060,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_58 ),
inference(avatar_component_clause,[],[f8058]) ).
thf(f9462,plain,
( spl44_115
| ~ spl44_57
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9286,f9001,f8052,f9459]) ).
thf(f8052,plain,
( spl44_57
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_57])]) ).
thf(f9286,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,zfact,min))) )
| ~ spl44_57
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8054,f9003]) ).
thf(f8054,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_57 ),
inference(avatar_component_clause,[],[f8052]) ).
thf(f9457,plain,
( spl44_114
| ~ spl44_56
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9285,f9001,f8046,f9454]) ).
thf(f8046,plain,
( spl44_56
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_56])]) ).
thf(f9285,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_56
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8048,f9003]) ).
thf(f8048,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_56 ),
inference(avatar_component_clause,[],[f8046]) ).
thf(f9452,plain,
( spl44_113
| ~ spl44_55
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9284,f9001,f8041,f9449]) ).
thf(f8041,plain,
( spl44_55
<=> ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_55])]) ).
thf(f9284,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,zfact,min))) )
| ~ spl44_55
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8043,f9003]) ).
thf(f8043,plain,
( ( $true = vAPP(int,$o,zprime,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_55 ),
inference(avatar_component_clause,[],[f8041]) ).
thf(f9447,plain,
( spl44_112
| ~ spl44_54
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9283,f9001,f8034,f9444]) ).
thf(f8034,plain,
( spl44_54
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_54])]) ).
thf(f9283,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,zfact,min)) )
| ~ spl44_54
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8036,f9003]) ).
thf(f8036,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit1,zero_zero_int)) )
| ~ spl44_54 ),
inference(avatar_component_clause,[],[f8034]) ).
thf(f9442,plain,
( spl44_111
| ~ spl44_52
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9282,f9001,f8022,f9439]) ).
thf(f8022,plain,
( spl44_52
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_52])]) ).
thf(f9282,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,zfact,min)) )
| ~ spl44_52
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8024,f9003]) ).
thf(f8024,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(int,int,bit1,zero_zero_int)) )
| ~ spl44_52 ),
inference(avatar_component_clause,[],[f8022]) ).
thf(f9437,plain,
( spl44_110
| ~ spl44_51
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9281,f9001,f8016,f9434]) ).
thf(f8016,plain,
( spl44_51
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_51])]) ).
thf(f9281,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,zfact,min)),t) )
| ~ spl44_51
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8018,f9003]) ).
thf(f8018,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit1,zero_zero_int)),t) )
| ~ spl44_51 ),
inference(avatar_component_clause,[],[f8016]) ).
thf(f9432,plain,
( spl44_109
| ~ spl44_48
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9280,f9001,f8000,f9429]) ).
thf(f8000,plain,
( spl44_48
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_48])]) ).
thf(f9280,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_48
| ~ spl44_97 ),
inference(backward_demodulation,[],[f8002,f9003]) ).
thf(f8002,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_48 ),
inference(avatar_component_clause,[],[f8000]) ).
thf(f9427,plain,
( spl44_108
| ~ spl44_47
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9279,f9001,f7991,f9424]) ).
thf(f7991,plain,
( spl44_47
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_47])]) ).
thf(f9279,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,zfact,min)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))))) )
| ~ spl44_47
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7993,f9003]) ).
thf(f7993,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK43),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_47 ),
inference(avatar_component_clause,[],[f7991]) ).
thf(f9407,plain,
( spl44_107
| ~ spl44_44
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9217,f9001,f7801,f9404]) ).
thf(f7801,plain,
( spl44_44
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_44])]) ).
thf(f9217,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))) )
| ~ spl44_44
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7803,f9003]) ).
thf(f7803,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_44 ),
inference(avatar_component_clause,[],[f7801]) ).
thf(f9399,plain,
( spl44_106
| ~ spl44_43
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9213,f9001,f7740,f9396]) ).
thf(f7740,plain,
( spl44_43
<=> ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_43])]) ).
thf(f9213,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) = vAPP(int,int,zfact,min) )
| ~ spl44_43
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7742,f9003]) ).
thf(f7742,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,min),min) )
| ~ spl44_43 ),
inference(avatar_component_clause,[],[f7740]) ).
thf(f9364,plain,
( ~ spl44_105
| spl44_26
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9133,f9001,f7347,f9361]) ).
thf(f7347,plain,
( spl44_26
<=> ( t = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_26])]) ).
thf(f9133,plain,
( ( t != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,min)) )
| spl44_26
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7349,f9003]) ).
thf(f7349,plain,
( ( t != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| spl44_26 ),
inference(avatar_component_clause,[],[f7347]) ).
thf(f9359,plain,
( spl44_104
| ~ spl44_17
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9132,f9001,f7299,f9356]) ).
thf(f7299,plain,
( spl44_17
<=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_17])]) ).
thf(f9132,plain,
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min))) )
| ~ spl44_17
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7301,f9003]) ).
thf(f7301,plain,
( ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_17 ),
inference(avatar_component_clause,[],[f7299]) ).
thf(f9354,plain,
( spl44_103
| ~ spl44_15
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9131,f9001,f7288,f9351]) ).
thf(f7288,plain,
( spl44_15
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_15])]) ).
thf(f9131,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_15
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7290,f9003]) ).
thf(f7290,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_15 ),
inference(avatar_component_clause,[],[f7288]) ).
thf(f9349,plain,
( spl44_102
| ~ spl44_14
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9130,f9001,f7283,f9346]) ).
thf(f7283,plain,
( spl44_14
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_14])]) ).
thf(f9130,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_14
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7285,f9003]) ).
thf(f7285,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_14 ),
inference(avatar_component_clause,[],[f7283]) ).
thf(f9344,plain,
( spl44_101
| ~ spl44_13
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9129,f9001,f7278,f9341]) ).
thf(f7278,plain,
( spl44_13
<=> ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_13])]) ).
thf(f9129,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,zfact,min)))) )
| ~ spl44_13
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7280,f9003]) ).
thf(f7280,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_13 ),
inference(avatar_component_clause,[],[f7278]) ).
thf(f9339,plain,
( ~ spl44_100
| spl44_5
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9128,f9001,f7232,f9336]) ).
thf(f7232,plain,
( spl44_5
<=> ( zero_zero_int = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_5])]) ).
thf(f9128,plain,
( ( zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,zfact,min)) )
| spl44_5
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7234,f9003]) ).
thf(f7234,plain,
( ( zero_zero_int != vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) )
| spl44_5 ),
inference(avatar_component_clause,[],[f7232]) ).
thf(f9334,plain,
( ~ spl44_99
| spl44_4
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9127,f9001,f7226,f9331]) ).
thf(f7226,plain,
( spl44_4
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_4])]) ).
thf(f9127,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,zfact,min)) )
| spl44_4
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7228,f9003]) ).
thf(f7228,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) )
| spl44_4 ),
inference(avatar_component_clause,[],[f7226]) ).
thf(f9329,plain,
( ~ spl44_98
| spl44_3
| ~ spl44_97 ),
inference(avatar_split_clause,[],[f9126,f9001,f7219,f9326]) ).
thf(f7219,plain,
( spl44_3
<=> ( vAPP(int,real,number267125858f_real,zero_zero_int) = vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_3])]) ).
thf(f9126,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,zfact,min)) )
| spl44_3
| ~ spl44_97 ),
inference(backward_demodulation,[],[f7221,f9003]) ).
thf(f7221,plain,
( ( vAPP(int,real,number267125858f_real,zero_zero_int) != vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) )
| spl44_3 ),
inference(avatar_component_clause,[],[f7219]) ).
thf(f9004,plain,
( spl44_97
| ~ spl44_50 ),
inference(avatar_split_clause,[],[f8993,f8010,f9001]) ).
thf(f8010,plain,
( spl44_50
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_50])]) ).
thf(f8993,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,min) )
| ~ spl44_50 ),
inference(trivial_inequality_removal,[],[f8988]) ).
thf(f8988,plain,
( ( $true != $true )
| ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,zfact,min) )
| ~ spl44_50 ),
inference(superposition,[],[f7461,f8012]) ).
thf(f8012,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,min),zero_zero_int) )
| ~ spl44_50 ),
inference(avatar_component_clause,[],[f8010]) ).
thf(f8999,plain,
spl44_96,
inference(avatar_split_clause,[],[f8994,f8996]) ).
thf(f8896,plain,
( spl44_95
| ~ spl44_50 ),
inference(avatar_split_clause,[],[f8891,f8010,f8893]) ).
thf(f8893,plain,
( spl44_95
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_95])]) ).
thf(f8891,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,min) )
| ~ spl44_50 ),
inference(trivial_inequality_removal,[],[f8886]) ).
thf(f8886,plain,
( ( $true != $true )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,min) )
| ~ spl44_50 ),
inference(superposition,[],[f6177,f8012]) ).
thf(f8841,plain,
spl44_94,
inference(avatar_split_clause,[],[f8830,f8838]) ).
thf(f8838,plain,
( spl44_94
<=> ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),standardRes,zero_zero_int),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_94])]) ).
thf(f8754,plain,
( spl44_93
| ~ spl44_43 ),
inference(avatar_split_clause,[],[f8742,f7740,f8751]) ).
thf(f8742,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,min),vAPP(int,int,bit1,zero_zero_int)) )
| ~ spl44_43 ),
inference(superposition,[],[f5341,f7742]) ).
thf(f8556,plain,
( spl44_92
| spl44_91 ),
inference(avatar_split_clause,[],[f8550,f8540,f8553]) ).
thf(f8540,plain,
( spl44_91
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_91])]) ).
thf(f8550,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) )
| spl44_91 ),
inference(trivial_inequality_removal,[],[f8549]) ).
thf(f8549,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) )
| spl44_91 ),
inference(superposition,[],[f8542,f1202]) ).
thf(f8542,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) )
| spl44_91 ),
inference(avatar_component_clause,[],[f8540]) ).
thf(f8546,plain,
~ spl44_91,
inference(avatar_split_clause,[],[f8533,f8540]) ).
thf(f8545,plain,
( ~ spl44_91
| ~ spl44_43 ),
inference(avatar_split_clause,[],[f8532,f7740,f8540]) ).
thf(f8532,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),zero_zero_int) )
| ~ spl44_43 ),
inference(superposition,[],[f4717,f7742]) ).
thf(f8543,plain,
~ spl44_91,
inference(avatar_split_clause,[],[f8530,f8540]) ).
thf(f8515,plain,
( spl44_90
| ~ spl44_86 ),
inference(avatar_split_clause,[],[f8483,f8382,f8509]) ).
thf(f8483,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_86 ),
inference(trivial_inequality_removal,[],[f8470]) ).
thf(f8470,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_86 ),
inference(superposition,[],[f8384,f8441]) ).
thf(f8514,plain,
( spl44_89
| spl44_88 ),
inference(avatar_split_clause,[],[f8484,f8501,f8504]) ).
thf(f8504,plain,
( spl44_89
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),dvd_dvd_int,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_89])]) ).
thf(f8501,plain,
( spl44_88
<=> ! [X0: int] : ( zero_zero_int = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_88])]) ).
thf(f8513,plain,
( spl44_89
| spl44_88 ),
inference(avatar_split_clause,[],[f8485,f8501,f8504]) ).
thf(f8512,plain,
( spl44_90
| ~ spl44_86 ),
inference(avatar_split_clause,[],[f8491,f8382,f8509]) ).
thf(f8491,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_86 ),
inference(trivial_inequality_removal,[],[f8462]) ).
thf(f8462,plain,
( ( $true = $false )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),vAPP(sTfun(int,$o),int,sK17,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int))) )
| ~ spl44_86 ),
inference(superposition,[],[f8441,f8384]) ).
thf(f8507,plain,
( spl44_88
| spl44_89 ),
inference(avatar_split_clause,[],[f8492,f8504,f8501]) ).
thf(f8393,plain,
( spl44_87
| spl44_36 ),
inference(avatar_split_clause,[],[f8388,f7399,f8390]) ).
thf(f8390,plain,
( spl44_87
<=> ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_87])]) ).
thf(f7399,plain,
( spl44_36
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_36])]) ).
thf(f8388,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),min) )
| spl44_36 ),
inference(trivial_inequality_removal,[],[f8387]) ).
thf(f8387,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),min) )
| spl44_36 ),
inference(superposition,[],[f7401,f1202]) ).
thf(f7401,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),min) )
| spl44_36 ),
inference(avatar_component_clause,[],[f7399]) ).
thf(f8385,plain,
( spl44_86
| spl44_34 ),
inference(avatar_split_clause,[],[f8380,f7389,f8382]) ).
thf(f7389,plain,
( spl44_34
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_34])]) ).
thf(f8380,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min) )
| spl44_34 ),
inference(trivial_inequality_removal,[],[f8379]) ).
thf(f8379,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min) )
| spl44_34 ),
inference(superposition,[],[f7391,f1202]) ).
thf(f7391,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,zero_zero_int),min) )
| spl44_34 ),
inference(avatar_component_clause,[],[f7389]) ).
thf(f8341,plain,
( spl44_85
| spl44_73 ),
inference(avatar_split_clause,[],[f8336,f8206,f8338]) ).
thf(f8206,plain,
( spl44_73
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_73])]) ).
thf(f8336,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) )
| spl44_73 ),
inference(trivial_inequality_removal,[],[f8335]) ).
thf(f8335,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) )
| spl44_73 ),
inference(superposition,[],[f8208,f1202]) ).
thf(f8208,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) )
| spl44_73 ),
inference(avatar_component_clause,[],[f8206]) ).
thf(f8334,plain,
( ~ spl44_84
| spl44_26 ),
inference(avatar_split_clause,[],[f8329,f7347,f8331]) ).
thf(f8331,plain,
( spl44_84
<=> ( t = vAPP(int,int,bit1,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_84])]) ).
thf(f8329,plain,
( ( t != vAPP(int,int,bit1,zero_zero_int) )
| spl44_26 ),
inference(superposition,[],[f7349,f4464]) ).
thf(f8300,plain,
( spl44_83
| ~ spl44_64
| ~ spl44_81 ),
inference(avatar_split_clause,[],[f8290,f8285,f8116,f8297]) ).
thf(f8116,plain,
( spl44_64
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_64])]) ).
thf(f8290,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_64
| ~ spl44_81 ),
inference(backward_demodulation,[],[f8118,f8287]) ).
thf(f8118,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),dvd_dvd_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s))) )
| ~ spl44_64 ),
inference(avatar_component_clause,[],[f8116]) ).
thf(f8295,plain,
( spl44_82
| ~ spl44_72
| ~ spl44_81 ),
inference(avatar_split_clause,[],[f8289,f8285,f8200,f8292]) ).
thf(f8200,plain,
( spl44_72
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_72])]) ).
thf(f8289,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_72
| ~ spl44_81 ),
inference(backward_demodulation,[],[f8202,f8287]) ).
thf(f8202,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) )
| ~ spl44_72 ),
inference(avatar_component_clause,[],[f8200]) ).
thf(f8288,plain,
( spl44_81
| ~ spl44_76
| ~ spl44_78 ),
inference(avatar_split_clause,[],[f8283,f8257,f8240,f8285]) ).
thf(f8240,plain,
( spl44_76
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_76])]) ).
thf(f8283,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_76
| ~ spl44_78 ),
inference(forward_demodulation,[],[f8242,f8259]) ).
thf(f8242,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) )
| ~ spl44_76 ),
inference(avatar_component_clause,[],[f8240]) ).
thf(f8280,plain,
( ~ spl44_80
| spl44_9 ),
inference(avatar_split_clause,[],[f8275,f7258,f8277]) ).
thf(f8277,plain,
( spl44_80
<=> ( zero_zero_int = vAPP(int,int,number_number_of_int,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_80])]) ).
thf(f7258,plain,
( spl44_9
<=> ( vAPP(int,int,number_number_of_int,min) = vAPP(int,int,number_number_of_int,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_9])]) ).
thf(f8275,plain,
( ( zero_zero_int != vAPP(int,int,number_number_of_int,min) )
| spl44_9 ),
inference(forward_demodulation,[],[f7260,f4464]) ).
thf(f7260,plain,
( ( vAPP(int,int,number_number_of_int,min) != vAPP(int,int,number_number_of_int,zero_zero_int) )
| spl44_9 ),
inference(avatar_component_clause,[],[f7258]) ).
thf(f8270,plain,
( spl44_79
| ~ spl44_19 ),
inference(avatar_split_clause,[],[f8265,f7311,f8267]) ).
thf(f7311,plain,
( spl44_19
<=> ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_19])]) ).
thf(f8265,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_19 ),
inference(forward_demodulation,[],[f8264,f4464]) ).
thf(f8264,plain,
( ( vAPP(int,int,bit1,zero_zero_int) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_19 ),
inference(forward_demodulation,[],[f8263,f4464]) ).
thf(f8263,plain,
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_19 ),
inference(forward_demodulation,[],[f8262,f4464]) ).
thf(f8262,plain,
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_19 ),
inference(forward_demodulation,[],[f8261,f4759]) ).
thf(f8261,plain,
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ~ spl44_19 ),
inference(forward_demodulation,[],[f7313,f4757]) ).
thf(f7313,plain,
( ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),legendre,vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_19 ),
inference(avatar_component_clause,[],[f7311]) ).
thf(f8260,plain,
( spl44_78
| ~ spl44_20 ),
inference(avatar_split_clause,[],[f8255,f7316,f8257]) ).
thf(f7316,plain,
( spl44_20
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_20])]) ).
thf(f8255,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_20 ),
inference(forward_demodulation,[],[f8254,f4464]) ).
thf(f8254,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_20 ),
inference(forward_demodulation,[],[f8253,f4759]) ).
thf(f8253,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_20 ),
inference(forward_demodulation,[],[f8252,f4757]) ).
thf(f8252,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,bit1,zero_zero_int))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_20 ),
inference(forward_demodulation,[],[f7318,f4464]) ).
thf(f7318,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(product_prod_int_int,int,twoSqu2057625106sum2sq,vAPP(int,product_prod_int_int,vAPP(int,sTfun(int,product_prod_int_int),product_Pair_int_int,s),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_20 ),
inference(avatar_component_clause,[],[f7316]) ).
thf(f8251,plain,
( spl44_77
| ~ spl44_21 ),
inference(avatar_split_clause,[],[f8246,f7321,f8248]) ).
thf(f7321,plain,
( spl44_21
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_21])]) ).
thf(f8246,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) )
| ~ spl44_21 ),
inference(forward_demodulation,[],[f8245,f4464]) ).
thf(f8245,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)),min) )
| ~ spl44_21 ),
inference(forward_demodulation,[],[f8244,f6100]) ).
thf(f8244,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),min) )
| ~ spl44_21 ),
inference(forward_demodulation,[],[f7323,f4464]) ).
thf(f7323,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)) )
| ~ spl44_21 ),
inference(avatar_component_clause,[],[f7321]) ).
thf(f8243,plain,
( spl44_76
| ~ spl44_22 ),
inference(avatar_split_clause,[],[f8238,f7326,f8240]) ).
thf(f7326,plain,
( spl44_22
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_22])]) ).
thf(f8238,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) )
| ~ spl44_22 ),
inference(forward_demodulation,[],[f8237,f4464]) ).
thf(f8237,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),t) )
| ~ spl44_22 ),
inference(forward_demodulation,[],[f8236,f4759]) ).
thf(f8236,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),t) )
| ~ spl44_22 ),
inference(forward_demodulation,[],[f8235,f4757]) ).
thf(f8235,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,bit1,zero_zero_int))),t) )
| ~ spl44_22 ),
inference(forward_demodulation,[],[f8234,f4464]) ).
thf(f8234,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) )
| ~ spl44_22 ),
inference(forward_demodulation,[],[f8233,f6100]) ).
thf(f8233,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) )
| ~ spl44_22 ),
inference(forward_demodulation,[],[f7328,f4757]) ).
thf(f7328,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),t) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl44_22 ),
inference(avatar_component_clause,[],[f7326]) ).
thf(f8232,plain,
( spl44_75
| ~ spl44_23 ),
inference(avatar_split_clause,[],[f8227,f7331,f8229]) ).
thf(f7331,plain,
( spl44_23
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_23])]) ).
thf(f8227,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_23 ),
inference(forward_demodulation,[],[f8226,f4464]) ).
thf(f8226,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_23 ),
inference(forward_demodulation,[],[f8225,f4464]) ).
thf(f8225,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_23 ),
inference(forward_demodulation,[],[f8224,f4759]) ).
thf(f8224,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ~ spl44_23 ),
inference(forward_demodulation,[],[f7333,f4757]) ).
thf(f7333,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_23 ),
inference(avatar_component_clause,[],[f7331]) ).
thf(f8223,plain,
( spl44_74
| ~ spl44_24 ),
inference(avatar_split_clause,[],[f8218,f7336,f8220]) ).
thf(f7336,plain,
( spl44_24
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_24])]) ).
thf(f8218,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_24 ),
inference(forward_demodulation,[],[f8217,f4464]) ).
thf(f8217,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_24 ),
inference(forward_demodulation,[],[f8216,f4464]) ).
thf(f8216,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_24 ),
inference(forward_demodulation,[],[f8215,f4759]) ).
thf(f8215,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ~ spl44_24 ),
inference(forward_demodulation,[],[f7338,f4757]) ).
thf(f7338,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,s),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_24 ),
inference(avatar_component_clause,[],[f7336]) ).
thf(f8209,plain,
( ~ spl44_73
| spl44_28 ),
inference(avatar_split_clause,[],[f8204,f7359,f8206]) ).
thf(f7359,plain,
( spl44_28
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_28])]) ).
thf(f8204,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,bit1,zero_zero_int)),t) )
| spl44_28 ),
inference(forward_demodulation,[],[f7361,f4464]) ).
thf(f7361,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t) )
| spl44_28 ),
inference(avatar_component_clause,[],[f7359]) ).
thf(f8203,plain,
( spl44_72
| ~ spl44_29 ),
inference(avatar_split_clause,[],[f8198,f7364,f8200]) ).
thf(f7364,plain,
( spl44_29
<=> ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_29])]) ).
thf(f8198,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,s),s)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) )
| ~ spl44_29 ),
inference(forward_demodulation,[],[f8197,f6100]) ).
thf(f8197,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))) )
| ~ spl44_29 ),
inference(forward_demodulation,[],[f8196,f4757]) ).
thf(f8196,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,bit1,zero_zero_int)) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) )
| ~ spl44_29 ),
inference(forward_demodulation,[],[f8195,f4464]) ).
thf(f8195,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))),sK7) )
| ~ spl44_29 ),
inference(forward_demodulation,[],[f8194,f4464]) ).
thf(f8194,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))),sK7) )
| ~ spl44_29 ),
inference(forward_demodulation,[],[f8193,f4759]) ).
thf(f8193,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))),sK7) )
| ~ spl44_29 ),
inference(forward_demodulation,[],[f7366,f4757]) ).
thf(f7366,plain,
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,s),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),sK7) )
| ~ spl44_29 ),
inference(avatar_component_clause,[],[f7364]) ).
thf(f8192,plain,
( spl44_71
| ~ spl44_30 ),
inference(avatar_split_clause,[],[f8187,f7369,f8189]) ).
thf(f7369,plain,
( spl44_30
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_30])]) ).
thf(f8187,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_30 ),
inference(forward_demodulation,[],[f8186,f4464]) ).
thf(f8186,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_30 ),
inference(forward_demodulation,[],[f8185,f4464]) ).
thf(f8185,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_30 ),
inference(forward_demodulation,[],[f8184,f4759]) ).
thf(f8184,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ~ spl44_30 ),
inference(forward_demodulation,[],[f7371,f4757]) ).
thf(f7371,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,s1),sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_30 ),
inference(avatar_component_clause,[],[f7369]) ).
thf(f8183,plain,
( spl44_70
| ~ spl44_31 ),
inference(avatar_split_clause,[],[f8178,f7374,f8180]) ).
thf(f7374,plain,
( spl44_31
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_31])]) ).
thf(f8178,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_31 ),
inference(forward_demodulation,[],[f8177,f4464]) ).
thf(f8177,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_31 ),
inference(forward_demodulation,[],[f8176,f4464]) ).
thf(f8176,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_31 ),
inference(forward_demodulation,[],[f8175,f4759]) ).
thf(f8175,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ~ spl44_31 ),
inference(forward_demodulation,[],[f7376,f4757]) ).
thf(f7376,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,sK8),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_31 ),
inference(avatar_component_clause,[],[f7374]) ).
thf(f8174,plain,
( spl44_69
| ~ spl44_33 ),
inference(avatar_split_clause,[],[f8169,f7384,f8171]) ).
thf(f7384,plain,
( spl44_33
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_33])]) ).
thf(f8169,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,sK9),sK9)),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_33 ),
inference(forward_demodulation,[],[f8168,f6100]) ).
thf(f8168,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),min),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_33 ),
inference(forward_demodulation,[],[f8167,f4464]) ).
thf(f8167,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,zero_zero_int)),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_33 ),
inference(forward_demodulation,[],[f8166,f4464]) ).
thf(f8166,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))))) )
| ~ spl44_33 ),
inference(forward_demodulation,[],[f8165,f4464]) ).
thf(f8165,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,m),vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))))) )
| ~ spl44_33 ),
inference(forward_demodulation,[],[f8164,f4759]) ).
thf(f8164,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m))) )
| ~ spl44_33 ),
inference(forward_demodulation,[],[f7386,f4757]) ).
thf(f7386,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vAPP(int,sTfun(int,sTfun(int,$o)),zcong,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,sK9),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),vAPP(int,int,number_number_of_int,min)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl44_33 ),
inference(avatar_component_clause,[],[f7384]) ).
thf(f8163,plain,
spl44_68,
inference(avatar_split_clause,[],[f8158,f8160]) ).
thf(f8152,plain,
spl44_67,
inference(avatar_split_clause,[],[f8147,f8149]) ).
thf(f8141,plain,
spl44_66,
inference(avatar_split_clause,[],[f8136,f8138]) ).
thf(f8130,plain,
spl44_65,
inference(avatar_split_clause,[],[f8125,f8127]) ).
thf(f8119,plain,
spl44_64,
inference(avatar_split_clause,[],[f8114,f8116]) ).
thf(f8108,plain,
spl44_63,
inference(avatar_split_clause,[],[f8103,f8105]) ).
thf(f8098,plain,
spl44_62,
inference(avatar_split_clause,[],[f8093,f8095]) ).
thf(f8088,plain,
spl44_61,
inference(avatar_split_clause,[],[f8083,f8085]) ).
thf(f8079,plain,
spl44_60,
inference(avatar_split_clause,[],[f8074,f8076]) ).
thf(f8070,plain,
spl44_59,
inference(avatar_split_clause,[],[f8065,f8067]) ).
thf(f8061,plain,
spl44_58,
inference(avatar_split_clause,[],[f8056,f8058]) ).
thf(f8055,plain,
spl44_57,
inference(avatar_split_clause,[],[f8050,f8052]) ).
thf(f8049,plain,
spl44_56,
inference(avatar_split_clause,[],[f6752,f8046]) ).
thf(f8044,plain,
spl44_55,
inference(avatar_split_clause,[],[f8039,f8041]) ).
thf(f8037,plain,
spl44_54,
inference(avatar_split_clause,[],[f8032,f8034]) ).
thf(f8031,plain,
spl44_53,
inference(avatar_split_clause,[],[f5952,f8027]) ).
thf(f8027,plain,
( spl44_53
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),zero_zero_int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_53])]) ).
thf(f8030,plain,
spl44_53,
inference(avatar_split_clause,[],[f6748,f8027]) ).
thf(f8025,plain,
spl44_52,
inference(avatar_split_clause,[],[f8020,f8022]) ).
thf(f8019,plain,
spl44_51,
inference(avatar_split_clause,[],[f8014,f8016]) ).
thf(f8013,plain,
spl44_50,
inference(avatar_split_clause,[],[f6744,f8010]) ).
thf(f8008,plain,
spl44_49,
inference(avatar_split_clause,[],[f5941,f8005]) ).
thf(f8003,plain,
spl44_48,
inference(avatar_split_clause,[],[f7998,f8000]) ).
thf(f7994,plain,
spl44_47,
inference(avatar_split_clause,[],[f7989,f7991]) ).
thf(f7860,plain,
spl44_46,
inference(avatar_split_clause,[],[f7859,f7839]) ).
thf(f7839,plain,
( spl44_46
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_eq_int,vAPP(int,int,bit0,zero_zero_int)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_46])]) ).
thf(f7856,plain,
~ spl44_45,
inference(avatar_split_clause,[],[f7855,f7832]) ).
thf(f7832,plain,
( spl44_45
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,bit0,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_45])]) ).
thf(f7842,plain,
spl44_46,
inference(avatar_split_clause,[],[f7837,f7839]) ).
thf(f7835,plain,
~ spl44_45,
inference(avatar_split_clause,[],[f7830,f7832]) ).
thf(f7806,plain,
spl44_44,
inference(avatar_split_clause,[],[f7805,f7801]) ).
thf(f7804,plain,
spl44_44,
inference(avatar_split_clause,[],[f7799,f7801]) ).
thf(f7743,plain,
spl44_43,
inference(avatar_split_clause,[],[f7738,f7740]) ).
thf(f7574,plain,
~ spl44_37,
inference(avatar_split_clause,[],[f7573,f7404]) ).
thf(f7404,plain,
( spl44_37
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_37])]) ).
thf(f7571,plain,
~ spl44_39,
inference(avatar_split_clause,[],[f7570,f7510]) ).
thf(f7510,plain,
( spl44_39
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(int,real,number267125858f_real,zero_zero_int)),vAPP(int,real,number267125858f_real,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_39])]) ).
thf(f7536,plain,
spl44_42,
inference(avatar_split_clause,[],[f6784,f7533]) ).
thf(f7533,plain,
( spl44_42
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_42])]) ).
thf(f7531,plain,
spl44_41,
inference(avatar_split_clause,[],[f6783,f7527]) ).
thf(f7527,plain,
( spl44_41
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_41])]) ).
thf(f7530,plain,
spl44_41,
inference(avatar_split_clause,[],[f6782,f7527]) ).
thf(f7525,plain,
spl44_40,
inference(avatar_split_clause,[],[f6781,f7522]) ).
thf(f7522,plain,
( spl44_40
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),dvd_dvd_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_40])]) ).
thf(f7513,plain,
~ spl44_39,
inference(avatar_split_clause,[],[f7508,f7510]) ).
thf(f7507,plain,
spl44_15,
inference(avatar_split_clause,[],[f6778,f7288]) ).
thf(f7506,plain,
spl44_13,
inference(avatar_split_clause,[],[f6777,f7278]) ).
thf(f7498,plain,
spl44_7,
inference(avatar_split_clause,[],[f6774,f7245]) ).
thf(f7245,plain,
( spl44_7
<=> ( min = vAPP(int,int,bit1,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_7])]) ).
thf(f7497,plain,
spl44_7,
inference(avatar_split_clause,[],[f6773,f7245]) ).
thf(f7496,plain,
spl44_8,
inference(avatar_split_clause,[],[f6772,f7250]) ).
thf(f7250,plain,
( spl44_8
<=> ( zero_zero_int = vAPP(int,int,bit0,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_8])]) ).
thf(f7495,plain,
spl44_8,
inference(avatar_split_clause,[],[f6771,f7250]) ).
thf(f7494,plain,
~ spl44_38,
inference(avatar_split_clause,[],[f6770,f7491]) ).
thf(f7491,plain,
( spl44_38
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_38])]) ).
thf(f7408,plain,
~ spl44_37,
inference(avatar_split_clause,[],[f6030,f7404]) ).
thf(f7407,plain,
~ spl44_37,
inference(avatar_split_clause,[],[f6029,f7404]) ).
thf(f7402,plain,
~ spl44_36,
inference(avatar_split_clause,[],[f6028,f7399]) ).
thf(f7397,plain,
~ spl44_35,
inference(avatar_split_clause,[],[f4456,f7394]) ).
thf(f7394,plain,
( spl44_35
<=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,min),min) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_35])]) ).
thf(f7392,plain,
~ spl44_34,
inference(avatar_split_clause,[],[f6027,f7389]) ).
thf(f7387,plain,
spl44_33,
inference(avatar_split_clause,[],[f6026,f7384]) ).
thf(f7382,plain,
spl44_32,
inference(avatar_split_clause,[],[f4451,f7379]) ).
thf(f7377,plain,
spl44_31,
inference(avatar_split_clause,[],[f6025,f7374]) ).
thf(f7372,plain,
spl44_30,
inference(avatar_split_clause,[],[f6024,f7369]) ).
thf(f7367,plain,
spl44_29,
inference(avatar_split_clause,[],[f6023,f7364]) ).
thf(f7362,plain,
~ spl44_28,
inference(avatar_split_clause,[],[f7357,f7359]) ).
thf(f7356,plain,
spl44_27,
inference(avatar_split_clause,[],[f7351,f7353]) ).
thf(f7353,plain,
( spl44_27
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),quadRes,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),times_times_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),m)),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))),vAPP(int,int,number_number_of_int,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_27])]) ).
thf(f7350,plain,
~ spl44_26,
inference(avatar_split_clause,[],[f7345,f7347]) ).
thf(f7344,plain,
spl44_25,
inference(avatar_split_clause,[],[f4444,f7341]) ).
thf(f7339,plain,
spl44_24,
inference(avatar_split_clause,[],[f6019,f7336]) ).
thf(f7334,plain,
spl44_23,
inference(avatar_split_clause,[],[f6018,f7331]) ).
thf(f7329,plain,
spl44_22,
inference(avatar_split_clause,[],[f6017,f7326]) ).
thf(f7324,plain,
spl44_21,
inference(avatar_split_clause,[],[f6016,f7321]) ).
thf(f7319,plain,
spl44_20,
inference(avatar_split_clause,[],[f6015,f7316]) ).
thf(f7314,plain,
spl44_19,
inference(avatar_split_clause,[],[f6014,f7311]) ).
thf(f7309,plain,
spl44_18,
inference(avatar_split_clause,[],[f6013,f7305]) ).
thf(f7305,plain,
( spl44_18
<=> ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_18])]) ).
thf(f7308,plain,
spl44_18,
inference(avatar_split_clause,[],[f6012,f7305]) ).
thf(f7303,plain,
spl44_17,
inference(avatar_split_clause,[],[f6011,f7299]) ).
thf(f7302,plain,
spl44_17,
inference(avatar_split_clause,[],[f6010,f7299]) ).
thf(f7297,plain,
spl44_16,
inference(avatar_split_clause,[],[f6009,f7293]) ).
thf(f7293,plain,
( spl44_16
<=> ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_16])]) ).
thf(f7296,plain,
spl44_16,
inference(avatar_split_clause,[],[f6008,f7293]) ).
thf(f7291,plain,
spl44_15,
inference(avatar_split_clause,[],[f6007,f7288]) ).
thf(f7286,plain,
spl44_14,
inference(avatar_split_clause,[],[f6006,f7283]) ).
thf(f7281,plain,
spl44_13,
inference(avatar_split_clause,[],[f6005,f7278]) ).
thf(f7276,plain,
spl44_12,
inference(avatar_split_clause,[],[f6004,f7273]) ).
thf(f7273,plain,
( spl44_12
<=> ( vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_12])]) ).
thf(f7271,plain,
spl44_11,
inference(avatar_split_clause,[],[f6003,f7268]) ).
thf(f7268,plain,
( spl44_11
<=> ( vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_11])]) ).
thf(f7266,plain,
spl44_10,
inference(avatar_split_clause,[],[f6002,f7263]) ).
thf(f7263,plain,
( spl44_10
<=> ( vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int)) = vAPP(nat,real,vAPP(real,sTfun(nat,real),power_power_real,vAPP(int,real,number267125858f_real,vAPP(int,int,bit1,zero_zero_int))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_10])]) ).
thf(f7261,plain,
~ spl44_9,
inference(avatar_split_clause,[],[f5994,f7258]) ).
thf(f7256,plain,
spl44_1,
inference(avatar_split_clause,[],[f5993,f7209]) ).
thf(f7209,plain,
( spl44_1
<=> ( zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_1])]) ).
thf(f7255,plain,
spl44_1,
inference(avatar_split_clause,[],[f5992,f7209]) ).
thf(f7254,plain,
spl44_1,
inference(avatar_split_clause,[],[f5991,f7209]) ).
thf(f7253,plain,
spl44_8,
inference(avatar_split_clause,[],[f5988,f7250]) ).
thf(f7248,plain,
spl44_7,
inference(avatar_split_clause,[],[f4405,f7245]) ).
thf(f7243,plain,
~ spl44_6,
inference(avatar_split_clause,[],[f5985,f7239]) ).
thf(f7242,plain,
~ spl44_6,
inference(avatar_split_clause,[],[f5984,f7239]) ).
thf(f7237,plain,
~ spl44_5,
inference(avatar_split_clause,[],[f5983,f7232]) ).
thf(f7236,plain,
~ spl44_5,
inference(avatar_split_clause,[],[f5982,f7232]) ).
thf(f7235,plain,
~ spl44_5,
inference(avatar_split_clause,[],[f5981,f7232]) ).
thf(f7230,plain,
~ spl44_4,
inference(avatar_split_clause,[],[f5980,f7226]) ).
thf(f7229,plain,
~ spl44_4,
inference(avatar_split_clause,[],[f5979,f7226]) ).
thf(f7224,plain,
~ spl44_3,
inference(avatar_split_clause,[],[f5978,f7219]) ).
thf(f7223,plain,
~ spl44_3,
inference(avatar_split_clause,[],[f5977,f7219]) ).
thf(f7222,plain,
~ spl44_3,
inference(avatar_split_clause,[],[f5976,f7219]) ).
thf(f7217,plain,
~ spl44_2,
inference(avatar_split_clause,[],[f1201,f7214]) ).
thf(f7214,plain,
( spl44_2
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_2])]) ).
thf(f7212,plain,
spl44_1,
inference(avatar_split_clause,[],[f5974,f7209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 14:11:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (20064)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.45 % (20067)WARNING: value z3 for option sas not known
% 0.21/0.45 % (20066)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.45 % (20065)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.45 % (20067)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.45 % (20070)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.45 % (20071)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.45 % (20069)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.45 % (20068)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.55 % (20071)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.57 % Exception at run slice level% Exception at run slice level
% 0.21/0.57 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.57
% 0.21/0.57 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.14/0.57 % Exception at run slice level
% 1.14/0.57 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.14/0.58 % (20119)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 1.14/0.58 % (20120)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 1.14/0.58 % (20123)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 1.44/0.64 % (20120)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.44/0.64 % (20119)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.44/0.65 % Exception at run slice level
% 1.44/0.65 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.44/0.66 % (20172)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 4.71/1.08 % (20172)First to succeed.
% 4.71/1.13 % (20123)Also succeeded, but the first one will report.
% 4.71/1.14 % (20305)WARNING: value z3 for option sas not known
% 4.71/1.14 % (20305)ott-11_10:1_aac=none:add=off:afr=on:amm=off:anc=all_dependent:bd=off:fsd=off:fde=none:gsp=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sas=z3:sp=occurrence_186 on theBenchmark for (186ds/0Mi)
% 5.35/1.19 % (20305)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.56/1.21 % (20172)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20064"
% 5.56/1.22 % (20172)Refutation found. Thanks to Tanya!
% 5.56/1.22 % SZS status Theorem for theBenchmark
% 5.56/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 5.64/1.25 % (20172)------------------------------
% 5.64/1.25 % (20172)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.64/1.25 % (20172)Termination reason: Refutation
% 5.64/1.25
% 5.64/1.25 % (20172)Memory used [KB]: 7572
% 5.64/1.25 % (20172)Time elapsed: 0.554 s
% 5.64/1.25 % (20172)Instructions burned: 2083 (million)
% 5.64/1.25 % (20064)Success in time 0.889 s
%------------------------------------------------------------------------------