TSTP Solution File: NUM925_3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925_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 : n023.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 08:43:20 EDT 2024
% Result : Theorem 1.31s 0.60s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 605
% Syntax : Number of formulae : 1520 ( 701 unt; 140 typ; 0 def)
% Number of atoms : 2791 (1142 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 2200 ( 789 ~; 703 |; 277 &)
% ( 343 <=>; 84 =>; 0 <=; 4 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 14 ( 13 usr)
% Number of type conns : 156 ( 83 >; 73 *; 0 +; 0 <<)
% Number of predicates : 266 ( 264 usr; 246 prp; 0-3 aty)
% Number of functors : 108 ( 108 usr; 44 con; 0-3 aty)
% Number of variables : 1422 (1389 !; 33 ?;1422 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(type_def_9,type,
fun_int_bool: $tType ).
tff(type_def_10,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_11,type,
fun_nat_bool: $tType ).
tff(type_def_12,type,
fun_nat_int: $tType ).
tff(type_def_13,type,
fun_nat_nat: $tType ).
tff(type_def_14,type,
fun_nat_real: $tType ).
tff(type_def_15,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_16,type,
fun_real_bool: $tType ).
tff(type_def_17,type,
fun_re413263731l_bool: $tType ).
tff(func_def_0,type,
abs_abs_int: int > int ).
tff(func_def_1,type,
abs_abs_real: real > real ).
tff(func_def_2,type,
minus_minus_int: ( int * int ) > int ).
tff(func_def_3,type,
minus_minus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
minus_minus_real: ( real * real ) > real ).
tff(func_def_5,type,
one_one_int: int ).
tff(func_def_6,type,
one_one_nat: nat ).
tff(func_def_7,type,
one_one_real: real ).
tff(func_def_8,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_9,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_10,type,
plus_plus_real: ( real * real ) > real ).
tff(func_def_11,type,
times_times_int: ( int * int ) > int ).
tff(func_def_12,type,
times_times_nat: ( nat * nat ) > nat ).
tff(func_def_13,type,
times_times_real: ( real * real ) > real ).
tff(func_def_14,type,
zero_zero_int: int ).
tff(func_def_15,type,
zero_zero_nat: nat ).
tff(func_def_16,type,
zero_zero_real: real ).
tff(func_def_17,type,
if_int: ( bool * int * int ) > int ).
tff(func_def_18,type,
if_nat: ( bool * nat * nat ) > nat ).
tff(func_def_19,type,
zcong: ( int * int ) > fun_int_bool ).
tff(func_def_20,type,
zprime: fun_int_bool ).
tff(func_def_21,type,
bit0: int > int ).
tff(func_def_22,type,
bit1: int > int ).
tff(func_def_23,type,
min: int ).
tff(func_def_24,type,
pls: int ).
tff(func_def_25,type,
nat_1: int > nat ).
tff(func_def_26,type,
number_number_of_int: int > int ).
tff(func_def_27,type,
number_number_of_nat: int > nat ).
tff(func_def_28,type,
number267125858f_real: int > real ).
tff(func_def_29,type,
succ: int > int ).
tff(func_def_30,type,
semiri1621563631at_int: fun_nat_int ).
tff(func_def_31,type,
semiri984289939at_nat: fun_nat_nat ).
tff(func_def_32,type,
semiri132038758t_real: fun_nat_real ).
tff(func_def_33,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_34,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_35,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_36,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_37,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_38,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_39,type,
power_power_int: int > fun_nat_int ).
tff(func_def_40,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_41,type,
power_power_real: real > fun_nat_real ).
tff(func_def_42,type,
legendre: ( int * int ) > int ).
tff(func_def_43,type,
quadRes: int > fun_int_bool ).
tff(func_def_44,type,
dvd_dvd_int: fun_int_fun_int_bool ).
tff(func_def_45,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(func_def_46,type,
twoSqu820444569sum2sq: fun_int_bool ).
tff(func_def_47,type,
fFalse: bool ).
tff(func_def_48,type,
fTrue: bool ).
tff(func_def_49,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_50,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_51,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_52,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_53,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_54,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_55,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_56,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_57,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_58,type,
m: int ).
tff(func_def_59,type,
m1: int ).
tff(func_def_60,type,
n: nat ).
tff(func_def_61,type,
s1: int ).
tff(func_def_62,type,
s: int ).
tff(func_def_63,type,
t: int ).
tff(func_def_64,type,
tn: nat ).
tff(func_def_65,type,
x: int ).
tff(func_def_66,type,
y: int ).
tff(func_def_67,type,
sK18: int ).
tff(func_def_68,type,
sK19: int ).
tff(func_def_69,type,
sK20: int ).
tff(func_def_70,type,
sK21: int ).
tff(func_def_71,type,
sK22: int ).
tff(func_def_72,type,
sK23: int ).
tff(func_def_73,type,
sK24: int ).
tff(func_def_74,type,
sK25: int ).
tff(func_def_75,type,
sK26: int ).
tff(func_def_76,type,
sK27: int ).
tff(func_def_77,type,
sK28: int ).
tff(func_def_78,type,
sK29: int > nat ).
tff(func_def_79,type,
sK30: int > int ).
tff(func_def_80,type,
sK31: fun_nat_bool > int ).
tff(func_def_81,type,
sK32: fun_nat_bool > nat ).
tff(func_def_82,type,
sK33: fun_int_bool > nat ).
tff(func_def_83,type,
sK34: fun_int_bool > int ).
tff(func_def_84,type,
sK35: fun_nat_bool > nat ).
tff(func_def_85,type,
sK36: fun_nat_bool > int ).
tff(func_def_86,type,
sK37: fun_int_bool > int ).
tff(func_def_87,type,
sK38: fun_int_bool > nat ).
tff(func_def_88,type,
sK39: ( nat * fun_nat_bool ) > nat ).
tff(func_def_89,type,
sK40: ( real * nat ) > real ).
tff(func_def_90,type,
sK41: ( real * nat ) > real ).
tff(func_def_91,type,
sK42: ( int * int ) > int ).
tff(func_def_92,type,
sK43: ( nat * nat ) > nat ).
tff(func_def_93,type,
sK44: ( fun_nat_bool * int ) > nat ).
tff(func_def_94,type,
sK45: ( int * int ) > int ).
tff(func_def_95,type,
sK46: ( nat * nat ) > nat ).
tff(func_def_96,type,
sK47: ( int * int ) > nat ).
tff(func_def_97,type,
sK48: ( fun_int_bool * int ) > int ).
tff(func_def_98,type,
sK49: ( fun_int_bool * int ) > int ).
tff(func_def_99,type,
sK50: ( fun_int_bool * int ) > int ).
tff(func_def_100,type,
sK51: ( int * fun_nat_int * nat ) > nat ).
tff(func_def_101,type,
sK52: ( fun_nat_int * nat ) > nat ).
tff(func_def_102,type,
sK53: ( int * fun_nat_int * nat ) > nat ).
tff(func_def_103,type,
sK54: ( fun_nat_int * nat ) > nat ).
tff(func_def_104,type,
sK55: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_105,type,
sK56: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_106,type,
sK57: ( int * int * int ) > int ).
tff(func_def_107,type,
sK58: int ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: int > $o ).
tff(pred_def_3,type,
sP1: ( nat * int ) > $o ).
tff(pred_def_4,type,
sP2: ( nat * int ) > $o ).
tff(pred_def_5,type,
sP3: ( int * int ) > $o ).
tff(pred_def_6,type,
sP4: ( fun_nat_bool * int ) > $o ).
tff(pred_def_7,type,
sP5: ( nat * int ) > $o ).
tff(pred_def_8,type,
sP6: ( real * real ) > $o ).
tff(pred_def_9,type,
sP7: ( real * real ) > $o ).
tff(pred_def_10,type,
sP8: ( int * int ) > $o ).
tff(pred_def_11,type,
sP9: ( int * int ) > $o ).
tff(pred_def_12,type,
sP10: ( bool * int * bool ) > $o ).
tff(pred_def_13,type,
sP11: ( bool * int * bool ) > $o ).
tff(pred_def_14,type,
sP12: ( nat * nat * fun_nat_fun_nat_bool ) > $o ).
tff(pred_def_15,type,
sP13: ( fun_nat_bool * nat * nat ) > $o ).
tff(pred_def_16,type,
sP14: ( fun_nat_bool * nat * nat ) > $o ).
tff(pred_def_17,type,
sP15: ( fun_int_bool * nat * nat ) > $o ).
tff(pred_def_18,type,
sP16: ( real * real * real ) > $o ).
tff(pred_def_19,type,
sP17: ( int * int * int ) > $o ).
tff(f8495,plain,
$false,
inference(avatar_sat_refutation,[],[f6948,f6953,f6958,f6963,f6968,f6973,f6978,f6983,f6988,f6993,f6997,f7002,f7007,f7011,f7015,f7020,f7026,f7035,f7040,f7045,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7087,f7091,f7095,f7099,f7103,f7107,f7111,f7115,f7119,f7123,f7127,f7131,f7135,f7139,f7143,f7147,f7152,f7158,f7162,f7166,f7170,f7174,f7181,f7193,f7198,f7203,f7208,f7213,f7218,f7223,f7228,f7233,f7238,f7243,f7248,f7253,f7257,f7261,f7265,f7269,f7273,f7277,f7281,f7285,f7289,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7333,f7337,f7341,f7345,f7349,f7353,f7357,f7362,f7367,f7372,f7377,f7382,f7386,f7391,f7395,f7399,f7404,f7409,f7417,f7446,f7465,f7469,f7473,f7477,f7481,f7485,f7491,f7495,f7499,f7503,f7507,f7511,f7515,f7519,f7523,f7527,f7532,f7536,f7540,f7545,f7550,f7690,f7721,f7726,f7730,f7734,f7738,f7742,f7746,f7750,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7791,f7795,f7799,f7803,f7807,f7811,f7815,f7819,f7823,f7827,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7864,f7869,f7873,f7878,f7882,f7886,f7890,f7894,f7898,f7902,f7907,f7913,f7918,f7923,f7928,f7933,f7964,f8015,f8070,f8091,f8127,f8132,f8148,f8153,f8157,f8161,f8165,f8169,f8174,f8178,f8182,f8186,f8190,f8194,f8198,f8202,f8206,f8210,f8214,f8218,f8223,f8228,f8232,f8236,f8240,f8244,f8248,f8301,f8314,f8344,f8351,f8356,f8360,f8364,f8368,f8372,f8377,f8381,f8385,f8389,f8393,f8397,f8401,f8405,f8409,f8413,f8417,f8422,f8426,f8430,f8434,f8438,f8442,f8446,f8450,f8454,f8458,f8462,f8467,f8471,f8475,f8479,f8484,f8491,f8494]) ).
tff(f8494,plain,
( ~ spl59_100
| ~ spl59_245 ),
inference(avatar_contradiction_clause,[],[f8492]) ).
tff(f8492,plain,
( $false
| ~ spl59_100
| ~ spl59_245 ),
inference(resolution,[],[f8490,f7398]) ).
tff(f7398,plain,
( ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1))
| ~ spl59_100 ),
inference(avatar_component_clause,[],[f7397]) ).
tff(f7397,plain,
( spl59_100
<=> ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_100])]) ).
tff(f8490,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
| ~ spl59_245 ),
inference(avatar_component_clause,[],[f8488]) ).
tff(f8488,plain,
( spl59_245
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_245])]) ).
tff(f8491,plain,
( spl59_245
| ~ spl59_110
| ~ spl59_122
| ~ spl59_190
| ~ spl59_196
| ~ spl59_244 ),
inference(avatar_split_clause,[],[f8486,f8481,f8196,f8171,f7534,f7483,f8488]) ).
tff(f7483,plain,
( spl59_110
<=> ! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_110])]) ).
tff(f7534,plain,
( spl59_122
<=> ! [X0: int] : ( minus_minus_int(X0,min) = plus_plus_int(X0,one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_122])]) ).
tff(f8171,plain,
( spl59_190
<=> ( pls = hAPP_nat_int(power_power_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)),plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_190])]) ).
tff(f8196,plain,
( spl59_196
<=> ! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_196])]) ).
tff(f8481,plain,
( spl59_244
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_244])]) ).
tff(f8486,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
| ~ spl59_110
| ~ spl59_122
| ~ spl59_190
| ~ spl59_196
| ~ spl59_244 ),
inference(forward_demodulation,[],[f8485,f8293]) ).
tff(f8293,plain,
( ( pls = minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min) )
| ~ spl59_190
| ~ spl59_196 ),
inference(trivial_inequality_removal,[],[f8287]) ).
tff(f8287,plain,
( ( pls != pls )
| ( pls = minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min) )
| ~ spl59_190
| ~ spl59_196 ),
inference(superposition,[],[f8197,f8173]) ).
tff(f8173,plain,
( ( pls = hAPP_nat_int(power_power_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)),plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl59_190 ),
inference(avatar_component_clause,[],[f8171]) ).
tff(f8197,plain,
( ! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) )
| ~ spl59_196 ),
inference(avatar_component_clause,[],[f8196]) ).
tff(f8485,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl59_110
| ~ spl59_122
| ~ spl59_244 ),
inference(forward_demodulation,[],[f8483,f7691]) ).
tff(f7691,plain,
( ! [X0: int] : ( minus_minus_int(X0,min) = plus_plus_int(one_one_int,X0) )
| ~ spl59_110
| ~ spl59_122 ),
inference(superposition,[],[f7535,f7484]) ).
tff(f7484,plain,
( ! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) )
| ~ spl59_110 ),
inference(avatar_component_clause,[],[f7483]) ).
tff(f7535,plain,
( ! [X0: int] : ( minus_minus_int(X0,min) = plus_plus_int(X0,one_one_int) )
| ~ spl59_122 ),
inference(avatar_component_clause,[],[f7534]) ).
tff(f8483,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl59_244 ),
inference(avatar_component_clause,[],[f8481]) ).
tff(f8484,plain,
spl59_244,
inference(avatar_split_clause,[],[f5377,f8481]) ).
tff(f5377,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f3638,f3551]) ).
tff(f3551,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
tff(f3638,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f8479,plain,
spl59_243,
inference(avatar_split_clause,[],[f5062,f8477]) ).
tff(f8477,plain,
( spl59_243
<=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_243])]) ).
tff(f5062,plain,
! [X2: nat,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3437]) ).
tff(f3437,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( ( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP14(X0,X1,X2) )
& ( sP14(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
inference(nnf_transformation,[],[f3003]) ).
tff(f3003,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> sP14(X0,X1,X2) ),
inference(definition_folding,[],[f2856,f3002]) ).
tff(f3002,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( sP14(X0,X1,X2)
<=> ( ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( plus_plus_nat(X2,X3) != X1 ) )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
tff(f2856,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ( ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( plus_plus_nat(X2,X3) != X1 ) )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2102]) ).
tff(f2102,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ~ ( ? [X3: nat] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& ( plus_plus_nat(X2,X3) = X1 ) )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(rectify,[],[f795]) ).
tff(f795,axiom,
! [X51: fun_nat_bool,X2: nat,X78: nat] :
( hBOOL(hAPP_nat_bool(X51,minus_minus_nat(X2,X78)))
<=> ~ ( ? [X377: nat] :
( ~ hBOOL(hAPP_nat_bool(X51,X377))
& ( plus_plus_nat(X78,X377) = X2 ) )
| ( ~ hBOOL(hAPP_nat_bool(X51,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X78)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_nat__diff__split__asm) ).
tff(f8475,plain,
spl59_242,
inference(avatar_split_clause,[],[f5061,f8473]) ).
tff(f8473,plain,
( spl59_242
<=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
( sP14(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_242])]) ).
tff(f5061,plain,
! [X2: nat,X0: fun_nat_bool,X1: nat] :
( sP14(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ),
inference(cnf_transformation,[],[f3437]) ).
tff(f8471,plain,
spl59_241,
inference(avatar_split_clause,[],[f5054,f8469]) ).
tff(f8469,plain,
( spl59_241
<=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_241])]) ).
tff(f5054,plain,
! [X2: nat,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f3431]) ).
tff(f3431,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( ( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP13(X0,X1,X2) )
& ( sP13(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
inference(nnf_transformation,[],[f3001]) ).
tff(f3001,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> sP13(X0,X1,X2) ),
inference(definition_folding,[],[f2855,f3000]) ).
tff(f3000,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( sP13(X0,X1,X2)
<=> ( ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( plus_plus_nat(X2,X3) != X1 ) )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
tff(f2855,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ( ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( plus_plus_nat(X2,X3) != X1 ) )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2101]) ).
tff(f2101,plain,
! [X0: fun_nat_bool,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ( ! [X3: nat] :
( ( plus_plus_nat(X2,X3) = X1 )
=> hBOOL(hAPP_nat_bool(X0,X3)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) ),
inference(rectify,[],[f796]) ).
tff(f796,axiom,
! [X51: fun_nat_bool,X2: nat,X78: nat] :
( hBOOL(hAPP_nat_bool(X51,minus_minus_nat(X2,X78)))
<=> ( ! [X377: nat] :
( ( plus_plus_nat(X78,X377) = X2 )
=> hBOOL(hAPP_nat_bool(X51,X377)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X78))
=> hBOOL(hAPP_nat_bool(X51,zero_zero_nat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_nat__diff__split) ).
tff(f8467,plain,
spl59_240,
inference(avatar_split_clause,[],[f5053,f8465]) ).
tff(f8465,plain,
( spl59_240
<=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_240])]) ).
tff(f5053,plain,
! [X2: nat,X0: fun_nat_bool,X1: nat] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ),
inference(cnf_transformation,[],[f3431]) ).
tff(f8462,plain,
spl59_239,
inference(avatar_split_clause,[],[f5034,f8460]) ).
tff(f8460,plain,
( spl59_239
<=> ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_239])]) ).
tff(f5034,plain,
! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f3417]) ).
tff(f3417,plain,
! [X0: nat,X1: nat,X2: fun_nat_fun_nat_bool] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
| ~ sP12(X0,X1,X2) ),
inference(rectify,[],[f3416]) ).
tff(f3416,plain,
! [X1: nat,X2: nat,X0: fun_nat_fun_nat_bool] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ~ sP12(X1,X2,X0) ),
inference(nnf_transformation,[],[f2998]) ).
tff(f2998,plain,
! [X1: nat,X2: nat,X0: fun_nat_fun_nat_bool] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ~ sP12(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
tff(f8458,plain,
spl59_238,
inference(avatar_split_clause,[],[f5033,f8456]) ).
tff(f8456,plain,
( spl59_238
<=> ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_238])]) ).
tff(f5033,plain,
! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f3417]) ).
tff(f8454,plain,
spl59_237,
inference(avatar_split_clause,[],[f4965,f8452]) ).
tff(f8452,plain,
( spl59_237
<=> ! [X2: int,X0: int,X1: int] :
( ( X1 = X2 )
| ( plus_plus_int(X0,X1) != plus_plus_int(X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_237])]) ).
tff(f4965,plain,
! [X2: int,X0: int,X1: int] :
( ( X1 = X2 )
| ( plus_plus_int(X0,X1) != plus_plus_int(X0,X2) ) ),
inference(cnf_transformation,[],[f2765]) ).
tff(f2765,plain,
! [X0: int,X1: int,X2: int] :
( ( X1 = X2 )
| ( plus_plus_int(X0,X1) != plus_plus_int(X0,X2) ) ),
inference(ennf_transformation,[],[f2046]) ).
tff(f2046,plain,
! [X0: int,X1: int,X2: int] :
( ( plus_plus_int(X0,X1) = plus_plus_int(X0,X2) )
=> ( X1 = X2 ) ),
inference(rectify,[],[f323]) ).
tff(f323,axiom,
! [X100: int,X101: int,X102: int] :
( ( plus_plus_int(X100,X101) = plus_plus_int(X100,X102) )
=> ( X101 = X102 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_add__left__imp__eq) ).
tff(f8450,plain,
spl59_236,
inference(avatar_split_clause,[],[f4964,f8448]) ).
tff(f8448,plain,
( spl59_236
<=> ! [X2: int,X0: int,X1: int] :
( ( X0 = X2 )
| ( plus_plus_int(X0,X1) != plus_plus_int(X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_236])]) ).
tff(f4964,plain,
! [X2: int,X0: int,X1: int] :
( ( X0 = X2 )
| ( plus_plus_int(X0,X1) != plus_plus_int(X2,X1) ) ),
inference(cnf_transformation,[],[f2764]) ).
tff(f2764,plain,
! [X0: int,X1: int,X2: int] :
( ( X0 = X2 )
| ( plus_plus_int(X0,X1) != plus_plus_int(X2,X1) ) ),
inference(ennf_transformation,[],[f2045]) ).
tff(f2045,plain,
! [X0: int,X1: int,X2: int] :
( ( plus_plus_int(X0,X1) = plus_plus_int(X2,X1) )
=> ( X0 = X2 ) ),
inference(rectify,[],[f317]) ).
tff(f317,axiom,
! [X94: int,X95: int,X96: int] :
( ( plus_plus_int(X94,X95) = plus_plus_int(X96,X95) )
=> ( X94 = X96 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_add__right__imp__eq) ).
tff(f8446,plain,
spl59_235,
inference(avatar_split_clause,[],[f4963,f8444]) ).
tff(f8444,plain,
( spl59_235
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus_nat(X0,X1) != plus_plus_nat(X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_235])]) ).
tff(f4963,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus_nat(X0,X1) != plus_plus_nat(X2,X1) ) ),
inference(cnf_transformation,[],[f2763]) ).
tff(f2763,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( plus_plus_nat(X0,X1) != plus_plus_nat(X2,X1) ) ),
inference(ennf_transformation,[],[f2044]) ).
tff(f2044,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus_nat(X0,X1) = plus_plus_nat(X2,X1) )
=> ( X0 = X2 ) ),
inference(rectify,[],[f318]) ).
tff(f318,axiom,
! [X94: nat,X95: nat,X96: nat] :
( ( plus_plus_nat(X94,X95) = plus_plus_nat(X96,X95) )
=> ( X94 = X96 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_add__right__imp__eq) ).
tff(f8442,plain,
spl59_234,
inference(avatar_split_clause,[],[f4961,f8440]) ).
tff(f8440,plain,
( spl59_234
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X1 = X2 )
| ( plus_plus_nat(X0,X1) != plus_plus_nat(X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_234])]) ).
tff(f4961,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X1 = X2 )
| ( plus_plus_nat(X0,X1) != plus_plus_nat(X0,X2) ) ),
inference(cnf_transformation,[],[f2761]) ).
tff(f2761,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X1 = X2 )
| ( plus_plus_nat(X0,X1) != plus_plus_nat(X0,X2) ) ),
inference(ennf_transformation,[],[f2042]) ).
tff(f2042,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus_nat(X0,X1) = plus_plus_nat(X0,X2) )
=> ( X1 = X2 ) ),
inference(rectify,[],[f321]) ).
tff(f321,axiom,
! [X97: nat,X98: nat,X99: nat] :
( ( plus_plus_nat(X97,X98) = plus_plus_nat(X97,X99) )
=> ( X98 = X99 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_add__imp__eq) ).
tff(f8438,plain,
spl59_233,
inference(avatar_split_clause,[],[f4959,f8436]) ).
tff(f8436,plain,
( spl59_233
<=> ! [X2: real,X0: real,X1: real] :
( ( X1 = X2 )
| ( plus_plus_real(X0,X1) != plus_plus_real(X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_233])]) ).
tff(f4959,plain,
! [X2: real,X0: real,X1: real] :
( ( X1 = X2 )
| ( plus_plus_real(X0,X1) != plus_plus_real(X0,X2) ) ),
inference(cnf_transformation,[],[f2759]) ).
tff(f2759,plain,
! [X0: real,X1: real,X2: real] :
( ( X1 = X2 )
| ( plus_plus_real(X0,X1) != plus_plus_real(X0,X2) ) ),
inference(ennf_transformation,[],[f2040]) ).
tff(f2040,plain,
! [X0: real,X1: real,X2: real] :
( ( plus_plus_real(X0,X1) = plus_plus_real(X0,X2) )
=> ( X1 = X2 ) ),
inference(rectify,[],[f322]) ).
tff(f322,axiom,
! [X97: real,X98: real,X99: real] :
( ( plus_plus_real(X97,X98) = plus_plus_real(X97,X99) )
=> ( X98 = X99 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_add__imp__eq) ).
tff(f8434,plain,
spl59_232,
inference(avatar_split_clause,[],[f4958,f8432]) ).
tff(f8432,plain,
( spl59_232
<=> ! [X2: real,X0: real,X1: real] :
( ( X0 = X2 )
| ( plus_plus_real(X0,X1) != plus_plus_real(X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_232])]) ).
tff(f4958,plain,
! [X2: real,X0: real,X1: real] :
( ( X0 = X2 )
| ( plus_plus_real(X0,X1) != plus_plus_real(X2,X1) ) ),
inference(cnf_transformation,[],[f2758]) ).
tff(f2758,plain,
! [X0: real,X1: real,X2: real] :
( ( X0 = X2 )
| ( plus_plus_real(X0,X1) != plus_plus_real(X2,X1) ) ),
inference(ennf_transformation,[],[f2039]) ).
tff(f2039,plain,
! [X0: real,X1: real,X2: real] :
( ( plus_plus_real(X0,X1) = plus_plus_real(X2,X1) )
=> ( X0 = X2 ) ),
inference(rectify,[],[f319]) ).
tff(f319,axiom,
! [X94: real,X95: real,X96: real] :
( ( plus_plus_real(X94,X95) = plus_plus_real(X96,X95) )
=> ( X94 = X96 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_add__right__imp__eq) ).
tff(f8430,plain,
spl59_231,
inference(avatar_split_clause,[],[f4781,f8428]) ).
tff(f8428,plain,
( spl59_231
<=> ! [X2: bool,X0: int,X1: int] :
( ( nat_1(X1) = nat_1(if_int(X2,X0,X1)) )
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_231])]) ).
tff(f4781,plain,
! [X2: bool,X0: int,X1: int] :
( ( nat_1(X1) = nat_1(if_int(X2,X0,X1)) )
| hBOOL(X2) ),
inference(cnf_transformation,[],[f2542]) ).
tff(f2542,plain,
! [X0: int,X1: int,X2: bool] :
( ( ( nat_1(X1) = nat_1(if_int(X2,X0,X1)) )
| hBOOL(X2) )
& ( ( nat_1(X0) = nat_1(if_int(X2,X0,X1)) )
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f1898]) ).
tff(f1898,plain,
! [X0: int,X1: int,X2: bool] :
( ( ~ hBOOL(X2)
=> ( nat_1(X1) = nat_1(if_int(X2,X0,X1)) ) )
& ( hBOOL(X2)
=> ( nat_1(X0) = nat_1(if_int(X2,X0,X1)) ) ) ),
inference(rectify,[],[f477]) ).
tff(f477,axiom,
! [X0: int,X1: int,X51: bool] :
( ( ~ hBOOL(X51)
=> ( nat_1(if_int(X51,X0,X1)) = nat_1(X1) ) )
& ( hBOOL(X51)
=> ( nat_1(X0) = nat_1(if_int(X51,X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_nat__if__cong) ).
tff(f8426,plain,
spl59_230,
inference(avatar_split_clause,[],[f4780,f8424]) ).
tff(f8424,plain,
( spl59_230
<=> ! [X2: bool,X0: int,X1: int] :
( ( nat_1(X0) = nat_1(if_int(X2,X0,X1)) )
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_230])]) ).
tff(f4780,plain,
! [X2: bool,X0: int,X1: int] :
( ( nat_1(X0) = nat_1(if_int(X2,X0,X1)) )
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f2542]) ).
tff(f8422,plain,
( spl59_229
| ~ spl59_113
| ~ spl59_209 ),
inference(avatar_split_clause,[],[f8328,f8298,f7497,f8419]) ).
tff(f8419,plain,
( spl59_229
<=> ( one_one_int = minus_minus_int(pls,hAPP_nat_int(semiri1621563631at_int,n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_229])]) ).
tff(f7497,plain,
( spl59_113
<=> ! [X0: int,X1: int] : ( minus_minus_int(plus_plus_int(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_113])]) ).
tff(f8298,plain,
( spl59_209
<=> ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_209])]) ).
tff(f8328,plain,
( ( one_one_int = minus_minus_int(pls,hAPP_nat_int(semiri1621563631at_int,n)) )
| ~ spl59_113
| ~ spl59_209 ),
inference(superposition,[],[f7498,f8300]) ).
tff(f8300,plain,
( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ spl59_209 ),
inference(avatar_component_clause,[],[f8298]) ).
tff(f7498,plain,
( ! [X0: int,X1: int] : ( minus_minus_int(plus_plus_int(X0,X1),X1) = X0 )
| ~ spl59_113 ),
inference(avatar_component_clause,[],[f7497]) ).
tff(f8417,plain,
spl59_228,
inference(avatar_split_clause,[],[f4700,f8415]) ).
tff(f8415,plain,
( spl59_228
<=> ! [X2: int,X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(times_times_int(X0,X1),times_times_int(X2,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_228])]) ).
tff(f4700,plain,
! [X2: int,X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(times_times_int(X0,X1),times_times_int(X2,X1)),X1)),
inference(cnf_transformation,[],[f1818]) ).
tff(f1818,plain,
! [X0: int,X1: int,X2: int] : hBOOL(hAPP_int_bool(zcong(times_times_int(X0,X1),times_times_int(X2,X1)),X1)),
inference(rectify,[],[f1129]) ).
tff(f1129,axiom,
! [X148: int,X12: int,X152: int] : hBOOL(hAPP_int_bool(zcong(times_times_int(X148,X12),times_times_int(X152,X12)),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_zcong__zmult__self) ).
tff(f8413,plain,
spl59_227,
inference(avatar_split_clause,[],[f4517,f8411]) ).
tff(f8411,plain,
( spl59_227
<=> ! [X0: int,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1))
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_227])]) ).
tff(f4517,plain,
! [X0: int,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1))
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f3269]) ).
tff(f3269,plain,
! [X0: int,X1: nat] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1))
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1)) ) ),
inference(nnf_transformation,[],[f2985]) ).
tff(f2985,plain,
! [X0: int,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1))
<=> sP5(X1,X0) ),
inference(definition_folding,[],[f2539,f2984]) ).
tff(f2984,plain,
! [X1: nat,X0: int] :
( sP5(X1,X0)
<=> ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f2539,plain,
! [X0: int,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1))
<=> ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
inference(ennf_transformation,[],[f1768]) ).
tff(f1768,plain,
! [X0: int,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1))
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( zero_zero_nat = X1 ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1))) ) ) ),
inference(rectify,[],[f1078]) ).
tff(f1078,axiom,
! [X27: int,X26: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X27)),X26))
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X27))
=> ( zero_zero_nat = X26 ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X27))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X27),hAPP_nat_int(semiri1621563631at_int,X26))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_nat__dvd__iff) ).
tff(f8409,plain,
spl59_226,
inference(avatar_split_clause,[],[f4516,f8407]) ).
tff(f8407,plain,
( spl59_226
<=> ! [X0: int,X1: nat] :
( sP5(X1,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_226])]) ).
tff(f4516,plain,
! [X0: int,X1: nat] :
( sP5(X1,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat_1(X0)),X1)) ),
inference(cnf_transformation,[],[f3269]) ).
tff(f8405,plain,
spl59_225,
inference(avatar_split_clause,[],[f4502,f8403]) ).
tff(f8403,plain,
( spl59_225
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_225])]) ).
tff(f4502,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
inference(cnf_transformation,[],[f3262]) ).
tff(f3262,plain,
! [X0: nat,X1: nat] :
( ( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ) ),
inference(nnf_transformation,[],[f222]) ).
tff(f222,axiom,
! [X0: nat,X1: nat] :
( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
tff(f8401,plain,
spl59_224,
inference(avatar_split_clause,[],[f4500,f8399]) ).
tff(f8399,plain,
( spl59_224
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_224])]) ).
tff(f4500,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ),
inference(cnf_transformation,[],[f3261]) ).
tff(f3261,plain,
! [X0: nat,X1: nat] :
( ( ( hAPP_nat_nat(semiri984289939at_nat,X0) = hAPP_nat_nat(semiri984289939at_nat,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ) ),
inference(nnf_transformation,[],[f1764]) ).
tff(f1764,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(semiri984289939at_nat,X0) = hAPP_nat_nat(semiri984289939at_nat,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f220]) ).
tff(f220,axiom,
! [X26: nat,X15: nat] :
( ( hAPP_nat_nat(semiri984289939at_nat,X15) = hAPP_nat_nat(semiri984289939at_nat,X26) )
<=> ( X15 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
tff(f8397,plain,
spl59_223,
inference(avatar_split_clause,[],[f4498,f8395]) ).
tff(f8395,plain,
( spl59_223
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_223])]) ).
tff(f4498,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ),
inference(cnf_transformation,[],[f3260]) ).
tff(f3260,plain,
! [X0: nat,X1: nat] :
( ( ( hAPP_nat_real(semiri132038758t_real,X0) = hAPP_nat_real(semiri132038758t_real,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ) ),
inference(nnf_transformation,[],[f1763]) ).
tff(f1763,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_real(semiri132038758t_real,X0) = hAPP_nat_real(semiri132038758t_real,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f219]) ).
tff(f219,axiom,
! [X26: nat,X15: nat] :
( ( hAPP_nat_real(semiri132038758t_real,X15) = hAPP_nat_real(semiri132038758t_real,X26) )
<=> ( X15 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_of__nat__eq__iff) ).
tff(f8393,plain,
spl59_222,
inference(avatar_split_clause,[],[f4185,f8391]) ).
tff(f8391,plain,
( spl59_222
<=> ! [X0: int,X1: int] :
( ( one_one_int = abs_abs_int(X0) )
| ( one_one_int != abs_abs_int(times_times_int(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_222])]) ).
tff(f4185,plain,
! [X0: int,X1: int] :
( ( one_one_int = abs_abs_int(X0) )
| ( one_one_int != abs_abs_int(times_times_int(X0,X1)) ) ),
inference(cnf_transformation,[],[f2339]) ).
tff(f2339,plain,
! [X0: int,X1: int] :
( ( one_one_int = abs_abs_int(X0) )
| ( one_one_int != abs_abs_int(times_times_int(X0,X1)) ) ),
inference(ennf_transformation,[],[f1593]) ).
tff(f1593,plain,
! [X0: int,X1: int] :
( ( one_one_int = abs_abs_int(times_times_int(X0,X1)) )
=> ( one_one_int = abs_abs_int(X0) ) ),
inference(rectify,[],[f1161]) ).
tff(f1161,axiom,
! [X12: int,X13: int] :
( ( one_one_int = abs_abs_int(times_times_int(X12,X13)) )
=> ( one_one_int = abs_abs_int(X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_abs__zmult__eq__1) ).
tff(f8389,plain,
spl59_221,
inference(avatar_split_clause,[],[f4088,f8387]) ).
tff(f8387,plain,
( spl59_221
<=> ! [X0: int,X1: int] : ( number267125858f_real(times_times_int(X0,X1)) = times_times_real(number267125858f_real(X0),number267125858f_real(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_221])]) ).
tff(f4088,plain,
! [X0: int,X1: int] : ( number267125858f_real(times_times_int(X0,X1)) = times_times_real(number267125858f_real(X0),number267125858f_real(X1)) ),
inference(cnf_transformation,[],[f1507]) ).
tff(f1507,plain,
! [X0: int,X1: int] : ( number267125858f_real(times_times_int(X0,X1)) = times_times_real(number267125858f_real(X0),number267125858f_real(X1)) ),
inference(rectify,[],[f457]) ).
tff(f457,axiom,
! [X185: int,X186: int] : ( number267125858f_real(times_times_int(X185,X186)) = times_times_real(number267125858f_real(X185),number267125858f_real(X186)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_number__of__mult) ).
tff(f8385,plain,
spl59_220,
inference(avatar_split_clause,[],[f4087,f8383]) ).
tff(f8383,plain,
( spl59_220
<=> ! [X0: int,X1: int] : ( number267125858f_real(plus_plus_int(X0,X1)) = plus_plus_real(number267125858f_real(X0),number267125858f_real(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_220])]) ).
tff(f4087,plain,
! [X0: int,X1: int] : ( number267125858f_real(plus_plus_int(X0,X1)) = plus_plus_real(number267125858f_real(X0),number267125858f_real(X1)) ),
inference(cnf_transformation,[],[f1506]) ).
tff(f1506,plain,
! [X0: int,X1: int] : ( number267125858f_real(plus_plus_int(X0,X1)) = plus_plus_real(number267125858f_real(X0),number267125858f_real(X1)) ),
inference(rectify,[],[f126]) ).
tff(f126,axiom,
! [X36: int,X37: int] : ( number267125858f_real(plus_plus_int(X36,X37)) = plus_plus_real(number267125858f_real(X36),number267125858f_real(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_number__of__add) ).
tff(f8381,plain,
spl59_219,
inference(avatar_split_clause,[],[f4086,f8379]) ).
tff(f8379,plain,
( spl59_219
<=> ! [X0: int,X1: int] : ( number267125858f_real(minus_minus_int(X0,X1)) = minus_minus_real(number267125858f_real(X0),number267125858f_real(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_219])]) ).
tff(f4086,plain,
! [X0: int,X1: int] : ( number267125858f_real(minus_minus_int(X0,X1)) = minus_minus_real(number267125858f_real(X0),number267125858f_real(X1)) ),
inference(cnf_transformation,[],[f1505]) ).
tff(f1505,plain,
! [X0: int,X1: int] : ( number267125858f_real(minus_minus_int(X0,X1)) = minus_minus_real(number267125858f_real(X0),number267125858f_real(X1)) ),
inference(rectify,[],[f469]) ).
tff(f469,axiom,
! [X199: int,X200: int] : ( number267125858f_real(minus_minus_int(X199,X200)) = minus_minus_real(number267125858f_real(X199),number267125858f_real(X200)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_number__of__diff) ).
tff(f8377,plain,
( ~ spl59_218
| ~ spl59_123
| ~ spl59_209 ),
inference(avatar_split_clause,[],[f8326,f8298,f7538,f8374]) ).
tff(f8374,plain,
( spl59_218
<=> ( pls = plus_plus_int(pls,hAPP_nat_int(semiri1621563631at_int,n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_218])]) ).
tff(f7538,plain,
( spl59_123
<=> ! [X0: int] : ( pls != plus_plus_int(plus_plus_int(one_one_int,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_123])]) ).
tff(f8326,plain,
( ( pls != plus_plus_int(pls,hAPP_nat_int(semiri1621563631at_int,n)) )
| ~ spl59_123
| ~ spl59_209 ),
inference(superposition,[],[f7539,f8300]) ).
tff(f7539,plain,
( ! [X0: int] : ( pls != plus_plus_int(plus_plus_int(one_one_int,X0),X0) )
| ~ spl59_123 ),
inference(avatar_component_clause,[],[f7538]) ).
tff(f8372,plain,
spl59_217,
inference(avatar_split_clause,[],[f4048,f8370]) ).
tff(f8370,plain,
( spl59_217
<=> ! [X4: nat,X0: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X0,nat_1(sK36(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_217])]) ).
tff(f4048,plain,
! [X0: fun_nat_bool,X4: nat] :
( hBOOL(hAPP_nat_bool(X0,nat_1(sK36(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ),
inference(cnf_transformation,[],[f3125]) ).
tff(f3125,plain,
! [X0: fun_nat_bool] :
( ( hBOOL(hAPP_nat_bool(X0,sK35(X0)))
| ! [X2: int] :
( ~ hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( ( hBOOL(hAPP_nat_bool(X0,nat_1(sK36(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK36(X0))) )
| ! [X4: nat] : ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f3122,f3124,f3123]) ).
tff(f3123,plain,
! [X0: fun_nat_bool] :
( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
=> hBOOL(hAPP_nat_bool(X0,sK35(X0))) ),
introduced(choice_axiom,[]) ).
tff(f3124,plain,
! [X0: fun_nat_bool] :
( ? [X3: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X3)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) )
=> ( hBOOL(hAPP_nat_bool(X0,nat_1(sK36(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK36(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f3122,plain,
! [X0: fun_nat_bool] :
( ( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
| ! [X2: int] :
( ~ hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( ? [X3: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X3)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) )
| ! [X4: nat] : ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
inference(rectify,[],[f3121]) ).
tff(f3121,plain,
! [X0: fun_nat_bool] :
( ( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
| ! [X2: int] :
( ~ hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( ? [X2: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
| ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
inference(nnf_transformation,[],[f1470]) ).
tff(f1470,plain,
! [X0: fun_nat_bool] :
( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ? [X2: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(rectify,[],[f533]) ).
tff(f533,axiom,
! [X51: fun_nat_bool] :
( ? [X245: nat] : hBOOL(hAPP_nat_bool(X51,X245))
<=> ? [X149: int] :
( hBOOL(hAPP_nat_bool(X51,nat_1(X149)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X149)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_ex__nat) ).
tff(f8368,plain,
spl59_216,
inference(avatar_split_clause,[],[f4043,f8366]) ).
tff(f8366,plain,
( spl59_216
<=> ! [X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ~ hBOOL(hAPP_nat_bool(X0,nat_1(sK31(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_216])]) ).
tff(f4043,plain,
! [X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ~ hBOOL(hAPP_nat_bool(X0,nat_1(sK31(X0)))) ),
inference(cnf_transformation,[],[f3115]) ).
tff(f3115,plain,
! [X0: fun_nat_bool] :
( ( ! [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
| ( ~ hBOOL(hAPP_nat_bool(X0,nat_1(sK31(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK31(X0))) ) )
& ( ! [X3: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) )
| ~ hBOOL(hAPP_nat_bool(X0,sK32(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f3112,f3114,f3113]) ).
tff(f3113,plain,
! [X0: fun_nat_bool] :
( ? [X2: int] :
( ~ hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
=> ( ~ hBOOL(hAPP_nat_bool(X0,nat_1(sK31(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK31(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f3114,plain,
! [X0: fun_nat_bool] :
( ? [X4: nat] : ~ hBOOL(hAPP_nat_bool(X0,X4))
=> ~ hBOOL(hAPP_nat_bool(X0,sK32(X0))) ),
introduced(choice_axiom,[]) ).
tff(f3112,plain,
! [X0: fun_nat_bool] :
( ( ! [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
| ? [X2: int] :
( ~ hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( ! [X3: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) )
| ? [X4: nat] : ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
inference(rectify,[],[f3111]) ).
tff(f3111,plain,
! [X0: fun_nat_bool] :
( ( ! [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
| ? [X2: int] :
( ~ hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( ! [X2: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
| ? [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
inference(nnf_transformation,[],[f2286]) ).
tff(f2286,plain,
! [X0: fun_nat_bool] :
( ! [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ! [X2: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f1468]) ).
tff(f1468,plain,
! [X0: fun_nat_bool] :
( ! [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ! [X2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(hAPP_nat_bool(X0,nat_1(X2))) ) ),
inference(rectify,[],[f532]) ).
tff(f532,axiom,
! [X51: fun_nat_bool] :
( ! [X245: nat] : hBOOL(hAPP_nat_bool(X51,X245))
<=> ! [X149: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X149))
=> hBOOL(hAPP_nat_bool(X51,nat_1(X149))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_all__nat) ).
tff(f8364,plain,
spl59_215,
inference(avatar_split_clause,[],[f3932,f8362]) ).
tff(f8362,plain,
( spl59_215
<=> ! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
| ( one_one_int != abs_abs_int(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_215])]) ).
tff(f3932,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
| ( one_one_int != abs_abs_int(X0) ) ),
inference(cnf_transformation,[],[f3056]) ).
tff(f3056,plain,
! [X0: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
| ( one_one_int != abs_abs_int(X0) ) )
& ( ( one_one_int = abs_abs_int(X0) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ) ),
inference(nnf_transformation,[],[f1159]) ).
tff(f1159,axiom,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
<=> ( one_one_int = abs_abs_int(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_zdvd1__eq) ).
tff(f8360,plain,
spl59_214,
inference(avatar_split_clause,[],[f3931,f8358]) ).
tff(f8358,plain,
( spl59_214
<=> ! [X0: int] :
( ( one_one_int = abs_abs_int(X0) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_214])]) ).
tff(f3931,plain,
! [X0: int] :
( ( one_one_int = abs_abs_int(X0) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
inference(cnf_transformation,[],[f3056]) ).
tff(f8356,plain,
spl59_213,
inference(avatar_split_clause,[],[f3821,f8354]) ).
tff(f8354,plain,
( spl59_213
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,times_times_nat(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_213])]) ).
tff(f3821,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,times_times_nat(X0,X0)))),
inference(cnf_transformation,[],[f1361]) ).
tff(f1361,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,times_times_nat(X0,X0)))),
inference(rectify,[],[f846]) ).
tff(f846,axiom,
! [X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),times_times_nat(X12,times_times_nat(X12,X12)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_le__cube) ).
tff(f8351,plain,
( spl59_212
| ~ spl59_110
| ~ spl59_122
| ~ spl59_190
| ~ spl59_196
| ~ spl59_211 ),
inference(avatar_split_clause,[],[f8346,f8341,f8196,f8171,f7534,f7483,f8348]) ).
tff(f8348,plain,
( spl59_212
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_212])]) ).
tff(f8341,plain,
( spl59_211
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_211])]) ).
tff(f8346,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),pls))
| ~ spl59_110
| ~ spl59_122
| ~ spl59_190
| ~ spl59_196
| ~ spl59_211 ),
inference(forward_demodulation,[],[f8345,f8293]) ).
tff(f8345,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl59_110
| ~ spl59_122
| ~ spl59_211 ),
inference(forward_demodulation,[],[f8343,f7691]) ).
tff(f8343,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl59_211 ),
inference(avatar_component_clause,[],[f8341]) ).
tff(f8344,plain,
spl59_211,
inference(avatar_split_clause,[],[f3637,f8341]) ).
tff(f3637,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f149]) ).
tff(f149,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mn) ).
tff(f8314,plain,
( spl59_210
| ~ spl59_122
| ~ spl59_202 ),
inference(avatar_split_clause,[],[f8224,f8220,f7534,f8311]) ).
tff(f8311,plain,
( spl59_210
<=> ( hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) = minus_minus_int(one_one_int,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_210])]) ).
tff(f8220,plain,
( spl59_202
<=> ( plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_202])]) ).
tff(f8224,plain,
( ( hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) = minus_minus_int(one_one_int,min) )
| ~ spl59_122
| ~ spl59_202 ),
inference(forward_demodulation,[],[f8222,f7535]) ).
tff(f8222,plain,
( ( plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl59_202 ),
inference(avatar_component_clause,[],[f8220]) ).
tff(f8301,plain,
( spl59_209
| ~ spl59_53
| ~ spl59_196 ),
inference(avatar_split_clause,[],[f8292,f8196,f7190,f8298]) ).
tff(f7190,plain,
( spl59_53
<=> ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(pls,min),min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_53])]) ).
tff(f8292,plain,
( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ spl59_53
| ~ spl59_196 ),
inference(trivial_inequality_removal,[],[f8289]) ).
tff(f8289,plain,
( ( pls != pls )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ spl59_53
| ~ spl59_196 ),
inference(superposition,[],[f8197,f7192]) ).
tff(f7192,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(pls,min),min))) )
| ~ spl59_53 ),
inference(avatar_component_clause,[],[f7190]) ).
tff(f8248,plain,
( spl59_208
| ~ spl59_106
| ~ spl59_184 ),
inference(avatar_split_clause,[],[f8149,f8146,f7467,f8246]) ).
tff(f8246,plain,
( spl59_208
<=> ! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(one_one_real,abs_abs_real(X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_208])]) ).
tff(f7467,plain,
( spl59_106
<=> ! [X0: real,X1: real] : ( plus_plus_real(X0,X1) = plus_plus_real(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_106])]) ).
tff(f8146,plain,
( spl59_184
<=> ! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_184])]) ).
tff(f8149,plain,
( ! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(one_one_real,abs_abs_real(X0))),X0))
| ~ spl59_106
| ~ spl59_184 ),
inference(forward_demodulation,[],[f8147,f7468]) ).
tff(f7468,plain,
( ! [X0: real,X1: real] : ( plus_plus_real(X0,X1) = plus_plus_real(X1,X0) )
| ~ spl59_106 ),
inference(avatar_component_clause,[],[f7467]) ).
tff(f8147,plain,
( ! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0))
| ~ spl59_184 ),
inference(avatar_component_clause,[],[f8146]) ).
tff(f8244,plain,
spl59_207,
inference(avatar_split_clause,[],[f6664,f8242]) ).
tff(f8242,plain,
( spl59_207
<=> ! [X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),pls))
| sP5(zero_zero_nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_207])]) ).
tff(f6664,plain,
! [X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),pls))
| sP5(zero_zero_nat,X1) ),
inference(forward_demodulation,[],[f6077,f5346]) ).
tff(f5346,plain,
pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(definition_unfolding,[],[f3586,f3551]) ).
tff(f3586,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(cnf_transformation,[],[f294]) ).
tff(f294,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
tff(f6077,plain,
! [X1: int] :
( sP5(zero_zero_nat,X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,zero_zero_nat))) ),
inference(equality_resolution,[],[f4515]) ).
tff(f4515,plain,
! [X0: nat,X1: int] :
( sP5(X0,X1)
| ( zero_zero_nat != X0 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,X0))) ),
inference(cnf_transformation,[],[f3268]) ).
tff(f3268,plain,
! [X0: nat,X1: int] :
( ( sP5(X0,X1)
| ( ( zero_zero_nat != X0 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( ( zero_zero_nat = X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f3267]) ).
tff(f3267,plain,
! [X1: nat,X0: int] :
( ( sP5(X1,X0)
| ( ( zero_zero_nat != X1 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP5(X1,X0) ) ),
inference(flattening,[],[f3266]) ).
tff(f3266,plain,
! [X1: nat,X0: int] :
( ( sP5(X1,X0)
| ( ( zero_zero_nat != X1 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP5(X1,X0) ) ),
inference(nnf_transformation,[],[f2984]) ).
tff(f8240,plain,
spl59_206,
inference(avatar_split_clause,[],[f6636,f8238]) ).
tff(f8238,plain,
( spl59_206
<=> ! [X0: int,X1: int] :
( ( min = X1 )
| ( one_one_int = X1 )
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_206])]) ).
tff(f6636,plain,
! [X0: int,X1: int] :
( ( min = X1 )
| ( one_one_int = X1 )
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f4375,f3679]) ).
tff(f3679,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f1219]) ).
tff(f1219,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(rectify,[],[f178]) ).
tff(f178,axiom,
! [X18: int] : ( number_number_of_int(X18) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_number__of__is__id) ).
tff(f4375,plain,
! [X0: int,X1: int] :
( ( number_number_of_int(min) = X1 )
| ( one_one_int = X1 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3180]) ).
tff(f3180,plain,
! [X0: int,X1: int] :
( ( sP3(X0,X1)
| ( ( ( number_number_of_int(min) != X0 )
| ( number_number_of_int(min) != X1 ) )
& ( ( one_one_int != X0 )
| ( one_one_int != X1 ) ) ) )
& ( ( ( number_number_of_int(min) = X0 )
& ( number_number_of_int(min) = X1 ) )
| ( ( one_one_int = X0 )
& ( one_one_int = X1 ) )
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f3179]) ).
tff(f3179,plain,
! [X1: int,X0: int] :
( ( sP3(X1,X0)
| ( ( ( number_number_of_int(min) != X1 )
| ( number_number_of_int(min) != X0 ) )
& ( ( one_one_int != X1 )
| ( one_one_int != X0 ) ) ) )
& ( ( ( number_number_of_int(min) = X1 )
& ( number_number_of_int(min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) )
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f3178]) ).
tff(f3178,plain,
! [X1: int,X0: int] :
( ( sP3(X1,X0)
| ( ( ( number_number_of_int(min) != X1 )
| ( number_number_of_int(min) != X0 ) )
& ( ( one_one_int != X1 )
| ( one_one_int != X0 ) ) ) )
& ( ( ( number_number_of_int(min) = X1 )
& ( number_number_of_int(min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f2980]) ).
tff(f2980,plain,
! [X1: int,X0: int] :
( sP3(X1,X0)
<=> ( ( ( number_number_of_int(min) = X1 )
& ( number_number_of_int(min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f8236,plain,
spl59_205,
inference(avatar_split_clause,[],[f6635,f8234]) ).
tff(f8234,plain,
( spl59_205
<=> ! [X0: int,X1: int] :
( ( min = X1 )
| ( one_one_int = X0 )
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_205])]) ).
tff(f6635,plain,
! [X0: int,X1: int] :
( ( min = X1 )
| ( one_one_int = X0 )
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f4376,f3679]) ).
tff(f4376,plain,
! [X0: int,X1: int] :
( ( number_number_of_int(min) = X1 )
| ( one_one_int = X0 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3180]) ).
tff(f8232,plain,
spl59_204,
inference(avatar_split_clause,[],[f6634,f8230]) ).
tff(f8230,plain,
( spl59_204
<=> ! [X0: int,X1: int] :
( ( min = X0 )
| ( one_one_int = X1 )
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_204])]) ).
tff(f6634,plain,
! [X0: int,X1: int] :
( ( min = X0 )
| ( one_one_int = X1 )
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f4377,f3679]) ).
tff(f4377,plain,
! [X0: int,X1: int] :
( ( number_number_of_int(min) = X0 )
| ( one_one_int = X1 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3180]) ).
tff(f8228,plain,
spl59_203,
inference(avatar_split_clause,[],[f6633,f8226]) ).
tff(f8226,plain,
( spl59_203
<=> ! [X0: int,X1: int] :
( ( min = X0 )
| ( one_one_int = X0 )
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_203])]) ).
tff(f6633,plain,
! [X0: int,X1: int] :
( ( min = X0 )
| ( one_one_int = X0 )
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f4378,f3679]) ).
tff(f4378,plain,
! [X0: int,X1: int] :
( ( number_number_of_int(min) = X0 )
| ( one_one_int = X0 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3180]) ).
tff(f8223,plain,
spl59_202,
inference(avatar_split_clause,[],[f6214,f8220]) ).
tff(f6214,plain,
plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6213,f6184]) ).
tff(f6184,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat_1(plus_plus_int(one_one_int,one_one_int)),
inference(forward_demodulation,[],[f6183,f6181]) ).
tff(f6181,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5361,f5331]) ).
tff(f5331,plain,
pls = plus_plus_int(pls,pls),
inference(definition_unfolding,[],[f3563,f3767]) ).
tff(f3767,plain,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
inference(cnf_transformation,[],[f1307]) ).
tff(f1307,plain,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X18: int] : ( bit0(X18) = plus_plus_int(X18,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
tff(f3563,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
tff(f5361,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f3618,f3767,f5319]) ).
tff(f5319,plain,
! [X0: int] : ( bit1(X0) = minus_minus_int(plus_plus_int(X0,X0),min) ),
inference(definition_unfolding,[],[f3768,f3764,f3767]) ).
tff(f3764,plain,
! [X0: int] : ( succ(X0) = minus_minus_int(X0,min) ),
inference(cnf_transformation,[],[f1304]) ).
tff(f1304,plain,
! [X0: int] : ( succ(X0) = minus_minus_int(X0,min) ),
inference(rectify,[],[f1022]) ).
tff(f1022,axiom,
! [X18: int] : ( succ(X18) = minus_minus_int(X18,min) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_diff__bin__simps_I2_J) ).
tff(f3768,plain,
! [X0: int] : ( bit1(X0) = succ(bit0(X0)) ),
inference(cnf_transformation,[],[f1308]) ).
tff(f1308,plain,
! [X0: int] : ( bit1(X0) = succ(bit0(X0)) ),
inference(rectify,[],[f810]) ).
tff(f810,axiom,
! [X18: int] : ( bit1(X18) = succ(bit0(X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_succ__Bit0) ).
tff(f3618,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(cnf_transformation,[],[f19]) ).
tff(f19,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).
tff(f6183,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat_1(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min)))),
inference(forward_demodulation,[],[f5363,f5331]) ).
tff(f5363,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min)))),
inference(definition_unfolding,[],[f3620,f3766,f3767,f5319]) ).
tff(f3766,plain,
! [X0: int] : ( number_number_of_nat(X0) = nat_1(number_number_of_int(X0)) ),
inference(cnf_transformation,[],[f1306]) ).
tff(f1306,plain,
! [X0: int] : ( number_number_of_nat(X0) = nat_1(number_number_of_int(X0)) ),
inference(rectify,[],[f768]) ).
tff(f768,axiom,
! [X10: int] : ( number_number_of_nat(X10) = nat_1(number_number_of_int(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).
tff(f3620,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
tff(f6213,plain,
plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,nat_1(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6212,f6181]) ).
tff(f6212,plain,
number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))) = hAPP_nat_int(semiri1621563631at_int,nat_1(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5378,f5331]) ).
tff(f5378,plain,
number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))) = hAPP_nat_int(semiri1621563631at_int,nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3639,f3767,f5319,f3766,f3767,f5319]) ).
tff(f3639,plain,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f152]) ).
tff(f152,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_transfer__int__nat__numerals_I3_J) ).
tff(f8218,plain,
spl59_201,
inference(avatar_split_clause,[],[f6078,f8216]) ).
tff(f8216,plain,
( spl59_201
<=> ! [X1: int] :
( sP5(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_201])]) ).
tff(f6078,plain,
! [X1: int] :
( sP5(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(equality_resolution,[],[f5776]) ).
tff(f5776,plain,
! [X0: nat,X1: int] :
( sP5(X0,X1)
| ( zero_zero_nat != X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f4514,f3551]) ).
tff(f4514,plain,
! [X0: nat,X1: int] :
( sP5(X0,X1)
| ( zero_zero_nat != X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3268]) ).
tff(f8214,plain,
spl59_200,
inference(avatar_split_clause,[],[f6048,f8212]) ).
tff(f8212,plain,
( spl59_200
<=> ! [X0: fun_nat_bool,X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ~ sP4(X0,hAPP_nat_int(semiri1621563631at_int,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_200])]) ).
tff(f6048,plain,
! [X3: nat,X0: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ~ sP4(X0,hAPP_nat_int(semiri1621563631at_int,X3)) ),
inference(equality_resolution,[],[f4418]) ).
tff(f4418,plain,
! [X3: nat,X0: fun_nat_bool,X1: int] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( hAPP_nat_int(semiri1621563631at_int,X3) != X1 )
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3206]) ).
tff(f3206,plain,
! [X0: fun_nat_bool,X1: int] :
( ( sP4(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ( ~ hBOOL(hAPP_nat_bool(X0,sK44(X0,X1)))
& ( hAPP_nat_int(semiri1621563631at_int,sK44(X0,X1)) = X1 ) ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( hAPP_nat_int(semiri1621563631at_int,X3) != X1 ) ) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f3204,f3205]) ).
tff(f3205,plain,
! [X0: fun_nat_bool,X1: int] :
( ? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& ( hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK44(X0,X1)))
& ( hAPP_nat_int(semiri1621563631at_int,sK44(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f3204,plain,
! [X0: fun_nat_bool,X1: int] :
( ( sP4(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& ( hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ( hAPP_nat_int(semiri1621563631at_int,X3) != X1 ) ) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f3203]) ).
tff(f3203,plain,
! [X0: fun_nat_bool,X1: int] :
( ( sP4(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& ( hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2: nat] :
( hBOOL(hAPP_nat_bool(X0,X2))
| ( hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) ) )
| ~ sP4(X0,X1) ) ),
inference(flattening,[],[f3202]) ).
tff(f3202,plain,
! [X0: fun_nat_bool,X1: int] :
( ( sP4(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& ( hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2: nat] :
( hBOOL(hAPP_nat_bool(X0,X2))
| ( hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) ) )
| ~ sP4(X0,X1) ) ),
inference(nnf_transformation,[],[f2982]) ).
tff(f2982,plain,
! [X0: fun_nat_bool,X1: int] :
( sP4(X0,X1)
<=> ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2: nat] :
( hBOOL(hAPP_nat_bool(X0,X2))
| ( hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f8210,plain,
spl59_199,
inference(avatar_split_clause,[],[f6011,f8208]) ).
tff(f8208,plain,
( spl59_199
<=> ! [X1: int] :
( sP2(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_199])]) ).
tff(f6011,plain,
! [X1: int] :
( sP2(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(equality_resolution,[],[f5725]) ).
tff(f5725,plain,
! [X0: nat,X1: int] :
( sP2(X0,X1)
| ( zero_zero_nat != X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f4358,f3551]) ).
tff(f4358,plain,
! [X0: nat,X1: int] :
( sP2(X0,X1)
| ( zero_zero_nat != X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3168]) ).
tff(f3168,plain,
! [X0: nat,X1: int] :
( ( sP2(X0,X1)
| ( ( zero_zero_nat != X0 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( ( hAPP_nat_int(semiri1621563631at_int,X0) != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( ( zero_zero_nat = X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X0) = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f3167]) ).
tff(f3167,plain,
! [X1: nat,X0: int] :
( ( sP2(X1,X0)
| ( ( zero_zero_nat != X1 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( ( hAPP_nat_int(semiri1621563631at_int,X1) != X0 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f3166]) ).
tff(f3166,plain,
! [X1: nat,X0: int] :
( ( sP2(X1,X0)
| ( ( zero_zero_nat != X1 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( ( hAPP_nat_int(semiri1621563631at_int,X1) != X0 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f2978]) ).
tff(f2978,plain,
! [X1: nat,X0: int] :
( sP2(X1,X0)
<=> ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f8206,plain,
spl59_198,
inference(avatar_split_clause,[],[f6006,f8204]) ).
tff(f8204,plain,
( spl59_198
<=> ! [X1: int] :
( sP1(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_198])]) ).
tff(f6006,plain,
! [X1: int] :
( sP1(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(equality_resolution,[],[f5720]) ).
tff(f5720,plain,
! [X0: nat,X1: int] :
( sP1(X0,X1)
| ( zero_zero_nat != X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f4350,f3551]) ).
tff(f4350,plain,
! [X0: nat,X1: int] :
( sP1(X0,X1)
| ( zero_zero_nat != X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3164]) ).
tff(f3164,plain,
! [X0: nat,X1: int] :
( ( sP1(X0,X1)
| ( ( zero_zero_nat != X0 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( ( hAPP_nat_int(semiri1621563631at_int,X0) != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( ( zero_zero_nat = X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X0) = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f3163]) ).
tff(f3163,plain,
! [X0: nat,X1: int] :
( ( sP1(X0,X1)
| ( ( zero_zero_nat != X0 )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( ( hAPP_nat_int(semiri1621563631at_int,X0) != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( ( zero_zero_nat = X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X0) = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f2976]) ).
tff(f2976,plain,
! [X0: nat,X1: int] :
( sP1(X0,X1)
<=> ( ( ( zero_zero_nat = X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X0) = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f8202,plain,
spl59_197,
inference(avatar_split_clause,[],[f5766,f8200]) ).
tff(f8200,plain,
( spl59_197
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_197])]) ).
tff(f5766,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),pls)) ),
inference(definition_unfolding,[],[f4487,f3551]) ).
tff(f4487,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int)) ),
inference(cnf_transformation,[],[f3253]) ).
tff(f3253,plain,
! [X0: int,X1: int] :
( ( hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int)) ) ),
inference(nnf_transformation,[],[f1759]) ).
tff(f1759,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(zcong(X0,X1),zero_zero_int))
<=> ( X0 = X1 ) ),
inference(rectify,[],[f1127]) ).
tff(f1127,axiom,
! [X2: int,X78: int] :
( hBOOL(hAPP_int_bool(zcong(X2,X78),zero_zero_int))
<=> ( X2 = X78 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_IntPrimes_Ozcong__zero) ).
tff(f8198,plain,
spl59_196,
inference(avatar_split_clause,[],[f5649,f8196]) ).
tff(f5649,plain,
! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) ),
inference(definition_unfolding,[],[f4163,f3551,f3551]) ).
tff(f4163,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f2307]) ).
tff(f2307,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[],[f1574]) ).
tff(f1574,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != X1 )
=> ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) ) ),
inference(rectify,[],[f232]) ).
tff(f232,axiom,
! [X61: nat,X62: int] :
( ( zero_zero_int != X62 )
=> ( zero_zero_int != hAPP_nat_int(power_power_int(X62),X61) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
tff(f8194,plain,
spl59_195,
inference(avatar_split_clause,[],[f5619,f8192]) ).
tff(f8192,plain,
( spl59_195
<=> ! [X0: int,X1: int] : ( plus_plus_int(X0,X0) != minus_minus_int(plus_plus_int(X1,X1),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_195])]) ).
tff(f5619,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X0) != minus_minus_int(plus_plus_int(X1,X1),min) ),
inference(definition_unfolding,[],[f4054,f3767,f5319]) ).
tff(f4054,plain,
! [X0: int,X1: int] : ( bit0(X0) != bit1(X1) ),
inference(cnf_transformation,[],[f1473]) ).
tff(f1473,plain,
! [X0: int,X1: int] : ( bit0(X0) != bit1(X1) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X18: int,X28: int] : ( bit1(X28) != bit0(X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I49_J) ).
tff(f8190,plain,
spl59_194,
inference(avatar_split_clause,[],[f5468,f8188]) ).
tff(f8188,plain,
( spl59_194
<=> ! [X0: nat] :
( ( pls = hAPP_nat_int(power_power_int(pls),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_194])]) ).
tff(f5468,plain,
! [X0: nat] :
( ( pls = hAPP_nat_int(power_power_int(pls),X0) )
| ( zero_zero_nat = X0 ) ),
inference(definition_unfolding,[],[f3844,f3551,f3551]) ).
tff(f3844,plain,
! [X0: nat] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f2261]) ).
tff(f2261,plain,
! [X0: nat] :
( ( ( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) )
& ( ( one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f1381]) ).
tff(f1381,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
=> ( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) ) )
& ( ( zero_zero_nat = X0 )
=> ( one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) ) ) ),
inference(rectify,[],[f161]) ).
tff(f161,axiom,
! [X47: nat] :
( ( ( zero_zero_nat != X47 )
=> ( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X47) ) )
& ( ( zero_zero_nat = X47 )
=> ( one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),X47) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_power__0__left) ).
tff(f8186,plain,
spl59_193,
inference(avatar_split_clause,[],[f4435,f8184]) ).
tff(f8184,plain,
( spl59_193
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_193])]) ).
tff(f4435,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
inference(cnf_transformation,[],[f3217]) ).
tff(f3217,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = hAPP_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 != hAPP_nat_nat(power_power_nat(X0),X1) ) ) ),
inference(flattening,[],[f3216]) ).
tff(f3216,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = hAPP_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 != hAPP_nat_nat(power_power_nat(X0),X1) ) ) ),
inference(nnf_transformation,[],[f1743]) ).
tff(f1743,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(X0),X1) )
<=> ( ( zero_zero_nat = X0 )
& ( zero_zero_nat != X1 ) ) ),
inference(rectify,[],[f403]) ).
tff(f403,axiom,
! [X26: nat,X15: nat] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(X26),X15) )
<=> ( ( zero_zero_nat = X26 )
& ( zero_zero_nat != X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_nat__power__eq__0__iff) ).
tff(f8182,plain,
spl59_192,
inference(avatar_split_clause,[],[f4160,f8180]) ).
tff(f8180,plain,
( spl59_192
<=> ! [X0: nat,X1: real] :
( ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) )
| ( zero_zero_real = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_192])]) ).
tff(f4160,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) )
| ( zero_zero_real = X1 ) ),
inference(cnf_transformation,[],[f2302]) ).
tff(f2302,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) )
| ( zero_zero_real = X1 ) ),
inference(ennf_transformation,[],[f1571]) ).
tff(f1571,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != X1 )
=> ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) ) ),
inference(rectify,[],[f233]) ).
tff(f233,axiom,
! [X61: nat,X62: real] :
( ( zero_zero_real != X62 )
=> ( zero_zero_real != hAPP_nat_real(power_power_real(X62),X61) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_field__power__not__zero) ).
tff(f8178,plain,
spl59_191,
inference(avatar_split_clause,[],[f3927,f8176]) ).
tff(f8176,plain,
( spl59_191
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_191])]) ).
tff(f3927,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
inference(cnf_transformation,[],[f3054]) ).
tff(f3054,plain,
! [X0: nat] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
| ( zero_zero_nat != X0 ) )
& ( ( zero_zero_nat = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
inference(nnf_transformation,[],[f1421]) ).
tff(f1421,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
<=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f872]) ).
tff(f872,axiom,
! [X15: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),zero_zero_nat))
<=> ( zero_zero_nat = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_le__0__eq) ).
tff(f8174,plain,
( spl59_190
| ~ spl59_110
| ~ spl59_122
| ~ spl59_126
| ~ spl59_182 ),
inference(avatar_split_clause,[],[f8143,f8124,f7687,f7534,f7483,f8171]) ).
tff(f7687,plain,
( spl59_126
<=> ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(one_one_int,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_126])]) ).
tff(f8124,plain,
( spl59_182
<=> ( plus_plus_nat(one_one_nat,one_one_nat) = nat_1(minus_minus_int(one_one_int,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_182])]) ).
tff(f8143,plain,
( ( pls = hAPP_nat_int(power_power_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)),plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl59_110
| ~ spl59_122
| ~ spl59_126
| ~ spl59_182 ),
inference(forward_demodulation,[],[f8138,f7691]) ).
tff(f8138,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl59_126
| ~ spl59_182 ),
inference(superposition,[],[f7689,f8126]) ).
tff(f8126,plain,
( ( plus_plus_nat(one_one_nat,one_one_nat) = nat_1(minus_minus_int(one_one_int,min)) )
| ~ spl59_182 ),
inference(avatar_component_clause,[],[f8124]) ).
tff(f7689,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(one_one_int,min))) )
| ~ spl59_126 ),
inference(avatar_component_clause,[],[f7687]) ).
tff(f8169,plain,
spl59_189,
inference(avatar_split_clause,[],[f3925,f8167]) ).
tff(f8167,plain,
( spl59_189
<=> ! [X0: nat] :
( ( one_one_nat = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_189])]) ).
tff(f3925,plain,
! [X0: nat] :
( ( one_one_nat = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ),
inference(cnf_transformation,[],[f3053]) ).
tff(f3053,plain,
! [X0: nat] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
| ( one_one_nat != X0 ) )
& ( ( one_one_nat = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ) ),
inference(nnf_transformation,[],[f1420]) ).
tff(f1420,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
<=> ( one_one_nat = X0 ) ),
inference(rectify,[],[f1056]) ).
tff(f1056,axiom,
! [X26: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X26),one_one_nat))
<=> ( one_one_nat = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_nat__dvd__1__iff__1) ).
tff(f8165,plain,
spl59_188,
inference(avatar_split_clause,[],[f3860,f8163]) ).
tff(f8163,plain,
( spl59_188
<=> ! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_188])]) ).
tff(f3860,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f2268]) ).
tff(f2268,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f1391]) ).
tff(f1391,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(rectify,[],[f197]) ).
tff(f197,axiom,
! [X13: nat] :
( ( zero_zero_nat != X13 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_gr0I) ).
tff(f8161,plain,
spl59_187,
inference(avatar_split_clause,[],[f3842,f8159]) ).
tff(f8159,plain,
( spl59_187
<=> ! [X0: nat] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_187])]) ).
tff(f3842,plain,
! [X0: nat] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f2260]) ).
tff(f2260,plain,
! [X0: nat] :
( ( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) )
& ( ( one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f1380]) ).
tff(f1380,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
=> ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) ) )
& ( ( zero_zero_nat = X0 )
=> ( one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) ) ) ),
inference(rectify,[],[f162]) ).
tff(f162,axiom,
! [X47: nat] :
( ( ( zero_zero_nat != X47 )
=> ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X47) ) )
& ( ( zero_zero_nat = X47 )
=> ( one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X47) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_power__0__left) ).
tff(f8157,plain,
spl59_186,
inference(avatar_split_clause,[],[f3840,f8155]) ).
tff(f8155,plain,
( spl59_186
<=> ! [X0: nat] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_186])]) ).
tff(f3840,plain,
! [X0: nat] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f2259]) ).
tff(f2259,plain,
! [X0: nat] :
( ( ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) )
& ( ( one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) )
| ( zero_zero_nat != X0 ) ) ),
inference(ennf_transformation,[],[f1379]) ).
tff(f1379,plain,
! [X0: nat] :
( ( ( zero_zero_nat != X0 )
=> ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) ) )
& ( ( zero_zero_nat = X0 )
=> ( one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) ) ) ),
inference(rectify,[],[f163]) ).
tff(f163,axiom,
! [X47: nat] :
( ( ( zero_zero_nat != X47 )
=> ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X47) ) )
& ( ( zero_zero_nat = X47 )
=> ( one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),X47) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_power__0__left) ).
tff(f8153,plain,
spl59_185,
inference(avatar_split_clause,[],[f3814,f8151]) ).
tff(f8151,plain,
( spl59_185
<=> ! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_185])]) ).
tff(f3814,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X0)))),
inference(cnf_transformation,[],[f1354]) ).
tff(f1354,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X0)))),
inference(rectify,[],[f1178]) ).
tff(f1178,axiom,
! [X5: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X5)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_abs__add__one__gt__zero) ).
tff(f8148,plain,
spl59_184,
inference(avatar_split_clause,[],[f3809,f8146]) ).
tff(f3809,plain,
! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0)),
inference(cnf_transformation,[],[f1349]) ).
tff(f1349,plain,
! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0)),
inference(rectify,[],[f1177]) ).
tff(f1177,axiom,
! [X5: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X5),one_one_real)),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_abs__add__one__not__less__self) ).
tff(f8132,plain,
( spl59_183
| ~ spl59_122
| ~ spl59_176 ),
inference(avatar_split_clause,[],[f7929,f7925,f7534,f8129]) ).
tff(f8129,plain,
( spl59_183
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),minus_minus_int(one_one_int,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_183])]) ).
tff(f7925,plain,
( spl59_176
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(one_one_int,one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_176])]) ).
tff(f7929,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),minus_minus_int(one_one_int,min)))
| ~ spl59_122
| ~ spl59_176 ),
inference(forward_demodulation,[],[f7927,f7535]) ).
tff(f7927,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(one_one_int,one_one_int)))
| ~ spl59_176 ),
inference(avatar_component_clause,[],[f7925]) ).
tff(f8127,plain,
( spl59_182
| ~ spl59_122
| ~ spl59_172 ),
inference(avatar_split_clause,[],[f7908,f7904,f7534,f8124]) ).
tff(f7904,plain,
( spl59_172
<=> ( plus_plus_nat(one_one_nat,one_one_nat) = nat_1(plus_plus_int(one_one_int,one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_172])]) ).
tff(f7908,plain,
( ( plus_plus_nat(one_one_nat,one_one_nat) = nat_1(minus_minus_int(one_one_int,min)) )
| ~ spl59_122
| ~ spl59_172 ),
inference(forward_demodulation,[],[f7906,f7535]) ).
tff(f7906,plain,
( ( plus_plus_nat(one_one_nat,one_one_nat) = nat_1(plus_plus_int(one_one_int,one_one_int)) )
| ~ spl59_172 ),
inference(avatar_component_clause,[],[f7904]) ).
tff(f8091,plain,
( spl59_181
| ~ spl59_122
| ~ spl59_162 ),
inference(avatar_split_clause,[],[f7865,f7861,f7534,f8088]) ).
tff(f8088,plain,
( spl59_181
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(one_one_int,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_181])]) ).
tff(f7861,plain,
( spl59_162
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_162])]) ).
tff(f7865,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(one_one_int,min)))
| ~ spl59_122
| ~ spl59_162 ),
inference(forward_demodulation,[],[f7863,f7535]) ).
tff(f7863,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,one_one_int)))
| ~ spl59_162 ),
inference(avatar_component_clause,[],[f7861]) ).
tff(f8070,plain,
( ~ spl59_180
| ~ spl59_100
| ~ spl59_137 ),
inference(avatar_split_clause,[],[f7975,f7760,f7397,f8067]) ).
tff(f8067,plain,
( spl59_180
<=> sP0(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_180])]) ).
tff(f7760,plain,
( spl59_137
<=> ! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_137])]) ).
tff(f7975,plain,
( ~ sP0(one_one_int)
| ~ spl59_100
| ~ spl59_137 ),
inference(resolution,[],[f7761,f7398]) ).
tff(f7761,plain,
( ! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
| ~ sP0(X0) )
| ~ spl59_137 ),
inference(avatar_component_clause,[],[f7760]) ).
tff(f8015,plain,
( ~ spl59_179
| spl59_92
| ~ spl59_137 ),
inference(avatar_split_clause,[],[f7974,f7760,f7359,f8012]) ).
tff(f8012,plain,
( spl59_179
<=> sP0(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_179])]) ).
tff(f7359,plain,
( spl59_92
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_92])]) ).
tff(f7974,plain,
( ~ sP0(pls)
| spl59_92
| ~ spl59_137 ),
inference(resolution,[],[f7761,f7361]) ).
tff(f7361,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls))
| spl59_92 ),
inference(avatar_component_clause,[],[f7359]) ).
tff(f7964,plain,
( spl59_178
| ~ spl59_47
| ~ spl59_131 ),
inference(avatar_split_clause,[],[f7945,f7736,f7155,f7961]) ).
tff(f7961,plain,
( spl59_178
<=> ( pls = abs_abs_int(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_178])]) ).
tff(f7155,plain,
( spl59_47
<=> ( pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_47])]) ).
tff(f7736,plain,
( spl59_131
<=> ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_131])]) ).
tff(f7945,plain,
( ( pls = abs_abs_int(pls) )
| ~ spl59_47
| ~ spl59_131 ),
inference(superposition,[],[f7737,f7157]) ).
tff(f7157,plain,
( ( pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
| ~ spl59_47 ),
inference(avatar_component_clause,[],[f7155]) ).
tff(f7737,plain,
( ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) )
| ~ spl59_131 ),
inference(avatar_component_clause,[],[f7736]) ).
tff(f7933,plain,
spl59_177,
inference(avatar_split_clause,[],[f6286,f7931]) ).
tff(f7931,plain,
( spl59_177
<=> ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),minus_minus_int(X0,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_177])]) ).
tff(f6286,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),minus_minus_int(X0,min))),
inference(forward_demodulation,[],[f3807,f5430]) ).
tff(f5430,plain,
! [X0: int] : ( minus_minus_int(X0,min) = plus_plus_int(X0,one_one_int) ),
inference(definition_unfolding,[],[f3765,f3764]) ).
tff(f3765,plain,
! [X0: int] : ( succ(X0) = plus_plus_int(X0,one_one_int) ),
inference(cnf_transformation,[],[f1305]) ).
tff(f1305,plain,
! [X0: int] : ( succ(X0) = plus_plus_int(X0,one_one_int) ),
inference(rectify,[],[f815]) ).
tff(f815,axiom,
! [X18: int] : ( succ(X18) = plus_plus_int(X18,one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_succ__def) ).
tff(f3807,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(X0,one_one_int))),
inference(cnf_transformation,[],[f1347]) ).
tff(f1347,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(X0,one_one_int))),
inference(rectify,[],[f270]) ).
tff(f270,axiom,
! [X77: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X77),plus_plus_int(X77,one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__add__one) ).
tff(f7928,plain,
spl59_176,
inference(avatar_split_clause,[],[f6210,f7925]) ).
tff(f6210,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6209,f6181]) ).
tff(f6209,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5373,f5331]) ).
tff(f5373,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3633,f3551,f3767,f5319]) ).
tff(f3633,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
inference(cnf_transformation,[],[f824]) ).
tff(f824,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
tff(f7923,plain,
spl59_175,
inference(avatar_split_clause,[],[f6204,f7920]) ).
tff(f7920,plain,
( spl59_175
<=> ( pls = hAPP_nat_int(power_power_int(pls),plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_175])]) ).
tff(f6204,plain,
pls = hAPP_nat_int(power_power_int(pls),plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6203,f6184]) ).
tff(f6203,plain,
pls = hAPP_nat_int(power_power_int(pls),nat_1(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6202,f6181]) ).
tff(f6202,plain,
pls = hAPP_nat_int(power_power_int(pls),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5371,f5331]) ).
tff(f5371,plain,
pls = hAPP_nat_int(power_power_int(pls),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3630,f3551,f3551,f3766,f3767,f5319]) ).
tff(f3630,plain,
zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zero__power2) ).
tff(f7918,plain,
spl59_174,
inference(avatar_split_clause,[],[f6201,f7915]) ).
tff(f7915,plain,
( spl59_174
<=> ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_174])]) ).
tff(f6201,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6200,f6184]) ).
tff(f6200,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),nat_1(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6199,f6181]) ).
tff(f6199,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5370,f5331]) ).
tff(f5370,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3629,f3766,f3767,f5319]) ).
tff(f3629,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zero__power2) ).
tff(f7913,plain,
spl59_173,
inference(avatar_split_clause,[],[f6198,f7910]) ).
tff(f7910,plain,
( spl59_173
<=> ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_173])]) ).
tff(f6198,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6197,f6184]) ).
tff(f6197,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat_1(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6196,f6181]) ).
tff(f6196,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5369,f5331]) ).
tff(f5369,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3628,f3766,f3767,f5319]) ).
tff(f3628,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__power2) ).
tff(f7907,plain,
spl59_172,
inference(avatar_split_clause,[],[f6184,f7904]) ).
tff(f7902,plain,
spl59_171,
inference(avatar_split_clause,[],[f5744,f7900]) ).
tff(f7900,plain,
( spl59_171
<=> ! [X0: int,X1: int] :
( ( pls = X1 )
| ( plus_plus_int(X0,X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_171])]) ).
tff(f5744,plain,
! [X0: int,X1: int] :
( ( pls = X1 )
| ( plus_plus_int(X0,X1) != X0 ) ),
inference(definition_unfolding,[],[f4416,f3551]) ).
tff(f4416,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( plus_plus_int(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f3201]) ).
tff(f3201,plain,
! [X0: int,X1: int] :
( ( ( plus_plus_int(X0,X1) = X0 )
| ( zero_zero_int != X1 ) )
& ( ( zero_zero_int = X1 )
| ( plus_plus_int(X0,X1) != X0 ) ) ),
inference(nnf_transformation,[],[f1738]) ).
tff(f1738,plain,
! [X0: int,X1: int] :
( ( plus_plus_int(X0,X1) = X0 )
<=> ( zero_zero_int = X1 ) ),
inference(rectify,[],[f356]) ).
tff(f356,axiom,
! [X78: int,X2: int] :
( ( plus_plus_int(X78,X2) = X78 )
<=> ( zero_zero_int = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
tff(f7898,plain,
spl59_170,
inference(avatar_split_clause,[],[f5718,f7896]) ).
tff(f7896,plain,
( spl59_170
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( pls != minus_minus_int(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_170])]) ).
tff(f5718,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( pls != minus_minus_int(X0,X1) ) ),
inference(definition_unfolding,[],[f4340,f3551]) ).
tff(f4340,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( zero_zero_int != minus_minus_int(X0,X1) ) ),
inference(cnf_transformation,[],[f3159]) ).
tff(f3159,plain,
! [X0: int,X1: int] :
( ( ( X0 = X1 )
| ( zero_zero_int != minus_minus_int(X0,X1) ) )
& ( ( zero_zero_int = minus_minus_int(X0,X1) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f1716]) ).
tff(f1716,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
<=> ( zero_zero_int = minus_minus_int(X0,X1) ) ),
inference(rectify,[],[f595]) ).
tff(f595,axiom,
! [X2: int,X78: int] :
( ( X2 = X78 )
<=> ( zero_zero_int = minus_minus_int(X2,X78) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_eq__iff__diff__eq__0) ).
tff(f7894,plain,
spl59_169,
inference(avatar_split_clause,[],[f5516,f7892]) ).
tff(f7892,plain,
( spl59_169
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_169])]) ).
tff(f5516,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
inference(definition_unfolding,[],[f3919,f3551]) ).
tff(f3919,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
inference(cnf_transformation,[],[f3050]) ).
tff(f3050,plain,
! [X0: nat] :
( ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0) )
| ( zero_zero_nat != X0 ) )
& ( ( zero_zero_nat = X0 )
| ( zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ) ),
inference(nnf_transformation,[],[f1417]) ).
tff(f1417,plain,
! [X0: nat] :
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0) )
<=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X15: nat] :
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X15) )
<=> ( zero_zero_nat = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_int__eq__0__conv) ).
tff(f7890,plain,
spl59_168,
inference(avatar_split_clause,[],[f5506,f7888]) ).
tff(f7888,plain,
( spl59_168
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus_int(X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_168])]) ).
tff(f5506,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus_int(X0,X0) ) ),
inference(definition_unfolding,[],[f3899,f3767]) ).
tff(f3899,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f3038]) ).
tff(f3038,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f1410]) ).
tff(f1410,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X9: int] :
( ( pls = bit0(X9) )
<=> ( pls = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_rel__simps_I38_J) ).
tff(f7886,plain,
spl59_167,
inference(avatar_split_clause,[],[f5442,f7884]) ).
tff(f7884,plain,
( spl59_167
<=> ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_167])]) ).
tff(f5442,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X0))),
inference(definition_unfolding,[],[f3806,f3551]) ).
tff(f3806,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X0))),
inference(cnf_transformation,[],[f1346]) ).
tff(f1346,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X0))),
inference(rectify,[],[f535]) ).
tff(f535,axiom,
! [X246: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X246,X246))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_zero__le__square) ).
tff(f7882,plain,
spl59_166,
inference(avatar_split_clause,[],[f5440,f7880]) ).
tff(f7880,plain,
( spl59_166
<=> ! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_166])]) ).
tff(f5440,plain,
! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(definition_unfolding,[],[f3801,f3551]) ).
tff(f3801,plain,
! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(cnf_transformation,[],[f1341]) ).
tff(f1341,plain,
! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(rectify,[],[f788]) ).
tff(f788,axiom,
! [X13: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_zero__zle__int) ).
tff(f7878,plain,
( ~ spl59_165
| ~ spl59_48
| ~ spl59_122 ),
inference(avatar_split_clause,[],[f7696,f7534,f7160,f7875]) ).
tff(f7875,plain,
( spl59_165
<=> ( min = minus_minus_int(one_one_int,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_165])]) ).
tff(f7160,plain,
( spl59_48
<=> ! [X0: int] : ( min != plus_plus_int(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_48])]) ).
tff(f7696,plain,
( ( min != minus_minus_int(one_one_int,min) )
| ~ spl59_48
| ~ spl59_122 ),
inference(superposition,[],[f7161,f7535]) ).
tff(f7161,plain,
( ! [X0: int] : ( min != plus_plus_int(X0,X0) )
| ~ spl59_48 ),
inference(avatar_component_clause,[],[f7160]) ).
tff(f7873,plain,
spl59_164,
inference(avatar_split_clause,[],[f5437,f7871]) ).
tff(f7871,plain,
( spl59_164
<=> ! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_164])]) ).
tff(f5437,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),pls)),
inference(definition_unfolding,[],[f3795,f3551]) ).
tff(f3795,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f1335]) ).
tff(f1335,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),zero_zero_int)),
inference(rectify,[],[f764]) ).
tff(f764,axiom,
! [X374: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X374,X374)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_not__square__less__zero) ).
tff(f7869,plain,
spl59_163,
inference(avatar_split_clause,[],[f5435,f7867]) ).
tff(f7867,plain,
( spl59_163
<=> ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_163])]) ).
tff(f5435,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f3792,f3551]) ).
tff(f3792,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f1332]) ).
tff(f1332,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(rectify,[],[f288]) ).
tff(f288,axiom,
! [X85: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X85)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
tff(f7864,plain,
spl59_162,
inference(avatar_split_clause,[],[f5365,f7861]) ).
tff(f5365,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,one_one_int))),
inference(definition_unfolding,[],[f3624,f3551]) ).
tff(f3624,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,one_one_int))),
inference(cnf_transformation,[],[f167]) ).
tff(f167,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_zero__less__two) ).
tff(f7859,plain,
spl59_161,
inference(avatar_split_clause,[],[f5032,f7857]) ).
tff(f7857,plain,
( spl59_161
<=> ! [X2: int,X0: bool,X1: bool] :
( sP11(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_161])]) ).
tff(f5032,plain,
! [X2: int,X0: bool,X1: bool] :
( sP11(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f3415]) ).
tff(f3415,plain,
! [X0: bool,X1: bool,X2: int] :
( sP11(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(flattening,[],[f3414]) ).
tff(f3414,plain,
! [X0: bool,X1: bool,X2: int] :
( sP11(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(nnf_transformation,[],[f2997]) ).
tff(f2997,plain,
! [X0: bool,X1: bool,X2: int] :
( sP11(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(definition_folding,[],[f2848,f2996]) ).
tff(f2996,plain,
! [X0: bool,X2: int,X1: bool] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP11(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
tff(f2848,plain,
! [X0: bool,X1: bool,X2: int] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f2097]) ).
tff(f2097,plain,
! [X0: bool,X1: bool,X2: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(X1) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(X0) ) ) ),
inference(rectify,[],[f1148]) ).
tff(f1148,axiom,
! [X392: bool,X51: bool,X0: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( hBOOL(X51)
<=> hBOOL(X392) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(X51) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(X392) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_imp__le__cong) ).
tff(f7855,plain,
spl59_160,
inference(avatar_split_clause,[],[f5031,f7853]) ).
tff(f7853,plain,
( spl59_160
<=> ! [X2: int,X0: bool,X1: bool] :
( sP11(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_160])]) ).
tff(f5031,plain,
! [X2: int,X0: bool,X1: bool] :
( sP11(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f3415]) ).
tff(f7851,plain,
spl59_159,
inference(avatar_split_clause,[],[f5025,f7849]) ).
tff(f7849,plain,
( spl59_159
<=> ! [X2: int,X0: bool,X1: bool] :
( sP10(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_159])]) ).
tff(f5025,plain,
! [X2: int,X0: bool,X1: bool] :
( sP10(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f3410]) ).
tff(f3410,plain,
! [X0: bool,X1: bool,X2: int] :
( sP10(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(flattening,[],[f3409]) ).
tff(f3409,plain,
! [X0: bool,X1: bool,X2: int] :
( sP10(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(nnf_transformation,[],[f2995]) ).
tff(f2995,plain,
! [X0: bool,X1: bool,X2: int] :
( sP10(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(definition_folding,[],[f2847,f2994]) ).
tff(f2994,plain,
! [X0: bool,X2: int,X1: bool] :
( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP10(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
tff(f2847,plain,
! [X0: bool,X1: bool,X2: int] :
( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f2096]) ).
tff(f2096,plain,
! [X0: bool,X1: bool,X2: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) ),
inference(rectify,[],[f1147]) ).
tff(f1147,axiom,
! [X392: bool,X51: bool,X0: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( hBOOL(X51)
<=> hBOOL(X392) ) )
=> ( ( hBOOL(X51)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
<=> ( hBOOL(X392)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_conj__le__cong) ).
tff(f7847,plain,
spl59_158,
inference(avatar_split_clause,[],[f5024,f7845]) ).
tff(f7845,plain,
( spl59_158
<=> ! [X2: int,X0: bool,X1: bool] :
( sP10(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_158])]) ).
tff(f5024,plain,
! [X2: int,X0: bool,X1: bool] :
( sP10(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f3410]) ).
tff(f7843,plain,
spl59_157,
inference(avatar_split_clause,[],[f4425,f7841]) ).
tff(f7841,plain,
( spl59_157
<=> ! [X0: fun_nat_bool,X1: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X1)))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_157])]) ).
tff(f4425,plain,
! [X0: fun_nat_bool,X1: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X1)))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3207]) ).
tff(f3207,plain,
! [X0: fun_nat_bool,X1: int] :
( ( hBOOL(hAPP_nat_bool(X0,nat_1(X1)))
| ~ sP4(X0,X1) )
& ( sP4(X0,X1)
| ~ hBOOL(hAPP_nat_bool(X0,nat_1(X1))) ) ),
inference(nnf_transformation,[],[f2983]) ).
tff(f2983,plain,
! [X0: fun_nat_bool,X1: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X1)))
<=> sP4(X0,X1) ),
inference(definition_folding,[],[f2538,f2982]) ).
tff(f2538,plain,
! [X0: fun_nat_bool,X1: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X1)))
<=> ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2: nat] :
( hBOOL(hAPP_nat_bool(X0,X2))
| ( hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) ) ) ),
inference(ennf_transformation,[],[f1739]) ).
tff(f1739,plain,
! [X0: fun_nat_bool,X1: int] :
( hBOOL(hAPP_nat_bool(X0,nat_1(X1)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
=> hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) )
& ! [X2: nat] :
( ( hAPP_nat_int(semiri1621563631at_int,X2) = X1 )
=> hBOOL(hAPP_nat_bool(X0,X2)) ) ) ),
inference(rectify,[],[f818]) ).
tff(f818,axiom,
! [X51: fun_nat_bool,X52: int] :
( hBOOL(hAPP_nat_bool(X51,nat_1(X52)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X52),zero_zero_int))
=> hBOOL(hAPP_nat_bool(X51,zero_zero_nat)) )
& ! [X87: nat] :
( ( hAPP_nat_int(semiri1621563631at_int,X87) = X52 )
=> hBOOL(hAPP_nat_bool(X51,X87)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_split__nat) ).
tff(f7839,plain,
spl59_156,
inference(avatar_split_clause,[],[f4424,f7837]) ).
tff(f7837,plain,
( spl59_156
<=> ! [X0: fun_nat_bool,X1: int] :
( sP4(X0,X1)
| ~ hBOOL(hAPP_nat_bool(X0,nat_1(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_156])]) ).
tff(f4424,plain,
! [X0: fun_nat_bool,X1: int] :
( sP4(X0,X1)
| ~ hBOOL(hAPP_nat_bool(X0,nat_1(X1))) ),
inference(cnf_transformation,[],[f3207]) ).
tff(f7835,plain,
spl59_155,
inference(avatar_split_clause,[],[f4412,f7833]) ).
tff(f7833,plain,
( spl59_155
<=> ! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( plus_plus_real(X0,X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_155])]) ).
tff(f4412,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( plus_plus_real(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f3199]) ).
tff(f3199,plain,
! [X0: real,X1: real] :
( ( ( plus_plus_real(X0,X1) = X0 )
| ( zero_zero_real != X1 ) )
& ( ( zero_zero_real = X1 )
| ( plus_plus_real(X0,X1) != X0 ) ) ),
inference(nnf_transformation,[],[f1736]) ).
tff(f1736,plain,
! [X0: real,X1: real] :
( ( plus_plus_real(X0,X1) = X0 )
<=> ( zero_zero_real = X1 ) ),
inference(rectify,[],[f358]) ).
tff(f358,axiom,
! [X78: real,X2: real] :
( ( plus_plus_real(X78,X2) = X78 )
<=> ( zero_zero_real = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_add__0__iff) ).
tff(f7831,plain,
spl59_154,
inference(avatar_split_clause,[],[f4403,f7829]) ).
tff(f7829,plain,
( spl59_154
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_154])]) ).
tff(f4403,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ),
inference(cnf_transformation,[],[f3194]) ).
tff(f3194,plain,
! [X0: int,X1: int] :
( ( ( number_number_of_int(X0) = number_number_of_int(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ) ),
inference(nnf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: int,X1: int] :
( ( number_number_of_int(X0) = number_number_of_int(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_eq__number__of) ).
tff(f7827,plain,
spl59_153,
inference(avatar_split_clause,[],[f4401,f7825]) ).
tff(f7825,plain,
( spl59_153
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number267125858f_real(X0) != number267125858f_real(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_153])]) ).
tff(f4401,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number267125858f_real(X0) != number267125858f_real(X1) ) ),
inference(cnf_transformation,[],[f3193]) ).
tff(f3193,plain,
! [X0: int,X1: int] :
( ( ( number267125858f_real(X0) = number267125858f_real(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( number267125858f_real(X0) != number267125858f_real(X1) ) ) ),
inference(nnf_transformation,[],[f58]) ).
tff(f58,axiom,
! [X0: int,X1: int] :
( ( number267125858f_real(X0) = number267125858f_real(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_eq__number__of) ).
tff(f7823,plain,
spl59_152,
inference(avatar_split_clause,[],[f4391,f7821]) ).
tff(f7821,plain,
( spl59_152
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( zero_zero_nat != plus_plus_nat(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_152])]) ).
tff(f4391,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( zero_zero_nat != plus_plus_nat(X0,X1) ) ),
inference(cnf_transformation,[],[f3187]) ).
tff(f3187,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_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 != plus_plus_nat(X0,X1) ) ) ),
inference(flattening,[],[f3186]) ).
tff(f3186,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_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 != plus_plus_nat(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1729]) ).
tff(f1729,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = plus_plus_nat(X0,X1) )
<=> ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) ) ),
inference(rectify,[],[f213]) ).
tff(f213,axiom,
! [X26: nat,X15: nat] :
( ( zero_zero_nat = plus_plus_nat(X26,X15) )
<=> ( ( zero_zero_nat = X15 )
& ( zero_zero_nat = X26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__is__0) ).
tff(f7819,plain,
spl59_151,
inference(avatar_split_clause,[],[f4390,f7817]) ).
tff(f7817,plain,
( spl59_151
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != plus_plus_nat(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_151])]) ).
tff(f4390,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != plus_plus_nat(X0,X1) ) ),
inference(cnf_transformation,[],[f3187]) ).
tff(f7815,plain,
spl59_150,
inference(avatar_split_clause,[],[f4382,f7813]) ).
tff(f7813,plain,
( spl59_150
<=> ! [X0: int,X1: int] :
( ( one_one_int = times_times_int(X0,X1) )
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_150])]) ).
tff(f4382,plain,
! [X0: int,X1: int] :
( ( one_one_int = times_times_int(X0,X1) )
| ~ sP3(X1,X0) ),
inference(cnf_transformation,[],[f3181]) ).
tff(f3181,plain,
! [X0: int,X1: int] :
( ( ( one_one_int = times_times_int(X0,X1) )
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| ( one_one_int != times_times_int(X0,X1) ) ) ),
inference(nnf_transformation,[],[f2981]) ).
tff(f2981,plain,
! [X0: int,X1: int] :
( ( one_one_int = times_times_int(X0,X1) )
<=> sP3(X1,X0) ),
inference(definition_folding,[],[f1725,f2980]) ).
tff(f1725,plain,
! [X0: int,X1: int] :
( ( one_one_int = times_times_int(X0,X1) )
<=> ( ( ( number_number_of_int(min) = X1 )
& ( number_number_of_int(min) = X0 ) )
| ( ( one_one_int = X1 )
& ( one_one_int = X0 ) ) ) ),
inference(rectify,[],[f1030]) ).
tff(f1030,axiom,
! [X26: int,X15: int] :
( ( one_one_int = times_times_int(X26,X15) )
<=> ( ( ( number_number_of_int(min) = X15 )
& ( number_number_of_int(min) = X26 ) )
| ( ( one_one_int = X15 )
& ( one_one_int = X26 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_zmult__eq__1__iff) ).
tff(f7811,plain,
spl59_149,
inference(avatar_split_clause,[],[f4381,f7809]) ).
tff(f7809,plain,
( spl59_149
<=> ! [X0: int,X1: int] :
( sP3(X1,X0)
| ( one_one_int != times_times_int(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_149])]) ).
tff(f4381,plain,
! [X0: int,X1: int] :
( sP3(X1,X0)
| ( one_one_int != times_times_int(X0,X1) ) ),
inference(cnf_transformation,[],[f3181]) ).
tff(f7807,plain,
spl59_148,
inference(avatar_split_clause,[],[f4367,f7805]) ).
tff(f7805,plain,
( spl59_148
<=> ! [X0: nat,X1: nat] :
( ( one_one_nat = X1 )
| ( one_one_nat != times_times_nat(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_148])]) ).
tff(f4367,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = X1 )
| ( one_one_nat != times_times_nat(X0,X1) ) ),
inference(cnf_transformation,[],[f3173]) ).
tff(f3173,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_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 != times_times_nat(X0,X1) ) ) ),
inference(flattening,[],[f3172]) ).
tff(f3172,plain,
! [X0: nat,X1: nat] :
( ( ( one_one_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 != times_times_nat(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1722]) ).
tff(f1722,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = times_times_nat(X0,X1) )
<=> ( ( one_one_nat = X1 )
& ( one_one_nat = X0 ) ) ),
inference(rectify,[],[f898]) ).
tff(f898,axiom,
! [X26: nat,X15: nat] :
( ( one_one_nat = times_times_nat(X26,X15) )
<=> ( ( one_one_nat = X15 )
& ( one_one_nat = X26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_nat__1__eq__mult__iff) ).
tff(f7803,plain,
spl59_147,
inference(avatar_split_clause,[],[f4366,f7801]) ).
tff(f7801,plain,
( spl59_147
<=> ! [X0: nat,X1: nat] :
( ( one_one_nat = X0 )
| ( one_one_nat != times_times_nat(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_147])]) ).
tff(f4366,plain,
! [X0: nat,X1: nat] :
( ( one_one_nat = X0 )
| ( one_one_nat != times_times_nat(X0,X1) ) ),
inference(cnf_transformation,[],[f3173]) ).
tff(f7799,plain,
spl59_146,
inference(avatar_split_clause,[],[f4338,f7797]) ).
tff(f7797,plain,
( spl59_146
<=> ! [X0: real,X1: real] :
( ( X0 = X1 )
| ( zero_zero_real != minus_minus_real(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_146])]) ).
tff(f4338,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( zero_zero_real != minus_minus_real(X0,X1) ) ),
inference(cnf_transformation,[],[f3158]) ).
tff(f3158,plain,
! [X0: real,X1: real] :
( ( ( X0 = X1 )
| ( zero_zero_real != minus_minus_real(X0,X1) ) )
& ( ( zero_zero_real = minus_minus_real(X0,X1) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f1715]) ).
tff(f1715,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
<=> ( zero_zero_real = minus_minus_real(X0,X1) ) ),
inference(rectify,[],[f594]) ).
tff(f594,axiom,
! [X2: real,X78: real] :
( ( X2 = X78 )
<=> ( zero_zero_real = minus_minus_real(X2,X78) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_eq__iff__diff__eq__0) ).
tff(f7795,plain,
spl59_145,
inference(avatar_split_clause,[],[f4182,f7793]) ).
tff(f7793,plain,
( spl59_145
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( plus_plus_nat(X0,X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_145])]) ).
tff(f4182,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( plus_plus_nat(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f2335]) ).
tff(f2335,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( plus_plus_nat(X0,X1) != X0 ) ),
inference(ennf_transformation,[],[f1590]) ).
tff(f1590,plain,
! [X0: nat,X1: nat] :
( ( plus_plus_nat(X0,X1) = X0 )
=> ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f212]) ).
tff(f212,axiom,
! [X12: nat,X13: nat] :
( ( plus_plus_nat(X12,X13) = X12 )
=> ( zero_zero_nat = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__eq__self__zero) ).
tff(f7791,plain,
( spl59_144
| ~ spl59_101
| ~ spl59_121 ),
inference(avatar_split_clause,[],[f7614,f7529,f7401,f7788]) ).
tff(f7788,plain,
( spl59_144
<=> ( one_one_real = number267125858f_real(one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_144])]) ).
tff(f7401,plain,
( spl59_101
<=> ( one_one_real = number267125858f_real(minus_minus_int(pls,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_101])]) ).
tff(f7529,plain,
( spl59_121
<=> ( one_one_int = minus_minus_int(pls,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_121])]) ).
tff(f7614,plain,
( ( one_one_real = number267125858f_real(one_one_int) )
| ~ spl59_101
| ~ spl59_121 ),
inference(superposition,[],[f7403,f7531]) ).
tff(f7531,plain,
( ( one_one_int = minus_minus_int(pls,min) )
| ~ spl59_121 ),
inference(avatar_component_clause,[],[f7529]) ).
tff(f7403,plain,
( ( one_one_real = number267125858f_real(minus_minus_int(pls,min)) )
| ~ spl59_101 ),
inference(avatar_component_clause,[],[f7401]) ).
tff(f7786,plain,
spl59_143,
inference(avatar_split_clause,[],[f4084,f7784]) ).
tff(f7784,plain,
( spl59_143
<=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_143])]) ).
tff(f4084,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X0,X1)),X0)),
inference(cnf_transformation,[],[f1503]) ).
tff(f1503,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X0,X1)),X0)),
inference(rectify,[],[f909]) ).
tff(f909,axiom,
! [X12: nat,X13: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X12,X13)),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_Nat_Odiff__le__self) ).
tff(f7782,plain,
spl59_142,
inference(avatar_split_clause,[],[f4083,f7780]) ).
tff(f7780,plain,
( spl59_142
<=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_142])]) ).
tff(f4083,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X0,X1))),
inference(cnf_transformation,[],[f1502]) ).
tff(f1502,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X0,X1))),
inference(rectify,[],[f893]) ).
tff(f893,axiom,
! [X13: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),plus_plus_nat(X13,X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_le__add1) ).
tff(f7778,plain,
spl59_141,
inference(avatar_split_clause,[],[f4082,f7776]) ).
tff(f7776,plain,
( spl59_141
<=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_141])]) ).
tff(f4082,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X1,X0))),
inference(cnf_transformation,[],[f1501]) ).
tff(f1501,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X1,X0))),
inference(rectify,[],[f894]) ).
tff(f894,axiom,
! [X13: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),plus_plus_nat(X12,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_le__add2) ).
tff(f7774,plain,
spl59_140,
inference(avatar_split_clause,[],[f4081,f7772]) ).
tff(f7772,plain,
( spl59_140
<=> ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_140])]) ).
tff(f4081,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X0)),
inference(cnf_transformation,[],[f1500]) ).
tff(f1500,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X0)),
inference(rectify,[],[f176]) ).
tff(f176,axiom,
! [X19: nat,X20: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X19,X20)),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_not__add__less1) ).
tff(f7770,plain,
spl59_139,
inference(avatar_split_clause,[],[f4080,f7768]) ).
tff(f7768,plain,
( spl59_139
<=> ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_139])]) ).
tff(f4080,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X1)),
inference(cnf_transformation,[],[f1499]) ).
tff(f1499,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X1)),
inference(rectify,[],[f177]) ).
tff(f177,axiom,
! [X20: nat,X19: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X20,X19)),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_not__add__less2) ).
tff(f7766,plain,
spl59_138,
inference(avatar_split_clause,[],[f3915,f7764]) ).
tff(f7764,plain,
( spl59_138
<=> ! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != plus_plus_real(X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_138])]) ).
tff(f3915,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != plus_plus_real(X0,X0) ) ),
inference(cnf_transformation,[],[f3048]) ).
tff(f3048,plain,
! [X0: real] :
( ( ( zero_zero_real = plus_plus_real(X0,X0) )
| ( zero_zero_real != X0 ) )
& ( ( zero_zero_real = X0 )
| ( zero_zero_real != plus_plus_real(X0,X0) ) ) ),
inference(nnf_transformation,[],[f1415]) ).
tff(f1415,plain,
! [X0: real] :
( ( zero_zero_real = plus_plus_real(X0,X0) )
<=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f369]) ).
tff(f369,axiom,
! [X2: real] :
( ( zero_zero_real = plus_plus_real(X2,X2) )
<=> ( zero_zero_real = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_double__zero__sym) ).
tff(f7762,plain,
spl59_137,
inference(avatar_split_clause,[],[f3907,f7760]) ).
tff(f3907,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f3046]) ).
tff(f3046,plain,
! [X0: int] :
( ( sP0(X0)
| ( ( sK30(X0) != X0 )
& ( one_one_int != sK30(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(X0)),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK30(X0))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
& ( ( ! [X2: int] :
( ( X0 = X2 )
| ( one_one_int = X2 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f3044,f3045]) ).
tff(f3045,plain,
! [X0: int] :
( ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> ( ( sK30(X0) != X0 )
& ( one_one_int != sK30(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK30(X0)),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK30(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f3044,plain,
! [X0: int] :
( ( sP0(X0)
| ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
& ( ( ! [X2: int] :
( ( X0 = X2 )
| ( one_one_int = X2 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f3043]) ).
tff(f3043,plain,
! [X0: int] :
( ( sP0(X0)
| ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
& ( ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
| ~ sP0(X0) ) ),
inference(flattening,[],[f3042]) ).
tff(f3042,plain,
! [X0: int] :
( ( sP0(X0)
| ? [X1: int] :
( ( X0 != X1 )
& ( one_one_int != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
& ( ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f2974]) ).
tff(f2974,plain,
! [X0: int] :
( sP0(X0)
<=> ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f7758,plain,
spl59_136,
inference(avatar_split_clause,[],[f3808,f7756]) ).
tff(f7756,plain,
( spl59_136
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_136])]) ).
tff(f3808,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,X0))),
inference(cnf_transformation,[],[f1348]) ).
tff(f1348,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,X0))),
inference(rectify,[],[f845]) ).
tff(f845,axiom,
! [X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),times_times_nat(X12,X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_le__square) ).
tff(f7754,plain,
spl59_135,
inference(avatar_split_clause,[],[f3805,f7752]) ).
tff(f7752,plain,
( spl59_135
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),plus_plus_nat(X0,one_one_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_135])]) ).
tff(f3805,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),plus_plus_nat(X0,one_one_nat))),
inference(cnf_transformation,[],[f1345]) ).
tff(f1345,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),plus_plus_nat(X0,one_one_nat))),
inference(rectify,[],[f271]) ).
tff(f271,axiom,
! [X77: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X77),plus_plus_nat(X77,one_one_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__add__one) ).
tff(f7750,plain,
spl59_134,
inference(avatar_split_clause,[],[f3804,f7748]) ).
tff(f7748,plain,
( spl59_134
<=> ! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),plus_plus_real(X0,one_one_real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_134])]) ).
tff(f3804,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),plus_plus_real(X0,one_one_real))),
inference(cnf_transformation,[],[f1344]) ).
tff(f1344,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),plus_plus_real(X0,one_one_real))),
inference(rectify,[],[f272]) ).
tff(f272,axiom,
! [X77: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X77),plus_plus_real(X77,one_one_real))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_less__add__one) ).
tff(f7746,plain,
spl59_133,
inference(avatar_split_clause,[],[f3803,f7744]) ).
tff(f7744,plain,
( spl59_133
<=> ! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_133])]) ).
tff(f3803,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0))),
inference(cnf_transformation,[],[f1343]) ).
tff(f1343,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0))),
inference(rectify,[],[f534]) ).
tff(f534,axiom,
! [X246: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X246,X246))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_zero__le__square) ).
tff(f7742,plain,
spl59_132,
inference(avatar_split_clause,[],[f3799,f7740]) ).
tff(f7740,plain,
( spl59_132
<=> ! [X0: nat] : ( hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_132])]) ).
tff(f3799,plain,
! [X0: nat] : ( hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(cnf_transformation,[],[f1339]) ).
tff(f1339,plain,
! [X0: nat] : ( hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X38: nat] : ( number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X38)) = hAPP_nat_real(semiri132038758t_real,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_number__of__int) ).
tff(f7738,plain,
spl59_131,
inference(avatar_split_clause,[],[f3797,f7736]) ).
tff(f3797,plain,
! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(cnf_transformation,[],[f1337]) ).
tff(f1337,plain,
! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(rectify,[],[f1160]) ).
tff(f1160,axiom,
! [X12: nat] : ( hAPP_nat_int(semiri1621563631at_int,X12) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_abs__int__eq) ).
tff(f7734,plain,
spl59_130,
inference(avatar_split_clause,[],[f3794,f7732]) ).
tff(f7732,plain,
( spl59_130
<=> ! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X0,X0)),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_130])]) ).
tff(f3794,plain,
! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X0,X0)),zero_zero_real)),
inference(cnf_transformation,[],[f1334]) ).
tff(f1334,plain,
! [X0: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X0,X0)),zero_zero_real)),
inference(rectify,[],[f763]) ).
tff(f763,axiom,
! [X374: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X374,X374)),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_not__square__less__zero) ).
tff(f7730,plain,
spl59_129,
inference(avatar_split_clause,[],[f3790,f7728]) ).
tff(f7728,plain,
( spl59_129
<=> ! [X0: nat] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_129])]) ).
tff(f3790,plain,
! [X0: nat] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)),
inference(cnf_transformation,[],[f1330]) ).
tff(f1330,plain,
! [X0: nat] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)),
inference(rectify,[],[f290]) ).
tff(f290,axiom,
! [X85: nat] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X85)),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_of__nat__less__0__iff) ).
tff(f7726,plain,
spl59_128,
inference(avatar_split_clause,[],[f3623,f7723]) ).
tff(f7723,plain,
( spl59_128
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_128])]) ).
tff(f3623,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat))),
inference(cnf_transformation,[],[f168]) ).
tff(f168,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_zero__less__two) ).
tff(f7721,plain,
spl59_127,
inference(avatar_split_clause,[],[f3622,f7718]) ).
tff(f7718,plain,
( spl59_127
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,one_one_real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_127])]) ).
tff(f3622,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,one_one_real))),
inference(cnf_transformation,[],[f169]) ).
tff(f169,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,one_one_real))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_zero__less__two) ).
tff(f7690,plain,
( spl59_126
| ~ spl59_53
| ~ spl59_121 ),
inference(avatar_split_clause,[],[f7615,f7529,f7190,f7687]) ).
tff(f7615,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(one_one_int,min))) )
| ~ spl59_53
| ~ spl59_121 ),
inference(superposition,[],[f7192,f7531]) ).
tff(f7550,plain,
spl59_125,
inference(avatar_split_clause,[],[f6170,f7547]) ).
tff(f7547,plain,
( spl59_125
<=> ( one_one_nat = nat_1(number_number_of_int(minus_minus_int(pls,min))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_125])]) ).
tff(f6170,plain,
one_one_nat = nat_1(number_number_of_int(minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5339,f5331]) ).
tff(f5339,plain,
one_one_nat = nat_1(number_number_of_int(minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f3573,f3766,f5319]) ).
tff(f3573,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(cnf_transformation,[],[f56]) ).
tff(f56,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Numeral1__eq1__nat) ).
tff(f7545,plain,
spl59_124,
inference(avatar_split_clause,[],[f5970,f7542]) ).
tff(f7542,plain,
( spl59_124
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_124])]) ).
tff(f5970,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)),
inference(equality_resolution,[],[f5559]) ).
tff(f5559,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| ( pls != X0 ) ),
inference(definition_unfolding,[],[f3978,f3551]) ).
tff(f3978,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f3079]) ).
tff(f3079,plain,
! [X0: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| ( zero_zero_int != X0 ) )
& ( ( zero_zero_int = X0 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ) ),
inference(nnf_transformation,[],[f1441]) ).
tff(f1441,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
<=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f1163]) ).
tff(f1163,axiom,
! [X27: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X27)),one_one_int))
<=> ( zero_zero_int = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_zabs__less__one__iff) ).
tff(f7540,plain,
spl59_123,
inference(avatar_split_clause,[],[f5433,f7538]) ).
tff(f5433,plain,
! [X0: int] : ( pls != plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(definition_unfolding,[],[f3788,f3551]) ).
tff(f3788,plain,
! [X0: int] : ( zero_zero_int != plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(cnf_transformation,[],[f1328]) ).
tff(f1328,plain,
! [X0: int] : ( zero_zero_int != plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X14: int] : ( zero_zero_int != plus_plus_int(plus_plus_int(one_one_int,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_odd__nonzero) ).
tff(f7536,plain,
spl59_122,
inference(avatar_split_clause,[],[f5430,f7534]) ).
tff(f7532,plain,
( spl59_121
| ~ spl59_11
| ~ spl59_102 ),
inference(avatar_split_clause,[],[f7460,f7406,f6995,f7529]) ).
tff(f6995,plain,
( spl59_11
<=> ! [X0: int] : ( number_number_of_int(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_11])]) ).
tff(f7406,plain,
( spl59_102
<=> ( one_one_int = number_number_of_int(minus_minus_int(pls,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_102])]) ).
tff(f7460,plain,
( ( one_one_int = minus_minus_int(pls,min) )
| ~ spl59_11
| ~ spl59_102 ),
inference(superposition,[],[f7408,f6996]) ).
tff(f6996,plain,
( ! [X0: int] : ( number_number_of_int(X0) = X0 )
| ~ spl59_11 ),
inference(avatar_component_clause,[],[f6995]) ).
tff(f7408,plain,
( ( one_one_int = number_number_of_int(minus_minus_int(pls,min)) )
| ~ spl59_102 ),
inference(avatar_component_clause,[],[f7406]) ).
tff(f7527,plain,
spl59_120,
inference(avatar_split_clause,[],[f5412,f7525]) ).
tff(f7525,plain,
( spl59_120
<=> ! [X0: int] : ( pls != minus_minus_int(plus_plus_int(X0,X0),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_120])]) ).
tff(f5412,plain,
! [X0: int] : ( pls != minus_minus_int(plus_plus_int(X0,X0),min) ),
inference(definition_unfolding,[],[f3675,f5319]) ).
tff(f3675,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f1215]) ).
tff(f1215,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X28: int] : ( pls != bit1(X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rel__simps_I39_J) ).
tff(f7523,plain,
spl59_119,
inference(avatar_split_clause,[],[f4361,f7521]) ).
tff(f7521,plain,
( spl59_119
<=> ! [X0: int,X1: nat] :
( ( nat_1(X0) = X1 )
| ~ sP2(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_119])]) ).
tff(f4361,plain,
! [X0: int,X1: nat] :
( ( nat_1(X0) = X1 )
| ~ sP2(X1,X0) ),
inference(cnf_transformation,[],[f3169]) ).
tff(f3169,plain,
! [X0: int,X1: nat] :
( ( ( nat_1(X0) = X1 )
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ( nat_1(X0) != X1 ) ) ),
inference(nnf_transformation,[],[f2979]) ).
tff(f2979,plain,
! [X0: int,X1: nat] :
( ( nat_1(X0) = X1 )
<=> sP2(X1,X0) ),
inference(definition_folding,[],[f2537,f2978]) ).
tff(f2537,plain,
! [X0: int,X1: nat] :
( ( nat_1(X0) = X1 )
<=> ( ( ( zero_zero_nat = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
inference(ennf_transformation,[],[f1719]) ).
tff(f1719,plain,
! [X0: int,X1: nat] :
( ( nat_1(X0) = X1 )
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( zero_zero_nat = X1 ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 ) ) ) ),
inference(rectify,[],[f743]) ).
tff(f743,axiom,
! [X22: int,X26: nat] :
( ( nat_1(X22) = X26 )
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X22))
=> ( zero_zero_nat = X26 ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X22))
=> ( hAPP_nat_int(semiri1621563631at_int,X26) = X22 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_nat__eq__iff) ).
tff(f7519,plain,
spl59_118,
inference(avatar_split_clause,[],[f4353,f7517]) ).
tff(f7517,plain,
( spl59_118
<=> ! [X0: nat,X1: int] :
( ( nat_1(X1) = X0 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_118])]) ).
tff(f4353,plain,
! [X0: nat,X1: int] :
( ( nat_1(X1) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3165]) ).
tff(f3165,plain,
! [X0: nat,X1: int] :
( ( ( nat_1(X1) = X0 )
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ( nat_1(X1) != X0 ) ) ),
inference(nnf_transformation,[],[f2977]) ).
tff(f2977,plain,
! [X0: nat,X1: int] :
( ( nat_1(X1) = X0 )
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f2536,f2976]) ).
tff(f2536,plain,
! [X0: nat,X1: int] :
( ( nat_1(X1) = X0 )
<=> ( ( ( zero_zero_nat = X0 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( ( hAPP_nat_int(semiri1621563631at_int,X0) = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
inference(ennf_transformation,[],[f1718]) ).
tff(f1718,plain,
! [X0: nat,X1: int] :
( ( nat_1(X1) = X0 )
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> ( zero_zero_nat = X0 ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> ( hAPP_nat_int(semiri1621563631at_int,X0) = X1 ) ) ) ),
inference(rectify,[],[f742]) ).
tff(f742,axiom,
! [X26: nat,X22: int] :
( ( nat_1(X22) = X26 )
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X22))
=> ( zero_zero_nat = X26 ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X22))
=> ( hAPP_nat_int(semiri1621563631at_int,X26) = X22 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_nat__eq__iff2) ).
tff(f7515,plain,
spl59_117,
inference(avatar_split_clause,[],[f4079,f7513]) ).
tff(f7513,plain,
( spl59_117
<=> ! [X0: int,X1: int] : ( plus_plus_int(minus_minus_int(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_117])]) ).
tff(f4079,plain,
! [X0: int,X1: int] : ( plus_plus_int(minus_minus_int(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f1498]) ).
tff(f1498,plain,
! [X0: int,X1: int] : ( plus_plus_int(minus_minus_int(X0,X1),X1) = X0 ),
inference(rectify,[],[f607]) ).
tff(f607,axiom,
! [X299: int,X300: int] : ( plus_plus_int(minus_minus_int(X299,X300),X300) = X299 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_diff__add__cancel) ).
tff(f7511,plain,
spl59_116,
inference(avatar_split_clause,[],[f4078,f7509]) ).
tff(f7509,plain,
( spl59_116
<=> ! [X0: real,X1: real] : ( plus_plus_real(minus_minus_real(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_116])]) ).
tff(f4078,plain,
! [X0: real,X1: real] : ( plus_plus_real(minus_minus_real(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f1497]) ).
tff(f1497,plain,
! [X0: real,X1: real] : ( plus_plus_real(minus_minus_real(X0,X1),X1) = X0 ),
inference(rectify,[],[f606]) ).
tff(f606,axiom,
! [X299: real,X300: real] : ( plus_plus_real(minus_minus_real(X299,X300),X300) = X299 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_diff__add__cancel) ).
tff(f7507,plain,
spl59_115,
inference(avatar_split_clause,[],[f4077,f7505]) ).
tff(f7505,plain,
( spl59_115
<=> ! [X0: nat,X1: nat] : ( minus_minus_nat(plus_plus_nat(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_115])]) ).
tff(f4077,plain,
! [X0: nat,X1: nat] : ( minus_minus_nat(plus_plus_nat(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f1496]) ).
tff(f1496,plain,
! [X0: nat,X1: nat] : ( minus_minus_nat(plus_plus_nat(X0,X1),X1) = X0 ),
inference(rectify,[],[f704]) ).
tff(f704,axiom,
! [X12: nat,X13: nat] : ( minus_minus_nat(plus_plus_nat(X12,X13),X13) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_diff__add__inverse2) ).
tff(f7503,plain,
spl59_114,
inference(avatar_split_clause,[],[f4076,f7501]) ).
tff(f7501,plain,
( spl59_114
<=> ! [X0: nat,X1: nat] : ( minus_minus_nat(plus_plus_nat(X0,X1),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_114])]) ).
tff(f4076,plain,
! [X0: nat,X1: nat] : ( minus_minus_nat(plus_plus_nat(X0,X1),X0) = X1 ),
inference(cnf_transformation,[],[f1495]) ).
tff(f1495,plain,
! [X0: nat,X1: nat] : ( minus_minus_nat(plus_plus_nat(X0,X1),X0) = X1 ),
inference(rectify,[],[f705]) ).
tff(f705,axiom,
! [X13: nat,X12: nat] : ( minus_minus_nat(plus_plus_nat(X13,X12),X13) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_diff__add__inverse) ).
tff(f7499,plain,
spl59_113,
inference(avatar_split_clause,[],[f4075,f7497]) ).
tff(f4075,plain,
! [X0: int,X1: int] : ( minus_minus_int(plus_plus_int(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f1494]) ).
tff(f1494,plain,
! [X0: int,X1: int] : ( minus_minus_int(plus_plus_int(X0,X1),X1) = X0 ),
inference(rectify,[],[f605]) ).
tff(f605,axiom,
! [X297: int,X298: int] : ( minus_minus_int(plus_plus_int(X297,X298),X298) = X297 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_add__diff__cancel) ).
tff(f7495,plain,
spl59_112,
inference(avatar_split_clause,[],[f4074,f7493]) ).
tff(f7493,plain,
( spl59_112
<=> ! [X0: real,X1: real] : ( minus_minus_real(plus_plus_real(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_112])]) ).
tff(f4074,plain,
! [X0: real,X1: real] : ( minus_minus_real(plus_plus_real(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f1493]) ).
tff(f1493,plain,
! [X0: real,X1: real] : ( minus_minus_real(plus_plus_real(X0,X1),X1) = X0 ),
inference(rectify,[],[f604]) ).
tff(f604,axiom,
! [X297: real,X298: real] : ( minus_minus_real(plus_plus_real(X297,X298),X298) = X297 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_add__diff__cancel) ).
tff(f7491,plain,
spl59_111,
inference(avatar_split_clause,[],[f4072,f7489]) ).
tff(f7489,plain,
( spl59_111
<=> ! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_111])]) ).
tff(f4072,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(cnf_transformation,[],[f1491]) ).
tff(f1491,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(rectify,[],[f450]) ).
tff(f450,axiom,
! [X14: int,X11: int] : ( times_times_int(X14,X11) = times_times_int(X11,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_zmult__commute) ).
tff(f7485,plain,
spl59_110,
inference(avatar_split_clause,[],[f4070,f7483]) ).
tff(f4070,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f1489]) ).
tff(f1489,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X14: int,X11: int] : ( plus_plus_int(X14,X11) = plus_plus_int(X11,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
tff(f7481,plain,
spl59_109,
inference(avatar_split_clause,[],[f4068,f7479]) ).
tff(f7479,plain,
( spl59_109
<=> ! [X0: nat,X1: nat] : ( times_times_nat(X0,X1) = times_times_nat(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_109])]) ).
tff(f4068,plain,
! [X0: nat,X1: nat] : ( times_times_nat(X0,X1) = times_times_nat(X1,X0) ),
inference(cnf_transformation,[],[f1487]) ).
tff(f1487,plain,
! [X0: nat,X1: nat] : ( times_times_nat(X0,X1) = times_times_nat(X1,X0) ),
inference(rectify,[],[f416]) ).
tff(f416,axiom,
! [X153: nat,X154: nat] : ( times_times_nat(X153,X154) = times_times_nat(X154,X153) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f7477,plain,
spl59_108,
inference(avatar_split_clause,[],[f4066,f7475]) ).
tff(f7475,plain,
( spl59_108
<=> ! [X0: nat,X1: nat] : ( plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_108])]) ).
tff(f4066,plain,
! [X0: nat,X1: nat] : ( plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0) ),
inference(cnf_transformation,[],[f1485]) ).
tff(f1485,plain,
! [X0: nat,X1: nat] : ( plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0) ),
inference(rectify,[],[f351]) ).
tff(f351,axiom,
! [X123: nat,X124: nat] : ( plus_plus_nat(X123,X124) = plus_plus_nat(X124,X123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f7473,plain,
spl59_107,
inference(avatar_split_clause,[],[f4064,f7471]) ).
tff(f7471,plain,
( spl59_107
<=> ! [X0: real,X1: real] : ( times_times_real(X0,X1) = times_times_real(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_107])]) ).
tff(f4064,plain,
! [X0: real,X1: real] : ( times_times_real(X0,X1) = times_times_real(X1,X0) ),
inference(cnf_transformation,[],[f1483]) ).
tff(f1483,plain,
! [X0: real,X1: real] : ( times_times_real(X0,X1) = times_times_real(X1,X0) ),
inference(rectify,[],[f979]) ).
tff(f979,axiom,
! [X14: real,X11: real] : ( times_times_real(X14,X11) = times_times_real(X11,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_real__mult__commute) ).
tff(f7469,plain,
spl59_106,
inference(avatar_split_clause,[],[f4063,f7467]) ).
tff(f4063,plain,
! [X0: real,X1: real] : ( plus_plus_real(X0,X1) = plus_plus_real(X1,X0) ),
inference(cnf_transformation,[],[f1482]) ).
tff(f1482,plain,
! [X0: real,X1: real] : ( plus_plus_real(X0,X1) = plus_plus_real(X1,X0) ),
inference(rectify,[],[f352]) ).
tff(f352,axiom,
! [X123: real,X124: real] : ( plus_plus_real(X123,X124) = plus_plus_real(X124,X123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f7465,plain,
spl59_105,
inference(avatar_split_clause,[],[f4062,f7463]) ).
tff(f7463,plain,
( spl59_105
<=> ! [X0: nat,X1: nat] : ( zero_zero_nat = minus_minus_nat(X0,plus_plus_nat(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_105])]) ).
tff(f4062,plain,
! [X0: nat,X1: nat] : ( zero_zero_nat = minus_minus_nat(X0,plus_plus_nat(X0,X1)) ),
inference(cnf_transformation,[],[f1481]) ).
tff(f1481,plain,
! [X0: nat,X1: nat] : ( zero_zero_nat = minus_minus_nat(X0,plus_plus_nat(X0,X1)) ),
inference(rectify,[],[f772]) ).
tff(f772,axiom,
! [X13: nat,X12: nat] : ( zero_zero_nat = minus_minus_nat(X13,plus_plus_nat(X13,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_diff__add__0) ).
tff(f7446,plain,
( spl59_104
| ~ spl59_14
| ~ spl59_74 ),
inference(avatar_split_clause,[],[f7413,f7287,f7009,f7444]) ).
tff(f7444,plain,
( spl59_104
<=> ! [X0: nat] : sP1(X0,hAPP_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_104])]) ).
tff(f7009,plain,
( spl59_14
<=> ! [X1: int] : sP1(nat_1(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_14])]) ).
tff(f7287,plain,
( spl59_74
<=> ! [X0: nat] : ( nat_1(hAPP_nat_int(semiri1621563631at_int,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_74])]) ).
tff(f7413,plain,
( ! [X0: nat] : sP1(X0,hAPP_nat_int(semiri1621563631at_int,X0))
| ~ spl59_14
| ~ spl59_74 ),
inference(superposition,[],[f7010,f7288]) ).
tff(f7288,plain,
( ! [X0: nat] : ( nat_1(hAPP_nat_int(semiri1621563631at_int,X0)) = X0 )
| ~ spl59_74 ),
inference(avatar_component_clause,[],[f7287]) ).
tff(f7010,plain,
( ! [X1: int] : sP1(nat_1(X1),X1)
| ~ spl59_14 ),
inference(avatar_component_clause,[],[f7009]) ).
tff(f7417,plain,
( spl59_103
| ~ spl59_15
| ~ spl59_74 ),
inference(avatar_split_clause,[],[f7412,f7287,f7013,f7415]) ).
tff(f7415,plain,
( spl59_103
<=> ! [X0: nat] : sP2(X0,hAPP_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_103])]) ).
tff(f7013,plain,
( spl59_15
<=> ! [X0: int] : sP2(nat_1(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_15])]) ).
tff(f7412,plain,
( ! [X0: nat] : sP2(X0,hAPP_nat_int(semiri1621563631at_int,X0))
| ~ spl59_15
| ~ spl59_74 ),
inference(superposition,[],[f7014,f7288]) ).
tff(f7014,plain,
( ! [X0: int] : sP2(nat_1(X0),X0)
| ~ spl59_15 ),
inference(avatar_component_clause,[],[f7013]) ).
tff(f7409,plain,
spl59_102,
inference(avatar_split_clause,[],[f6173,f7406]) ).
tff(f6173,plain,
one_one_int = number_number_of_int(minus_minus_int(pls,min)),
inference(forward_demodulation,[],[f5342,f5331]) ).
tff(f5342,plain,
one_one_int = number_number_of_int(minus_minus_int(plus_plus_int(pls,pls),min)),
inference(definition_unfolding,[],[f3577,f5319]) ).
tff(f3577,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_numeral__1__eq__1) ).
tff(f7404,plain,
spl59_101,
inference(avatar_split_clause,[],[f6167,f7401]) ).
tff(f6167,plain,
one_one_real = number267125858f_real(minus_minus_int(pls,min)),
inference(forward_demodulation,[],[f5336,f5331]) ).
tff(f5336,plain,
one_one_real = number267125858f_real(minus_minus_int(plus_plus_int(pls,pls),min)),
inference(definition_unfolding,[],[f3569,f5319]) ).
tff(f3569,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(cnf_transformation,[],[f29]) ).
tff(f29,axiom,
one_one_real = number267125858f_real(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_numeral__1__eq__1) ).
tff(f7399,plain,
spl59_100,
inference(avatar_split_clause,[],[f6066,f7397]) ).
tff(f6066,plain,
! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(equality_resolution,[],[f4481]) ).
tff(f4481,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f3247]) ).
tff(f3247,plain,
! [X0: int,X1: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( ( X0 != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(flattening,[],[f3246]) ).
tff(f3246,plain,
! [X0: int,X1: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( ( X0 != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f1756]) ).
tff(f1756,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( ( X0 != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(rectify,[],[f719]) ).
tff(f719,axiom,
! [X27: int,X22: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),X22))
<=> ( ( X22 != X27 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X27),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_zless__le) ).
tff(f7395,plain,
spl59_99,
inference(avatar_split_clause,[],[f6060,f7393]) ).
tff(f7393,plain,
( spl59_99
<=> ! [X1: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_99])]) ).
tff(f6060,plain,
! [X1: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)),
inference(equality_resolution,[],[f4449]) ).
tff(f4449,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
inference(cnf_transformation,[],[f3226]) ).
tff(f3226,plain,
! [X0: real,X1: real] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
& ( ( ( X0 != X1 )
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
inference(flattening,[],[f3225]) ).
tff(f3225,plain,
! [X0: real,X1: real] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
& ( ( ( X0 != X1 )
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
inference(nnf_transformation,[],[f880]) ).
tff(f880,axiom,
! [X0: real,X1: real] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
<=> ( ( X0 != X1 )
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_real__less__def) ).
tff(f7391,plain,
spl59_98,
inference(avatar_split_clause,[],[f5940,f7388]) ).
tff(f7388,plain,
( spl59_98
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK58)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_98])]) ).
tff(f5940,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK58)),
inference(definition_unfolding,[],[f5315,f3551]) ).
tff(f5315,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK58)),
inference(cnf_transformation,[],[f3539]) ).
tff(f3539,plain,
( ! [X1: int] :
( ( sK58 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(zcong(s1,sK58),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK58),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK58)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f2973,f3538]) ).
tff(f3538,plain,
( ? [X0: int] :
( ! [X1: int] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
=> ( ! [X1: int] :
( ( sK58 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(zcong(s1,sK58),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK58),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK58)) ) ),
introduced(choice_axiom,[]) ).
tff(f2973,plain,
? [X0: int] :
( ! [X1: int] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(flattening,[],[f2972]) ).
tff(f2972,plain,
? [X0: int] :
( ! [X1: int] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f2249]) ).
tff(f2249,plain,
? [X0: int] :
( ! [X1: int] :
( ( hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> ( X0 = X1 ) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(rectify,[],[f1084]) ).
tff(f1084,axiom,
? [X149: int] :
( ! [X150: int] :
( ( hBOOL(hAPP_int_bool(zcong(s1,X150),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X150),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X150)) )
=> ( X149 = X150 ) )
& hBOOL(hAPP_int_bool(zcong(s1,X149),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X149),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X149)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s) ).
tff(f7386,plain,
spl59_97,
inference(avatar_split_clause,[],[f5432,f7384]) ).
tff(f7384,plain,
( spl59_97
<=> ! [X0: int] : hBOOL(hAPP_int_bool(zcong(X0,pls),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_97])]) ).
tff(f5432,plain,
! [X0: int] : hBOOL(hAPP_int_bool(zcong(X0,pls),X0)),
inference(definition_unfolding,[],[f3786,f3551]) ).
tff(f3786,plain,
! [X0: int] : hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X0)),
inference(cnf_transformation,[],[f1326]) ).
tff(f1326,plain,
! [X0: int] : hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X0)),
inference(rectify,[],[f1059]) ).
tff(f1059,axiom,
! [X12: int] : hBOOL(hAPP_int_bool(zcong(X12,zero_zero_int),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_zcong__id) ).
tff(f7382,plain,
spl59_96,
inference(avatar_split_clause,[],[f5408,f7379]) ).
tff(f7379,plain,
( spl59_96
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_96])]) ).
tff(f5408,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK22)),
inference(definition_unfolding,[],[f3667,f3551]) ).
tff(f3667,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK22)),
inference(cnf_transformation,[],[f3017]) ).
tff(f3017,plain,
( hBOOL(hAPP_int_bool(zcong(s1,sK22),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK22),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK22)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f2255,f3016]) ).
tff(f3016,plain,
( ? [X0: int] :
( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
=> ( hBOOL(hAPP_int_bool(zcong(s1,sK22),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK22),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK22)) ) ),
introduced(choice_axiom,[]) ).
tff(f2255,plain,
? [X0: int] :
( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f1211]) ).
tff(f1211,plain,
~ ! [X0: int] :
~ ( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(rectify,[],[f1086]) ).
tff(f1086,axiom,
~ ! [X390: int] :
~ ( hBOOL(hAPP_int_bool(zcong(s1,X390),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X390),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X390)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085__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) ).
tff(f7377,plain,
spl59_95,
inference(avatar_split_clause,[],[f5397,f7374]) ).
tff(f7374,plain,
( spl59_95
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),s)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_95])]) ).
tff(f5397,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),s)),
inference(definition_unfolding,[],[f3656,f3551]) ).
tff(f3656,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)),
inference(cnf_transformation,[],[f1039]) ).
tff(f1039,axiom,
( hBOOL(hAPP_int_bool(zcong(s1,s),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_s0p) ).
tff(f7372,plain,
spl59_94,
inference(avatar_split_clause,[],[f5355,f7369]) ).
tff(f7369,plain,
( spl59_94
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_94])]) ).
tff(f5355,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
inference(definition_unfolding,[],[f3612,f3551]) ).
tff(f3612,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f782]) ).
tff(f782,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
tff(f7367,plain,
spl59_93,
inference(avatar_split_clause,[],[f5353,f7364]) ).
tff(f7364,plain,
( spl59_93
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_93])]) ).
tff(f5353,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
inference(definition_unfolding,[],[f3606,f3551]) ).
tff(f3606,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f264]) ).
tff(f264,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_zero__less__one) ).
tff(f7362,plain,
~ spl59_92,
inference(avatar_split_clause,[],[f5350,f7359]) ).
tff(f5350,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)),
inference(definition_unfolding,[],[f3593,f3551]) ).
tff(f3593,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f261]) ).
tff(f261,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_not__one__less__zero) ).
tff(f7357,plain,
spl59_91,
inference(avatar_split_clause,[],[f4061,f7355]) ).
tff(f7355,plain,
( spl59_91
<=> ! [X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_91])]) ).
tff(f4061,plain,
! [X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
inference(cnf_transformation,[],[f1480]) ).
tff(f1480,plain,
! [X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
inference(rectify,[],[f1125]) ).
tff(f1125,axiom,
! [X18: int,X12: int] : hBOOL(hAPP_int_bool(zcong(X18,X18),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_zcong__refl) ).
tff(f7353,plain,
spl59_90,
inference(avatar_split_clause,[],[f4060,f7351]) ).
tff(f7351,plain,
( spl59_90
<=> ! [X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_90])]) ).
tff(f4060,plain,
! [X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
inference(cnf_transformation,[],[f1479]) ).
tff(f1479,plain,
! [X0: int,X1: int] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
inference(rectify,[],[f1128]) ).
tff(f1128,axiom,
! [X148: int,X152: int] : hBOOL(hAPP_int_bool(zcong(X148,X152),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_zcong__1) ).
tff(f7349,plain,
spl59_89,
inference(avatar_split_clause,[],[f4059,f7347]) ).
tff(f7347,plain,
( spl59_89
<=> ! [X0: nat,X1: nat] : ( if_nat(fFalse,X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_89])]) ).
tff(f4059,plain,
! [X0: nat,X1: nat] : ( if_nat(fFalse,X0,X1) = X1 ),
inference(cnf_transformation,[],[f1478]) ).
tff(f1478,plain,
! [X0: nat,X1: nat] : ( if_nat(fFalse,X0,X1) = X1 ),
inference(rectify,[],[f1203]) ).
tff(f1203,axiom,
! [X5: nat,X7: nat] : ( if_nat(fFalse,X5,X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
tff(f7345,plain,
spl59_88,
inference(avatar_split_clause,[],[f4058,f7343]) ).
tff(f7343,plain,
( spl59_88
<=> ! [X0: int,X1: int] : ( if_int(fFalse,X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_88])]) ).
tff(f4058,plain,
! [X0: int,X1: int] : ( if_int(fFalse,X0,X1) = X1 ),
inference(cnf_transformation,[],[f1477]) ).
tff(f1477,plain,
! [X0: int,X1: int] : ( if_int(fFalse,X0,X1) = X1 ),
inference(rectify,[],[f1200]) ).
tff(f1200,axiom,
! [X5: int,X7: int] : ( if_int(fFalse,X5,X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Int__Oint_T) ).
tff(f7341,plain,
spl59_87,
inference(avatar_split_clause,[],[f4057,f7339]) ).
tff(f7339,plain,
( spl59_87
<=> ! [X0: int,X1: int] : ( if_int(fTrue,X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_87])]) ).
tff(f4057,plain,
! [X0: int,X1: int] : ( if_int(fTrue,X0,X1) = X0 ),
inference(cnf_transformation,[],[f1476]) ).
tff(f1476,plain,
! [X0: int,X1: int] : ( if_int(fTrue,X0,X1) = X0 ),
inference(rectify,[],[f1199]) ).
tff(f1199,axiom,
! [X5: int,X7: int] : ( if_int(fTrue,X5,X7) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Int__Oint_T) ).
tff(f7337,plain,
spl59_86,
inference(avatar_split_clause,[],[f4056,f7335]) ).
tff(f7335,plain,
( spl59_86
<=> ! [X0: nat,X1: nat] : ( if_nat(fTrue,X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_86])]) ).
tff(f4056,plain,
! [X0: nat,X1: nat] : ( if_nat(fTrue,X0,X1) = X0 ),
inference(cnf_transformation,[],[f1475]) ).
tff(f1475,plain,
! [X0: nat,X1: nat] : ( if_nat(fTrue,X0,X1) = X0 ),
inference(rectify,[],[f1202]) ).
tff(f1202,axiom,
! [X5: nat,X7: nat] : ( if_nat(fTrue,X5,X7) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).
tff(f7333,plain,
spl59_85,
inference(avatar_split_clause,[],[f3914,f7331]) ).
tff(f7331,plain,
( spl59_85
<=> ! [X0: int] :
( hBOOL(hAPP_int_bool(zprime,X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_85])]) ).
tff(f3914,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(zprime,X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f3047]) ).
tff(f3047,plain,
! [X0: int] :
( ( hBOOL(hAPP_int_bool(zprime,X0))
| ~ sP0(X0) )
& ( sP0(X0)
| ~ hBOOL(hAPP_int_bool(zprime,X0)) ) ),
inference(nnf_transformation,[],[f2975]) ).
tff(f2975,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(zprime,X0))
<=> sP0(X0) ),
inference(definition_folding,[],[f2285,f2974]) ).
tff(f2285,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ),
inference(flattening,[],[f2284]) ).
tff(f2284,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( ! [X1: int] :
( ( X0 = X1 )
| ( one_one_int = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ),
inference(ennf_transformation,[],[f1414]) ).
tff(f1414,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( ! [X1: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> ( ( X0 = X1 )
| ( one_one_int = X1 ) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ),
inference(rectify,[],[f1143]) ).
tff(f1143,axiom,
! [X388: int] :
( hBOOL(hAPP_int_bool(zprime,X388))
<=> ( ! [X391: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X391),X388))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X391)) )
=> ( ( X388 = X391 )
| ( one_one_int = X391 ) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X388)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_zprime__def) ).
tff(f7329,plain,
spl59_84,
inference(avatar_split_clause,[],[f3913,f7327]) ).
tff(f7327,plain,
( spl59_84
<=> ! [X0: int] :
( sP0(X0)
| ~ hBOOL(hAPP_int_bool(zprime,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_84])]) ).
tff(f3913,plain,
! [X0: int] :
( sP0(X0)
| ~ hBOOL(hAPP_int_bool(zprime,X0)) ),
inference(cnf_transformation,[],[f3047]) ).
tff(f7325,plain,
spl59_83,
inference(avatar_split_clause,[],[f3857,f7323]) ).
tff(f7323,plain,
( spl59_83
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_83])]) ).
tff(f3857,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f1388]) ).
tff(f1388,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f1201]) ).
tff(f1201,axiom,
! [X398: bool] :
( ( fFalse = X398 )
| ( fTrue = X398 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Int__Oint_T) ).
tff(f7321,plain,
spl59_82,
inference(avatar_split_clause,[],[f3787,f7319]) ).
tff(f7319,plain,
( spl59_82
<=> ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_82])]) ).
tff(f3787,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(cnf_transformation,[],[f1327]) ).
tff(f1327,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(rectify,[],[f449]) ).
tff(f449,axiom,
! [X11: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_zle__refl) ).
tff(f7317,plain,
spl59_81,
inference(avatar_split_clause,[],[f3785,f7315]) ).
tff(f7315,plain,
( spl59_81
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_81])]) ).
tff(f3785,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(cnf_transformation,[],[f1325]) ).
tff(f1325,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(rectify,[],[f844]) ).
tff(f844,axiom,
! [X13: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_le__refl) ).
tff(f7313,plain,
spl59_80,
inference(avatar_split_clause,[],[f3784,f7311]) ).
tff(f7311,plain,
( spl59_80
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_80])]) ).
tff(f3784,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)),
inference(cnf_transformation,[],[f1324]) ).
tff(f1324,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)),
inference(rectify,[],[f1085]) ).
tff(f1085,axiom,
! [X5: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_dvd_Oorder__refl) ).
tff(f7309,plain,
spl59_79,
inference(avatar_split_clause,[],[f3783,f7307]) ).
tff(f7307,plain,
( spl59_79
<=> ! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_79])]) ).
tff(f3783,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
inference(cnf_transformation,[],[f1323]) ).
tff(f1323,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
inference(rectify,[],[f978]) ).
tff(f978,axiom,
! [X11: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_real__le__refl) ).
tff(f7305,plain,
spl59_78,
inference(avatar_split_clause,[],[f3781,f7303]) ).
tff(f7303,plain,
( spl59_78
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_78])]) ).
tff(f3781,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(cnf_transformation,[],[f1321]) ).
tff(f1321,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(rectify,[],[f835]) ).
tff(f835,axiom,
! [X13: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_le0) ).
tff(f7301,plain,
spl59_77,
inference(avatar_split_clause,[],[f3777,f7299]) ).
tff(f7299,plain,
( spl59_77
<=> ! [X0: int] : ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_77])]) ).
tff(f3777,plain,
! [X0: int] : ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f1317]) ).
tff(f1317,plain,
! [X0: int] : ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
inference(rectify,[],[f216]) ).
tff(f216,axiom,
! [X60: int] : ( hAPP_nat_int(power_power_int(X60),one_one_nat) = X60 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_power__one__right) ).
tff(f7297,plain,
spl59_76,
inference(avatar_split_clause,[],[f3773,f7295]) ).
tff(f7295,plain,
( spl59_76
<=> ! [X0: nat] : ( hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_76])]) ).
tff(f3773,plain,
! [X0: nat] : ( hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f1313]) ).
tff(f1313,plain,
! [X0: nat] : ( hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ),
inference(rectify,[],[f401]) ).
tff(f401,axiom,
! [X147: nat] : ( hAPP_nat_nat(power_power_nat(X147),one_one_nat) = X147 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
tff(f7293,plain,
spl59_75,
inference(avatar_split_clause,[],[f3771,f7291]) ).
tff(f7291,plain,
( spl59_75
<=> ! [X0: real] : ( hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_75])]) ).
tff(f3771,plain,
! [X0: real] : ( hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f1311]) ).
tff(f1311,plain,
! [X0: real] : ( hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ),
inference(rectify,[],[f402]) ).
tff(f402,axiom,
! [X147: real] : ( hAPP_nat_real(power_power_real(X147),one_one_nat) = X147 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
tff(f7289,plain,
spl59_74,
inference(avatar_split_clause,[],[f3770,f7287]) ).
tff(f3770,plain,
! [X0: nat] : ( nat_1(hAPP_nat_int(semiri1621563631at_int,X0)) = X0 ),
inference(cnf_transformation,[],[f1310]) ).
tff(f1310,plain,
! [X0: nat] : ( nat_1(hAPP_nat_int(semiri1621563631at_int,X0)) = X0 ),
inference(rectify,[],[f653]) ).
tff(f653,axiom,
! [X13: nat] : ( nat_1(hAPP_nat_int(semiri1621563631at_int,X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_nat__int) ).
tff(f7285,plain,
spl59_73,
inference(avatar_split_clause,[],[f3762,f7283]) ).
tff(f7283,plain,
( spl59_73
<=> ! [X0: int] : ( one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_73])]) ).
tff(f3762,plain,
! [X0: int] : ( one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f1302]) ).
tff(f1302,plain,
! [X0: int] : ( one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ),
inference(rectify,[],[f291]) ).
tff(f291,axiom,
! [X86: int] : ( one_one_int = hAPP_nat_int(power_power_int(X86),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_power__0) ).
tff(f7281,plain,
spl59_72,
inference(avatar_split_clause,[],[f3761,f7279]) ).
tff(f7279,plain,
( spl59_72
<=> ! [X0: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_72])]) ).
tff(f3761,plain,
! [X0: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ),
inference(cnf_transformation,[],[f1301]) ).
tff(f1301,plain,
! [X0: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ),
inference(rectify,[],[f234]) ).
tff(f234,axiom,
! [X63: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_power__one) ).
tff(f7277,plain,
spl59_71,
inference(avatar_split_clause,[],[f3759,f7275]) ).
tff(f7275,plain,
( spl59_71
<=> ! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_71])]) ).
tff(f3759,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f1299]) ).
tff(f1299,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ),
inference(rectify,[],[f292]) ).
tff(f292,axiom,
! [X86: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X86),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_power__0) ).
tff(f7273,plain,
spl59_70,
inference(avatar_split_clause,[],[f3758,f7271]) ).
tff(f7271,plain,
( spl59_70
<=> ! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_70])]) ).
tff(f3758,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ),
inference(cnf_transformation,[],[f1298]) ).
tff(f1298,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ),
inference(rectify,[],[f235]) ).
tff(f235,axiom,
! [X63: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_power__one) ).
tff(f7269,plain,
spl59_69,
inference(avatar_split_clause,[],[f3756,f7267]) ).
tff(f7267,plain,
( spl59_69
<=> ! [X0: real] : ( one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_69])]) ).
tff(f3756,plain,
! [X0: real] : ( one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f1296]) ).
tff(f1296,plain,
! [X0: real] : ( one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ),
inference(rectify,[],[f293]) ).
tff(f293,axiom,
! [X86: real] : ( one_one_real = hAPP_nat_real(power_power_real(X86),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_power__0) ).
tff(f7265,plain,
spl59_68,
inference(avatar_split_clause,[],[f3755,f7263]) ).
tff(f7263,plain,
( spl59_68
<=> ! [X0: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_68])]) ).
tff(f3755,plain,
! [X0: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ),
inference(cnf_transformation,[],[f1295]) ).
tff(f1295,plain,
! [X0: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ),
inference(rectify,[],[f236]) ).
tff(f236,axiom,
! [X63: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_power__one) ).
tff(f7261,plain,
spl59_67,
inference(avatar_split_clause,[],[f3753,f7259]) ).
tff(f7259,plain,
( spl59_67
<=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_67])]) ).
tff(f3753,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(cnf_transformation,[],[f1293]) ).
tff(f1293,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(rectify,[],[f187]) ).
tff(f187,axiom,
! [X13: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_less__irrefl__nat) ).
tff(f7257,plain,
spl59_66,
inference(avatar_split_clause,[],[f3750,f7255]) ).
tff(f7255,plain,
( spl59_66
<=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_66])]) ).
tff(f3750,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(cnf_transformation,[],[f1290]) ).
tff(f1290,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(rectify,[],[f173]) ).
tff(f173,axiom,
! [X13: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_less__zeroE) ).
tff(f7253,plain,
spl59_65,
inference(avatar_split_clause,[],[f3610,f7250]) ).
tff(f7250,plain,
( spl59_65
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_65])]) ).
tff(f3610,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(cnf_transformation,[],[f406]) ).
tff(f406,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_tpos) ).
tff(f7248,plain,
spl59_64,
inference(avatar_split_clause,[],[f3609,f7245]) ).
tff(f7245,plain,
( spl59_64
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_64])]) ).
tff(f3609,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
inference(cnf_transformation,[],[f1009]) ).
tff(f1009,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_rel__simps_I23_J) ).
tff(f7243,plain,
spl59_63,
inference(avatar_split_clause,[],[f3605,f7240]) ).
tff(f7240,plain,
( spl59_63
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_63])]) ).
tff(f3605,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
tff(f7238,plain,
spl59_62,
inference(avatar_split_clause,[],[f3603,f7235]) ).
tff(f7235,plain,
( spl59_62
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_62])]) ).
tff(f3603,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
inference(cnf_transformation,[],[f1003]) ).
tff(f1003,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_rel__simps_I6_J) ).
tff(f7233,plain,
spl59_61,
inference(avatar_split_clause,[],[f3602,f7230]) ).
tff(f7230,plain,
( spl59_61
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_61])]) ).
tff(f3602,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
inference(cnf_transformation,[],[f265]) ).
tff(f265,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_zero__less__one) ).
tff(f7228,plain,
spl59_60,
inference(avatar_split_clause,[],[f3601,f7225]) ).
tff(f7225,plain,
( spl59_60
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_60])]) ).
tff(f3601,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n0) ).
tff(f7223,plain,
spl59_59,
inference(avatar_split_clause,[],[f3600,f7220]) ).
tff(f7220,plain,
( spl59_59
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_59])]) ).
tff(f3600,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
inference(cnf_transformation,[],[f172]) ).
tff(f172,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_tn0) ).
tff(f7218,plain,
spl59_58,
inference(avatar_split_clause,[],[f3599,f7215]) ).
tff(f7215,plain,
( spl59_58
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_58])]) ).
tff(f3599,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
inference(cnf_transformation,[],[f266]) ).
tff(f266,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_zero__less__one) ).
tff(f7213,plain,
spl59_57,
inference(avatar_split_clause,[],[f3598,f7210]) ).
tff(f7210,plain,
( spl59_57
<=> ( tn = minus_minus_nat(nat_1(t),one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_57])]) ).
tff(f3598,plain,
tn = minus_minus_nat(nat_1(t),one_one_nat),
inference(cnf_transformation,[],[f411]) ).
tff(f411,axiom,
tn = minus_minus_nat(nat_1(t),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_tn) ).
tff(f7208,plain,
~ spl59_56,
inference(avatar_split_clause,[],[f3597,f7205]) ).
tff(f7205,plain,
( spl59_56
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_56])]) ).
tff(f3597,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
inference(cnf_transformation,[],[f1010]) ).
tff(f1010,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_rel__simps_I20_J) ).
tff(f7203,plain,
~ spl59_55,
inference(avatar_split_clause,[],[f3594,f7200]) ).
tff(f7200,plain,
( spl59_55
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_55])]) ).
tff(f3594,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
inference(cnf_transformation,[],[f1004]) ).
tff(f1004,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_rel__simps_I3_J) ).
tff(f7198,plain,
~ spl59_54,
inference(avatar_split_clause,[],[f3590,f7195]) ).
tff(f7195,plain,
( spl59_54
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_54])]) ).
tff(f3590,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
inference(cnf_transformation,[],[f263]) ).
tff(f263,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_not__one__less__zero) ).
tff(f7193,plain,
( spl59_53
| ~ spl59_11
| ~ spl59_42
| ~ spl59_43
| ~ spl59_52 ),
inference(avatar_split_clause,[],[f7188,f7178,f7137,f7133,f6995,f7190]) ).
tff(f7133,plain,
( spl59_42
<=> ! [X0: int] : ( plus_plus_int(X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_42])]) ).
tff(f7137,plain,
( spl59_43
<=> ! [X0: int] : ( plus_plus_int(pls,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_43])]) ).
tff(f7178,plain,
( spl59_52
<=> ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_52])]) ).
tff(f7188,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(pls,min),min))) )
| ~ spl59_11
| ~ spl59_42
| ~ spl59_43
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7187,f7134]) ).
tff(f7134,plain,
( ! [X0: int] : ( plus_plus_int(X0,pls) = X0 )
| ~ spl59_42 ),
inference(avatar_component_clause,[],[f7133]) ).
tff(f7187,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(plus_plus_int(pls,pls),min),min))) )
| ~ spl59_11
| ~ spl59_43
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7186,f7138]) ).
tff(f7138,plain,
( ! [X0: int] : ( plus_plus_int(pls,X0) = X0 )
| ~ spl59_43 ),
inference(avatar_component_clause,[],[f7137]) ).
tff(f7186,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(plus_plus_int(pls,plus_plus_int(pls,pls)),min),min))) )
| ~ spl59_11
| ~ spl59_43
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7185,f4070]) ).
tff(f7185,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(plus_plus_int(plus_plus_int(pls,pls),pls),min),min))) )
| ~ spl59_11
| ~ spl59_43
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7184,f7138]) ).
tff(f7184,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(plus_plus_int(pls,plus_plus_int(plus_plus_int(pls,pls),pls)),min),min))) )
| ~ spl59_11
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7183,f4729]) ).
tff(f4729,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)) ),
inference(cnf_transformation,[],[f1847]) ).
tff(f1847,plain,
! [X0: int,X1: int,X2: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)) ),
inference(rectify,[],[f347]) ).
tff(f347,axiom,
! [X120: int,X121: int,X122: int] : ( plus_plus_int(X120,plus_plus_int(X121,X122)) = plus_plus_int(X121,plus_plus_int(X120,X122)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f7183,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(minus_minus_int(minus_minus_int(plus_plus_int(plus_plus_int(pls,pls),plus_plus_int(pls,pls)),min),min))) )
| ~ spl59_11
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7182,f5434]) ).
tff(f5434,plain,
! [X0: int] : ( minus_minus_int(minus_minus_int(plus_plus_int(X0,X0),min),min) = plus_plus_int(minus_minus_int(X0,min),minus_minus_int(X0,min)) ),
inference(definition_unfolding,[],[f3789,f3764,f5319,f3767,f3764]) ).
tff(f3789,plain,
! [X0: int] : ( succ(bit1(X0)) = bit0(succ(X0)) ),
inference(cnf_transformation,[],[f1329]) ).
tff(f1329,plain,
! [X0: int] : ( succ(bit1(X0)) = bit0(succ(X0)) ),
inference(rectify,[],[f811]) ).
tff(f811,axiom,
! [X18: int] : ( succ(bit1(X18)) = bit0(succ(X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_succ__Bit1) ).
tff(f7182,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min)))) )
| ~ spl59_11
| ~ spl59_52 ),
inference(forward_demodulation,[],[f7180,f6996]) ).
tff(f7180,plain,
( ( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))) )
| ~ spl59_52 ),
inference(avatar_component_clause,[],[f7178]) ).
tff(f7181,plain,
spl59_52,
inference(avatar_split_clause,[],[f5320,f7178]) ).
tff(f5320,plain,
pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3540,f3551,f3766,f3767,f5319]) ).
tff(f3540,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1207]) ).
tff(f1207,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f1206]) ).
tff(f1206,negated_conjecture,
( ~ zero_zero_int != hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f1205]) ).
tff(f1205,conjecture,
zero_zero_int != hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f7174,plain,
spl59_51,
inference(avatar_split_clause,[],[f6285,f7172]) ).
tff(f7172,plain,
( spl59_51
<=> ! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_51])]) ).
tff(f6285,plain,
! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = X0 ),
inference(forward_demodulation,[],[f6284,f3770]) ).
tff(f6284,plain,
! [X0: nat] : ( nat_1(hAPP_nat_int(semiri1621563631at_int,X0)) = hAPP_nat_nat(semiri984289939at_nat,X0) ),
inference(forward_demodulation,[],[f5439,f3679]) ).
tff(f5439,plain,
! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = nat_1(number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X0))) ),
inference(definition_unfolding,[],[f3800,f3766]) ).
tff(f3800,plain,
! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(cnf_transformation,[],[f1340]) ).
tff(f1340,plain,
! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X38: nat] : ( number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X38)) = hAPP_nat_nat(semiri984289939at_nat,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_number__of__int) ).
tff(f7170,plain,
spl59_50,
inference(avatar_split_clause,[],[f5420,f7168]) ).
tff(f7168,plain,
( spl59_50
<=> ! [X0: int] : ( pls = minus_minus_int(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_50])]) ).
tff(f5420,plain,
! [X0: int] : ( pls = minus_minus_int(X0,X0) ),
inference(definition_unfolding,[],[f3698,f3551]) ).
tff(f3698,plain,
! [X0: int] : ( zero_zero_int = minus_minus_int(X0,X0) ),
inference(cnf_transformation,[],[f1238]) ).
tff(f1238,plain,
! [X0: int] : ( zero_zero_int = minus_minus_int(X0,X0) ),
inference(rectify,[],[f597]) ).
tff(f597,axiom,
! [X291: int] : ( zero_zero_int = minus_minus_int(X291,X291) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_diff__self) ).
tff(f7166,plain,
spl59_49,
inference(avatar_split_clause,[],[f5416,f7164]) ).
tff(f7164,plain,
( spl59_49
<=> ! [X0: int] : ( pls = times_times_int(X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_49])]) ).
tff(f5416,plain,
! [X0: int] : ( pls = times_times_int(X0,pls) ),
inference(definition_unfolding,[],[f3694,f3551,f3551]) ).
tff(f3694,plain,
! [X0: int] : ( zero_zero_int = times_times_int(X0,zero_zero_int) ),
inference(cnf_transformation,[],[f1234]) ).
tff(f1234,plain,
! [X0: int] : ( zero_zero_int = times_times_int(X0,zero_zero_int) ),
inference(rectify,[],[f613]) ).
tff(f613,axiom,
! [X302: int] : ( zero_zero_int = times_times_int(X302,zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_mult__zero__right) ).
tff(f7162,plain,
spl59_48,
inference(avatar_split_clause,[],[f5414,f7160]) ).
tff(f5414,plain,
! [X0: int] : ( min != plus_plus_int(X0,X0) ),
inference(definition_unfolding,[],[f3677,f3767]) ).
tff(f3677,plain,
! [X0: int] : ( min != bit0(X0) ),
inference(cnf_transformation,[],[f1217]) ).
tff(f1217,plain,
! [X0: int] : ( min != bit0(X0) ),
inference(rectify,[],[f1014]) ).
tff(f1014,axiom,
! [X28: int] : ( bit0(X28) != min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_rel__simps_I42_J) ).
tff(f7158,plain,
spl59_47,
inference(avatar_split_clause,[],[f5346,f7155]) ).
tff(f7152,plain,
spl59_46,
inference(avatar_split_clause,[],[f5327,f7149]) ).
tff(f7149,plain,
( spl59_46
<=> ( zero_zero_nat = nat_1(number_number_of_int(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_46])]) ).
tff(f5327,plain,
zero_zero_nat = nat_1(number_number_of_int(pls)),
inference(definition_unfolding,[],[f3559,f3766]) ).
tff(f3559,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_semiring__numeral__0__eq__0) ).
tff(f7147,plain,
spl59_45,
inference(avatar_split_clause,[],[f3746,f7145]) ).
tff(f7145,plain,
( spl59_45
<=> ! [X0: int] : ( times_times_int(one_one_int,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_45])]) ).
tff(f3746,plain,
! [X0: int] : ( times_times_int(one_one_int,X0) = X0 ),
inference(cnf_transformation,[],[f1286]) ).
tff(f1286,plain,
! [X0: int] : ( times_times_int(one_one_int,X0) = X0 ),
inference(rectify,[],[f671]) ).
tff(f671,axiom,
! [X330: int] : ( times_times_int(one_one_int,X330) = X330 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_mult__1__left) ).
tff(f7143,plain,
spl59_44,
inference(avatar_split_clause,[],[f3742,f7141]) ).
tff(f7141,plain,
( spl59_44
<=> ! [X0: int] : ( times_times_int(X0,one_one_int) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_44])]) ).
tff(f3742,plain,
! [X0: int] : ( times_times_int(X0,one_one_int) = X0 ),
inference(cnf_transformation,[],[f1282]) ).
tff(f1282,plain,
! [X0: int] : ( times_times_int(X0,one_one_int) = X0 ),
inference(rectify,[],[f659]) ).
tff(f659,axiom,
! [X326: int] : ( times_times_int(X326,one_one_int) = X326 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
tff(f7139,plain,
spl59_43,
inference(avatar_split_clause,[],[f3737,f7137]) ).
tff(f3737,plain,
! [X0: int] : ( plus_plus_int(pls,X0) = X0 ),
inference(cnf_transformation,[],[f1277]) ).
tff(f1277,plain,
! [X0: int] : ( plus_plus_int(pls,X0) = X0 ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X18: int] : ( plus_plus_int(pls,X18) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__Pls) ).
tff(f7135,plain,
spl59_42,
inference(avatar_split_clause,[],[f3732,f7133]) ).
tff(f3732,plain,
! [X0: int] : ( plus_plus_int(X0,pls) = X0 ),
inference(cnf_transformation,[],[f1272]) ).
tff(f1272,plain,
! [X0: int] : ( plus_plus_int(X0,pls) = X0 ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X18: int] : ( plus_plus_int(X18,pls) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
tff(f7131,plain,
spl59_41,
inference(avatar_split_clause,[],[f3728,f7129]) ).
tff(f7129,plain,
( spl59_41
<=> ! [X0: nat] : ( times_times_nat(one_one_nat,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_41])]) ).
tff(f3728,plain,
! [X0: nat] : ( times_times_nat(one_one_nat,X0) = X0 ),
inference(cnf_transformation,[],[f1268]) ).
tff(f1268,plain,
! [X0: nat] : ( times_times_nat(one_one_nat,X0) = X0 ),
inference(rectify,[],[f670]) ).
tff(f670,axiom,
! [X330: nat] : ( times_times_nat(one_one_nat,X330) = X330 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_mult__1__left) ).
tff(f7127,plain,
spl59_40,
inference(avatar_split_clause,[],[f3724,f7125]) ).
tff(f7125,plain,
( spl59_40
<=> ! [X0: nat] : ( times_times_nat(X0,one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_40])]) ).
tff(f3724,plain,
! [X0: nat] : ( times_times_nat(X0,one_one_nat) = X0 ),
inference(cnf_transformation,[],[f1264]) ).
tff(f1264,plain,
! [X0: nat] : ( times_times_nat(X0,one_one_nat) = X0 ),
inference(rectify,[],[f661]) ).
tff(f661,axiom,
! [X327: nat] : ( times_times_nat(X327,one_one_nat) = X327 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_mult__1__right) ).
tff(f7123,plain,
spl59_39,
inference(avatar_split_clause,[],[f3720,f7121]) ).
tff(f7121,plain,
( spl59_39
<=> ! [X0: nat] : ( plus_plus_nat(zero_zero_nat,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_39])]) ).
tff(f3720,plain,
! [X0: nat] : ( plus_plus_nat(zero_zero_nat,X0) = X0 ),
inference(cnf_transformation,[],[f1260]) ).
tff(f1260,plain,
! [X0: nat] : ( plus_plus_nat(zero_zero_nat,X0) = X0 ),
inference(rectify,[],[f215]) ).
tff(f215,axiom,
! [X13: nat] : ( plus_plus_nat(zero_zero_nat,X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_plus__nat_Oadd__0) ).
tff(f7119,plain,
spl59_38,
inference(avatar_split_clause,[],[f3716,f7117]) ).
tff(f7117,plain,
( spl59_38
<=> ! [X0: nat] : ( plus_plus_nat(X0,zero_zero_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_38])]) ).
tff(f3716,plain,
! [X0: nat] : ( plus_plus_nat(X0,zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f1256]) ).
tff(f1256,plain,
! [X0: nat] : ( plus_plus_nat(X0,zero_zero_nat) = X0 ),
inference(rectify,[],[f363]) ).
tff(f363,axiom,
! [X126: nat] : ( plus_plus_nat(X126,zero_zero_nat) = X126 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
tff(f7115,plain,
spl59_37,
inference(avatar_split_clause,[],[f3712,f7113]) ).
tff(f7113,plain,
( spl59_37
<=> ! [X0: real] : ( times_times_real(one_one_real,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_37])]) ).
tff(f3712,plain,
! [X0: real] : ( times_times_real(one_one_real,X0) = X0 ),
inference(cnf_transformation,[],[f1252]) ).
tff(f1252,plain,
! [X0: real] : ( times_times_real(one_one_real,X0) = X0 ),
inference(rectify,[],[f902]) ).
tff(f902,axiom,
! [X14: real] : ( times_times_real(one_one_real,X14) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_real__mult__1) ).
tff(f7111,plain,
spl59_36,
inference(avatar_split_clause,[],[f3709,f7109]) ).
tff(f7109,plain,
( spl59_36
<=> ! [X0: real] : ( times_times_real(X0,one_one_real) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_36])]) ).
tff(f3709,plain,
! [X0: real] : ( times_times_real(X0,one_one_real) = X0 ),
inference(cnf_transformation,[],[f1249]) ).
tff(f1249,plain,
! [X0: real] : ( times_times_real(X0,one_one_real) = X0 ),
inference(rectify,[],[f660]) ).
tff(f660,axiom,
! [X327: real] : ( times_times_real(X327,one_one_real) = X327 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_mult__1__right) ).
tff(f7107,plain,
spl59_35,
inference(avatar_split_clause,[],[f3706,f7105]) ).
tff(f7105,plain,
( spl59_35
<=> ! [X0: real] : ( plus_plus_real(zero_zero_real,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_35])]) ).
tff(f3706,plain,
! [X0: real] : ( plus_plus_real(zero_zero_real,X0) = X0 ),
inference(cnf_transformation,[],[f1246]) ).
tff(f1246,plain,
! [X0: real] : ( plus_plus_real(zero_zero_real,X0) = X0 ),
inference(rectify,[],[f378]) ).
tff(f378,axiom,
! [X130: real] : ( plus_plus_real(zero_zero_real,X130) = X130 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_add__0__left) ).
tff(f7103,plain,
spl59_34,
inference(avatar_split_clause,[],[f3703,f7101]) ).
tff(f7101,plain,
( spl59_34
<=> ! [X0: real] : ( plus_plus_real(X0,zero_zero_real) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_34])]) ).
tff(f3703,plain,
! [X0: real] : ( plus_plus_real(X0,zero_zero_real) = X0 ),
inference(cnf_transformation,[],[f1243]) ).
tff(f1243,plain,
! [X0: real] : ( plus_plus_real(X0,zero_zero_real) = X0 ),
inference(rectify,[],[f361]) ).
tff(f361,axiom,
! [X125: real] : ( plus_plus_real(X125,zero_zero_real) = X125 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_add_Ocomm__neutral) ).
tff(f7099,plain,
spl59_33,
inference(avatar_split_clause,[],[f3702,f7097]) ).
tff(f7097,plain,
( spl59_33
<=> ! [X0: nat] : ( minus_minus_nat(X0,zero_zero_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_33])]) ).
tff(f3702,plain,
! [X0: nat] : ( minus_minus_nat(X0,zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f1242]) ).
tff(f1242,plain,
! [X0: nat] : ( minus_minus_nat(X0,zero_zero_nat) = X0 ),
inference(rectify,[],[f630]) ).
tff(f630,axiom,
! [X12: nat] : ( minus_minus_nat(X12,zero_zero_nat) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_minus__nat_Odiff__0) ).
tff(f7095,plain,
spl59_32,
inference(avatar_split_clause,[],[f3700,f7093]) ).
tff(f7093,plain,
( spl59_32
<=> ! [X0: int] : ( minus_minus_int(X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_32])]) ).
tff(f3700,plain,
! [X0: int] : ( minus_minus_int(X0,pls) = X0 ),
inference(cnf_transformation,[],[f1240]) ).
tff(f1240,plain,
! [X0: int] : ( minus_minus_int(X0,pls) = X0 ),
inference(rectify,[],[f862]) ).
tff(f862,axiom,
! [X18: int] : ( minus_minus_int(X18,pls) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_diff__bin__simps_I1_J) ).
tff(f7091,plain,
spl59_31,
inference(avatar_split_clause,[],[f3699,f7089]) ).
tff(f7089,plain,
( spl59_31
<=> ! [X0: real] : ( minus_minus_real(X0,zero_zero_real) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_31])]) ).
tff(f3699,plain,
! [X0: real] : ( minus_minus_real(X0,zero_zero_real) = X0 ),
inference(cnf_transformation,[],[f1239]) ).
tff(f1239,plain,
! [X0: real] : ( minus_minus_real(X0,zero_zero_real) = X0 ),
inference(rectify,[],[f598]) ).
tff(f598,axiom,
! [X292: real] : ( minus_minus_real(X292,zero_zero_real) = X292 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_diff__0__right) ).
tff(f7087,plain,
( spl59_30
| ~ spl59_9
| ~ spl59_15 ),
inference(avatar_split_clause,[],[f7029,f7013,f6985,f7084]) ).
tff(f7084,plain,
( spl59_30
<=> sP2(one_one_nat,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_30])]) ).
tff(f6985,plain,
( spl59_9
<=> ( one_one_nat = nat_1(one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_9])]) ).
tff(f7029,plain,
( sP2(one_one_nat,one_one_int)
| ~ spl59_9
| ~ spl59_15 ),
inference(superposition,[],[f7014,f6987]) ).
tff(f6987,plain,
( ( one_one_nat = nat_1(one_one_int) )
| ~ spl59_9 ),
inference(avatar_component_clause,[],[f6985]) ).
tff(f7082,plain,
spl59_29,
inference(avatar_split_clause,[],[f3693,f7080]) ).
tff(f7080,plain,
( spl59_29
<=> ! [X0: int] : ( pls = times_times_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_29])]) ).
tff(f3693,plain,
! [X0: int] : ( pls = times_times_int(pls,X0) ),
inference(cnf_transformation,[],[f1233]) ).
tff(f1233,plain,
! [X0: int] : ( pls = times_times_int(pls,X0) ),
inference(rectify,[],[f709]) ).
tff(f709,axiom,
! [X11: int] : ( pls = times_times_int(pls,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_mult__Pls) ).
tff(f7078,plain,
spl59_28,
inference(avatar_split_clause,[],[f3692,f7076]) ).
tff(f7076,plain,
( spl59_28
<=> ! [X0: nat] : ( zero_zero_nat = minus_minus_nat(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_28])]) ).
tff(f3692,plain,
! [X0: nat] : ( zero_zero_nat = minus_minus_nat(X0,X0) ),
inference(cnf_transformation,[],[f1232]) ).
tff(f1232,plain,
! [X0: nat] : ( zero_zero_nat = minus_minus_nat(X0,X0) ),
inference(rectify,[],[f629]) ).
tff(f629,axiom,
! [X12: nat] : ( zero_zero_nat = minus_minus_nat(X12,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_diff__self__eq__0) ).
tff(f7074,plain,
spl59_27,
inference(avatar_split_clause,[],[f3689,f7072]) ).
tff(f7072,plain,
( spl59_27
<=> ! [X0: nat] : ( zero_zero_nat = times_times_nat(zero_zero_nat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_27])]) ).
tff(f3689,plain,
! [X0: nat] : ( zero_zero_nat = times_times_nat(zero_zero_nat,X0) ),
inference(cnf_transformation,[],[f1229]) ).
tff(f1229,plain,
! [X0: nat] : ( zero_zero_nat = times_times_nat(zero_zero_nat,X0) ),
inference(rectify,[],[f609]) ).
tff(f609,axiom,
! [X301: nat] : ( zero_zero_nat = times_times_nat(zero_zero_nat,X301) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_mult__zero__left) ).
tff(f7070,plain,
spl59_26,
inference(avatar_split_clause,[],[f3686,f7068]) ).
tff(f7068,plain,
( spl59_26
<=> ! [X0: nat] : ( zero_zero_nat = times_times_nat(X0,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_26])]) ).
tff(f3686,plain,
! [X0: nat] : ( zero_zero_nat = times_times_nat(X0,zero_zero_nat) ),
inference(cnf_transformation,[],[f1226]) ).
tff(f1226,plain,
! [X0: nat] : ( zero_zero_nat = times_times_nat(X0,zero_zero_nat) ),
inference(rectify,[],[f623]) ).
tff(f623,axiom,
! [X307: nat] : ( zero_zero_nat = times_times_nat(X307,zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(f7066,plain,
spl59_25,
inference(avatar_split_clause,[],[f3685,f7064]) ).
tff(f7064,plain,
( spl59_25
<=> ! [X0: nat] : ( zero_zero_nat = minus_minus_nat(zero_zero_nat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_25])]) ).
tff(f3685,plain,
! [X0: nat] : ( zero_zero_nat = minus_minus_nat(zero_zero_nat,X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f1225,plain,
! [X0: nat] : ( zero_zero_nat = minus_minus_nat(zero_zero_nat,X0) ),
inference(rectify,[],[f631]) ).
tff(f631,axiom,
! [X13: nat] : ( zero_zero_nat = minus_minus_nat(zero_zero_nat,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_diff__0__eq__0) ).
tff(f7062,plain,
spl59_24,
inference(avatar_split_clause,[],[f3684,f7060]) ).
tff(f7060,plain,
( spl59_24
<=> ! [X0: real] : ( zero_zero_real = minus_minus_real(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_24])]) ).
tff(f3684,plain,
! [X0: real] : ( zero_zero_real = minus_minus_real(X0,X0) ),
inference(cnf_transformation,[],[f1224]) ).
tff(f1224,plain,
! [X0: real] : ( zero_zero_real = minus_minus_real(X0,X0) ),
inference(rectify,[],[f596]) ).
tff(f596,axiom,
! [X291: real] : ( zero_zero_real = minus_minus_real(X291,X291) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_diff__self) ).
tff(f7058,plain,
spl59_23,
inference(avatar_split_clause,[],[f3682,f7056]) ).
tff(f7056,plain,
( spl59_23
<=> ! [X0: real] : ( zero_zero_real = times_times_real(zero_zero_real,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_23])]) ).
tff(f3682,plain,
! [X0: real] : ( zero_zero_real = times_times_real(zero_zero_real,X0) ),
inference(cnf_transformation,[],[f1222]) ).
tff(f1222,plain,
! [X0: real] : ( zero_zero_real = times_times_real(zero_zero_real,X0) ),
inference(rectify,[],[f625]) ).
tff(f625,axiom,
! [X308: real] : ( zero_zero_real = times_times_real(zero_zero_real,X308) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
tff(f7054,plain,
spl59_22,
inference(avatar_split_clause,[],[f3680,f7052]) ).
tff(f7052,plain,
( spl59_22
<=> ! [X0: real] : ( zero_zero_real = times_times_real(X0,zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_22])]) ).
tff(f3680,plain,
! [X0: real] : ( zero_zero_real = times_times_real(X0,zero_zero_real) ),
inference(cnf_transformation,[],[f1220]) ).
tff(f1220,plain,
! [X0: real] : ( zero_zero_real = times_times_real(X0,zero_zero_real) ),
inference(rectify,[],[f622]) ).
tff(f622,axiom,
! [X307: real] : ( zero_zero_real = times_times_real(X307,zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(f7050,plain,
spl59_21,
inference(avatar_split_clause,[],[f3584,f7047]) ).
tff(f7047,plain,
( spl59_21
<=> ( zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_21])]) ).
tff(f3584,plain,
zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat),
inference(cnf_transformation,[],[f296]) ).
tff(f296,axiom,
zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_of__nat__0) ).
tff(f7045,plain,
spl59_20,
inference(avatar_split_clause,[],[f3581,f7042]) ).
tff(f7042,plain,
( spl59_20
<=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_20])]) ).
tff(f3581,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(cnf_transformation,[],[f249]) ).
tff(f249,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_of__nat__1) ).
tff(f7040,plain,
( spl59_19
| ~ spl59_9
| ~ spl59_14 ),
inference(avatar_split_clause,[],[f7027,f7009,f6985,f7037]) ).
tff(f7037,plain,
( spl59_19
<=> sP1(one_one_nat,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_19])]) ).
tff(f7027,plain,
( sP1(one_one_nat,one_one_int)
| ~ spl59_9
| ~ spl59_14 ),
inference(superposition,[],[f7010,f6987]) ).
tff(f7035,plain,
spl59_18,
inference(avatar_split_clause,[],[f3572,f7032]) ).
tff(f7032,plain,
( spl59_18
<=> ( one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_18])]) ).
tff(f3572,plain,
one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat),
inference(cnf_transformation,[],[f251]) ).
tff(f251,axiom,
one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_of__nat__1) ).
tff(f7026,plain,
spl59_17,
inference(avatar_split_clause,[],[f6445,f7023]) ).
tff(f7023,plain,
( spl59_17
<=> ( one_one_int = abs_abs_int(min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_17])]) ).
tff(f6445,plain,
one_one_int = abs_abs_int(min),
inference(forward_demodulation,[],[f5957,f3679]) ).
tff(f5957,plain,
one_one_int = abs_abs_int(number_number_of_int(min)),
inference(equality_resolution,[],[f3892]) ).
tff(f3892,plain,
! [X0: int] :
( ( one_one_int = abs_abs_int(X0) )
| ( number_number_of_int(min) != X0 ) ),
inference(cnf_transformation,[],[f3034]) ).
tff(f3034,plain,
! [X0: int] :
( ( ( one_one_int = abs_abs_int(X0) )
| ( ( number_number_of_int(min) != X0 )
& ( one_one_int != X0 ) ) )
& ( ( number_number_of_int(min) = X0 )
| ( one_one_int = X0 )
| ( one_one_int != abs_abs_int(X0) ) ) ),
inference(flattening,[],[f3033]) ).
tff(f3033,plain,
! [X0: int] :
( ( ( one_one_int = abs_abs_int(X0) )
| ( ( number_number_of_int(min) != X0 )
& ( one_one_int != X0 ) ) )
& ( ( number_number_of_int(min) = X0 )
| ( one_one_int = X0 )
| ( one_one_int != abs_abs_int(X0) ) ) ),
inference(nnf_transformation,[],[f1406]) ).
tff(f1406,plain,
! [X0: int] :
( ( one_one_int = abs_abs_int(X0) )
<=> ( ( number_number_of_int(min) = X0 )
| ( one_one_int = X0 ) ) ),
inference(rectify,[],[f1164]) ).
tff(f1164,axiom,
! [X27: int] :
( ( one_one_int = abs_abs_int(X27) )
<=> ( ( number_number_of_int(min) = X27 )
| ( one_one_int = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_abs__eq__1__iff) ).
tff(f7020,plain,
~ spl59_16,
inference(avatar_split_clause,[],[f6166,f7017]) ).
tff(f7017,plain,
( spl59_16
<=> ( pls = number_number_of_int(min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_16])]) ).
tff(f6166,plain,
pls != number_number_of_int(min),
inference(forward_demodulation,[],[f3568,f5332]) ).
tff(f5332,plain,
pls = number_number_of_int(pls),
inference(definition_unfolding,[],[f3564,f3551]) ).
tff(f3564,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
tff(f3568,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(cnf_transformation,[],[f1012]) ).
tff(f1012,axiom,
number_number_of_int(pls) != number_number_of_int(min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_eq__number__of__Pls__Min) ).
tff(f7015,plain,
spl59_15,
inference(avatar_split_clause,[],[f6013,f7013]) ).
tff(f6013,plain,
! [X0: int] : sP2(nat_1(X0),X0),
inference(equality_resolution,[],[f4360]) ).
tff(f4360,plain,
! [X0: int,X1: nat] :
( sP2(X1,X0)
| ( nat_1(X0) != X1 ) ),
inference(cnf_transformation,[],[f3169]) ).
tff(f7011,plain,
spl59_14,
inference(avatar_split_clause,[],[f6008,f7009]) ).
tff(f6008,plain,
! [X1: int] : sP1(nat_1(X1),X1),
inference(equality_resolution,[],[f4352]) ).
tff(f4352,plain,
! [X0: nat,X1: int] :
( sP1(X0,X1)
| ( nat_1(X1) != X0 ) ),
inference(cnf_transformation,[],[f3165]) ).
tff(f7007,plain,
spl59_13,
inference(avatar_split_clause,[],[f5958,f7004]) ).
tff(f7004,plain,
( spl59_13
<=> ( one_one_int = abs_abs_int(one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_13])]) ).
tff(f5958,plain,
one_one_int = abs_abs_int(one_one_int),
inference(equality_resolution,[],[f3891]) ).
tff(f3891,plain,
! [X0: int] :
( ( one_one_int = abs_abs_int(X0) )
| ( one_one_int != X0 ) ),
inference(cnf_transformation,[],[f3034]) ).
tff(f7002,plain,
spl59_12,
inference(avatar_split_clause,[],[f5325,f6999]) ).
tff(f6999,plain,
( spl59_12
<=> ( zero_zero_nat = nat_1(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_12])]) ).
tff(f5325,plain,
zero_zero_nat = nat_1(pls),
inference(definition_unfolding,[],[f3557,f3551]) ).
tff(f3557,plain,
zero_zero_nat = nat_1(zero_zero_int),
inference(cnf_transformation,[],[f762]) ).
tff(f762,axiom,
zero_zero_nat = nat_1(zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_nat__0) ).
tff(f6997,plain,
spl59_11,
inference(avatar_split_clause,[],[f3679,f6995]) ).
tff(f6993,plain,
spl59_10,
inference(avatar_split_clause,[],[f3554,f6990]) ).
tff(f6990,plain,
( spl59_10
<=> ( zero_zero_real = number267125858f_real(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_10])]) ).
tff(f3554,plain,
zero_zero_real = number267125858f_real(pls),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
zero_zero_real = number267125858f_real(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_number__of__Pls) ).
tff(f6988,plain,
spl59_9,
inference(avatar_split_clause,[],[f3553,f6985]) ).
tff(f3553,plain,
one_one_nat = nat_1(one_one_int),
inference(cnf_transformation,[],[f769]) ).
tff(f769,axiom,
one_one_nat = nat_1(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_transfer__nat__int__numerals_I2_J) ).
tff(f6983,plain,
spl59_8,
inference(avatar_split_clause,[],[f6632,f6980]) ).
tff(f6980,plain,
( spl59_8
<=> sP3(min,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_8])]) ).
tff(f6632,plain,
sP3(min,min),
inference(forward_demodulation,[],[f6025,f3679]) ).
tff(f6025,plain,
sP3(number_number_of_int(min),number_number_of_int(min)),
inference(equality_resolution,[],[f6024]) ).
tff(f6024,plain,
! [X1: int] :
( sP3(number_number_of_int(min),X1)
| ( number_number_of_int(min) != X1 ) ),
inference(equality_resolution,[],[f4380]) ).
tff(f4380,plain,
! [X0: int,X1: int] :
( sP3(X0,X1)
| ( number_number_of_int(min) != X0 )
| ( number_number_of_int(min) != X1 ) ),
inference(cnf_transformation,[],[f3180]) ).
tff(f6978,plain,
spl59_7,
inference(avatar_split_clause,[],[f6631,f6975]) ).
tff(f6975,plain,
( spl59_7
<=> sP2(zero_zero_nat,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_7])]) ).
tff(f6631,plain,
sP2(zero_zero_nat,pls),
inference(forward_demodulation,[],[f6010,f5346]) ).
tff(f6010,plain,
sP2(zero_zero_nat,hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)),
inference(equality_resolution,[],[f6009]) ).
tff(f6009,plain,
! [X1: int] :
( sP2(zero_zero_nat,X1)
| ( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != X1 ) ),
inference(equality_resolution,[],[f4359]) ).
tff(f4359,plain,
! [X0: nat,X1: int] :
( sP2(X0,X1)
| ( zero_zero_nat != X0 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != X1 ) ),
inference(cnf_transformation,[],[f3168]) ).
tff(f6973,plain,
spl59_6,
inference(avatar_split_clause,[],[f6630,f6970]) ).
tff(f6970,plain,
( spl59_6
<=> sP1(zero_zero_nat,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_6])]) ).
tff(f6630,plain,
sP1(zero_zero_nat,pls),
inference(forward_demodulation,[],[f6005,f5346]) ).
tff(f6005,plain,
sP1(zero_zero_nat,hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)),
inference(equality_resolution,[],[f6004]) ).
tff(f6004,plain,
! [X1: int] :
( sP1(zero_zero_nat,X1)
| ( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != X1 ) ),
inference(equality_resolution,[],[f4351]) ).
tff(f4351,plain,
! [X0: nat,X1: int] :
( sP1(X0,X1)
| ( zero_zero_nat != X0 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != X1 ) ),
inference(cnf_transformation,[],[f3164]) ).
tff(f6968,plain,
spl59_5,
inference(avatar_split_clause,[],[f6027,f6965]) ).
tff(f6965,plain,
( spl59_5
<=> sP3(one_one_int,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_5])]) ).
tff(f6027,plain,
sP3(one_one_int,one_one_int),
inference(equality_resolution,[],[f6026]) ).
tff(f6026,plain,
! [X1: int] :
( sP3(one_one_int,X1)
| ( one_one_int != X1 ) ),
inference(equality_resolution,[],[f4379]) ).
tff(f4379,plain,
! [X0: int,X1: int] :
( sP3(X0,X1)
| ( one_one_int != X0 )
| ( one_one_int != X1 ) ),
inference(cnf_transformation,[],[f3180]) ).
tff(f6963,plain,
~ spl59_4,
inference(avatar_split_clause,[],[f5321,f6960]) ).
tff(f6960,plain,
( spl59_4
<=> ( one_one_int = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_4])]) ).
tff(f5321,plain,
one_one_int != pls,
inference(definition_unfolding,[],[f3548,f3551]) ).
tff(f3548,plain,
zero_zero_int != one_one_int,
inference(cnf_transformation,[],[f226]) ).
tff(f226,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_one__neq__zero) ).
tff(f6958,plain,
~ spl59_3,
inference(avatar_split_clause,[],[f3546,f6955]) ).
tff(f6955,plain,
( spl59_3
<=> ( pls = min ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_3])]) ).
tff(f3546,plain,
pls != min,
inference(cnf_transformation,[],[f1016]) ).
tff(f1016,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_rel__simps_I40_J) ).
tff(f6953,plain,
~ spl59_2,
inference(avatar_split_clause,[],[f3543,f6950]) ).
tff(f6950,plain,
( spl59_2
<=> ( zero_zero_real = one_one_real ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_2])]) ).
tff(f3543,plain,
zero_zero_real != one_one_real,
inference(cnf_transformation,[],[f231]) ).
tff(f231,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_zero__neq__one) ).
tff(f6948,plain,
~ spl59_1,
inference(avatar_split_clause,[],[f3541,f6945]) ).
tff(f6945,plain,
( spl59_1
<=> ( one_one_nat = zero_zero_nat ) ),
introduced(avatar_definition,[new_symbols(naming,[spl59_1])]) ).
tff(f3541,plain,
one_one_nat != zero_zero_nat,
inference(cnf_transformation,[],[f230]) ).
tff(f230,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_zero__neq__one) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM925_3 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 15:24:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (24289)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.45 % (24290)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.45 % (24292)WARNING: value z3 for option sas not known
% 0.21/0.45 % (24292)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 % (24293)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.45 % (24295)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 % (24294)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 % (24296)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 % (24291)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 1.14/0.58 % (24294)First to succeed.
% 1.14/0.60 % (24294)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24289"
% 1.31/0.60 % (24294)Refutation found. Thanks to Tanya!
% 1.31/0.60 % SZS status Theorem for theBenchmark
% 1.31/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.61 % (24294)------------------------------
% 1.31/0.61 % (24294)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.31/0.61 % (24294)Termination reason: Refutation
% 1.31/0.61
% 1.31/0.61 % (24294)Memory used [KB]: 4829
% 1.31/0.61 % (24294)Time elapsed: 0.147 s
% 1.31/0.61 % (24294)Instructions burned: 300 (million)
% 1.31/0.61 % (24289)Success in time 0.234 s
%------------------------------------------------------------------------------