TSTP Solution File: NUM925_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925_2 : 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 : n028.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 : Tue Apr 30 14:38:36 EDT 2024
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 343
% Syntax : Number of formulae : 827 ( 391 unt; 89 typ; 0 def)
% Number of atoms : 1352 ( 591 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 990 ( 376 ~; 305 |; 87 &)
% ( 178 <=>; 40 =>; 0 <=; 4 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 16 ( 15 usr)
% Number of type conns : 81 ( 52 >; 29 *; 0 +; 0 <<)
% Number of predicates : 134 ( 132 usr; 129 prp; 0-3 aty)
% Number of functors : 70 ( 70 usr; 22 con; 0-2 aty)
% Number of variables : 663 ( 647 !; 16 ?; 663 :)
% 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_int: $tType ).
tff(type_def_11,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_12,type,
fun_nat_bool: $tType ).
tff(type_def_13,type,
fun_nat_int: $tType ).
tff(type_def_14,type,
fun_nat_nat: $tType ).
tff(type_def_15,type,
fun_nat_real: $tType ).
tff(type_def_16,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_17,type,
fun_real_bool: $tType ).
tff(type_def_18,type,
fun_real_real: $tType ).
tff(type_def_19,type,
fun_re413263731l_bool: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
one_one_real: real ).
tff(func_def_3,type,
plus_plus_int: int > fun_int_int ).
tff(func_def_4,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_5,type,
plus_plus_real: real > fun_real_real ).
tff(func_def_6,type,
times_times_int: ( int * int ) > int ).
tff(func_def_7,type,
zero_zero_int: int ).
tff(func_def_8,type,
zero_zero_nat: nat ).
tff(func_def_9,type,
zero_zero_real: real ).
tff(func_def_10,type,
if_nat: ( bool * nat ) > fun_nat_nat ).
tff(func_def_11,type,
bit0: int > int ).
tff(func_def_12,type,
bit1: int > int ).
tff(func_def_13,type,
pls: int ).
tff(func_def_14,type,
number_number_of_int: int > int ).
tff(func_def_15,type,
number_number_of_nat: int > nat ).
tff(func_def_16,type,
number267125858f_real: int > real ).
tff(func_def_17,type,
succ: int > int ).
tff(func_def_18,type,
semiri1621563631at_int: fun_nat_int ).
tff(func_def_19,type,
semiri984289939at_nat: fun_nat_nat ).
tff(func_def_20,type,
semiri132038758t_real: fun_nat_real ).
tff(func_def_21,type,
sqrt: real > real ).
tff(func_def_22,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_23,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_24,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_25,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_26,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_27,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_28,type,
power_power_int: int > fun_nat_int ).
tff(func_def_29,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_30,type,
power_power_real: real > fun_nat_real ).
tff(func_def_31,type,
fFalse: bool ).
tff(func_def_32,type,
fTrue: bool ).
tff(func_def_33,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_34,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(func_def_35,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_36,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_37,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_38,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_39,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_40,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_41,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_42,type,
hAPP_real_real: ( fun_real_real * real ) > real ).
tff(func_def_43,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_44,type,
m1: int ).
tff(func_def_45,type,
n: nat ).
tff(func_def_46,type,
t: int ).
tff(func_def_47,type,
tn: nat ).
tff(func_def_48,type,
sK3: int > nat ).
tff(func_def_49,type,
sK4: int > nat ).
tff(func_def_50,type,
sK5: int > nat ).
tff(func_def_51,type,
sK6: int > nat ).
tff(func_def_52,type,
sK7: fun_int_bool > nat ).
tff(func_def_53,type,
sK8: fun_int_bool > int ).
tff(func_def_54,type,
sK9: fun_int_bool > int ).
tff(func_def_55,type,
sK10: fun_int_bool > nat ).
tff(func_def_56,type,
sK11: ( nat * fun_nat_bool ) > nat ).
tff(func_def_57,type,
sK12: ( nat * fun_nat_bool ) > nat ).
tff(func_def_58,type,
sK13: ( real * real ) > real ).
tff(func_def_59,type,
sK14: ( real * nat ) > real ).
tff(func_def_60,type,
sK15: ( real * nat ) > real ).
tff(func_def_61,type,
sK16: ( nat * nat ) > nat ).
tff(func_def_62,type,
sK17: ( nat * nat ) > nat ).
tff(func_def_63,type,
sK18: ( int * int ) > nat ).
tff(func_def_64,type,
sK19: ( fun_int_bool * int ) > int ).
tff(func_def_65,type,
sK20: ( fun_int_bool * int ) > int ).
tff(func_def_66,type,
sK21: fun_nat_nat > nat ).
tff(func_def_67,type,
sK22: fun_nat_nat > nat ).
tff(func_def_68,type,
sK23: fun_nat_nat > nat ).
tff(func_def_69,type,
sK24: fun_nat_nat > nat ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( bool * int * bool ) > $o ).
tff(pred_def_3,type,
sP1: ( bool * int * bool ) > $o ).
tff(pred_def_4,type,
sP2: ( nat * nat * fun_nat_fun_nat_bool ) > $o ).
tff(f4743,plain,
$false,
inference(avatar_sat_refutation,[],[f3935,f3940,f3945,f3950,f3955,f3959,f3964,f3969,f3974,f3979,f3984,f3989,f3994,f3999,f4004,f4009,f4014,f4019,f4024,f4029,f4034,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4124,f4129,f4134,f4139,f4143,f4147,f4151,f4155,f4187,f4192,f4210,f4214,f4218,f4223,f4230,f4235,f4242,f4248,f4255,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4372,f4376,f4380,f4384,f4388,f4392,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4424,f4428,f4432,f4436,f4441,f4445,f4449,f4453,f4457,f4461,f4465,f4470,f4475,f4612,f4616,f4620,f4624,f4628,f4632,f4636,f4640,f4644,f4648,f4652,f4660,f4665,f4702,f4713,f4719,f4724,f4728,f4733,f4739,f4742]) ).
tff(f4742,plain,
( ~ spl25_50
| ~ spl25_128 ),
inference(avatar_contradiction_clause,[],[f4740]) ).
tff(f4740,plain,
( $false
| ~ spl25_50
| ~ spl25_128 ),
inference(resolution,[],[f4738,f4154]) ).
tff(f4154,plain,
( ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1))
| ~ spl25_50 ),
inference(avatar_component_clause,[],[f4153]) ).
tff(f4153,plain,
( spl25_50
<=> ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_50])]) ).
tff(f4738,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
| ~ spl25_128 ),
inference(avatar_component_clause,[],[f4736]) ).
tff(f4736,plain,
( spl25_128
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_128])]) ).
tff(f4739,plain,
( spl25_128
| ~ spl25_109
| ~ spl25_127 ),
inference(avatar_split_clause,[],[f4734,f4730,f4609,f4736]) ).
tff(f4609,plain,
( spl25_109
<=> ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_109])]) ).
tff(f4730,plain,
( spl25_127
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_127])]) ).
tff(f4734,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
| ~ spl25_109
| ~ spl25_127 ),
inference(forward_demodulation,[],[f4732,f4611]) ).
tff(f4611,plain,
( ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ spl25_109 ),
inference(avatar_component_clause,[],[f4609]) ).
tff(f4732,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl25_127 ),
inference(avatar_component_clause,[],[f4730]) ).
tff(f4733,plain,
spl25_127,
inference(avatar_split_clause,[],[f3021,f4730]) ).
tff(f3021,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f2077,f2000]) ).
tff(f2000,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(f2077,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_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),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f4728,plain,
spl25_126,
inference(avatar_split_clause,[],[f2362,f4726]) ).
tff(f4726,plain,
( spl25_126
<=> ! [X2: nat,X0: fun_int_bool] :
( hBOOL(hAPP_int_bool(X0,sK9(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_126])]) ).
tff(f2362,plain,
! [X2: nat,X0: fun_int_bool] :
( hBOOL(hAPP_int_bool(X0,sK9(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(cnf_transformation,[],[f1800]) ).
tff(f1800,plain,
! [X0: fun_int_bool] :
( ( ( hBOOL(hAPP_int_bool(X0,sK9(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK9(X0))) )
| ! [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK10(X0))))
| ! [X4: int] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f1797,f1799,f1798]) ).
tff(f1798,plain,
! [X0: fun_int_bool] :
( ? [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> ( hBOOL(hAPP_int_bool(X0,sK9(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK9(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1799,plain,
! [X0: fun_int_bool] :
( ? [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
=> hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK10(X0)))) ),
introduced(choice_axiom,[]) ).
tff(f1797,plain,
! [X0: fun_int_bool] :
( ( ? [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ! [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ? [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ! [X4: int] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
inference(rectify,[],[f1796]) ).
tff(f1796,plain,
! [X0: fun_int_bool] :
( ( ? [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ! [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ? [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
| ! [X1: int] :
( ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
inference(nnf_transformation,[],[f889]) ).
tff(f889,plain,
! [X0: fun_int_bool] :
( ? [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
<=> ? [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(rectify,[],[f526]) ).
tff(f526,axiom,
! [X51: fun_int_bool] :
( ? [X149: int] :
( hBOOL(hAPP_int_bool(X51,X149))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X149)) )
<=> ? [X149: nat] : hBOOL(hAPP_int_bool(X51,hAPP_nat_int(semiri1621563631at_int,X149))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_transfer__int__nat__quantifiers_I2_J) ).
tff(f4724,plain,
spl25_125,
inference(avatar_split_clause,[],[f2358,f4722]) ).
tff(f4722,plain,
( spl25_125
<=> ! [X0: fun_int_bool,X3: nat] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ~ hBOOL(hAPP_int_bool(X0,sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_125])]) ).
tff(f2358,plain,
! [X3: nat,X0: fun_int_bool] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ~ hBOOL(hAPP_int_bool(X0,sK8(X0))) ),
inference(cnf_transformation,[],[f1795]) ).
tff(f1795,plain,
! [X0: fun_int_bool] :
( ( ! [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK7(X0)))) )
& ( ! [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ( ~ hBOOL(hAPP_int_bool(X0,sK8(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK8(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f1792,f1794,f1793]) ).
tff(f1793,plain,
! [X0: fun_int_bool] :
( ? [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
=> ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK7(X0)))) ),
introduced(choice_axiom,[]) ).
tff(f1794,plain,
! [X0: fun_int_bool] :
( ? [X4: int] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) )
=> ( ~ hBOOL(hAPP_int_bool(X0,sK8(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK8(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1792,plain,
! [X0: fun_int_bool] :
( ( ! [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ? [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ! [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ? [X4: int] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
inference(rectify,[],[f1791]) ).
tff(f1791,plain,
! [X0: fun_int_bool] :
( ( ! [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ? [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ! [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
| ? [X1: int] :
( ~ hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
inference(nnf_transformation,[],[f1315]) ).
tff(f1315,plain,
! [X0: fun_int_bool] :
( ! [X1: int] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
<=> ! [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(ennf_transformation,[],[f888]) ).
tff(f888,plain,
! [X0: fun_int_bool] :
( ! [X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> hBOOL(hAPP_int_bool(X0,X1)) )
<=> ! [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(rectify,[],[f527]) ).
tff(f527,axiom,
! [X51: fun_int_bool] :
( ! [X149: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X149))
=> hBOOL(hAPP_int_bool(X51,X149)) )
<=> ! [X149: nat] : hBOOL(hAPP_int_bool(X51,hAPP_nat_int(semiri1621563631at_int,X149))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_transfer__int__nat__quantifiers_I1_J) ).
tff(f4719,plain,
( spl25_124
| ~ spl25_109
| ~ spl25_123 ),
inference(avatar_split_clause,[],[f4714,f4710,f4609,f4716]) ).
tff(f4716,plain,
( spl25_124
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_124])]) ).
tff(f4710,plain,
( spl25_123
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_123])]) ).
tff(f4714,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),pls))
| ~ spl25_109
| ~ spl25_123 ),
inference(forward_demodulation,[],[f4712,f4611]) ).
tff(f4712,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl25_123 ),
inference(avatar_component_clause,[],[f4710]) ).
tff(f4713,plain,
spl25_123,
inference(avatar_split_clause,[],[f2076,f4710]) ).
tff(f2076,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(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),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mn) ).
tff(f4702,plain,
( ~ spl25_122
| ~ spl25_102
| ~ spl25_109 ),
inference(avatar_split_clause,[],[f4654,f4609,f4447,f4699]) ).
tff(f4699,plain,
( spl25_122
<=> ( pls = hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(semiri1621563631at_int,n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_122])]) ).
tff(f4447,plain,
( spl25_102
<=> ! [X0: int] : ( pls != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_102])]) ).
tff(f4654,plain,
( ( pls != hAPP_int_int(plus_plus_int(pls),hAPP_nat_int(semiri1621563631at_int,n)) )
| ~ spl25_102
| ~ spl25_109 ),
inference(superposition,[],[f4448,f4611]) ).
tff(f4448,plain,
( ! [X0: int] : ( pls != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) )
| ~ spl25_102 ),
inference(avatar_component_clause,[],[f4447]) ).
tff(f4665,plain,
spl25_121,
inference(avatar_split_clause,[],[f3622,f4662]) ).
tff(f4662,plain,
( spl25_121
<=> ( pls = hAPP_nat_int(power_power_int(pls),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_121])]) ).
tff(f3622,plain,
pls = hAPP_nat_int(power_power_int(pls),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(forward_demodulation,[],[f3621,f3028]) ).
tff(f3028,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),pls) = X0 ),
inference(definition_unfolding,[],[f2111,f2000]) ).
tff(f2111,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),zero_zero_int) = X0 ),
inference(cnf_transformation,[],[f739]) ).
tff(f739,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),zero_zero_int) = X0 ),
inference(rectify,[],[f358]) ).
tff(f358,axiom,
! [X122: int] : ( hAPP_int_int(plus_plus_int(X122),zero_zero_int) = X122 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
tff(f3621,plain,
pls = hAPP_nat_int(power_power_int(pls),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),pls)))),
inference(forward_demodulation,[],[f3620,f3024]) ).
tff(f3024,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(pls),X0) = X0 ),
inference(definition_unfolding,[],[f2106,f2000]) ).
tff(f2106,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
inference(cnf_transformation,[],[f734]) ).
tff(f734,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X14: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),X14) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zadd__0) ).
tff(f3620,plain,
pls = hAPP_nat_int(power_power_int(pls),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls))))),
inference(forward_demodulation,[],[f3323,f3465]) ).
tff(f3465,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),one_one_int) = hAPP_int_int(plus_plus_int(one_one_int),X0) ),
inference(forward_demodulation,[],[f3464,f2080]) ).
tff(f2080,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f708]) ).
tff(f708,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(rectify,[],[f177]) ).
tff(f177,axiom,
! [X18: int] : ( number_number_of_int(X18) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
tff(f3464,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),one_one_int) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) ),
inference(forward_demodulation,[],[f3041,f2080]) ).
tff(f3041,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),one_one_int)) ),
inference(definition_unfolding,[],[f2158,f2134]) ).
tff(f2134,plain,
! [X0: int] : ( succ(X0) = hAPP_int_int(plus_plus_int(X0),one_one_int) ),
inference(cnf_transformation,[],[f762]) ).
tff(f762,plain,
! [X0: int] : ( succ(X0) = hAPP_int_int(plus_plus_int(X0),one_one_int) ),
inference(rectify,[],[f574]) ).
tff(f574,axiom,
! [X18: int] : ( succ(X18) = hAPP_int_int(plus_plus_int(X18),one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_succ__def) ).
tff(f2158,plain,
! [X0: int] : ( number_number_of_int(succ(X0)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) ),
inference(cnf_transformation,[],[f786]) ).
tff(f786,plain,
! [X0: int] : ( number_number_of_int(succ(X0)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) ),
inference(rectify,[],[f584]) ).
tff(f584,axiom,
! [X230: int] : ( number_number_of_int(succ(X230)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X230)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_number__of__succ) ).
tff(f3323,plain,
pls = hAPP_nat_int(power_power_int(pls),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))),
inference(equality_resolution,[],[f3151]) ).
tff(f3151,plain,
! [X0: int] :
( ( pls = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))) )
| ( pls != X0 ) ),
inference(definition_unfolding,[],[f2330,f2000,f2135,f2970,f2000]) ).
tff(f2970,plain,
! [X0: int] : ( bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),one_one_int) ),
inference(definition_unfolding,[],[f2095,f2134,f2135]) ).
tff(f2095,plain,
! [X0: int] : ( bit1(X0) = succ(bit0(X0)) ),
inference(cnf_transformation,[],[f723]) ).
tff(f723,plain,
! [X0: int] : ( bit1(X0) = succ(bit0(X0)) ),
inference(rectify,[],[f569]) ).
tff(f569,axiom,
! [X18: int] : ( bit1(X18) = succ(bit0(X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_succ__Bit0) ).
tff(f2135,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f763]) ).
tff(f763,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X18: int] : ( bit0(X18) = hAPP_int_int(plus_plus_int(X18),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
tff(f2330,plain,
! [X0: int] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f1777]) ).
tff(f1777,plain,
! [X0: int] :
( ( ( zero_zero_int = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) )
| ( zero_zero_int != X0 ) )
& ( ( zero_zero_int = X0 )
| ( zero_zero_int != hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) ) ) ),
inference(nnf_transformation,[],[f874]) ).
tff(f874,plain,
! [X0: int] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) )
<=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X2: int] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))) )
<=> ( zero_zero_int = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_zero__eq__power2) ).
tff(f4660,plain,
spl25_120,
inference(avatar_split_clause,[],[f3616,f4657]) ).
tff(f4657,plain,
( spl25_120
<=> ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_120])]) ).
tff(f3616,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(forward_demodulation,[],[f3615,f3028]) ).
tff(f3615,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),pls)))),
inference(forward_demodulation,[],[f3614,f3024]) ).
tff(f3614,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls))),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls))))),
inference(forward_demodulation,[],[f3322,f3465]) ).
tff(f3322,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))),
inference(equality_resolution,[],[f3149]) ).
tff(f3149,plain,
! [X0: real] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))) )
| ( zero_zero_real != X0 ) ),
inference(definition_unfolding,[],[f2328,f2135,f2970]) ).
tff(f2328,plain,
! [X0: real] :
( ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real )
| ( zero_zero_real != X0 ) ),
inference(cnf_transformation,[],[f1776]) ).
tff(f1776,plain,
! [X0: real] :
( ( ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real )
| ( zero_zero_real != X0 ) )
& ( ( zero_zero_real = X0 )
| ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ) ),
inference(nnf_transformation,[],[f873]) ).
tff(f873,plain,
! [X0: real] :
( ( hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real )
<=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X2: real] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))) )
<=> ( zero_zero_real = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__eq__power2) ).
tff(f4652,plain,
spl25_119,
inference(avatar_split_clause,[],[f3296,f4650]) ).
tff(f4650,plain,
( spl25_119
<=> ! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_119])]) ).
tff(f3296,plain,
! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
inference(definition_unfolding,[],[f2894,f2000]) ).
tff(f2894,plain,
! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(cnf_transformation,[],[f1962]) ).
tff(f1962,plain,
! [X0: bool,X1: bool,X2: int] :
( sP1(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,[],[f1961]) ).
tff(f1961,plain,
! [X0: bool,X1: bool,X2: int] :
( sP1(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,[],[f1711]) ).
tff(f1711,plain,
! [X0: bool,X1: bool,X2: int] :
( sP1(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,[],[f1670,f1710]) ).
tff(f1710,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)) ) )
| ~ sP1(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1670,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,[],[f1243]) ).
tff(f1243,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,[],[f645]) ).
tff(f645,axiom,
! [X244: bool,X51: bool,X0: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( hBOOL(X51)
<=> hBOOL(X244) ) )
=> ( ( 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(X244) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_imp__le__cong) ).
tff(f4648,plain,
spl25_118,
inference(avatar_split_clause,[],[f3291,f4646]) ).
tff(f4646,plain,
( spl25_118
<=> ! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_118])]) ).
tff(f3291,plain,
! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
inference(definition_unfolding,[],[f2887,f2000]) ).
tff(f2887,plain,
! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(cnf_transformation,[],[f1957]) ).
tff(f1957,plain,
! [X0: bool,X1: bool,X2: int] :
( sP0(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,[],[f1956]) ).
tff(f1956,plain,
! [X0: bool,X1: bool,X2: int] :
( sP0(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,[],[f1709]) ).
tff(f1709,plain,
! [X0: bool,X1: bool,X2: int] :
( sP0(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,[],[f1669,f1708]) ).
tff(f1708,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)) ) )
| ~ sP0(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1669,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,[],[f1242]) ).
tff(f1242,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,[],[f644]) ).
tff(f644,axiom,
! [X244: bool,X51: bool,X0: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ( hBOOL(X51)
<=> hBOOL(X244) ) )
=> ( ( hBOOL(X51)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
<=> ( hBOOL(X244)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_conj__le__cong) ).
tff(f4644,plain,
spl25_117,
inference(avatar_split_clause,[],[f2898,f4642]) ).
tff(f4642,plain,
( spl25_117
<=> ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_117])]) ).
tff(f2898,plain,
! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f1964]) ).
tff(f1964,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)) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f1963]) ).
tff(f1963,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)) )
| ~ sP2(X1,X2,X0) ),
inference(nnf_transformation,[],[f1712]) ).
tff(f1712,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)) )
| ~ sP2(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f4640,plain,
spl25_116,
inference(avatar_split_clause,[],[f2897,f4638]) ).
tff(f4638,plain,
( spl25_116
<=> ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_116])]) ).
tff(f2897,plain,
! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f1964]) ).
tff(f4636,plain,
spl25_115,
inference(avatar_split_clause,[],[f2602,f4634]) ).
tff(f4634,plain,
( spl25_115
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_115])]) ).
tff(f2602,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f1874,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,[],[f1056]) ).
tff(f1056,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(semiri984289939at_nat,X0) = hAPP_nat_nat(semiri984289939at_nat,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f219]) ).
tff(f219,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_218_of__nat__eq__iff) ).
tff(f4632,plain,
spl25_114,
inference(avatar_split_clause,[],[f2596,f4630]) ).
tff(f4630,plain,
( spl25_114
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_114])]) ).
tff(f2596,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
inference(cnf_transformation,[],[f1871]) ).
tff(f1871,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,[],[f1054]) ).
tff(f1054,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f220]) ).
tff(f220,axiom,
! [X26: nat,X15: nat] :
( ( hAPP_nat_int(semiri1621563631at_int,X15) = hAPP_nat_int(semiri1621563631at_int,X26) )
<=> ( X15 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
tff(f4628,plain,
spl25_113,
inference(avatar_split_clause,[],[f2594,f4626]) ).
tff(f4626,plain,
( spl25_113
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_113])]) ).
tff(f2594,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f1870,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,[],[f1053]) ).
tff(f1053,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_real(semiri132038758t_real,X0) = hAPP_nat_real(semiri132038758t_real,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f218]) ).
tff(f218,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_217_of__nat__eq__iff) ).
tff(f4624,plain,
spl25_112,
inference(avatar_split_clause,[],[f2234,f4622]) ).
tff(f4622,plain,
( spl25_112
<=> ! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_112])]) ).
tff(f2234,plain,
! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(cnf_transformation,[],[f1729]) ).
tff(f1729,plain,
! [X0: int] :
( ( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ( zero_zero_nat != number_number_of_nat(X0) ) ) ),
inference(nnf_transformation,[],[f836]) ).
tff(f836,plain,
! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(rectify,[],[f558]) ).
tff(f558,axiom,
! [X56: int] :
( ( zero_zero_nat = number_number_of_nat(X56) )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X56),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_eq__0__number__of) ).
tff(f4620,plain,
spl25_111,
inference(avatar_split_clause,[],[f2233,f4618]) ).
tff(f4618,plain,
( spl25_111
<=> ! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ( zero_zero_nat != number_number_of_nat(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_111])]) ).
tff(f2233,plain,
! [X0: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ( zero_zero_nat != number_number_of_nat(X0) ) ),
inference(cnf_transformation,[],[f1729]) ).
tff(f4616,plain,
spl25_110,
inference(avatar_split_clause,[],[f2202,f4614]) ).
tff(f4614,plain,
( spl25_110
<=> ! [X0: real] :
( ( zero_zero_real != sqrt(X0) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_110])]) ).
tff(f2202,plain,
! [X0: real] :
( ( zero_zero_real != sqrt(X0) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
inference(cnf_transformation,[],[f1299]) ).
tff(f1299,plain,
! [X0: real] :
( ( zero_zero_real != sqrt(X0) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0)) ),
inference(ennf_transformation,[],[f820]) ).
tff(f820,plain,
! [X0: real] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X0))
=> ( zero_zero_real != sqrt(X0) ) ),
inference(rectify,[],[f695]) ).
tff(f695,axiom,
! [X5: real] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X5))
=> ( zero_zero_real != sqrt(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_real__sqrt__not__eq__zero) ).
tff(f4612,plain,
( spl25_109
| ~ spl25_54
| ~ spl25_105 ),
inference(avatar_split_clause,[],[f4601,f4459,f4207,f4609]) ).
tff(f4207,plain,
( spl25_54
<=> ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_54])]) ).
tff(f4459,plain,
( spl25_105
<=> ! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_105])]) ).
tff(f4601,plain,
( ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ spl25_54
| ~ spl25_105 ),
inference(trivial_inequality_removal,[],[f4600]) ).
tff(f4600,plain,
( ( pls != pls )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ spl25_54
| ~ spl25_105 ),
inference(superposition,[],[f4460,f4209]) ).
tff(f4209,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) )
| ~ spl25_54 ),
inference(avatar_component_clause,[],[f4207]) ).
tff(f4460,plain,
( ! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) )
| ~ spl25_105 ),
inference(avatar_component_clause,[],[f4459]) ).
tff(f4475,plain,
spl25_108,
inference(avatar_split_clause,[],[f3454,f4472]) ).
tff(f4472,plain,
( spl25_108
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_108])]) ).
tff(f3454,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(forward_demodulation,[],[f3453,f3449]) ).
tff(f3449,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),one_one_int)),hAPP_int_int(plus_plus_int(pls),one_one_int))),
inference(forward_demodulation,[],[f3013,f2979]) ).
tff(f2979,plain,
pls = hAPP_int_int(plus_plus_int(pls),pls),
inference(definition_unfolding,[],[f2011,f2135]) ).
tff(f2011,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(f3013,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int))),
inference(definition_unfolding,[],[f2066,f2135,f2970]) ).
tff(f2066,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__add__one__is__two) ).
tff(f3453,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),one_one_int)),hAPP_int_int(plus_plus_int(pls),one_one_int))))),
inference(forward_demodulation,[],[f3017,f2979]) ).
tff(f3017,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int))))),
inference(definition_unfolding,[],[f2072,f2000,f2135,f2970]) ).
tff(f2072,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,[],[f589]) ).
tff(f589,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_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
tff(f4470,plain,
spl25_107,
inference(avatar_split_clause,[],[f3452,f4467]) ).
tff(f4467,plain,
( spl25_107
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_107])]) ).
tff(f3452,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
inference(forward_demodulation,[],[f3451,f3445]) ).
tff(f3445,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),one_one_int)),hAPP_int_int(plus_plus_int(pls),one_one_int))),
inference(forward_demodulation,[],[f3009,f2979]) ).
tff(f3009,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int))),
inference(definition_unfolding,[],[f2062,f2135,f2970]) ).
tff(f2062,plain,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(cnf_transformation,[],[f46]) ).
tff(f46,axiom,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_nat__1__add__1) ).
tff(f3451,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),one_one_int)),hAPP_int_int(plus_plus_int(pls),one_one_int))))),
inference(forward_demodulation,[],[f3015,f2979]) ).
tff(f3015,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int))))),
inference(definition_unfolding,[],[f2069,f2135,f2970]) ).
tff(f2069,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
inference(cnf_transformation,[],[f297]) ).
tff(f297,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_pos2) ).
tff(f4465,plain,
spl25_106,
inference(avatar_split_clause,[],[f3219,f4463]) ).
tff(f4463,plain,
( spl25_106
<=> ! [X0: int,X1: int] :
( ( pls = X1 )
| ( hAPP_int_int(plus_plus_int(X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_106])]) ).
tff(f3219,plain,
! [X0: int,X1: int] :
( ( pls = X1 )
| ( hAPP_int_int(plus_plus_int(X0),X1) != X0 ) ),
inference(definition_unfolding,[],[f2562,f2000]) ).
tff(f2562,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( hAPP_int_int(plus_plus_int(X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f1844]) ).
tff(f1844,plain,
! [X0: int,X1: int] :
( ( ( hAPP_int_int(plus_plus_int(X0),X1) = X0 )
| ( zero_zero_int != X1 ) )
& ( ( zero_zero_int = X1 )
| ( hAPP_int_int(plus_plus_int(X0),X1) != X0 ) ) ),
inference(nnf_transformation,[],[f1043]) ).
tff(f1043,plain,
! [X0: int,X1: int] :
( ( hAPP_int_int(plus_plus_int(X0),X1) = X0 )
<=> ( zero_zero_int = X1 ) ),
inference(rectify,[],[f352]) ).
tff(f352,axiom,
! [X78: int,X2: int] :
( ( hAPP_int_int(plus_plus_int(X78),X2) = X78 )
<=> ( zero_zero_int = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
tff(f4461,plain,
spl25_105,
inference(avatar_split_clause,[],[f3186,f4459]) ).
tff(f3186,plain,
! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) ),
inference(definition_unfolding,[],[f2414,f2000,f2000]) ).
tff(f2414,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f1324]) ).
tff(f1324,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[],[f939]) ).
tff(f939,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(f4457,plain,
spl25_104,
inference(avatar_split_clause,[],[f3088,f4455]) ).
tff(f4455,plain,
( spl25_104
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != hAPP_int_int(plus_plus_int(X0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_104])]) ).
tff(f3088,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != hAPP_int_int(plus_plus_int(X0),X0) ) ),
inference(definition_unfolding,[],[f2237,f2135]) ).
tff(f2237,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f1731]) ).
tff(f1731,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f838]) ).
tff(f838,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X8: int] :
( ( pls = bit0(X8) )
<=> ( pls = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I44_J) ).
tff(f4453,plain,
spl25_103,
inference(avatar_split_clause,[],[f3060,f4451]) ).
tff(f4451,plain,
( spl25_103
<=> ! [X0: nat] :
( ( pls = hAPP_nat_int(power_power_int(pls),X0) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_103])]) ).
tff(f3060,plain,
! [X0: nat] :
( ( pls = hAPP_nat_int(power_power_int(pls),X0) )
| ( zero_zero_nat = X0 ) ),
inference(definition_unfolding,[],[f2185,f2000,f2000]) ).
tff(f2185,plain,
! [X0: nat] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f1290]) ).
tff(f1290,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,[],[f810]) ).
tff(f810,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(f4449,plain,
spl25_102,
inference(avatar_split_clause,[],[f3039,f4447]) ).
tff(f3039,plain,
! [X0: int] : ( pls != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
inference(definition_unfolding,[],[f2156,f2000]) ).
tff(f2156,plain,
! [X0: int] : ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f784]) ).
tff(f784,plain,
! [X0: int] : ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X14: int] : ( zero_zero_int != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X14)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_odd__nonzero) ).
tff(f4445,plain,
spl25_101,
inference(avatar_split_clause,[],[f3022,f4443]) ).
tff(f4443,plain,
( spl25_101
<=> ! [X0: int] : ( pls != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_101])]) ).
tff(f3022,plain,
! [X0: int] : ( pls != hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X0)),one_one_int) ),
inference(definition_unfolding,[],[f2078,f2970]) ).
tff(f2078,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f706]) ).
tff(f706,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X18: int] : ( pls != bit1(X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_rel__simps_I46_J) ).
tff(f4441,plain,
spl25_100,
inference(avatar_split_clause,[],[f3016,f4438]) ).
tff(f4438,plain,
( spl25_100
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_100])]) ).
tff(f3016,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(definition_unfolding,[],[f2071,f2000]) ).
tff(f2071,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_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),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_zero__less__two) ).
tff(f4436,plain,
( spl25_99
| ~ spl25_6
| ~ spl25_67 ),
inference(avatar_split_clause,[],[f4325,f4273,f3957,f4434]) ).
tff(f4434,plain,
( spl25_99
<=> ! [X0: int,X1: int] :
( ( number_number_of_int(X1) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_99])]) ).
tff(f3957,plain,
( spl25_6
<=> ! [X0: int] : ( number_number_of_int(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_6])]) ).
tff(f4273,plain,
( spl25_67
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_67])]) ).
tff(f4325,plain,
( ! [X0: int,X1: int] :
( ( number_number_of_int(X1) != X0 )
| ( X0 = X1 ) )
| ~ spl25_6
| ~ spl25_67 ),
inference(superposition,[],[f4274,f3958]) ).
tff(f3958,plain,
( ! [X0: int] : ( number_number_of_int(X0) = X0 )
| ~ spl25_6 ),
inference(avatar_component_clause,[],[f3957]) ).
tff(f4274,plain,
( ! [X0: int,X1: int] :
( ( number_number_of_int(X0) != number_number_of_int(X1) )
| ( X0 = X1 ) )
| ~ spl25_67 ),
inference(avatar_component_clause,[],[f4273]) ).
tff(f4432,plain,
spl25_98,
inference(avatar_split_clause,[],[f2560,f4430]) ).
tff(f4430,plain,
( spl25_98
<=> ! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( hAPP_real_real(plus_plus_real(X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_98])]) ).
tff(f2560,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( hAPP_real_real(plus_plus_real(X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f1843]) ).
tff(f1843,plain,
! [X0: real,X1: real] :
( ( ( hAPP_real_real(plus_plus_real(X0),X1) = X0 )
| ( zero_zero_real != X1 ) )
& ( ( zero_zero_real = X1 )
| ( hAPP_real_real(plus_plus_real(X0),X1) != X0 ) ) ),
inference(nnf_transformation,[],[f1042]) ).
tff(f1042,plain,
! [X0: real,X1: real] :
( ( hAPP_real_real(plus_plus_real(X0),X1) = X0 )
<=> ( zero_zero_real = X1 ) ),
inference(rectify,[],[f350]) ).
tff(f350,axiom,
! [X78: real,X2: real] :
( ( hAPP_real_real(plus_plus_real(X78),X2) = X78 )
<=> ( zero_zero_real = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_add__0__iff) ).
tff(f4428,plain,
spl25_97,
inference(avatar_split_clause,[],[f2555,f4426]) ).
tff(f4426,plain,
( spl25_97
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( zero_zero_nat != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_97])]) ).
tff(f2555,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( zero_zero_nat != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ),
inference(cnf_transformation,[],[f1840]) ).
tff(f1840,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = hAPP_nat_nat(plus_plus_nat(X0),X1) )
| ( zero_zero_nat != X1 )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ) ),
inference(flattening,[],[f1839]) ).
tff(f1839,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = hAPP_nat_nat(plus_plus_nat(X0),X1) )
| ( zero_zero_nat != X1 )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ) ),
inference(nnf_transformation,[],[f1040]) ).
tff(f1040,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = hAPP_nat_nat(plus_plus_nat(X0),X1) )
<=> ( ( zero_zero_nat = X1 )
& ( zero_zero_nat = X0 ) ) ),
inference(rectify,[],[f212]) ).
tff(f212,axiom,
! [X26: nat,X15: nat] :
( ( zero_zero_nat = hAPP_nat_nat(plus_plus_nat(X26),X15) )
<=> ( ( zero_zero_nat = X15 )
& ( zero_zero_nat = X26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__is__0) ).
tff(f4424,plain,
spl25_96,
inference(avatar_split_clause,[],[f2554,f4422]) ).
tff(f4422,plain,
( spl25_96
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_96])]) ).
tff(f2554,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != hAPP_nat_nat(plus_plus_nat(X0),X1) ) ),
inference(cnf_transformation,[],[f1840]) ).
tff(f4420,plain,
spl25_95,
inference(avatar_split_clause,[],[f2549,f4418]) ).
tff(f4418,plain,
( spl25_95
<=> ! [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,[spl25_95])]) ).
tff(f2549,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
inference(cnf_transformation,[],[f1836]) ).
tff(f1836,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,[],[f1835]) ).
tff(f1835,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,[],[f1038]) ).
tff(f1038,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,[],[f397]) ).
tff(f397,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_396_nat__power__eq__0__iff) ).
tff(f4416,plain,
spl25_94,
inference(avatar_split_clause,[],[f2426,f4414]) ).
tff(f4414,plain,
( spl25_94
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_94])]) ).
tff(f2426,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f1334]) ).
tff(f1334,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( hAPP_nat_nat(plus_plus_nat(X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f947]) ).
tff(f947,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(plus_plus_nat(X0),X1) = X0 )
=> ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f211]) ).
tff(f211,axiom,
! [X12: nat,X13: nat] :
( ( hAPP_nat_nat(plus_plus_nat(X12),X13) = X12 )
=> ( zero_zero_nat = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_add__eq__self__zero) ).
tff(f4412,plain,
spl25_93,
inference(avatar_split_clause,[],[f2413,f4410]) ).
tff(f4410,plain,
( spl25_93
<=> ! [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,[spl25_93])]) ).
tff(f2413,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) )
| ( zero_zero_real = X1 ) ),
inference(cnf_transformation,[],[f1323]) ).
tff(f1323,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) )
| ( zero_zero_real = X1 ) ),
inference(ennf_transformation,[],[f938]) ).
tff(f938,plain,
! [X0: nat,X1: real] :
( ( zero_zero_real != X1 )
=> ( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) ) ),
inference(rectify,[],[f231]) ).
tff(f231,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_230_field__power__not__zero) ).
tff(f4408,plain,
spl25_92,
inference(avatar_split_clause,[],[f2375,f4406]) ).
tff(f4406,plain,
( spl25_92
<=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_92])]) ).
tff(f2375,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1))),
inference(cnf_transformation,[],[f902]) ).
tff(f902,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),X1))),
inference(rectify,[],[f629]) ).
tff(f629,axiom,
! [X13: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),hAPP_nat_nat(plus_plus_nat(X13),X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_le__add1) ).
tff(f4404,plain,
spl25_91,
inference(avatar_split_clause,[],[f2374,f4402]) ).
tff(f4402,plain,
( spl25_91
<=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_91])]) ).
tff(f2374,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))),
inference(cnf_transformation,[],[f901]) ).
tff(f901,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(plus_plus_nat(X1),X0))),
inference(rectify,[],[f628]) ).
tff(f628,axiom,
! [X13: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),hAPP_nat_nat(plus_plus_nat(X12),X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_le__add2) ).
tff(f4400,plain,
spl25_90,
inference(avatar_split_clause,[],[f2372,f4398]) ).
tff(f4398,plain,
( spl25_90
<=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_90])]) ).
tff(f2372,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0) ),
inference(cnf_transformation,[],[f899]) ).
tff(f899,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(plus_plus_nat(X0),X1) = hAPP_nat_nat(plus_plus_nat(X1),X0) ),
inference(rectify,[],[f345]) ).
tff(f345,axiom,
! [X119: nat,X120: nat] : ( hAPP_nat_nat(plus_plus_nat(X119),X120) = hAPP_nat_nat(plus_plus_nat(X120),X119) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f4396,plain,
spl25_89,
inference(avatar_split_clause,[],[f2370,f4394]) ).
tff(f4394,plain,
( spl25_89
<=> ! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_89])]) ).
tff(f2370,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0) ),
inference(cnf_transformation,[],[f897]) ).
tff(f897,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X14: int,X11: int] : ( hAPP_int_int(plus_plus_int(X14),X11) = hAPP_int_int(plus_plus_int(X11),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
tff(f4392,plain,
( spl25_88
| ~ spl25_58
| ~ spl25_66 ),
inference(avatar_split_clause,[],[f4319,f4269,f4227,f4390]) ).
tff(f4390,plain,
( spl25_88
<=> ! [X0: int] :
( ( one_one_real != number267125858f_real(X0) )
| ( one_one_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_88])]) ).
tff(f4227,plain,
( spl25_58
<=> ( one_one_real = number267125858f_real(one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_58])]) ).
tff(f4269,plain,
( spl25_66
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number267125858f_real(X0) != number267125858f_real(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_66])]) ).
tff(f4319,plain,
( ! [X0: int] :
( ( one_one_real != number267125858f_real(X0) )
| ( one_one_int = X0 ) )
| ~ spl25_58
| ~ spl25_66 ),
inference(superposition,[],[f4270,f4229]) ).
tff(f4229,plain,
( ( one_one_real = number267125858f_real(one_one_int) )
| ~ spl25_58 ),
inference(avatar_component_clause,[],[f4227]) ).
tff(f4270,plain,
( ! [X0: int,X1: int] :
( ( number267125858f_real(X0) != number267125858f_real(X1) )
| ( X0 = X1 ) )
| ~ spl25_66 ),
inference(avatar_component_clause,[],[f4269]) ).
tff(f4388,plain,
spl25_87,
inference(avatar_split_clause,[],[f2369,f4386]) ).
tff(f4386,plain,
( spl25_87
<=> ! [X0: real,X1: real] : ( hAPP_real_real(plus_plus_real(X0),X1) = hAPP_real_real(plus_plus_real(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_87])]) ).
tff(f2369,plain,
! [X0: real,X1: real] : ( hAPP_real_real(plus_plus_real(X0),X1) = hAPP_real_real(plus_plus_real(X1),X0) ),
inference(cnf_transformation,[],[f896]) ).
tff(f896,plain,
! [X0: real,X1: real] : ( hAPP_real_real(plus_plus_real(X0),X1) = hAPP_real_real(plus_plus_real(X1),X0) ),
inference(rectify,[],[f344]) ).
tff(f344,axiom,
! [X119: real,X120: real] : ( hAPP_real_real(plus_plus_real(X119),X120) = hAPP_real_real(plus_plus_real(X120),X119) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f4384,plain,
spl25_86,
inference(avatar_split_clause,[],[f2368,f4382]) ).
tff(f4382,plain,
( spl25_86
<=> ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_86])]) ).
tff(f2368,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)),
inference(cnf_transformation,[],[f895]) ).
tff(f895,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X0)),
inference(rectify,[],[f175]) ).
tff(f175,axiom,
! [X19: nat,X20: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X19),X20)),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_not__add__less1) ).
tff(f4380,plain,
spl25_85,
inference(avatar_split_clause,[],[f2367,f4378]) ).
tff(f4378,plain,
( spl25_85
<=> ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_85])]) ).
tff(f2367,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)),
inference(cnf_transformation,[],[f894]) ).
tff(f894,plain,
! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X0),X1)),X1)),
inference(rectify,[],[f176]) ).
tff(f176,axiom,
! [X20: nat,X19: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X20),X19)),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_not__add__less2) ).
tff(f4376,plain,
spl25_84,
inference(avatar_split_clause,[],[f2251,f4374]) ).
tff(f4374,plain,
( spl25_84
<=> ! [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,[spl25_84])]) ).
tff(f2251,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,[],[f1738]) ).
tff(f1738,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,[],[f845]) ).
tff(f845,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
<=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f615]) ).
tff(f615,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_614_le__0__eq) ).
tff(f4372,plain,
spl25_83,
inference(avatar_split_clause,[],[f2243,f4370]) ).
tff(f4370,plain,
( spl25_83
<=> ! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != hAPP_real_real(plus_plus_real(X0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_83])]) ).
tff(f2243,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != hAPP_real_real(plus_plus_real(X0),X0) ) ),
inference(cnf_transformation,[],[f1734]) ).
tff(f1734,plain,
! [X0: real] :
( ( ( zero_zero_real = hAPP_real_real(plus_plus_real(X0),X0) )
| ( zero_zero_real != X0 ) )
& ( ( zero_zero_real = X0 )
| ( zero_zero_real != hAPP_real_real(plus_plus_real(X0),X0) ) ) ),
inference(nnf_transformation,[],[f841]) ).
tff(f841,plain,
! [X0: real] :
( ( zero_zero_real = hAPP_real_real(plus_plus_real(X0),X0) )
<=> ( zero_zero_real = X0 ) ),
inference(rectify,[],[f362]) ).
tff(f362,axiom,
! [X2: real] :
( ( zero_zero_real = hAPP_real_real(plus_plus_real(X2),X2) )
<=> ( zero_zero_real = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_double__zero__sym) ).
tff(f4368,plain,
spl25_82,
inference(avatar_split_clause,[],[f2201,f4366]) ).
tff(f4366,plain,
( spl25_82
<=> ! [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,[spl25_82])]) ).
tff(f2201,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f1298]) ).
tff(f1298,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f819]) ).
tff(f819,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(rectify,[],[f196]) ).
tff(f196,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_195_gr0I) ).
tff(f4364,plain,
spl25_81,
inference(avatar_split_clause,[],[f2183,f4362]) ).
tff(f4362,plain,
( spl25_81
<=> ! [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,[spl25_81])]) ).
tff(f2183,plain,
! [X0: nat] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f1289]) ).
tff(f1289,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,[],[f809]) ).
tff(f809,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(f4360,plain,
spl25_80,
inference(avatar_split_clause,[],[f2181,f4358]) ).
tff(f4358,plain,
( spl25_80
<=> ! [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,[spl25_80])]) ).
tff(f2181,plain,
! [X0: nat] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f1288]) ).
tff(f1288,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,[],[f808]) ).
tff(f808,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(f4356,plain,
spl25_79,
inference(avatar_split_clause,[],[f2161,f4354]) ).
tff(f4354,plain,
( spl25_79
<=> ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_79])]) ).
tff(f2161,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
inference(cnf_transformation,[],[f789]) ).
tff(f789,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
inference(rectify,[],[f271]) ).
tff(f271,axiom,
! [X77: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X77),hAPP_int_int(plus_plus_int(X77),one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__add__one) ).
tff(f4352,plain,
spl25_78,
inference(avatar_split_clause,[],[f2160,f4350]) ).
tff(f4350,plain,
( spl25_78
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),one_one_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_78])]) ).
tff(f2160,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),one_one_nat))),
inference(cnf_transformation,[],[f788]) ).
tff(f788,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(plus_plus_nat(X0),one_one_nat))),
inference(rectify,[],[f270]) ).
tff(f270,axiom,
! [X77: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X77),hAPP_nat_nat(plus_plus_nat(X77),one_one_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__add__one) ).
tff(f4348,plain,
( spl25_77
| ~ spl25_4
| ~ spl25_66 ),
inference(avatar_split_clause,[],[f4318,f4269,f3947,f4346]) ).
tff(f4346,plain,
( spl25_77
<=> ! [X0: int] :
( ( zero_zero_real != number267125858f_real(X0) )
| ( pls = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_77])]) ).
tff(f3947,plain,
( spl25_4
<=> ( zero_zero_real = number267125858f_real(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_4])]) ).
tff(f4318,plain,
( ! [X0: int] :
( ( zero_zero_real != number267125858f_real(X0) )
| ( pls = X0 ) )
| ~ spl25_4
| ~ spl25_66 ),
inference(superposition,[],[f4270,f3949]) ).
tff(f3949,plain,
( ( zero_zero_real = number267125858f_real(pls) )
| ~ spl25_4 ),
inference(avatar_component_clause,[],[f3947]) ).
tff(f4344,plain,
spl25_76,
inference(avatar_split_clause,[],[f2159,f4342]) ).
tff(f4342,plain,
( spl25_76
<=> ! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),hAPP_real_real(plus_plus_real(X0),one_one_real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_76])]) ).
tff(f2159,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),hAPP_real_real(plus_plus_real(X0),one_one_real))),
inference(cnf_transformation,[],[f787]) ).
tff(f787,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),hAPP_real_real(plus_plus_real(X0),one_one_real))),
inference(rectify,[],[f269]) ).
tff(f269,axiom,
! [X77: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X77),hAPP_real_real(plus_plus_real(X77),one_one_real))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_less__add__one) ).
tff(f4340,plain,
spl25_75,
inference(avatar_split_clause,[],[f2068,f4337]) ).
tff(f4337,plain,
( spl25_75
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_75])]) ).
tff(f2068,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_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),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_zero__less__two) ).
tff(f4303,plain,
spl25_74,
inference(avatar_split_clause,[],[f3092,f4301]) ).
tff(f4301,plain,
( spl25_74
<=> ! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_74])]) ).
tff(f3092,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
inference(definition_unfolding,[],[f2241,f2000]) ).
tff(f2241,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f1733,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,[],[f840]) ).
tff(f840,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(f4299,plain,
spl25_73,
inference(avatar_split_clause,[],[f3035,f4297]) ).
tff(f4297,plain,
( spl25_73
<=> ! [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,[spl25_73])]) ).
tff(f3035,plain,
! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(definition_unfolding,[],[f2152,f2000]) ).
tff(f2152,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,[],[f780]) ).
tff(f780,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,[],[f513]) ).
tff(f513,axiom,
! [X202: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X202))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_zero__le__imp__of__nat) ).
tff(f4295,plain,
spl25_72,
inference(avatar_split_clause,[],[f3033,f4293]) ).
tff(f4293,plain,
( spl25_72
<=> ! [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,[spl25_72])]) ).
tff(f3033,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f2143,f2000]) ).
tff(f2143,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,[],[f771]) ).
tff(f771,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X18: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X18)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
tff(f4291,plain,
spl25_71,
inference(avatar_split_clause,[],[f2896,f4289]) ).
tff(f4289,plain,
( spl25_71
<=> ! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_71])]) ).
tff(f2896,plain,
! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f1962]) ).
tff(f4287,plain,
spl25_70,
inference(avatar_split_clause,[],[f2895,f4285]) ).
tff(f4285,plain,
( spl25_70
<=> ! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_70])]) ).
tff(f2895,plain,
! [X2: int,X0: bool,X1: bool] :
( sP1(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f1962]) ).
tff(f4283,plain,
spl25_69,
inference(avatar_split_clause,[],[f2889,f4281]) ).
tff(f4281,plain,
( spl25_69
<=> ! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_69])]) ).
tff(f2889,plain,
! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f1957]) ).
tff(f4279,plain,
spl25_68,
inference(avatar_split_clause,[],[f2888,f4277]) ).
tff(f4277,plain,
( spl25_68
<=> ! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_68])]) ).
tff(f2888,plain,
! [X2: int,X0: bool,X1: bool] :
( sP0(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f1957]) ).
tff(f4275,plain,
spl25_67,
inference(avatar_split_clause,[],[f2536,f4273]) ).
tff(f2536,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ),
inference(cnf_transformation,[],[f1828]) ).
tff(f1828,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(f4271,plain,
spl25_66,
inference(avatar_split_clause,[],[f2534,f4269]) ).
tff(f2534,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number267125858f_real(X0) != number267125858f_real(X1) ) ),
inference(cnf_transformation,[],[f1827]) ).
tff(f1827,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(f4267,plain,
spl25_65,
inference(avatar_split_clause,[],[f2148,f4265]) ).
tff(f4265,plain,
( spl25_65
<=> ! [X0: nat] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_65])]) ).
tff(f2148,plain,
! [X0: nat] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X0))),
inference(cnf_transformation,[],[f776]) ).
tff(f776,plain,
! [X0: nat] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X0))),
inference(rectify,[],[f511]) ).
tff(f511,axiom,
! [X202: nat] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X202))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_zero__le__imp__of__nat) ).
tff(f4263,plain,
spl25_64,
inference(avatar_split_clause,[],[f2147,f4261]) ).
tff(f4261,plain,
( spl25_64
<=> ! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_64])]) ).
tff(f2147,plain,
! [X0: nat] : ( hAPP_nat_nat(semiri984289939at_nat,X0) = number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(cnf_transformation,[],[f775]) ).
tff(f775,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(f4259,plain,
spl25_63,
inference(avatar_split_clause,[],[f2146,f4257]) ).
tff(f4257,plain,
( spl25_63
<=> ! [X0: nat] : ( hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_63])]) ).
tff(f2146,plain,
! [X0: nat] : ( hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)) ),
inference(cnf_transformation,[],[f774]) ).
tff(f774,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(f4255,plain,
spl25_62,
inference(avatar_split_clause,[],[f2141,f4253]) ).
tff(f4253,plain,
( spl25_62
<=> ! [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,[spl25_62])]) ).
tff(f2141,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,[],[f769]) ).
tff(f769,plain,
! [X0: nat] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)),
inference(rectify,[],[f287]) ).
tff(f287,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_286_of__nat__less__0__iff) ).
tff(f4248,plain,
spl25_61,
inference(avatar_split_clause,[],[f3434,f4245]) ).
tff(f4245,plain,
( spl25_61
<=> ( one_one_int = number_number_of_int(hAPP_int_int(plus_plus_int(pls),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_61])]) ).
tff(f3434,plain,
one_one_int = number_number_of_int(hAPP_int_int(plus_plus_int(pls),one_one_int)),
inference(forward_demodulation,[],[f2986,f2979]) ).
tff(f2986,plain,
one_one_int = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),
inference(definition_unfolding,[],[f2020,f2970]) ).
tff(f2020,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(f4242,plain,
( spl25_60
| ~ spl25_48
| ~ spl25_59 ),
inference(avatar_split_clause,[],[f4237,f4232,f4145,f4239]) ).
tff(f4239,plain,
( spl25_60
<=> ( one_one_nat = number_number_of_nat(one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_60])]) ).
tff(f4145,plain,
( spl25_48
<=> ! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_48])]) ).
tff(f4232,plain,
( spl25_59
<=> ( one_one_nat = number_number_of_nat(hAPP_int_int(plus_plus_int(pls),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_59])]) ).
tff(f4237,plain,
( ( one_one_nat = number_number_of_nat(one_one_int) )
| ~ spl25_48
| ~ spl25_59 ),
inference(forward_demodulation,[],[f4236,f4146]) ).
tff(f4146,plain,
( ! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),pls) = X0 )
| ~ spl25_48 ),
inference(avatar_component_clause,[],[f4145]) ).
tff(f4236,plain,
( ( one_one_nat = number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),pls)) )
| ~ spl25_59 ),
inference(forward_demodulation,[],[f4234,f2370]) ).
tff(f4234,plain,
( ( one_one_nat = number_number_of_nat(hAPP_int_int(plus_plus_int(pls),one_one_int)) )
| ~ spl25_59 ),
inference(avatar_component_clause,[],[f4232]) ).
tff(f4235,plain,
spl25_59,
inference(avatar_split_clause,[],[f3431,f4232]) ).
tff(f3431,plain,
one_one_nat = number_number_of_nat(hAPP_int_int(plus_plus_int(pls),one_one_int)),
inference(forward_demodulation,[],[f2983,f2979]) ).
tff(f2983,plain,
one_one_nat = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),
inference(definition_unfolding,[],[f2016,f2970]) ).
tff(f2016,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(cnf_transformation,[],[f147]) ).
tff(f147,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_semiring__numeral__1__eq__1) ).
tff(f4230,plain,
( spl25_58
| ~ spl25_48
| ~ spl25_57 ),
inference(avatar_split_clause,[],[f4225,f4220,f4145,f4227]) ).
tff(f4220,plain,
( spl25_57
<=> ( one_one_real = number267125858f_real(hAPP_int_int(plus_plus_int(pls),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_57])]) ).
tff(f4225,plain,
( ( one_one_real = number267125858f_real(one_one_int) )
| ~ spl25_48
| ~ spl25_57 ),
inference(forward_demodulation,[],[f4224,f4146]) ).
tff(f4224,plain,
( ( one_one_real = number267125858f_real(hAPP_int_int(plus_plus_int(one_one_int),pls)) )
| ~ spl25_57 ),
inference(forward_demodulation,[],[f4222,f2370]) ).
tff(f4222,plain,
( ( one_one_real = number267125858f_real(hAPP_int_int(plus_plus_int(pls),one_one_int)) )
| ~ spl25_57 ),
inference(avatar_component_clause,[],[f4220]) ).
tff(f4223,plain,
spl25_57,
inference(avatar_split_clause,[],[f3428,f4220]) ).
tff(f3428,plain,
one_one_real = number267125858f_real(hAPP_int_int(plus_plus_int(pls),one_one_int)),
inference(forward_demodulation,[],[f2980,f2979]) ).
tff(f2980,plain,
one_one_real = number267125858f_real(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),
inference(definition_unfolding,[],[f2012,f2970]) ).
tff(f2012,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(cnf_transformation,[],[f27]) ).
tff(f27,axiom,
one_one_real = number267125858f_real(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_semiring__norm_I110_J) ).
tff(f4218,plain,
spl25_56,
inference(avatar_split_clause,[],[f2366,f4216]) ).
tff(f4216,plain,
( spl25_56
<=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(if_nat(fTrue,X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_56])]) ).
tff(f2366,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(if_nat(fTrue,X0),X1) = X0 ),
inference(cnf_transformation,[],[f893]) ).
tff(f893,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(if_nat(fTrue,X0),X1) = X0 ),
inference(rectify,[],[f700]) ).
tff(f700,axiom,
! [X5: nat,X7: nat] : ( hAPP_nat_nat(if_nat(fTrue,X5),X7) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).
tff(f4214,plain,
spl25_55,
inference(avatar_split_clause,[],[f2365,f4212]) ).
tff(f4212,plain,
( spl25_55
<=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(if_nat(fFalse,X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_55])]) ).
tff(f2365,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(if_nat(fFalse,X0),X1) = X1 ),
inference(cnf_transformation,[],[f892]) ).
tff(f892,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(if_nat(fFalse,X0),X1) = X1 ),
inference(rectify,[],[f701]) ).
tff(f701,axiom,
! [X5: nat,X7: nat] : ( hAPP_nat_nat(if_nat(fFalse,X5),X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
tff(f4210,plain,
( spl25_54
| ~ spl25_47
| ~ spl25_48
| ~ spl25_53 ),
inference(avatar_split_clause,[],[f4205,f4189,f4145,f4141,f4207]) ).
tff(f4141,plain,
( spl25_47
<=> ! [X0: int] : ( hAPP_int_int(plus_plus_int(pls),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_47])]) ).
tff(f4189,plain,
( spl25_53
<=> ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_53])]) ).
tff(f4205,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) )
| ~ spl25_47
| ~ spl25_48
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4204,f4146]) ).
tff(f4204,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4203,f2370]) ).
tff(f4203,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),one_one_int)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4202,f2726]) ).
tff(f2726,plain,
! [X2: int,X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)) ),
inference(cnf_transformation,[],[f1100]) ).
tff(f1100,plain,
! [X0: int,X1: int,X2: int] : ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X5: int,X7: int,X14: int] : ( hAPP_int_int(plus_plus_int(X5),hAPP_int_int(plus_plus_int(X7),X14)) = hAPP_int_int(plus_plus_int(X7),hAPP_int_int(plus_plus_int(X5),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zadd__left__commute) ).
tff(f4202,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4201,f2370]) ).
tff(f4201,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),pls))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4200,f4142]) ).
tff(f4142,plain,
( ! [X0: int] : ( hAPP_int_int(plus_plus_int(pls),X0) = X0 )
| ~ spl25_47 ),
inference(avatar_component_clause,[],[f4141]) ).
tff(f4200,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),pls)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4199,f2726]) ).
tff(f4199,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(pls),pls)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4198,f2370]) ).
tff(f4198,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4197,f4142]) ).
tff(f4197,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4196,f3929]) ).
tff(f3929,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3))) ),
inference(forward_demodulation,[],[f2952,f2728]) ).
tff(f2728,plain,
! [X2: int,X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) ),
inference(cnf_transformation,[],[f1102]) ).
tff(f1102,plain,
! [X0: int,X1: int,X2: int] : ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) ),
inference(rectify,[],[f340]) ).
tff(f340,axiom,
! [X113: int,X114: int,X115: int] : ( hAPP_int_int(plus_plus_int(X113),hAPP_int_int(plus_plus_int(X114),X115)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X113),X114)),X115) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f2952,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X2)),hAPP_int_int(plus_plus_int(X1),X3)) ),
inference(cnf_transformation,[],[f1270]) ).
tff(f1270,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X2)),hAPP_int_int(plus_plus_int(X1),X3)) ),
inference(rectify,[],[f322]) ).
tff(f322,axiom,
! [X99: int,X100: int,X101: int,X102: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X99),X100)),hAPP_int_int(plus_plus_int(X101),X102)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X99),X101)),hAPP_int_int(plus_plus_int(X100),X102)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
tff(f4196,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4195,f2370]) ).
tff(f4195,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(pls),one_one_int)))) )
| ~ spl25_47
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4194,f4142]) ).
tff(f4194,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(pls),one_one_int))))) )
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4193,f3929]) ).
tff(f4193,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),one_one_int)))) )
| ~ spl25_53 ),
inference(forward_demodulation,[],[f4191,f2726]) ).
tff(f4191,plain,
( ( pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))) )
| ~ spl25_53 ),
inference(avatar_component_clause,[],[f4189]) ).
tff(f4192,plain,
spl25_53,
inference(avatar_split_clause,[],[f2971,f4189]) ).
tff(f2971,plain,
pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))),
inference(definition_unfolding,[],[f1991,f2000,f2135,f2970]) ).
tff(f1991,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f705]) ).
tff(f705,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f704]) ).
tff(f704,negated_conjecture,
( ~ zero_zero_int != hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f703]) ).
tff(f703,conjecture,
zero_zero_int != hAPP_nat_int(power_power_int(hAPP_int_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(f4187,plain,
( spl25_51
| ~ spl25_52
| ~ spl25_42 ),
inference(avatar_split_clause,[],[f4173,f4117,f4184,f4181]) ).
tff(f4181,plain,
( spl25_51
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_51])]) ).
tff(f4184,plain,
( spl25_52
<=> ( fTrue = fFalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_52])]) ).
tff(f4117,plain,
( spl25_42
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_42])]) ).
tff(f4173,plain,
( ! [X0: bool] :
( ( fTrue != fFalse )
| ( fFalse = X0 ) )
| ~ spl25_42 ),
inference(equality_factoring,[],[f4118]) ).
tff(f4118,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl25_42 ),
inference(avatar_component_clause,[],[f4117]) ).
tff(f4155,plain,
spl25_50,
inference(avatar_split_clause,[],[f3374,f4153]) ).
tff(f3374,plain,
! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(equality_resolution,[],[f2581]) ).
tff(f2581,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f1859]) ).
tff(f1859,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,[],[f1858]) ).
tff(f1858,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,[],[f1048]) ).
tff(f1048,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,[],[f448]) ).
tff(f448,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_447_zless__le) ).
tff(f4151,plain,
spl25_49,
inference(avatar_split_clause,[],[f3369,f4149]) ).
tff(f4149,plain,
( spl25_49
<=> ! [X1: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_49])]) ).
tff(f3369,plain,
! [X1: real] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)),
inference(equality_resolution,[],[f2567]) ).
tff(f2567,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
inference(cnf_transformation,[],[f1847]) ).
tff(f1847,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,[],[f1846]) ).
tff(f1846,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,[],[f627]) ).
tff(f627,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_626_real__less__def) ).
tff(f4147,plain,
spl25_48,
inference(avatar_split_clause,[],[f3028,f4145]) ).
tff(f4143,plain,
spl25_47,
inference(avatar_split_clause,[],[f3024,f4141]) ).
tff(f4139,plain,
spl25_46,
inference(avatar_split_clause,[],[f2999,f4136]) ).
tff(f4136,plain,
( spl25_46
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_46])]) ).
tff(f2999,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
inference(definition_unfolding,[],[f2051,f2000]) ).
tff(f2051,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f522]) ).
tff(f522,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_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
tff(f4134,plain,
spl25_45,
inference(avatar_split_clause,[],[f2997,f4131]) ).
tff(f4131,plain,
( spl25_45
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_45])]) ).
tff(f2997,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
inference(definition_unfolding,[],[f2048,f2000]) ).
tff(f2048,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f265]) ).
tff(f265,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_264_zero__less__one) ).
tff(f4129,plain,
~ spl25_44,
inference(avatar_split_clause,[],[f2996,f4126]) ).
tff(f4126,plain,
( spl25_44
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_44])]) ).
tff(f2996,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)),
inference(definition_unfolding,[],[f2040,f2000]) ).
tff(f2040,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f495]) ).
tff(f495,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_not__one__le__zero) ).
tff(f4124,plain,
~ spl25_43,
inference(avatar_split_clause,[],[f2994,f4121]) ).
tff(f4121,plain,
( spl25_43
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_43])]) ).
tff(f2994,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)),
inference(definition_unfolding,[],[f2037,f2000]) ).
tff(f2037,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f262]) ).
tff(f262,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_261_not__one__less__zero) ).
tff(f4119,plain,
spl25_42,
inference(avatar_split_clause,[],[f2200,f4117]) ).
tff(f2200,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f818]) ).
tff(f818,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f702]) ).
tff(f702,axiom,
! [X280: bool] :
( ( fFalse = X280 )
| ( fTrue = X280 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Nat__Onat_T) ).
tff(f4115,plain,
spl25_41,
inference(avatar_split_clause,[],[f2132,f4113]) ).
tff(f4113,plain,
( spl25_41
<=> ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_41])]) ).
tff(f2132,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(cnf_transformation,[],[f760]) ).
tff(f760,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(rectify,[],[f439]) ).
tff(f439,axiom,
! [X11: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_zle__refl) ).
tff(f4111,plain,
spl25_40,
inference(avatar_split_clause,[],[f2130,f4109]) ).
tff(f4109,plain,
( spl25_40
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_40])]) ).
tff(f2130,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(cnf_transformation,[],[f758]) ).
tff(f758,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(rectify,[],[f621]) ).
tff(f621,axiom,
! [X13: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_le__refl) ).
tff(f4107,plain,
spl25_39,
inference(avatar_split_clause,[],[f2128,f4105]) ).
tff(f4105,plain,
( spl25_39
<=> ! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_39])]) ).
tff(f2128,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
inference(cnf_transformation,[],[f756]) ).
tff(f756,plain,
! [X0: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
inference(rectify,[],[f656]) ).
tff(f656,axiom,
! [X249: real] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X249),X249)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_order__refl) ).
tff(f4103,plain,
spl25_38,
inference(avatar_split_clause,[],[f2126,f4101]) ).
tff(f4101,plain,
( spl25_38
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_38])]) ).
tff(f2126,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(cnf_transformation,[],[f754]) ).
tff(f754,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(rectify,[],[f613]) ).
tff(f613,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_612_le0) ).
tff(f4099,plain,
spl25_37,
inference(avatar_split_clause,[],[f2122,f4097]) ).
tff(f4097,plain,
( spl25_37
<=> ! [X0: nat] : ( hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_37])]) ).
tff(f2122,plain,
! [X0: nat] : ( hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f750]) ).
tff(f750,plain,
! [X0: nat] : ( hAPP_nat_nat(plus_plus_nat(X0),zero_zero_nat) = X0 ),
inference(rectify,[],[f360]) ).
tff(f360,axiom,
! [X123: nat] : ( hAPP_nat_nat(plus_plus_nat(X123),zero_zero_nat) = X123 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_add__0__right) ).
tff(f4095,plain,
spl25_36,
inference(avatar_split_clause,[],[f2120,f4093]) ).
tff(f4093,plain,
( spl25_36
<=> ! [X0: nat] : ( hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_36])]) ).
tff(f2120,plain,
! [X0: nat] : ( hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f748]) ).
tff(f748,plain,
! [X0: nat] : ( hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ),
inference(rectify,[],[f216]) ).
tff(f216,axiom,
! [X60: nat] : ( hAPP_nat_nat(power_power_nat(X60),one_one_nat) = X60 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_power__one__right) ).
tff(f4091,plain,
spl25_35,
inference(avatar_split_clause,[],[f2116,f4089]) ).
tff(f4089,plain,
( spl25_35
<=> ! [X0: nat] : ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_35])]) ).
tff(f2116,plain,
! [X0: nat] : ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) = X0 ),
inference(cnf_transformation,[],[f744]) ).
tff(f744,plain,
! [X0: nat] : ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X0) = X0 ),
inference(rectify,[],[f214]) ).
tff(f214,axiom,
! [X13: nat] : ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_plus__nat_Oadd__0) ).
tff(f4087,plain,
spl25_34,
inference(avatar_split_clause,[],[f2104,f4085]) ).
tff(f4085,plain,
( spl25_34
<=> ! [X0: int] : ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_34])]) ).
tff(f2104,plain,
! [X0: int] : ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f732]) ).
tff(f732,plain,
! [X0: int] : ( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
inference(rectify,[],[f396]) ).
tff(f396,axiom,
! [X143: int] : ( hAPP_nat_int(power_power_int(X143),one_one_nat) = X143 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
tff(f4083,plain,
spl25_33,
inference(avatar_split_clause,[],[f2101,f4081]) ).
tff(f4081,plain,
( spl25_33
<=> ! [X0: real] : ( hAPP_real_real(plus_plus_real(X0),zero_zero_real) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_33])]) ).
tff(f2101,plain,
! [X0: real] : ( hAPP_real_real(plus_plus_real(X0),zero_zero_real) = X0 ),
inference(cnf_transformation,[],[f729]) ).
tff(f729,plain,
! [X0: real] : ( hAPP_real_real(plus_plus_real(X0),zero_zero_real) = X0 ),
inference(rectify,[],[f359]) ).
tff(f359,axiom,
! [X123: real] : ( hAPP_real_real(plus_plus_real(X123),zero_zero_real) = X123 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_add__0__right) ).
tff(f4079,plain,
spl25_32,
inference(avatar_split_clause,[],[f2098,f4077]) ).
tff(f4077,plain,
( spl25_32
<=> ! [X0: real] : ( hAPP_real_real(plus_plus_real(zero_zero_real),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_32])]) ).
tff(f2098,plain,
! [X0: real] : ( hAPP_real_real(plus_plus_real(zero_zero_real),X0) = X0 ),
inference(cnf_transformation,[],[f726]) ).
tff(f726,plain,
! [X0: real] : ( hAPP_real_real(plus_plus_real(zero_zero_real),X0) = X0 ),
inference(rectify,[],[f364]) ).
tff(f364,axiom,
! [X124: real] : ( hAPP_real_real(plus_plus_real(zero_zero_real),X124) = X124 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_add__0) ).
tff(f4075,plain,
spl25_31,
inference(avatar_split_clause,[],[f2096,f4073]) ).
tff(f4073,plain,
( spl25_31
<=> ! [X0: real] : ( hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_31])]) ).
tff(f2096,plain,
! [X0: real] : ( hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ),
inference(cnf_transformation,[],[f724]) ).
tff(f724,plain,
! [X0: real] : ( hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ),
inference(rectify,[],[f215]) ).
tff(f215,axiom,
! [X60: real] : ( hAPP_nat_real(power_power_real(X60),one_one_nat) = X60 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_power__one__right) ).
tff(f4071,plain,
spl25_30,
inference(avatar_split_clause,[],[f2093,f4069]) ).
tff(f4069,plain,
( spl25_30
<=> ! [X0: int] : ( one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_30])]) ).
tff(f2093,plain,
! [X0: int] : ( one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f721]) ).
tff(f721,plain,
! [X0: int] : ( one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ),
inference(rectify,[],[f303]) ).
tff(f303,axiom,
! [X89: int] : ( one_one_int = hAPP_nat_int(power_power_int(X89),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
tff(f4067,plain,
spl25_29,
inference(avatar_split_clause,[],[f2092,f4065]) ).
tff(f4065,plain,
( spl25_29
<=> ! [X0: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_29])]) ).
tff(f2092,plain,
! [X0: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ),
inference(cnf_transformation,[],[f720]) ).
tff(f720,plain,
! [X0: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ),
inference(rectify,[],[f235]) ).
tff(f235,axiom,
! [X63: nat] : ( one_one_int = hAPP_nat_int(power_power_int(one_one_int),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_power__one) ).
tff(f4063,plain,
spl25_28,
inference(avatar_split_clause,[],[f2090,f4061]) ).
tff(f4061,plain,
( spl25_28
<=> ! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_28])]) ).
tff(f2090,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f718]) ).
tff(f718,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ),
inference(rectify,[],[f291]) ).
tff(f291,axiom,
! [X86: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(X86),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_power__0) ).
tff(f4059,plain,
spl25_27,
inference(avatar_split_clause,[],[f2089,f4057]) ).
tff(f4057,plain,
( spl25_27
<=> ! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_27])]) ).
tff(f2089,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ),
inference(cnf_transformation,[],[f717]) ).
tff(f717,plain,
! [X0: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ),
inference(rectify,[],[f234]) ).
tff(f234,axiom,
! [X63: nat] : ( one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_power__one) ).
tff(f4055,plain,
spl25_26,
inference(avatar_split_clause,[],[f2087,f4053]) ).
tff(f4053,plain,
( spl25_26
<=> ! [X0: real] : ( one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_26])]) ).
tff(f2087,plain,
! [X0: real] : ( one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ),
inference(cnf_transformation,[],[f715]) ).
tff(f715,plain,
! [X0: real] : ( one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ),
inference(rectify,[],[f290]) ).
tff(f290,axiom,
! [X86: real] : ( one_one_real = hAPP_nat_real(power_power_real(X86),zero_zero_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_power__0) ).
tff(f4051,plain,
spl25_25,
inference(avatar_split_clause,[],[f2086,f4049]) ).
tff(f4049,plain,
( spl25_25
<=> ! [X0: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_25])]) ).
tff(f2086,plain,
! [X0: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ),
inference(cnf_transformation,[],[f714]) ).
tff(f714,plain,
! [X0: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ),
inference(rectify,[],[f233]) ).
tff(f233,axiom,
! [X63: nat] : ( one_one_real = hAPP_nat_real(power_power_real(one_one_real),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_power__one) ).
tff(f4047,plain,
spl25_24,
inference(avatar_split_clause,[],[f2084,f4045]) ).
tff(f4045,plain,
( spl25_24
<=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_24])]) ).
tff(f2084,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(cnf_transformation,[],[f712]) ).
tff(f712,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(rectify,[],[f174]) ).
tff(f174,axiom,
! [X13: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_less__not__refl) ).
tff(f4043,plain,
spl25_23,
inference(avatar_split_clause,[],[f2081,f4041]) ).
tff(f4041,plain,
( spl25_23
<=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_23])]) ).
tff(f2081,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(cnf_transformation,[],[f709]) ).
tff(f709,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(rectify,[],[f172]) ).
tff(f172,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_171_less__zeroE) ).
tff(f4039,plain,
spl25_22,
inference(avatar_split_clause,[],[f2050,f4036]) ).
tff(f4036,plain,
( spl25_22
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_22])]) ).
tff(f2050,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(f4034,plain,
spl25_21,
inference(avatar_split_clause,[],[f2047,f4031]) ).
tff(f4031,plain,
( spl25_21
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_21])]) ).
tff(f2047,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(f4029,plain,
spl25_20,
inference(avatar_split_clause,[],[f2046,f4026]) ).
tff(f4026,plain,
( spl25_20
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_20])]) ).
tff(f2046,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
inference(cnf_transformation,[],[f264]) ).
tff(f264,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_263_zero__less__one) ).
tff(f4024,plain,
spl25_19,
inference(avatar_split_clause,[],[f2045,f4021]) ).
tff(f4021,plain,
( spl25_19
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_19])]) ).
tff(f2045,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(f4019,plain,
spl25_18,
inference(avatar_split_clause,[],[f2044,f4016]) ).
tff(f4016,plain,
( spl25_18
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_18])]) ).
tff(f2044,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
inference(cnf_transformation,[],[f171]) ).
tff(f171,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_tn0) ).
tff(f4014,plain,
spl25_17,
inference(avatar_split_clause,[],[f2042,f4011]) ).
tff(f4011,plain,
( spl25_17
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_17])]) ).
tff(f2042,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
inference(cnf_transformation,[],[f496]) ).
tff(f496,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_zero__le__one) ).
tff(f4009,plain,
spl25_16,
inference(avatar_split_clause,[],[f2041,f4006]) ).
tff(f4006,plain,
( spl25_16
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_16])]) ).
tff(f2041,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
inference(cnf_transformation,[],[f263]) ).
tff(f263,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_262_zero__less__one) ).
tff(f4004,plain,
~ spl25_15,
inference(avatar_split_clause,[],[f2035,f4001]) ).
tff(f4001,plain,
( spl25_15
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_15])]) ).
tff(f2035,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(cnf_transformation,[],[f494]) ).
tff(f494,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_not__one__le__zero) ).
tff(f3999,plain,
~ spl25_14,
inference(avatar_split_clause,[],[f2034,f3996]) ).
tff(f3996,plain,
( spl25_14
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_14])]) ).
tff(f2034,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
inference(cnf_transformation,[],[f493]) ).
tff(f493,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_not__one__le__zero) ).
tff(f3994,plain,
~ spl25_13,
inference(avatar_split_clause,[],[f2033,f3991]) ).
tff(f3991,plain,
( spl25_13
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_13])]) ).
tff(f2033,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
inference(cnf_transformation,[],[f260]) ).
tff(f260,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_259_not__one__less__zero) ).
tff(f3989,plain,
spl25_12,
inference(avatar_split_clause,[],[f2990,f3986]) ).
tff(f3986,plain,
( spl25_12
<=> ( pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_12])]) ).
tff(f2990,plain,
pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(definition_unfolding,[],[f2029,f2000]) ).
tff(f2029,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(cnf_transformation,[],[f295]) ).
tff(f295,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_of__nat__0) ).
tff(f3984,plain,
spl25_11,
inference(avatar_split_clause,[],[f2028,f3981]) ).
tff(f3981,plain,
( spl25_11
<=> ( zero_zero_nat = hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_11])]) ).
tff(f2028,plain,
zero_zero_nat = hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat),
inference(cnf_transformation,[],[f294]) ).
tff(f294,axiom,
zero_zero_nat = hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
tff(f3979,plain,
spl25_10,
inference(avatar_split_clause,[],[f2027,f3976]) ).
tff(f3976,plain,
( spl25_10
<=> ( zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_10])]) ).
tff(f2027,plain,
zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat),
inference(cnf_transformation,[],[f293]) ).
tff(f293,axiom,
zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_of__nat__0) ).
tff(f3974,plain,
spl25_9,
inference(avatar_split_clause,[],[f2024,f3971]) ).
tff(f3971,plain,
( spl25_9
<=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_9])]) ).
tff(f2024,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(cnf_transformation,[],[f250]) ).
tff(f250,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_of__nat__1) ).
tff(f3969,plain,
spl25_8,
inference(avatar_split_clause,[],[f2019,f3966]) ).
tff(f3966,plain,
( spl25_8
<=> ( one_one_nat = hAPP_nat_nat(semiri984289939at_nat,one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_8])]) ).
tff(f2019,plain,
one_one_nat = hAPP_nat_nat(semiri984289939at_nat,one_one_nat),
inference(cnf_transformation,[],[f249]) ).
tff(f249,axiom,
one_one_nat = hAPP_nat_nat(semiri984289939at_nat,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_of__nat__1) ).
tff(f3964,plain,
spl25_7,
inference(avatar_split_clause,[],[f2015,f3961]) ).
tff(f3961,plain,
( spl25_7
<=> ( one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).
tff(f2015,plain,
one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat),
inference(cnf_transformation,[],[f248]) ).
tff(f248,axiom,
one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_of__nat__1) ).
tff(f3959,plain,
spl25_6,
inference(avatar_split_clause,[],[f2080,f3957]) ).
tff(f3955,plain,
spl25_5,
inference(avatar_split_clause,[],[f2004,f3952]) ).
tff(f3952,plain,
( spl25_5
<=> ( zero_zero_nat = number_number_of_nat(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_5])]) ).
tff(f2004,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_semiring__norm_I113_J) ).
tff(f3950,plain,
spl25_4,
inference(avatar_split_clause,[],[f2001,f3947]) ).
tff(f2001,plain,
zero_zero_real = number267125858f_real(pls),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
zero_zero_real = number267125858f_real(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_semiring__norm_I112_J) ).
tff(f3945,plain,
~ spl25_3,
inference(avatar_split_clause,[],[f2972,f3942]) ).
tff(f3942,plain,
( spl25_3
<=> ( one_one_int = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).
tff(f2972,plain,
one_one_int != pls,
inference(definition_unfolding,[],[f1997,f2000]) ).
tff(f1997,plain,
zero_zero_int != one_one_int,
inference(cnf_transformation,[],[f230]) ).
tff(f230,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_zero__neq__one) ).
tff(f3940,plain,
~ spl25_2,
inference(avatar_split_clause,[],[f1994,f3937]) ).
tff(f3937,plain,
( spl25_2
<=> ( zero_zero_real = one_one_real ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).
tff(f1994,plain,
zero_zero_real != one_one_real,
inference(cnf_transformation,[],[f228]) ).
tff(f228,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_zero__neq__one) ).
tff(f3935,plain,
~ spl25_1,
inference(avatar_split_clause,[],[f1992,f3932]) ).
tff(f3932,plain,
( spl25_1
<=> ( one_one_nat = zero_zero_nat ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).
tff(f1992,plain,
one_one_nat != zero_zero_nat,
inference(cnf_transformation,[],[f226]) ).
tff(f226,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_one__neq__zero) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 30 00:12:45 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (30112)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.39 % (30116)WARNING: value z3 for option sas not known
% 0.11/0.39 % (30116)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)
% 0.11/0.39 % (30117)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.39 % (30115)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.39 % (30119)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)
% 0.11/0.39 % (30118)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)
% 0.16/0.40 % (30120)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)
% 0.16/0.41 % (30114)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.45 % (30118)First to succeed.
% 0.16/0.46 % (30119)Also succeeded, but the first one will report.
% 0.16/0.46 % (30118)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (30118)------------------------------
% 0.16/0.47 % (30118)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.47 % (30118)Termination reason: Refutation
% 0.16/0.47
% 0.16/0.47 % (30118)Memory used [KB]: 2896
% 0.16/0.47 % (30118)Time elapsed: 0.076 s
% 0.16/0.47 % (30118)Instructions burned: 159 (million)
% 0.16/0.47 % (30118)------------------------------
% 0.16/0.47 % (30118)------------------------------
% 0.16/0.47 % (30112)Success in time 0.135 s
%------------------------------------------------------------------------------