%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM924_30 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:17:29 PM UTC 2026
% Result : Unsatisfiable 10.38s 2.49s
% Output : Refutation 11.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 23
% Syntax : Number of formulae : 144 ( 140 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 129 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 111 ( 111 usr; 28 con; 0-3 aty)
% Number of variables : 93 ( 93 !; 0 ?; 93 :)
% 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_bool_bool: $tType ).
tff(type_def_10,type,
fun_bo1549164019l_bool: $tType ).
tff(type_def_11,type,
fun_int_bool: $tType ).
tff(type_def_12,type,
fun_int_int: $tType ).
tff(type_def_13,type,
fun_in531499254l_bool: $tType ).
tff(type_def_14,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_15,type,
fun_nat_bool: $tType ).
tff(type_def_16,type,
fun_nat_int: $tType ).
tff(type_def_17,type,
fun_nat_nat: $tType ).
tff(type_def_18,type,
fun_nat_real: $tType ).
tff(type_def_19,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_20,type,
fun_real_bool: $tType ).
tff(type_def_21,type,
fun_real_real: $tType ).
tff(type_def_22,type,
fun_re413263731l_bool: $tType ).
tff(type_def_23,type,
product_prod_int_int: $tType ).
tff(func_def_0,type,
cOMBB_1652995168ol_int: ( fun_bo1549164019l_bool * fun_int_bool ) > fun_in531499254l_bool ).
tff(func_def_1,type,
cOMBC_int_int_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_2,type,
cOMBS_int_bool_bool: ( fun_in531499254l_bool * fun_int_bool ) > fun_int_bool ).
tff(func_def_3,type,
div_mod_int: int > fun_int_int ).
tff(func_def_4,type,
div_mod_nat: nat > fun_nat_nat ).
tff(func_def_5,type,
minus_minus_int: int > fun_int_int ).
tff(func_def_6,type,
minus_minus_nat: nat > fun_nat_nat ).
tff(func_def_7,type,
minus_minus_real: real > fun_real_real ).
tff(func_def_8,type,
one_one_int: int ).
tff(func_def_9,type,
one_one_nat: nat ).
tff(func_def_10,type,
one_one_real: real ).
tff(func_def_11,type,
plus_plus_int: int > fun_int_int ).
tff(func_def_12,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_13,type,
plus_plus_real: real > fun_real_real ).
tff(func_def_14,type,
times_times_int: int > fun_int_int ).
tff(func_def_15,type,
times_times_nat: nat > fun_nat_nat ).
tff(func_def_16,type,
times_times_real: real > fun_real_real ).
tff(func_def_17,type,
zero_zero_int: int ).
tff(func_def_18,type,
zero_zero_nat: nat ).
tff(func_def_19,type,
zero_zero_real: real ).
tff(func_def_20,type,
multInv: ( int * int ) > int ).
tff(func_def_21,type,
d22set: int > fun_int_bool ).
tff(func_def_22,type,
zfact: int > int ).
tff(func_def_23,type,
zcong: ( int * int ) > fun_int_bool ).
tff(func_def_24,type,
zprime: fun_int_bool ).
tff(func_def_25,type,
bit0: int > int ).
tff(func_def_26,type,
bit1: int > int ).
tff(func_def_27,type,
min: int ).
tff(func_def_28,type,
pls: int ).
tff(func_def_29,type,
number_number_of_int: int > int ).
tff(func_def_30,type,
number_number_of_nat: int > nat ).
tff(func_def_31,type,
number267125858f_real: int > real ).
tff(func_def_32,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_33,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_34,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_35,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_36,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_37,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_38,type,
power_power_int: int > fun_nat_int ).
tff(func_def_39,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_40,type,
power_power_real: real > fun_nat_real ).
tff(func_def_41,type,
product_Pair_int_int: ( int * int ) > product_prod_int_int ).
tff(func_def_42,type,
legendre: ( int * int ) > int ).
tff(func_def_43,type,
quadRes: int > fun_int_bool ).
tff(func_def_44,type,
sr: int > fun_int_bool ).
tff(func_def_45,type,
standardRes: ( int * int ) > int ).
tff(func_def_46,type,
dvd_dvd_int: fun_int_fun_int_bool ).
tff(func_def_47,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(func_def_48,type,
dvd_dvd_real: fun_re413263731l_bool ).
tff(func_def_49,type,
collect_int: fun_int_bool > fun_int_bool ).
tff(func_def_50,type,
twoSqu820444569sum2sq: fun_int_bool ).
tff(func_def_51,type,
twoSqu949963151sum2sq: product_prod_int_int > int ).
tff(func_def_52,type,
inv: ( int * int ) > int ).
tff(func_def_53,type,
wset: ( int * int ) > fun_int_bool ).
tff(func_def_54,type,
fconj: fun_bo1549164019l_bool ).
tff(func_def_55,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(func_def_56,type,
hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).
tff(func_def_57,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_58,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(func_def_59,type,
hAPP_i68813070l_bool: ( fun_in531499254l_bool * int ) > fun_bool_bool ).
tff(func_def_60,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_61,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_62,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_63,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_64,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_65,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_66,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_67,type,
hAPP_real_real: ( fun_real_real * real ) > real ).
tff(func_def_68,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_69,type,
member_int: ( int * fun_int_bool ) > bool ).
tff(func_def_70,type,
m: int ).
tff(func_def_71,type,
s1: int ).
tff(func_def_72,type,
s: int ).
tff(func_def_73,type,
t: int ).
tff(func_def_74,type,
sK1: int ).
tff(func_def_75,type,
sK2: int ).
tff(func_def_76,type,
sK3: int ).
tff(func_def_77,type,
sK4: int > int ).
tff(func_def_78,type,
sK5: int ).
tff(func_def_79,type,
sK6: ( int * int * int ) > int ).
tff(func_def_80,type,
sK7: ( int * int ) > int ).
tff(func_def_81,type,
sK8: ( real * nat ) > real ).
tff(func_def_82,type,
sK9: ( real * nat ) > real ).
tff(func_def_83,type,
sK10: ( nat * nat ) > nat ).
tff(func_def_84,type,
sK11: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_85,type,
sK12: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_86,type,
sK13: ( nat * fun_nat_bool ) > nat ).
tff(func_def_87,type,
sK14: int > int ).
tff(func_def_88,type,
sK15: ( fun_int_bool * int ) > int ).
tff(func_def_89,type,
sK16: ( fun_int_bool * int ) > int ).
tff(func_def_90,type,
sK17: ( int * int ) > int ).
tff(func_def_91,type,
sK18: int > int ).
tff(func_def_92,type,
sK19: int > int ).
tff(func_def_93,type,
sK20: ( fun_int_bool * int ) > int ).
tff(func_def_94,type,
sK21: fun_int_bool > int ).
tff(func_def_95,type,
sK22: ( fun_int_bool * int ) > int ).
tff(func_def_96,type,
sK23: ( fun_int_bool * int ) > int ).
tff(func_def_97,type,
sK24: ( fun_int_bool * int ) > int ).
tff(func_def_98,type,
sK25: fun_nat_nat > nat ).
tff(func_def_99,type,
sK26: fun_nat_nat > nat ).
tff(func_def_100,type,
sK27: ( nat * fun_nat_bool ) > nat ).
tff(func_def_101,type,
sK28: ( nat * nat ) > nat ).
tff(func_def_102,type,
sK29: ( int * int ) > int ).
tff(func_def_103,type,
sK30: ( fun_int_bool * int * int ) > int ).
tff(func_def_104,type,
sK31: ( fun_int_bool * int * int ) > int ).
tff(func_def_105,type,
sK32: ( fun_int_bool * int * int ) > int ).
tff(func_def_106,type,
sK33: ( fun_int_bool * int * int ) > int ).
tff(func_def_107,type,
sK34: ( int * int ) > int ).
tff(func_def_108,type,
sK35: ( nat * nat ) > nat ).
tff(func_def_109,type,
sK36: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_110,type,
sK37: ( fun_nat_bool * nat * nat ) > nat ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( fun_int_bool * int * int ) > $o ).
tff(f3,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(f4,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f35,axiom,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
tff(f156,axiom,
! [X0: int,X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_not__sum__squares__lt__zero) ).
tff(f173,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Pls__def) ).
tff(f183,axiom,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Bit0__def) ).
tff(f188,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(bit0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_double__number__of__Bit0) ).
tff(f237,axiom,
! [X0: int] : ( bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Bit1__def) ).
tff(f286,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(f325,axiom,
! [X0: int,X1: int,X2: int] : ( hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
tff(f328,axiom,
! [X0: int,X1: int,X2: int] : ( hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f331,axiom,
! [X0: int,X1: int] : ( hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f334,axiom,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f337,axiom,
! [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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f343,axiom,
! [X0: int,X1: int,X2: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
tff(f371,axiom,
! [X0: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
tff(f377,axiom,
! [X0: int,X1: int] :
( ( X0 = hAPP_int_int(plus_plus_int(X0),X1) )
<=> ( X1 = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_add__0__iff) ).
tff(f398,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),one_one_int) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
tff(f416,axiom,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
tff(f422,axiom,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X1) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
tff(f510,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(zero_zero_int),X0) = zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_mult__zero__left) ).
tff(f1069,axiom,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
tff(f1202,axiom,
! [X0: fun_int_fun_int_bool,X1: int,X2: int] : ( hAPP_int_bool(cOMBC_int_int_bool(X0,X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).
tff(f2200,plain,
! [X0: int,X1: int] :
( ( ( X0 = hAPP_int_int(plus_plus_int(X0),X1) )
| ( zero_zero_int != X1 ) )
& ( ( X1 = zero_zero_int )
| ( hAPP_int_int(plus_plus_int(X0),X1) != X0 ) ) ),
inference(nnf_transformation,[],[f377]) ).
tff(f2468,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
inference(cnf_transformation,[],[f3]) ).
tff(f2469,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f2512,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f35]) ).
tff(f2700,plain,
! [X0: int,X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),zero_zero_int)),
inference(cnf_transformation,[],[f156]) ).
tff(f2723,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f173]) ).
tff(f2737,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f183]) ).
tff(f2742,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(bit0(X0)) ),
inference(cnf_transformation,[],[f188]) ).
tff(f2802,plain,
! [X0: int] : ( bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f237]) ).
tff(f2864,plain,
! [X0: int] : ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(X0),X0) ),
inference(cnf_transformation,[],[f286]) ).
tff(f2914,plain,
! [X2: int,X0: int,X1: int] : ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f2917,plain,
! [X2: int,X0: int,X1: int] : ( hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) = hAPP_int_int(times_times_int(X1),hAPP_int_int(times_times_int(X0),X2)) ),
inference(cnf_transformation,[],[f328]) ).
tff(f2920,plain,
! [X0: int,X1: int] : ( hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0) ),
inference(cnf_transformation,[],[f331]) ).
tff(f2923,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0) ),
inference(cnf_transformation,[],[f334]) ).
tff(f2926,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,[],[f337]) ).
tff(f2932,plain,
! [X2: int,X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f2964,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),X0) = X0 ),
inference(cnf_transformation,[],[f371]) ).
tff(f2973,plain,
! [X0: int,X1: int] :
( ( hAPP_int_int(plus_plus_int(X0),X1) = X0 )
| ( zero_zero_int != X1 ) ),
inference(cnf_transformation,[],[f2200]) ).
tff(f3006,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),one_one_int) = X0 ),
inference(cnf_transformation,[],[f398]) ).
tff(f3024,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X0) ),
inference(cnf_transformation,[],[f416]) ).
tff(f3030,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X1)),X1) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X0),one_one_int)),X1) ),
inference(cnf_transformation,[],[f422]) ).
tff(f3152,plain,
! [X0: int] : ( zero_zero_int = hAPP_int_int(times_times_int(zero_zero_int),X0) ),
inference(cnf_transformation,[],[f510]) ).
tff(f3961,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t) = twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)),
inference(cnf_transformation,[],[f1069]) ).
tff(f4160,plain,
! [X2: int,X0: fun_int_fun_int_bool,X1: int] : ( hAPP_int_bool(cOMBC_int_int_bool(X0,X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f1202]) ).
tff(f4165,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),pls))),
inference(definition_unfolding,[],[f2468,f2737,f2737,f2802,f2737,f2737,f2802,f2723]) ).
tff(f4166,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int),
inference(definition_unfolding,[],[f2469,f2737,f2737,f2802,f2737,f2802]) ).
tff(f4291,plain,
! [X0: int,X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1))),pls)),
inference(definition_unfolding,[],[f2700,f2723]) ).
tff(f4325,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(X0)) = number_number_of_int(hAPP_int_int(plus_plus_int(X0),X0)) ),
inference(definition_unfolding,[],[f2742,f2737]) ).
tff(f4419,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = 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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ),
inference(definition_unfolding,[],[f2864,f2737,f2802]) ).
tff(f4443,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(pls),X0) = X0 ),
inference(definition_unfolding,[],[f2964,f2723]) ).
tff(f4445,plain,
! [X0: int,X1: int] :
( ( hAPP_int_int(plus_plus_int(X0),X1) = X0 )
| ( pls != X1 ) ),
inference(definition_unfolding,[],[f2973,f2723]) ).
tff(f4511,plain,
! [X0: int] : ( pls = hAPP_int_int(times_times_int(pls),X0) ),
inference(definition_unfolding,[],[f3152,f2723,f2723]) ).
tff(f4696,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t),
inference(definition_unfolding,[],[f3961,f2737,f2737,f2802]) ).
tff(f4828,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),pls) = X0 ),
inference(equality_resolution,[],[f4445]) ).
tff(f5100,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) ),
inference(forward_demodulation,[],[f4419,f2932]) ).
tff(f5196,plain,
! [X0: int,X1: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X0),X0)),hAPP_int_int(times_times_int(X1),X1)))),
inference(forward_demodulation,[],[f4291,f4160]) ).
tff(f5294,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
inference(forward_demodulation,[],[f4166,f2923]) ).
tff(f5295,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls)),pls))),
inference(forward_demodulation,[],[f4165,f3030]) ).
tff(f5326,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
inference(forward_demodulation,[],[f5100,f2932]) ).
tff(f5477,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),m)),one_one_int)),t),
inference(forward_demodulation,[],[f5294,f2932]) ).
tff(f5478,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls))),
inference(forward_demodulation,[],[f5295,f4828]) ).
tff(f5499,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) ),
inference(forward_demodulation,[],[f5326,f2926]) ).
tff(f5626,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),m)),t)),t),
inference(forward_demodulation,[],[f5477,f3030]) ).
tff(f5627,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t))),
inference(forward_demodulation,[],[f5478,f4160]) ).
tff(f5648,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) ),
inference(forward_demodulation,[],[f5499,f4443]) ).
tff(f5774,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),m)),t)),
inference(forward_demodulation,[],[f5626,f2923]) ).
tff(f5775,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls)),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(forward_demodulation,[],[f5627,f4696]) ).
tff(f5796,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) ),
inference(forward_demodulation,[],[f5648,f2926]) ).
tff(f5901,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),hAPP_int_int(times_times_int(m),t))),
inference(forward_demodulation,[],[f5774,f2914]) ).
tff(f5902,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls))),
inference(forward_demodulation,[],[f5775,f4160]) ).
tff(f5923,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ),
inference(forward_demodulation,[],[f5796,f4443]) ).
tff(f6017,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(m),t)),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f5901,f2920]) ).
tff(f6018,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(m),pls)))),
inference(forward_demodulation,[],[f5902,f2914]) ).
tff(f6039,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls))))) ),
inference(forward_demodulation,[],[f5923,f2932]) ).
tff(f6128,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6017,f2914]) ).
tff(f6129,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(m),pls)),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6018,f2920]) ).
tff(f6150,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls))))) ),
inference(forward_demodulation,[],[f6039,f2926]) ).
tff(f6237,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(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(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6128,f4325]) ).
tff(f6238,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6129,f2914]) ).
tff(f6259,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls))))) ),
inference(forward_demodulation,[],[f6150,f2926]) ).
tff(f6346,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),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(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6237,f2512]) ).
tff(f6347,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))),hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6238,f2917]) ).
tff(f6363,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))) ),
inference(forward_demodulation,[],[f6259,f4443]) ).
tff(f6450,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6346,f2932]) ).
tff(f6451,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))),pls)),
inference(forward_demodulation,[],[f6347,f4511]) ).
tff(f6467,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ),
inference(forward_demodulation,[],[f6363,f4828]) ).
tff(f6552,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6450,f2926]) ).
tff(f6553,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(forward_demodulation,[],[f6451,f4160]) ).
tff(f6634,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6552,f4443]) ).
tff(f6679,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6634,f2926]) ).
tff(f6715,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
inference(forward_demodulation,[],[f6679,f4443]) ).
tff(f6741,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls))))))),
inference(forward_demodulation,[],[f6715,f2932]) ).
tff(f6755,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls))))))),
inference(forward_demodulation,[],[f6741,f2926]) ).
tff(f6767,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls))))))),
inference(forward_demodulation,[],[f6755,f2926]) ).
tff(f6777,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls))))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))))),
inference(forward_demodulation,[],[f6767,f4443]) ).
tff(f6781,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))),
inference(forward_demodulation,[],[f6777,f4828]) ).
tff(f6785,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))),
inference(forward_demodulation,[],[f6781,f3024]) ).
tff(f6788,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),
inference(forward_demodulation,[],[f6785,f2932]) ).
tff(f6791,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),
inference(forward_demodulation,[],[f6788,f6467]) ).
tff(f6821,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),m)),one_one_int)),t),
inference(superposition,[],[f4696,f2512]) ).
tff(f6822,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),m)),t)),t),
inference(forward_demodulation,[],[f6821,f3030]) ).
tff(f6823,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),m)),t)),
inference(forward_demodulation,[],[f6822,f2923]) ).
tff(f6824,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),hAPP_int_int(times_times_int(m),t))),
inference(forward_demodulation,[],[f6823,f2914]) ).
tff(f6825,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(m),t)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),
inference(forward_demodulation,[],[f6824,f2920]) ).
tff(f6826,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))),
inference(forward_demodulation,[],[f6825,f2914]) ).
tff(f6827,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6826,f2932]) ).
tff(f6828,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6827,f2932]) ).
tff(f6829,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6828,f2932]) ).
tff(f6830,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6829,f2926]) ).
tff(f6831,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6830,f4443]) ).
tff(f6832,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6831,f2926]) ).
tff(f6833,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6832,f4443]) ).
tff(f6834,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6833,f2932]) ).
tff(f6835,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6834,f2932]) ).
tff(f6836,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6835,f2926]) ).
tff(f6837,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6836,f2926]) ).
tff(f6838,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),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(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6837,f4443]) ).
tff(f6839,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6838,f2926]) ).
tff(f6840,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6839,f2926]) ).
tff(f6841,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6840,f4443]) ).
tff(f6842,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6841,f2932]) ).
tff(f6843,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6842,f2932]) ).
tff(f6844,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6843,f2926]) ).
tff(f6845,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6844,f2926]) ).
tff(f6846,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))))),
inference(forward_demodulation,[],[f6845,f2926]) ).
tff(f6847,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6846,f4443]) ).
tff(f6848,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6847,f2926]) ).
tff(f6849,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6848,f2926]) ).
tff(f6850,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f6849,f2926]) ).
tff(f6851,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f6850,f4443]) ).
tff(f6852,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),pls)))))))),
inference(forward_demodulation,[],[f6851,f2932]) ).
tff(f6853,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls)))))))),
inference(forward_demodulation,[],[f6852,f2926]) ).
tff(f6854,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))))))),
inference(forward_demodulation,[],[f6853,f2926]) ).
tff(f6855,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))))))),
inference(forward_demodulation,[],[f6854,f2926]) ).
tff(f6856,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls)))))))),
inference(forward_demodulation,[],[f6855,f2926]) ).
tff(f6857,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),pls))))))),
inference(forward_demodulation,[],[f6856,f4443]) ).
tff(f6858,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(t),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),
inference(forward_demodulation,[],[f6857,f4828]) ).
tff(f6863,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)),
inference(superposition,[],[f6858,f6791]) ).
tff(f7402,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(X0),X0)))),
inference(superposition,[],[f5196,f3006]) ).
tff(f7411,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(superposition,[],[f7402,f6863]) ).
tff(f7412,plain,
$false,
inference(forward_subsumption_resolution,[],[f7411,f6553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924_30 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 21:41:02 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.32/2.09 % (1196779)Detected formulas, will run a generic FOF schedule.
% 8.32/2.09 % (1196919)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=447225663:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.32/2.09 % (1196919)Instruction limit reached!
% 8.32/2.09 % (1196919)------------------------------
% 8.32/2.09 % (1196919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.32/2.09 % (1196919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.32/2.09 % (1196919)CaDiCaL version: 2.1.3
% 8.32/2.09 % (1196919)Termination reason: Instruction limit
% 8.32/2.09 % (1196919)Termination phase: Saturation
% 8.32/2.09 % (1196919)Time elapsed: 0.036 s
% 8.32/2.09 % (1196919)Peak memory usage: 90 MB
% 8.32/2.09 % (1196919)Instructions burned: 139 (million)
% 8.32/2.09 % (1196916)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4037913361:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.32/2.09 % (1196917)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3979651753:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.32/2.09 % (1196915)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1624705541:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.32/2.09 % (1196914)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3827176453:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.32/2.09 % (1196918)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2452761251:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.32/2.09 % (1196917)Refutation not found, incomplete strategy
% 8.32/2.09 % (1196917)------------------------------
% 8.32/2.09 % (1196917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.32/2.09 % (1196917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.32/2.09 % (1196917)CaDiCaL version: 2.1.3
% 8.32/2.09 % (1196917)Termination reason: Refutation not found, incomplete strategy
% 8.32/2.09 % (1196917)Time elapsed: 0.004 s
% 8.32/2.09 % (1196917)Peak memory usage: 87 MB
% 8.32/2.09 % (1196917)Instructions burned: 5 (million)
% 8.32/2.09 % (1196918)Refutation not found, incomplete strategy
% 8.32/2.09 % (1196918)------------------------------
% 8.32/2.09 % (1196918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.32/2.09 % (1196918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.32/2.09 % (1196918)CaDiCaL version: 2.1.3
% 8.32/2.09 % (1196918)Termination reason: Refutation not found, incomplete strategy
% 8.32/2.09 % (1196918)Time elapsed: 0.004 s
% 8.32/2.09 % (1196918)Peak memory usage: 87 MB
% 8.32/2.09 % (1196918)Instructions burned: 5 (million)
% 8.32/2.09 % (1196920)dis-21_1_sil=8000:lcm=predicate:random_seed=522769083:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.32/2.09 % (1196920)Instruction limit reached!
% 8.32/2.09 % (1196920)------------------------------
% 8.32/2.09 % (1196920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.32/2.09 % (1196920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.32/2.09 % (1196920)CaDiCaL version: 2.1.3
% 8.32/2.09 % (1196920)Termination reason: Instruction limit
% 8.32/2.09 % (1196920)Termination phase: Property scanning
% 8.32/2.09 % (1196920)Time elapsed: 0.058 s
% 8.32/2.09 % (1196920)Peak memory usage: 88 MB
% 8.32/2.09 % (1196920)Instructions burned: 130 (million)
% 8.32/2.09 % (1196922)lrs+10_1_sil=8000:sp=occurrence:random_seed=3589977617:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.32/2.09 % (1196922)Refutation not found, incomplete strategy
% 8.32/2.09 % (1196922)------------------------------
% 8.32/2.09 % (1196922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.32/2.09 % (1196922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.32/2.09 % (1196922)CaDiCaL version: 2.1.3
% 8.32/2.09 % (1196922)Termination reason: Refutation not found, incomplete strategy
% 8.32/2.09 % (1196922)Time elapsed: 0.002 s
% 8.32/2.09 % (1196922)Peak memory usage: 87 MB
% 8.32/2.09 % (1196922)Instructions burned: 5 (million)
% 8.32/2.09 % (1196929)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2401493121:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.32/2.25 % (1196929)Refutation not found, incomplete strategy
% 9.32/2.25 % (1196929)------------------------------
% 9.32/2.25 % (1196929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.25 % (1196929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.25 % (1196929)CaDiCaL version: 2.1.3
% 9.32/2.25 % (1196929)Termination reason: Refutation not found, incomplete strategy
% 9.32/2.25 % (1196929)Time elapsed: 0.012 s
% 9.32/2.25 % (1196929)Peak memory usage: 88 MB
% 9.32/2.25 % (1196929)Instructions burned: 26 (million)
% 9.32/2.25 % (1196922)------------------------------
% 9.32/2.25 % (1196922)------------------------------
% 9.32/2.25 % (1196917)------------------------------
% 9.32/2.25 % (1196917)------------------------------
% 9.32/2.25 % (1196918)------------------------------
% 9.32/2.25 % (1196918)------------------------------
% 9.32/2.25 % (1196932)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2094581715:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 9.32/2.25 % (1196932)Refutation not found, incomplete strategy
% 9.32/2.25 % (1196932)------------------------------
% 9.32/2.25 % (1196932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.25 % (1196932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.25 % (1196932)CaDiCaL version: 2.1.3
% 9.32/2.25 % (1196932)Termination reason: Refutation not found, incomplete strategy
% 9.32/2.25 % (1196932)Time elapsed: 0.002 s
% 9.32/2.25 % (1196932)Peak memory usage: 87 MB
% 9.32/2.25 % (1196932)Instructions burned: 5 (million)
% 9.32/2.25 % (1196933)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=4150676314:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.32/2.25 % (1196934)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4023421109:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.32/2.25 % (1196934)Refutation not found, incomplete strategy
% 9.32/2.25 % (1196934)------------------------------
% 9.32/2.25 % (1196934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.25 % (1196934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.25 % (1196934)CaDiCaL version: 2.1.3
% 9.32/2.25 % (1196934)Termination reason: Refutation not found, incomplete strategy
% 9.32/2.25 % (1196934)Time elapsed: 0.006 s
% 9.32/2.25 % (1196934)Peak memory usage: 87 MB
% 9.32/2.25 % (1196934)Instructions burned: 8 (million)
% 9.32/2.25 % (1196929)------------------------------
% 9.32/2.25 % (1196929)------------------------------
% 9.32/2.25 % (1196932)------------------------------
% 9.32/2.25 % (1196932)------------------------------
% 9.32/2.25 % (1196933)Instruction limit reached!
% 9.32/2.25 % (1196933)------------------------------
% 9.32/2.25 % (1196933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.25 % (1196933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.25 % (1196933)CaDiCaL version: 2.1.3
% 9.32/2.25 % (1196933)Termination reason: Instruction limit
% 9.32/2.25 % (1196933)Termination phase: Saturation
% 9.32/2.25 % (1196933)Time elapsed: 0.131 s
% 9.32/2.25 % (1196933)Peak memory usage: 93 MB
% 9.32/2.25 % (1196933)Instructions burned: 249 (million)
% 9.32/2.25 % (1196939)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2245704483:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 9.32/2.25 % (1196939)Instruction limit reached!
% 9.32/2.25 % (1196939)------------------------------
% 9.32/2.25 % (1196939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.25 % (1196939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.25 % (1196939)CaDiCaL version: 2.1.3
% 9.32/2.25 % (1196939)Termination reason: Instruction limit
% 9.32/2.25 % (1196939)Termination phase: Saturation
% 9.32/2.25 % (1196939)Time elapsed: 0.029 s
% 9.32/2.25 % (1196939)Peak memory usage: 90 MB
% 9.32/2.25 % (1196939)Instructions burned: 113 (million)
% 9.32/2.25 % (1196938)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1850063782:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 9.32/2.25 % (1196934)------------------------------
% 9.32/2.25 % (1196934)------------------------------
% 9.32/2.25 % (1196940)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3075918542:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 10.38/2.48 % (1196943)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2852076805:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 10.38/2.48 % (1196940)Instruction limit reached!
% 10.38/2.48 % (1196940)------------------------------
% 10.38/2.48 % (1196940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.48 % (1196940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.48 % (1196940)CaDiCaL version: 2.1.3
% 10.38/2.48 % (1196940)Termination reason: Instruction limit
% 10.38/2.48 % (1196940)Termination phase: Property scanning
% 10.38/2.48 % (1196940)Time elapsed: 0.059 s
% 10.38/2.48 % (1196940)Peak memory usage: 88 MB
% 10.38/2.48 % (1196940)Instructions burned: 129 (million)
% 10.38/2.48 % (1196943)Instruction limit reached!
% 10.38/2.48 % (1196943)------------------------------
% 10.38/2.48 % (1196943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.48 % (1196943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196943)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196943)Termination reason: Instruction limit
% 10.38/2.49 % (1196943)Termination phase: Saturation
% 10.38/2.49 % (1196943)Time elapsed: 0.029 s
% 10.38/2.49 % (1196943)Peak memory usage: 89 MB
% 10.38/2.49 % (1196943)Instructions burned: 117 (million)
% 10.38/2.49 % (1196944)lrs+10_1_sil=8000:sp=occurrence:random_seed=2353947909:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.38/2.49 % (1196944)Refutation not found, incomplete strategy
% 10.38/2.49 % (1196944)------------------------------
% 10.38/2.49 % (1196944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196944)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196944)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.49 % (1196944)Time elapsed: 0.006 s
% 10.38/2.49 % (1196944)Peak memory usage: 87 MB
% 10.38/2.49 % (1196944)Instructions burned: 7 (million)
% 10.38/2.49 % (1196916)Refutation not found, incomplete strategy
% 10.38/2.49 % (1196916)------------------------------
% 10.38/2.49 % (1196916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196916)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196916)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.49 % (1196916)Time elapsed: 0.783 s
% 10.38/2.49 % (1196916)Peak memory usage: 137 MB
% 10.38/2.49 % (1196916)Instructions burned: 1229 (million)
% 10.38/2.49 % (1196948)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1241152109:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 10.38/2.49 % (1196947)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=708381160:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 10.38/2.49 % (1196947)Refutation not found, incomplete strategy
% 10.38/2.49 % (1196947)------------------------------
% 10.38/2.49 % (1196947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196947)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196947)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.49 % (1196947)Time elapsed: 0.081 s
% 10.38/2.49 % (1196947)Peak memory usage: 91 MB
% 10.38/2.49 % (1196947)Instructions burned: 158 (million)
% 10.38/2.49 % (1196944)------------------------------
% 10.38/2.49 % (1196944)------------------------------
% 10.38/2.49 [W927 21:41:03.187470562 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187508711 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187530084 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187536182 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187550087 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187555734 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187576631 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187582044 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187594484 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187628383 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187648397 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 [W927 21:41:03.187654404 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 10.38/2.49 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.38/2.49 % (1196916)------------------------------
% 10.38/2.49 % (1196916)------------------------------
% 10.38/2.49 % (1196948)Refutation not found, incomplete strategy
% 10.38/2.49 % (1196948)------------------------------
% 10.38/2.49 % (1196948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196948)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196948)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.49 % (1196948)Time elapsed: 0.323 s
% 10.38/2.49 % (1196948)Peak memory usage: 126 MB
% 10.38/2.49 % (1196948)Instructions burned: 839 (million)
% 10.38/2.49 % (1196915)First to succeed.
% 10.38/2.49 % (1196915)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1196779"
% 10.38/2.49 % (1196952)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3921810539:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.38/2.49 % (1196953)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2397711668:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 10.38/2.49 % (1196947)------------------------------
% 10.38/2.49 % (1196947)------------------------------
% 10.38/2.49 % (1196953)Refutation not found, incomplete strategy
% 10.38/2.49 % (1196953)------------------------------
% 10.38/2.49 % (1196953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196953)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196953)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.49 % (1196953)Time elapsed: 0.006 s
% 10.38/2.49 % (1196953)Peak memory usage: 87 MB
% 10.38/2.49 % (1196953)Instructions burned: 8 (million)
% 10.38/2.49 % (1196952)Instruction limit reached!
% 10.38/2.49 % (1196952)------------------------------
% 10.38/2.49 % (1196952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196952)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196952)Termination reason: Instruction limit
% 10.38/2.49 % (1196952)Termination phase: Saturation
% 10.38/2.49 % (1196952)Time elapsed: 0.071 s
% 10.38/2.49 % (1196952)Peak memory usage: 91 MB
% 10.38/2.49 % (1196952)Instructions burned: 136 (million)
% 10.38/2.49 % (1196914)Also succeeded, but the first one will report.
% 10.38/2.49 % (1196948)------------------------------
% 10.38/2.49 % (1196948)------------------------------
% 10.38/2.49 % (1196956)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3903495756:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 10.38/2.49 % (1196957)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2337196715:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2985 on theBenchmark for (2985ds/125Mi)
% 10.38/2.49 % (1196957)Refutation not found, incomplete strategy
% 10.38/2.49 % (1196957)------------------------------
% 10.38/2.49 % (1196957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.38/2.49 % (1196957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.38/2.49 % (1196957)CaDiCaL version: 2.1.3
% 10.38/2.49 % (1196957)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.49 % (1196957)Time elapsed: 0.016 s
% 10.38/2.49 % (1196957)Peak memory usage: 88 MB
% 10.38/2.49 % (1196957)Instructions burned: 31 (million)
% 10.38/2.49 % (1196958)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3049859012:i=134:gtgl=5:slsql=off:gtg=exists_sym_2985 on theBenchmark for (2985ds/134Mi)
% 10.38/2.49 % (1196915)Refutation found. Thanks to Tanya!
% 10.38/2.49 % SZS status Unsatisfiable for theBenchmark
% 10.38/2.49 % SZS output start Proof for theBenchmark
% See solution above
% 11.64/2.68 % (1196915)------------------------------
% 11.64/2.68 % (1196915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.64/2.68 % (1196915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.64/2.68 % (1196915)CaDiCaL version: 2.1.3
% 11.64/2.68 % (1196915)Termination reason: Refutation
% 11.64/2.68 % (1196915)Time elapsed: 1.142 s
% 11.64/2.68 % (1196915)Peak memory usage: 148 MB
% 11.64/2.68 % (1196915)Instructions burned: 1886 (million)
% 11.64/2.68 % (1196915)------------------------------
% 11.64/2.68 % (1196915)------------------------------
% 11.64/2.68 % (1196779)Success in time 1.622 s
% 11.64/2.68 % Vampire exiting
%------------------------------------------------------------------------------