%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM924_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:26:07 PM UTC 2026
% Result : Theorem 12.25s 4.64s
% Output : Refutation 12.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 29
% Syntax : Number of formulae : 187 ( 148 unt; 0 typ; 4 def)
% Number of atoms : 237 ( 97 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 99 ( 49 ~; 40 |; 3 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-5 aty)
% Number of functors : 111 ( 111 usr; 28 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 105 !; 0 ?; 105 :)
% 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,
sK0: int ).
tff(func_def_75,type,
sK1: int ).
tff(func_def_76,type,
sK2: int ).
tff(func_def_77,type,
sK3: int > int ).
tff(func_def_78,type,
sK4: int ).
tff(func_def_79,type,
sK5: ( int * int * int ) > int ).
tff(func_def_80,type,
sK6: ( int * int ) > int ).
tff(func_def_81,type,
sK7: ( real * nat ) > real ).
tff(func_def_82,type,
sK8: ( real * nat ) > real ).
tff(func_def_83,type,
sK9: ( nat * nat ) > nat ).
tff(func_def_84,type,
sK10: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_85,type,
sK11: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_86,type,
sK12: ( nat * fun_nat_bool ) > nat ).
tff(func_def_87,type,
sK13: int > int ).
tff(func_def_88,type,
sK14: ( fun_int_bool * int ) > int ).
tff(func_def_89,type,
sK15: ( fun_int_bool * int ) > int ).
tff(func_def_90,type,
sK16: ( int * int ) > int ).
tff(func_def_91,type,
sK17: int > int ).
tff(func_def_92,type,
sK18: int > int ).
tff(func_def_93,type,
sK19: ( fun_int_bool * int ) > int ).
tff(func_def_94,type,
sK20: fun_int_bool > int ).
tff(func_def_95,type,
sK21: ( fun_int_bool * int ) > int ).
tff(func_def_96,type,
sK22: ( fun_int_bool * int ) > int ).
tff(func_def_97,type,
sK23: ( fun_int_bool * int ) > int ).
tff(func_def_98,type,
sK24: fun_nat_nat > nat ).
tff(func_def_99,type,
sK25: fun_nat_nat > nat ).
tff(func_def_100,type,
sK26: ( nat * fun_nat_bool ) > nat ).
tff(func_def_101,type,
sK27: ( nat * nat ) > nat ).
tff(func_def_102,type,
sK28: ( int * int ) > int ).
tff(func_def_103,type,
sK29: ( fun_int_bool * int * int ) > int ).
tff(func_def_104,type,
sK30: ( fun_int_bool * int * int ) > int ).
tff(func_def_105,type,
sK31: ( fun_int_bool * int * int ) > int ).
tff(func_def_106,type,
sK32: ( 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,
sP33: ( int * int * int * int * fun_int_bool ) > $o ).
tff(f1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_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(f7,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_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))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
tff(f15,axiom,
! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__less__0) ).
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(f36,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_35_zmult__commute) ).
tff(f51,axiom,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
& ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zless__le) ).
tff(f75,axiom,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_le__number__of__eq__not__less) ).
tff(f88,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
tff(f93,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(one_one_int),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_zmult__1) ).
tff(f134,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_133_zadd__left__commute) ).
tff(f135,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_134_zadd__commute) ).
tff(f173,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Pls__def) ).
tff(f180,axiom,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__Pls__right) ).
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(f199,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_semiring__mult__2__right) ).
tff(f204,axiom,
! [X0: int] : ( hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_power2__eq__square) ).
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(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(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(f643,axiom,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_zero__le__mult__iff) ).
tff(f718,axiom,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_less__add__one) ).
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(f1205,conjecture,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f1206,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(negated_conjecture,[status(cth)],[f1205]) ).
tff(f1210,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(flattening,[],[f1206]) ).
tff(f2080,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),zero_zero_int)),
inference(cnf_transformation,[],[f1]) ).
tff(f2083,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(f2086,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_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))),
inference(cnf_transformation,[],[f7]) ).
tff(f2102,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(cnf_transformation,[],[f15]) ).
tff(f2126,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f35]) ).
tff(f2127,plain,
! [X0: int,X1: int] : ( hAPP_int_int(times_times_int(X0),X1) = hAPP_int_int(times_times_int(X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tff(f2150,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f51]) ).
tff(f2151,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ( X0 = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f51]) ).
tff(f2188,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X0)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
inference(cnf_transformation,[],[f75]) ).
tff(f2189,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
inference(cnf_transformation,[],[f75]) ).
tff(f2211,plain,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(cnf_transformation,[],[f88]) ).
tff(f2217,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(one_one_int),X0) = X0 ),
inference(cnf_transformation,[],[f93]) ).
tff(f2277,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,[],[f134]) ).
tff(f2278,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0) ),
inference(cnf_transformation,[],[f135]) ).
tff(f2330,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f173]) ).
tff(f2341,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),pls) = X0 ),
inference(cnf_transformation,[],[f180]) ).
tff(f2344,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f183]) ).
tff(f2360,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),number_number_of_int(bit0(bit1(pls)))) ),
inference(cnf_transformation,[],[f199]) ).
tff(f2365,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,[],[f204]) ).
tff(f2409,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(f2524,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(f2631,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(f2918,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X0),X1))) ),
inference(cnf_transformation,[],[f643]) ).
tff(f3021,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
inference(cnf_transformation,[],[f718]) ).
tff(f3519,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(f3725,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(f3728,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(cnf_transformation,[],[f1210]) ).
tff(f3730,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),pls)),
inference(definition_unfolding,[],[f2080,f2330]) ).
tff(f3732,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,[],[f2083,f2344,f2344,f2409,f2344,f2409]) ).
tff(f3734,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))),
inference(definition_unfolding,[],[f2086,f2330,f2344,f2344,f2409]) ).
tff(f3750,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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))))),pls)),
inference(definition_unfolding,[],[f2102,f2344,f2409,f2330]) ).
tff(f3807,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(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,[],[f2211,f2344,f2409]) ).
tff(f3902,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),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)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) ),
inference(definition_unfolding,[],[f2360,f2344,f2409]) ).
tff(f3907,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,[],[f2365,f2344,f2409]) ).
tff(f4113,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(times_times_int(X0),X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(definition_unfolding,[],[f2918,f2330,f2330,f2330]) ).
tff(f4238,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,[],[f3519,f2344,f2344,f2409]) ).
tff(f4330,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)),pls)),
inference(definition_unfolding,[],[f3728,f2344,f2409,f2330]) ).
tff(f4784,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(one_one_int),X0))),
inference(superposition,[],[f3021,f2278]) ).
tff(f6291,definition,
( spl38_26
<=> ( pls = 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)))) ) ),
introduced(definition,[new_symbols(definition,[spl38_26])],[avatar_definition]) ).
tff(f6292,plain,
( ( pls != 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)))) )
| spl38_26 ),
inference(avatar_component_clause,[],[f6291]) ).
tff(f6293,plain,
( ( pls = 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)))) )
| ~ spl38_26 ),
inference(avatar_component_clause,[],[f6291]) ).
tff(f6346,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))),pls))
| ~ spl38_26 ),
inference(superposition,[],[f4784,f6293]) ).
tff(f6360,plain,
( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))
| ~ spl38_26 ),
inference(forward_demodulation,[],[f6346,f3725]) ).
tff(f10635,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
inference(forward_demodulation,[],[f2188,f2126]) ).
tff(f10636,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
inference(forward_demodulation,[],[f10635,f2126]) ).
tff(f10637,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
inference(forward_demodulation,[],[f10636,f2126]) ).
tff(f10638,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
inference(forward_demodulation,[],[f10637,f2126]) ).
tff(f10668,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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(resolution,[],[f10638,f4330]) ).
tff(f10678,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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,[],[f10668,f2278]) ).
tff(f10680,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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)),pls))))))),
inference(forward_demodulation,[],[f10678,f2631]) ).
tff(f10681,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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),pls))))))),
inference(forward_demodulation,[],[f10680,f2341]) ).
tff(f10682,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
inference(forward_demodulation,[],[f10681,f2127]) ).
tff(f10683,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
inference(forward_demodulation,[],[f10682,f2341]) ).
tff(f10684,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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)))))),
inference(forward_demodulation,[],[f10683,f2217]) ).
tff(f10686,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
inference(forward_demodulation,[],[f2189,f2126]) ).
tff(f10687,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),number_number_of_int(X1))) ),
inference(forward_demodulation,[],[f10686,f2126]) ).
tff(f10688,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0)) ),
inference(forward_demodulation,[],[f10687,f2126]) ).
tff(f10689,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(forward_demodulation,[],[f10688,f2126]) ).
tff(f18597,plain,
( ( pls = 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)))) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)))))) ),
inference(resolution,[],[f10684,f2151]) ).
tff(f18605,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))))
| spl38_26 ),
inference(forward_subsumption_resolution,[],[f18597,f6292]) ).
tff(f21343,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(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)),pls))),
inference(forward_demodulation,[],[f3807,f2631]) ).
tff(f21344,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(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),pls))),
inference(forward_demodulation,[],[f21343,f2341]) ).
tff(f21345,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(forward_demodulation,[],[f21344,f2127]) ).
tff(f21346,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(forward_demodulation,[],[f21345,f2341]) ).
tff(f21347,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),
inference(forward_demodulation,[],[f21346,f2217]) ).
tff(f26909,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(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,[],[f3750,f3725]) ).
tff(f26910,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(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)),pls)))))),
inference(forward_demodulation,[],[f26909,f2631]) ).
tff(f26911,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(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),pls)))))),
inference(forward_demodulation,[],[f26910,f2341]) ).
tff(f26912,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),
inference(forward_demodulation,[],[f26911,f2127]) ).
tff(f26913,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),
inference(forward_demodulation,[],[f26912,f2341]) ).
tff(f26914,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),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,[],[f26913,f2217]) ).
tff(f26915,plain,
! [X0: int] : ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),
inference(forward_demodulation,[],[f26914,f21347]) ).
tff(f27390,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),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,[],[f3902,f2126]) ).
tff(f27391,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),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)),pls))) ),
inference(forward_demodulation,[],[f27390,f2631]) ).
tff(f27392,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),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),pls))) ),
inference(forward_demodulation,[],[f27391,f2341]) ).
tff(f27393,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ),
inference(forward_demodulation,[],[f27392,f2127]) ).
tff(f27394,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) ),
inference(forward_demodulation,[],[f27393,f2341]) ).
tff(f27395,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),X0) = hAPP_int_int(times_times_int(X0),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) ),
inference(forward_demodulation,[],[f27394,f2217]) ).
tff(f27953,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(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)),pls)))) ),
inference(forward_demodulation,[],[f3907,f2631]) ).
tff(f27954,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(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(one_one_int),pls)))) ),
inference(forward_demodulation,[],[f27953,f2341]) ).
tff(f27955,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(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) ),
inference(forward_demodulation,[],[f27954,f2127]) ).
tff(f27956,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(one_one_int),pls)))) ),
inference(forward_demodulation,[],[f27955,f27395]) ).
tff(f27957,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,[],[f27956,f2277]) ).
tff(f27958,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,[],[f27957,f2341]) ).
tff(f27959,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,[],[f27958,f2341]) ).
tff(f27960,plain,
! [X0: int] : ( hAPP_int_int(times_times_int(X0),X0) = hAPP_nat_int(power_power_int(X0),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) ),
inference(forward_demodulation,[],[f27959,f21347]) ).
tff(f30458,definition,
( spl38_131
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),t)) ),
introduced(definition,[new_symbols(definition,[spl38_131])],[avatar_definition]) ).
tff(f37362,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(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))))),m)))),
inference(forward_demodulation,[],[f3734,f2278]) ).
tff(f37363,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),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,[],[f37362,f2127]) ).
tff(f37364,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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,[],[f37363,f2126]) ).
tff(f37365,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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(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,[],[f37364,f2631]) ).
tff(f37366,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),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)),pls))))))),
inference(forward_demodulation,[],[f37365,f2631]) ).
tff(f37367,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),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),pls))))))),
inference(forward_demodulation,[],[f37366,f2341]) ).
tff(f37368,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
inference(forward_demodulation,[],[f37367,f2127]) ).
tff(f37369,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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,[],[f37368,f2524]) ).
tff(f37370,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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,[],[f37369,f27395]) ).
tff(f37371,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_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),one_one_int)),one_one_int))))))),
inference(forward_demodulation,[],[f37370,f2277]) ).
tff(f37372,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_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),one_one_int)))))))),
inference(forward_demodulation,[],[f37371,f2278]) ).
tff(f37373,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_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),one_one_int)))))))),
inference(forward_demodulation,[],[f37372,f2341]) ).
tff(f37374,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(m),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,[],[f37373,f2524]) ).
tff(f37375,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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,[],[f37374,f2217]) ).
tff(f39500,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(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))))),m))),t),
inference(forward_demodulation,[],[f4238,f2278]) ).
tff(f39501,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),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))))))),t),
inference(forward_demodulation,[],[f39500,f2127]) ).
tff(f39502,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))),t),
inference(forward_demodulation,[],[f39501,f2126]) ).
tff(f39503,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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(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)))))),t),
inference(forward_demodulation,[],[f39502,f2631]) ).
tff(f39504,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),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)),pls)))))),t),
inference(forward_demodulation,[],[f39503,f2631]) ).
tff(f39505,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),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),pls)))))),t),
inference(forward_demodulation,[],[f39504,f2341]) ).
tff(f39506,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),t),
inference(forward_demodulation,[],[f39505,f2127]) ).
tff(f39507,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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)))))),t),
inference(forward_demodulation,[],[f39506,f2524]) ).
tff(f39508,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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)))))),t),
inference(forward_demodulation,[],[f39507,f27395]) ).
tff(f39509,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_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),one_one_int)),one_one_int)))))),t),
inference(forward_demodulation,[],[f39508,f2277]) ).
tff(f39510,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_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),one_one_int))))))),t),
inference(forward_demodulation,[],[f39509,f2278]) ).
tff(f39511,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_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),one_one_int))))))),t),
inference(forward_demodulation,[],[f39510,f2341]) ).
tff(f39512,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(m),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))))))),t),
inference(forward_demodulation,[],[f39511,f2524]) ).
tff(f39513,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))),t),
inference(forward_demodulation,[],[f39512,f2217]) ).
tff(f39667,definition,
( spl38_190
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)))) ),
introduced(definition,[new_symbols(definition,[spl38_190])],[avatar_definition]) ).
tff(f39671,definition,
( spl38_191
<=> hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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))))))) ),
introduced(definition,[new_symbols(definition,[spl38_191])],[avatar_definition]) ).
tff(f42149,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),t))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))),pls)) ),
inference(superposition,[],[f4113,f39513]) ).
tff(f42155,plain,
( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),t)) ),
inference(forward_demodulation,[],[f42149,f3725]) ).
tff(f42168,plain,
( spl38_131
| ~ spl38_190
| spl38_191 ),
inference(avatar_split_clause,[],[f42155,f39671,f39667,f30458]) ).
tff(f45080,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,[],[f3732,f2278]) ).
tff(f45081,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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)),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(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)),pls))),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)),pls))))),m)),one_one_int)),t),
inference(forward_demodulation,[],[f45080,f2631]) ).
tff(f45082,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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)),pls))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(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)),pls))),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)),pls))))),m))),t),
inference(forward_demodulation,[],[f45081,f2278]) ).
tff(f45083,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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)),pls))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(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)),pls))),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)),pls))))))),t),
inference(forward_demodulation,[],[f45082,f2127]) ).
tff(f45084,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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)),pls))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(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)),pls))),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)),pls)))))),t),
inference(forward_demodulation,[],[f45083,f2126]) ).
tff(f45085,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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)),pls))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),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)),pls)))))),t),
inference(forward_demodulation,[],[f45084,f2631]) ).
tff(f45086,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(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),pls))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),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),pls)))))),t),
inference(forward_demodulation,[],[f45085,f2341]) ).
tff(f45087,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),t),
inference(forward_demodulation,[],[f45086,f2127]) ).
tff(f45088,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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)))))),t),
inference(forward_demodulation,[],[f45087,f2524]) ).
tff(f45089,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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)))))),t),
inference(forward_demodulation,[],[f45088,f27395]) ).
tff(f45090,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_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),one_one_int)),one_one_int)))))),t),
inference(forward_demodulation,[],[f45089,f2277]) ).
tff(f45091,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_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),one_one_int))))))),t),
inference(forward_demodulation,[],[f45090,f2278]) ).
tff(f45092,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_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),one_one_int))))))),t),
inference(forward_demodulation,[],[f45091,f2341]) ).
tff(f45093,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(times_times_int(m),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))))))),t),
inference(forward_demodulation,[],[f45092,f2524]) ).
tff(f45094,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))),t),
inference(forward_demodulation,[],[f45093,f2217]) ).
tff(f45095,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(times_times_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))),
inference(forward_demodulation,[],[f45094,f39513]) ).
tff(f45096,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = 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)))),
inference(forward_demodulation,[],[f45095,f27395]) ).
tff(f45097,plain,
twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
inference(forward_demodulation,[],[f45096,f21347]) ).
tff(f45098,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(forward_demodulation,[],[f45097,f27960]) ).
tff(f45898,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))))
| spl38_26 ),
inference(forward_demodulation,[],[f18605,f21347]) ).
tff(f45941,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))))
| spl38_26 ),
inference(forward_demodulation,[],[f45898,f27960]) ).
tff(f45967,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))))
| spl38_26 ),
inference(forward_demodulation,[],[f45941,f45098]) ).
tff(f50398,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),twoSqu949963151sum2sq(product_Pair_int_int(s,one_one_int))))
| spl38_26 ),
inference(resolution,[],[f45967,f2150]) ).
tff(f50428,plain,
( spl38_190
| spl38_26 ),
inference(avatar_split_clause,[],[f50398,f6291,f39667]) ).
tff(f59570,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))),pls)),
inference(resolution,[],[f10689,f37375]) ).
tff(f59579,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),t)),
inference(resolution,[],[f10689,f3730]) ).
tff(f59586,plain,
~ spl38_131,
inference(avatar_split_clause,[],[f59579,f30458]) ).
tff(f59594,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_eq_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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,[],[f59570,f3725]) ).
tff(f59603,plain,
~ spl38_191,
inference(avatar_split_clause,[],[f59594,f39671]) ).
tff(f59611,plain,
( hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))))
| ~ spl38_26 ),
inference(forward_demodulation,[],[f6360,f21347]) ).
tff(f60740,plain,
( $false
| ~ spl38_26 ),
inference(forward_subsumption_resolution,[],[f59611,f26915]) ).
tff(f60741,plain,
~ spl38_26,
inference(avatar_contradiction_clause,[],[f60740]) ).
cnf(s301,plain,
( spl38_131
| ~ spl38_190
| spl38_191 ),
inference(sat_conversion,[],[f42168]) ).
cnf(s460,plain,
( spl38_26
| spl38_190 ),
inference(sat_conversion,[],[f50428]) ).
cnf(s812,plain,
~ spl38_131,
inference(sat_conversion,[],[f59586]) ).
cnf(s813,plain,
~ spl38_191,
inference(sat_conversion,[],[f59603]) ).
cnf(s823,plain,
~ spl38_26,
inference(sat_conversion,[],[f60741]) ).
cnf(s920,plain,
spl38_190,
inference(rat,[],[s460,s823]) ).
cnf(s939,plain,
$false,
inference(rat,[],[s301,s813,s920,s812]) ).
tff(f63305,plain,
$false,
inference(avatar_sat_refutation,[],[s939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.40 % Computer : n013.cluster.edu
% 0.17/0.40 % Model : x86_64 x86_64
% 0.17/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.40 % Memory : 8046.5625MB
% 0.17/0.40 % OS : Linux 6.8.0-71-generic
% 0.17/0.40 % CPULimit : 300
% 0.17/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Sun Sep 27 21:40:21 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.44 Running first-order model finding
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.25/4.63 % (579567)Will run a generic schedule for satisfiability detection.
% 12.25/4.63 % (579573)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=806789001_2999 on theBenchmark for (2999ds/0Mi)
% 12.25/4.63 % (579577)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2020442511:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 12.25/4.63 % (579574)% WARNING: option uhcvi not known.
% 12.25/4.63 % (579575)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3186291768:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 12.25/4.63 % (579574)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=249461460:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 12.25/4.63 % (579578)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2473540474:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 12.25/4.63 % (579576)dis+10_1_sil=32000:sp=arity:random_seed=1465990317:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 12.25/4.63 % (579579)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3749613277:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 12.25/4.63 % (579577)Instruction limit reached!
% 12.25/4.63 % (579577)------------------------------
% 12.25/4.63 % (579577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579577)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579577)Termination reason: Instruction limit
% 12.25/4.63 % (579577)Termination phase: Property scanning
% 12.25/4.63 % (579577)Time elapsed: 0.087 s
% 12.25/4.63 % (579577)Peak memory usage: 13 MB
% 12.25/4.63 % (579577)Instructions burned: 117 (million)
% 12.25/4.63 % (579576)Instruction limit reached!
% 12.25/4.63 % (579576)------------------------------
% 12.25/4.63 % (579576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579576)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579576)Termination reason: Instruction limit
% 12.25/4.63 % (579576)Termination phase: Saturation
% 12.25/4.63 % (579576)Time elapsed: 0.091 s
% 12.25/4.63 % (579576)Peak memory usage: 13 MB
% 12.25/4.63 % (579576)Instructions burned: 103 (million)
% 12.25/4.63 % (579589)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3999549811:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 12.25/4.63 % (579590)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=243446262:i=131:bd=preordered:fsd=on_2997 on theBenchmark for (2997ds/131Mi)
% 12.25/4.63 % (579578)Instruction limit reached!
% 12.25/4.63 % (579578)------------------------------
% 12.25/4.63 % (579578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579578)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579578)Termination reason: Instruction limit
% 12.25/4.63 % (579578)Termination phase: Saturation
% 12.25/4.63 % (579578)Time elapsed: 0.116 s
% 12.25/4.63 % (579578)Peak memory usage: 14 MB
% 12.25/4.63 % (579578)Instructions burned: 132 (million)
% 12.25/4.63 % (579579)Instruction limit reached!
% 12.25/4.63 % (579579)------------------------------
% 12.25/4.63 % (579579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579579)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579579)Termination reason: Instruction limit
% 12.25/4.63 % (579579)Termination phase: Saturation
% 12.25/4.63 % (579579)Time elapsed: 0.149 s
% 12.25/4.63 % (579579)Peak memory usage: 15 MB
% 12.25/4.63 % (579579)Instructions burned: 159 (million)
% 12.25/4.63 % (579594)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2315796243:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2997 on theBenchmark for (2997ds/684Mi)
% 12.25/4.63 % (579596)ott-21_1_sil=16000:fs=off:random_seed=3474198953:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 12.25/4.63 % (579590)Instruction limit reached!
% 12.25/4.63 % (579590)------------------------------
% 12.25/4.63 % (579590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579590)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579590)Termination reason: Instruction limit
% 12.25/4.63 % (579590)Termination phase: Property scanning
% 12.25/4.63 % (579590)Time elapsed: 0.107 s
% 12.25/4.63 % (579590)Peak memory usage: 13 MB
% 12.25/4.63 % (579590)Instructions burned: 131 (million)
% 12.25/4.63 % (579599)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3352870126:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 12.25/4.63 % (579596)Instruction limit reached!
% 12.25/4.63 % (579596)------------------------------
% 12.25/4.63 % (579596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579596)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579596)Termination reason: Instruction limit
% 12.25/4.63 % (579596)Termination phase: Saturation
% 12.25/4.63 % (579596)Time elapsed: 0.159 s
% 12.25/4.63 % (579596)Peak memory usage: 14 MB
% 12.25/4.63 % (579596)Instructions burned: 181 (million)
% 12.25/4.63 % (579603)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1152707554:fmbsr=1.3:i=865:ins=25_2995 on theBenchmark for (2995ds/865Mi)
% 12.25/4.63 % (579599)Instruction limit reached!
% 12.25/4.63 % (579599)------------------------------
% 12.25/4.63 % (579599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579599)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579599)Termination reason: Instruction limit
% 12.25/4.63 % (579599)Termination phase: Saturation
% 12.25/4.63 % (579599)Time elapsed: 0.445 s
% 12.25/4.63 % (579599)Peak memory usage: 16 MB
% 12.25/4.63 % (579599)Instructions burned: 477 (million)
% 12.25/4.63 % (579589)Instruction limit reached!
% 12.25/4.63 % (579589)------------------------------
% 12.25/4.63 % (579589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579589)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579589)Termination reason: Instruction limit
% 12.25/4.63 % (579589)Termination phase: Finite model building preprocessing
% 12.25/4.63 % (579589)Time elapsed: 0.604 s
% 12.25/4.63 % (579589)Peak memory usage: 21 MB
% 12.25/4.63 % (579589)Instructions burned: 715 (million)
% 12.25/4.63 % (579608)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=971017742:i=1179_2991 on theBenchmark for (2991ds/1179Mi)
% 12.25/4.63 % (579609)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3364542109:i=889:ins=1_2991 on theBenchmark for (2991ds/889Mi)
% 12.25/4.63 % (579594)Instruction limit reached!
% 12.25/4.63 % (579594)------------------------------
% 12.25/4.63 % (579594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579594)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579594)Termination reason: Instruction limit
% 12.25/4.63 % (579594)Termination phase: Saturation
% 12.25/4.63 % (579594)Time elapsed: 0.715 s
% 12.25/4.63 % (579594)Peak memory usage: 20 MB
% 12.25/4.63 % (579594)Instructions burned: 684 (million)
% 12.25/4.63 % (579612)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1379722384:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2990 on theBenchmark for (2990ds/692Mi)
% 12.25/4.63 % (579603)Instruction limit reached!
% 12.25/4.63 % (579603)------------------------------
% 12.25/4.63 % (579603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579603)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579603)Termination reason: Instruction limit
% 12.25/4.63 % (579603)Termination phase: Finite model building preprocessing
% 12.25/4.63 % (579603)Time elapsed: 0.760 s
% 12.25/4.63 % (579603)Peak memory usage: 23 MB
% 12.25/4.63 % (579603)Instructions burned: 865 (million)
% 12.25/4.63 % (579616)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=438130088:i=879:kws=inv_precedence:fsr=off_2987 on theBenchmark for (2987ds/879Mi)
% 12.25/4.63 % (579609)Instruction limit reached!
% 12.25/4.63 % (579609)------------------------------
% 12.25/4.63 % (579609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579609)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579609)Termination reason: Instruction limit
% 12.25/4.63 % (579609)Termination phase: Finite model building preprocessing
% 12.25/4.63 % (579609)Time elapsed: 0.767 s
% 12.25/4.63 % (579609)Peak memory usage: 23 MB
% 12.25/4.63 % (579609)Instructions burned: 890 (million)
% 12.25/4.63 % (579620)fmb+10_1_sil=64000:random_seed=3830540705:i=22061:nm=2:gsp=on_2983 on theBenchmark for (2983ds/22061Mi)
% 12.25/4.63 % (579612)Instruction limit reached!
% 12.25/4.63 % (579612)------------------------------
% 12.25/4.63 % (579612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579612)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579612)Termination reason: Instruction limit
% 12.25/4.63 % (579612)Termination phase: Saturation
% 12.25/4.63 % (579612)Time elapsed: 0.667 s
% 12.25/4.63 % (579612)Peak memory usage: 19 MB
% 12.25/4.63 % (579612)Instructions burned: 693 (million)
% 12.25/4.63 % (579623)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1603678507:i=9515:nm=5_2983 on theBenchmark for (2983ds/9515Mi)
% 12.25/4.63 % TRYING [1,1,1,1,1]
% 12.25/4.63 % TRYING [2,1,1,1,1]
% 12.25/4.63 % TRYING [2,1,1,1,2]
% 12.25/4.63 % TRYING [2,1,1,2,2]
% 12.25/4.63 % (579608)Instruction limit reached!
% 12.25/4.63 % (579608)------------------------------
% 12.25/4.63 % (579608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579608)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579608)Termination reason: Instruction limit
% 12.25/4.63 % (579608)Termination phase: Saturation
% 12.25/4.63 % (579608)Time elapsed: 1.168 s
% 12.25/4.63 % (579608)Peak memory usage: 24 MB
% 12.25/4.63 % (579608)Instructions burned: 1179 (million)
% 12.25/4.63 % (579627)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1192410832:fmbsr=1.7:i=920_2979 on theBenchmark for (2979ds/920Mi)
% 12.25/4.63 % (579616)Instruction limit reached!
% 12.25/4.63 % (579616)------------------------------
% 12.25/4.63 % (579616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579616)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579616)Termination reason: Instruction limit
% 12.25/4.63 % (579616)Termination phase: Saturation
% 12.25/4.63 % (579616)Time elapsed: 0.763 s
% 12.25/4.63 % (579616)Peak memory usage: 19 MB
% 12.25/4.63 % (579616)Instructions burned: 880 (million)
% 12.25/4.63 % TRYING [2,1,2,2,2]
% 12.25/4.63 % (579629)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=284547302:i=5131_2979 on theBenchmark for (2979ds/5131Mi)
% 12.25/4.63 % TRYING [3,1,2,2,2]
% 12.25/4.63 % TRYING [2,2,2,2,2]
% 12.25/4.63 % (579627)Instruction limit reached!
% 12.25/4.63 % (579627)------------------------------
% 12.25/4.63 % (579627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.63 % (579627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.63 % (579627)CaDiCaL version: 2.1.3
% 12.25/4.63 % (579627)Termination reason: Instruction limit
% 12.25/4.63 % (579627)Termination phase: Finite model building preprocessing
% 12.25/4.63 % (579627)Time elapsed: 0.720 s
% 12.25/4.63 % (579627)Peak memory usage: 24 MB
% 12.25/4.63 % (579627)Instructions burned: 920 (million)
% 12.25/4.63 % (579634)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1965977726:i=1472:ins=7:fdi=8:gsp=on_2972 on theBenchmark for (2972ds/1472Mi)
% 12.25/4.64 % TRYING [2,1,3,2,2]
% 12.25/4.64 % TRYING [3,2,2,2,2]
% 12.25/4.64 % TRYING [2,1,3,2,3]
% 12.25/4.64 % TRYING [4,1,2,2,2]
% 12.25/4.64 % (579574) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579567-579574"...
% 12.25/4.64 % (579574)...printing done.
% 12.25/4.64 % (579574)Refutation found. Thanks to Tanya!
% 12.25/4.64 % SZS status Theorem for theBenchmark
% 12.25/4.64 % SZS output start Proof for theBenchmark
% See solution above
% 12.25/4.64 % (579574)------------------------------
% 12.25/4.64 % (579574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.25/4.64 % (579574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/4.64 % (579574)CaDiCaL version: 2.1.3
% 12.25/4.64 % (579574)Termination reason: Refutation
% 12.25/4.64 % (579574)Time elapsed: 4.018 s
% 12.25/4.64 % (579574)Peak memory usage: 38 MB
% 12.25/4.64 % (579574)Instructions burned: 4070 (million)
% 12.25/4.64 % (579567)Success in time 4.182 s
% 12.25/4.64 % Vampire exiting
%------------------------------------------------------------------------------