%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM926_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:17:36 PM UTC 2026
% Result : Theorem 5.92s 1.85s
% Output : Refutation 7.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 14 ( 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 : 115 ( 115 usr; 32 con; 0-3 aty)
% Number of variables : 30 ( 18 !; 12 ?; 30 :)
% 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 ).
tff(func_def_78,type,
sK5: int ).
tff(func_def_79,type,
sK6: int ).
tff(func_def_80,type,
sK7: int ).
tff(func_def_81,type,
sK8: int > int ).
tff(func_def_82,type,
sK9: int ).
tff(func_def_83,type,
sK10: ( int * int * int ) > int ).
tff(func_def_84,type,
sK11: ( int * int ) > int ).
tff(func_def_85,type,
sK12: ( real * nat ) > real ).
tff(func_def_86,type,
sK13: ( real * nat ) > real ).
tff(func_def_87,type,
sK14: ( nat * nat ) > nat ).
tff(func_def_88,type,
sK15: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_89,type,
sK16: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_90,type,
sK17: ( nat * fun_nat_bool ) > nat ).
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 ) > int ).
tff(func_def_95,type,
sK22: int > int ).
tff(func_def_96,type,
sK23: ( int * int ) > int ).
tff(func_def_97,type,
sK24: ( fun_int_bool * int ) > int ).
tff(func_def_98,type,
sK25: ( fun_int_bool * int ) > int ).
tff(func_def_99,type,
sK26: fun_int_bool > int ).
tff(func_def_100,type,
sK27: ( fun_int_bool * int ) > int ).
tff(func_def_101,type,
sK28: ( fun_int_bool * int ) > int ).
tff(func_def_102,type,
sK29: fun_nat_nat > nat ).
tff(func_def_103,type,
sK30: fun_nat_nat > nat ).
tff(func_def_104,type,
sK31: ( nat * fun_nat_bool ) > nat ).
tff(func_def_105,type,
sK32: ( nat * nat ) > nat ).
tff(func_def_106,type,
sK33: ( int * int ) > int ).
tff(func_def_107,type,
sK34: ( fun_int_bool * int * int ) > int ).
tff(func_def_108,type,
sK35: ( fun_int_bool * int * int ) > int ).
tff(func_def_109,type,
sK36: ( fun_int_bool * int * int ) > int ).
tff(func_def_110,type,
sK37: ( fun_int_bool * int * int ) > int ).
tff(func_def_111,type,
sK38: ( int * int ) > int ).
tff(func_def_112,type,
sK39: ( nat * nat ) > nat ).
tff(func_def_113,type,
sK40: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_114,type,
sK41: ( 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(f1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(f2,axiom,
( ( t = one_one_int )
=> ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = 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/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f3,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = 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/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f207,axiom,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Bit0__def) ).
tff(f254,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/sandbox/benchmark/theBenchmark.p',fact_253_Bit1__def) ).
tff(f359,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_Pls__def) ).
tff(f571,axiom,
! [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)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_order__le__neq__implies__less) ).
tff(f1205,conjecture,
? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = 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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f1206,negated_conjecture,
~ ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = 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(negated_conjecture,[status(cth)],[f1205]) ).
tff(f1210,plain,
( ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) )
| ( one_one_int != t ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f1211,plain,
( ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f1439,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(ennf_transformation,[],[f571]) ).
tff(f1440,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(flattening,[],[f1439]) ).
tff(f2083,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != 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(ennf_transformation,[],[f1206]) ).
tff(f2086,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK2),number_number_of_nat(bit0(bit1(pls))))) )
| ( one_one_int != t ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f1210]) ).
tff(f2087,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK4),number_number_of_nat(bit0(bit1(pls))))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f1211]) ).
tff(f2470,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(cnf_transformation,[],[f1]) ).
tff(f2471,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK2),number_number_of_nat(bit0(bit1(pls))))) )
| ( one_one_int != t ) ),
inference(cnf_transformation,[],[f2086]) ).
tff(f2472,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK4),number_number_of_nat(bit0(bit1(pls))))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(cnf_transformation,[],[f2087]) ).
tff(f2747,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f207]) ).
tff(f2794,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,[],[f254]) ).
tff(f2923,plain,
pls = zero_zero_int,
inference(cnf_transformation,[],[f359]) ).
tff(f3228,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,[],[f1440]) ).
tff(f4168,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != 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,[],[f2083]) ).
tff(f4169,plain,
( ( 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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK1),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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK2),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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) )
| ( one_one_int != t ) ),
inference(definition_unfolding,[],[f2471,f2747,f2747,f2794,f2923,f2747,f2794,f2923,f2747,f2794,f2923]) ).
tff(f4170,plain,
( ( 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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK3),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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK4),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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(definition_unfolding,[],[f2472,f2747,f2747,f2794,f2923,f2747,f2794,f2923,f2747,f2794,f2923]) ).
tff(f4566,plain,
! [X0: int,X1: 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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) != hAPP_int_int(plus_plus_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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(X1),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),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) ),
inference(definition_unfolding,[],[f4168,f2747,f2794,f2923,f2747,f2794,f2923,f2747,f2747,f2794,f2923]) ).
tff(f5053,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(forward_subsumption_resolution,[],[f4170,f4566]) ).
tff(f5054,plain,
one_one_int != t,
inference(forward_subsumption_resolution,[],[f4169,f4566]) ).
tff(f6092,plain,
$false,
inference(unit_resulting_resolution,[],[f3228,f5054,f5053,f2470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:44:11 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.92/1.85 % (3346580)Detected formulas, will run a generic FOF schedule.
% 5.92/1.85 % (3346586)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=548480465:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.92/1.85 % (3346585)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=4278596499:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.92/1.85 % (3346590)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=827404123:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.92/1.85 % (3346591)dis-21_1_sil=8000:lcm=predicate:random_seed=1261775349: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)
% 5.92/1.85 % (3346589)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3907974878:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.92/1.85 % (3346587)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=1840150787:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.92/1.85 % (3346588)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1488191786:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.92/1.85 % (3346591)Instruction limit reached!
% 5.92/1.85 % (3346591)------------------------------
% 5.92/1.85 % (3346591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346591)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346591)Termination reason: Instruction limit
% 5.92/1.85 % (3346591)Termination phase: Property scanning
% 5.92/1.85 % (3346591)Time elapsed: 0.055 s
% 5.92/1.85 % (3346591)Peak memory usage: 88 MB
% 5.92/1.85 % (3346591)Instructions burned: 129 (million)
% 5.92/1.85 % (3346588)Instruction limit reached!
% 5.92/1.85 % (3346588)------------------------------
% 5.92/1.85 % (3346588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346588)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346588)Termination reason: Instruction limit
% 5.92/1.85 % (3346588)Termination phase: Saturation
% 5.92/1.85 % (3346588)Time elapsed: 0.059 s
% 5.92/1.85 % (3346588)Peak memory usage: 90 MB
% 5.92/1.85 % (3346588)Instructions burned: 110 (million)
% 5.92/1.85 % (3346589)Instruction limit reached!
% 5.92/1.85 % (3346589)------------------------------
% 5.92/1.85 % (3346589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346589)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346589)Termination reason: Instruction limit
% 5.92/1.85 % (3346589)Termination phase: Saturation
% 5.92/1.85 % (3346589)Time elapsed: 0.062 s
% 5.92/1.85 % (3346589)Peak memory usage: 90 MB
% 5.92/1.85 % (3346589)Instructions burned: 120 (million)
% 5.92/1.85 % (3346590)Instruction limit reached!
% 5.92/1.85 % (3346590)------------------------------
% 5.92/1.85 % (3346590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346590)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346590)Termination reason: Instruction limit
% 5.92/1.85 % (3346590)Termination phase: Saturation
% 5.92/1.85 % (3346590)Time elapsed: 0.064 s
% 5.92/1.85 % (3346590)Peak memory usage: 90 MB
% 5.92/1.85 % (3346590)Instructions burned: 139 (million)
% 5.92/1.85 % (3346600)lrs+10_1_sil=32000:urr=on:br=off:random_seed=712787117:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.92/1.85 % (3346599)lrs+10_1_sil=8000:sp=occurrence:random_seed=878553220:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.92/1.85 % (3346601)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2801981547:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.92/1.85 % (3346602)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=3574959115:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.92/1.85 % (3346600)Instruction limit reached!
% 5.92/1.85 % (3346600)------------------------------
% 5.92/1.85 % (3346600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346600)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346600)Termination reason: Instruction limit
% 5.92/1.85 % (3346600)Termination phase: Saturation
% 5.92/1.85 % (3346600)Time elapsed: 0.077 s
% 5.92/1.85 % (3346600)Peak memory usage: 90 MB
% 5.92/1.85 % (3346600)Instructions burned: 157 (million)
% 5.92/1.85 % (3346599)Instruction limit reached!
% 5.92/1.85 % (3346599)------------------------------
% 5.92/1.85 % (3346599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346599)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346599)Termination reason: Instruction limit
% 5.92/1.85 % (3346599)Termination phase: Saturation
% 5.92/1.85 % (3346599)Time elapsed: 0.162 s
% 5.92/1.85 % (3346599)Peak memory usage: 92 MB
% 5.92/1.85 % (3346599)Instructions burned: 285 (million)
% 5.92/1.85 % (3346602)Instruction limit reached!
% 5.92/1.85 % (3346602)------------------------------
% 5.92/1.85 % (3346602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346602)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346602)Termination reason: Instruction limit
% 5.92/1.85 % (3346602)Termination phase: Saturation
% 5.92/1.85 % (3346602)Time elapsed: 0.143 s
% 5.92/1.85 % (3346602)Peak memory usage: 92 MB
% 5.92/1.85 % (3346602)Instructions burned: 248 (million)
% 5.92/1.85 % (3346601)Instruction limit reached!
% 5.92/1.85 % (3346601)------------------------------
% 5.92/1.85 % (3346601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346601)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346601)Termination reason: Instruction limit
% 5.92/1.85 % (3346601)Termination phase: Saturation
% 5.92/1.85 % (3346601)Time elapsed: 0.182 s
% 5.92/1.85 % (3346601)Peak memory usage: 92 MB
% 5.92/1.85 % (3346601)Instructions burned: 325 (million)
% 5.92/1.85 % (3346607)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4268817623:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.92/1.85 % (3346609)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=403207058:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.92/1.85 % (3346608)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=222760362:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.92/1.85 % (3346611)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1848677046:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.92/1.85 % (3346609)Instruction limit reached!
% 5.92/1.85 % (3346609)------------------------------
% 5.92/1.85 % (3346609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346609)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346609)Termination reason: Instruction limit
% 5.92/1.85 % (3346609)Termination phase: Saturation
% 5.92/1.85 % (3346609)Time elapsed: 0.052 s
% 5.92/1.85 % (3346609)Peak memory usage: 90 MB
% 5.92/1.85 % (3346609)Instructions burned: 114 (million)
% 5.92/1.85 % (3346607)Instruction limit reached!
% 5.92/1.85 % (3346607)------------------------------
% 5.92/1.85 % (3346607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346607)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346607)Termination reason: Instruction limit
% 5.92/1.85 % (3346607)Termination phase: Saturation
% 5.92/1.85 % (3346607)Time elapsed: 0.150 s
% 5.92/1.85 % (3346607)Peak memory usage: 92 MB
% 5.92/1.85 % (3346607)Instructions burned: 294 (million)
% 5.92/1.85 % (3346611)Instruction limit reached!
% 5.92/1.85 % (3346611)------------------------------
% 5.92/1.85 % (3346611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346611)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346611)Termination reason: Instruction limit
% 5.92/1.85 % (3346611)Termination phase: Property scanning
% 5.92/1.85 % (3346611)Time elapsed: 0.053 s
% 5.92/1.85 % (3346611)Peak memory usage: 88 MB
% 5.92/1.85 % (3346611)Instructions burned: 127 (million)
% 5.92/1.85 % (3346586)First to succeed.
% 5.92/1.85 % (3346586)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3346580"
% 5.92/1.85 % (3346615)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=447500390:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.92/1.85 % (3346616)lrs+10_1_sil=8000:sp=occurrence:random_seed=4014640892:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.92/1.85 % (3346617)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2231973770:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.92/1.85 % (3346615)Instruction limit reached!
% 5.92/1.85 % (3346615)------------------------------
% 5.92/1.85 % (3346615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.85 % (3346615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.85 % (3346615)CaDiCaL version: 2.1.3
% 5.92/1.85 % (3346615)Termination reason: Instruction limit
% 5.92/1.85 % (3346615)Termination phase: Saturation
% 5.92/1.85 % (3346615)Time elapsed: 0.058 s
% 5.92/1.85 % (3346615)Peak memory usage: 90 MB
% 5.92/1.85 % (3346615)Instructions burned: 115 (million)
% 5.92/1.85 % (3346586)Refutation found. Thanks to Tanya!
% 5.92/1.85 % SZS status Theorem for theBenchmark
% 5.92/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.19/2.04 % (3346586)------------------------------
% 7.19/2.04 % (3346586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.19/2.04 % (3346586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.19/2.04 % (3346586)CaDiCaL version: 2.1.3
% 7.19/2.04 % (3346586)Termination reason: Refutation
% 7.19/2.04 % (3346586)Time elapsed: 0.631 s
% 7.19/2.04 % (3346586)Peak memory usage: 150 MB
% 7.19/2.04 % (3346586)Instructions burned: 1766 (million)
% 7.19/2.04 % (3346586)------------------------------
% 7.19/2.04 % (3346586)------------------------------
% 7.19/2.04 % (3346580)Success in time 0.982 s
% 7.19/2.04 % Vampire exiting
%------------------------------------------------------------------------------