%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM924_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 : n020.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 12:17:30 PM UTC 2026
% Result : Theorem 5.31s 1.79s
% Output : Refutation 6.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 61 ( 58 unt; 0 typ; 1 def)
% Number of atoms : 64 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 10 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 18 ( 4 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 111 ( 111 usr; 28 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(type_def_9,type,
fun_bool_bool: $tType ).
tff(type_def_10,type,
fun_bo1549164019l_bool: $tType ).
tff(type_def_11,type,
fun_int_bool: $tType ).
tff(type_def_12,type,
fun_int_int: $tType ).
tff(type_def_13,type,
fun_in531499254l_bool: $tType ).
tff(type_def_14,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_15,type,
fun_nat_bool: $tType ).
tff(type_def_16,type,
fun_nat_int: $tType ).
tff(type_def_17,type,
fun_nat_nat: $tType ).
tff(type_def_18,type,
fun_nat_real: $tType ).
tff(type_def_19,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_20,type,
fun_real_bool: $tType ).
tff(type_def_21,type,
fun_real_real: $tType ).
tff(type_def_22,type,
fun_re413263731l_bool: $tType ).
tff(type_def_23,type,
product_prod_int_int: $tType ).
tff(func_def_0,type,
cOMBB_1652995168ol_int: ( fun_bo1549164019l_bool * fun_int_bool ) > fun_in531499254l_bool ).
tff(func_def_1,type,
cOMBC_int_int_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_2,type,
cOMBS_int_bool_bool: ( fun_in531499254l_bool * fun_int_bool ) > fun_int_bool ).
tff(func_def_3,type,
div_mod_int: int > fun_int_int ).
tff(func_def_4,type,
div_mod_nat: nat > fun_nat_nat ).
tff(func_def_5,type,
minus_minus_int: int > fun_int_int ).
tff(func_def_6,type,
minus_minus_nat: nat > fun_nat_nat ).
tff(func_def_7,type,
minus_minus_real: real > fun_real_real ).
tff(func_def_8,type,
one_one_int: int ).
tff(func_def_9,type,
one_one_nat: nat ).
tff(func_def_10,type,
one_one_real: real ).
tff(func_def_11,type,
plus_plus_int: int > fun_int_int ).
tff(func_def_12,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_13,type,
plus_plus_real: real > fun_real_real ).
tff(func_def_14,type,
times_times_int: int > fun_int_int ).
tff(func_def_15,type,
times_times_nat: nat > fun_nat_nat ).
tff(func_def_16,type,
times_times_real: real > fun_real_real ).
tff(func_def_17,type,
zero_zero_int: int ).
tff(func_def_18,type,
zero_zero_nat: nat ).
tff(func_def_19,type,
zero_zero_real: real ).
tff(func_def_20,type,
multInv: ( int * int ) > int ).
tff(func_def_21,type,
d22set: int > fun_int_bool ).
tff(func_def_22,type,
zfact: int > int ).
tff(func_def_23,type,
zcong: ( int * int ) > fun_int_bool ).
tff(func_def_24,type,
zprime: fun_int_bool ).
tff(func_def_25,type,
bit0: int > int ).
tff(func_def_26,type,
bit1: int > int ).
tff(func_def_27,type,
min: int ).
tff(func_def_28,type,
pls: int ).
tff(func_def_29,type,
number_number_of_int: int > int ).
tff(func_def_30,type,
number_number_of_nat: int > nat ).
tff(func_def_31,type,
number267125858f_real: int > real ).
tff(func_def_32,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_33,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_34,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_35,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_36,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_37,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_38,type,
power_power_int: int > fun_nat_int ).
tff(func_def_39,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_40,type,
power_power_real: real > fun_nat_real ).
tff(func_def_41,type,
product_Pair_int_int: ( int * int ) > product_prod_int_int ).
tff(func_def_42,type,
legendre: ( int * int ) > int ).
tff(func_def_43,type,
quadRes: int > fun_int_bool ).
tff(func_def_44,type,
sr: int > fun_int_bool ).
tff(func_def_45,type,
standardRes: ( int * int ) > int ).
tff(func_def_46,type,
dvd_dvd_int: fun_int_fun_int_bool ).
tff(func_def_47,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(func_def_48,type,
dvd_dvd_real: fun_re413263731l_bool ).
tff(func_def_49,type,
collect_int: fun_int_bool > fun_int_bool ).
tff(func_def_50,type,
twoSqu820444569sum2sq: fun_int_bool ).
tff(func_def_51,type,
twoSqu949963151sum2sq: product_prod_int_int > int ).
tff(func_def_52,type,
inv: ( int * int ) > int ).
tff(func_def_53,type,
wset: ( int * int ) > fun_int_bool ).
tff(func_def_54,type,
fconj: fun_bo1549164019l_bool ).
tff(func_def_55,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(func_def_56,type,
hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).
tff(func_def_57,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_58,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(func_def_59,type,
hAPP_i68813070l_bool: ( fun_in531499254l_bool * int ) > fun_bool_bool ).
tff(func_def_60,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_61,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_62,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_63,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_64,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_65,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_66,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_67,type,
hAPP_real_real: ( fun_real_real * real ) > real ).
tff(func_def_68,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_69,type,
member_int: ( int * fun_int_bool ) > bool ).
tff(func_def_70,type,
m: int ).
tff(func_def_71,type,
s1: int ).
tff(func_def_72,type,
s: int ).
tff(func_def_73,type,
t: int ).
tff(func_def_74,type,
sK1: int ).
tff(func_def_75,type,
sK2: int ).
tff(func_def_76,type,
sK3: int ).
tff(func_def_77,type,
sK4: int > int ).
tff(func_def_78,type,
sK5: int ).
tff(func_def_79,type,
sK6: ( int * int * int ) > int ).
tff(func_def_80,type,
sK7: ( int * int ) > int ).
tff(func_def_81,type,
sK8: ( real * nat ) > real ).
tff(func_def_82,type,
sK9: ( real * nat ) > real ).
tff(func_def_83,type,
sK10: ( nat * nat ) > nat ).
tff(func_def_84,type,
sK11: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_85,type,
sK12: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_86,type,
sK13: ( nat * fun_nat_bool ) > nat ).
tff(func_def_87,type,
sK14: int > int ).
tff(func_def_88,type,
sK15: ( fun_int_bool * int ) > int ).
tff(func_def_89,type,
sK16: ( fun_int_bool * int ) > int ).
tff(func_def_90,type,
sK17: ( int * int ) > int ).
tff(func_def_91,type,
sK18: int > int ).
tff(func_def_92,type,
sK19: int > int ).
tff(func_def_93,type,
sK20: ( fun_int_bool * int ) > int ).
tff(func_def_94,type,
sK21: fun_int_bool > int ).
tff(func_def_95,type,
sK22: ( fun_int_bool * int ) > int ).
tff(func_def_96,type,
sK23: ( fun_int_bool * int ) > int ).
tff(func_def_97,type,
sK24: ( fun_int_bool * int ) > int ).
tff(func_def_98,type,
sK25: fun_nat_nat > nat ).
tff(func_def_99,type,
sK26: fun_nat_nat > nat ).
tff(func_def_100,type,
sK27: ( nat * fun_nat_bool ) > nat ).
tff(func_def_101,type,
sK28: ( nat * nat ) > nat ).
tff(func_def_102,type,
sK29: ( int * int ) > int ).
tff(func_def_103,type,
sK30: ( fun_int_bool * int * int ) > int ).
tff(func_def_104,type,
sK31: ( fun_int_bool * int * int ) > int ).
tff(func_def_105,type,
sK32: ( fun_int_bool * int * int ) > int ).
tff(func_def_106,type,
sK33: ( fun_int_bool * int * int ) > int ).
tff(func_def_107,type,
sK34: ( int * int ) > int ).
tff(func_def_108,type,
sK35: ( nat * nat ) > nat ).
tff(func_def_109,type,
sK36: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_110,type,
sK37: ( fun_nat_bool * nat * nat ) > nat ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( fun_int_bool * int * int ) > $o ).
tff(f3,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(f4,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
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/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
tff(f42,axiom,
! [X0: int,X1: int,X2: int] : ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zmult__assoc) ).
tff(f89,axiom,
! [X0: int] : ( hAPP_int_int(times_times_int(pls),X0) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mult__Pls) ).
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/sandbox/benchmark/theBenchmark.p',fact_134_zadd__commute) ).
tff(f173,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Pls__def) ).
tff(f181,axiom,
! [X0: int] : ( hAPP_int_int(plus_plus_int(pls),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_add__Pls) ).
tff(f183,axiom,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_Bit0__def) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f419,axiom,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
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/sandbox/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/sandbox/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(f2471,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
inference(cnf_transformation,[],[f3]) ).
tff(f2472,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(f2516,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(f2525,plain,
! [X2: int,X0: int,X1: int] : ( hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X0),X1)),X2) = hAPP_int_int(times_times_int(X0),hAPP_int_int(times_times_int(X1),X2)) ),
inference(cnf_transformation,[],[f42]) ).
tff(f2601,plain,
! [X0: int] : ( pls = hAPP_int_int(times_times_int(pls),X0) ),
inference(cnf_transformation,[],[f89]) ).
tff(f2674,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(f2726,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f173]) ).
tff(f2738,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(pls),X0) = X0 ),
inference(cnf_transformation,[],[f181]) ).
tff(f2740,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f183]) ).
tff(f2761,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(f2805,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(f2920,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(f3030,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(X0),hAPP_int_int(times_times_int(X1),X0)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X1),one_one_int)),X0) ),
inference(cnf_transformation,[],[f419]) ).
tff(f4163,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(f4166,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(f4169,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),pls))),
inference(definition_unfolding,[],[f2471,f2740,f2740,f2805,f2740,f2740,f2805,f2726]) ).
tff(f4170,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,[],[f2472,f2740,f2740,f2805,f2740,f2805]) ).
tff(f4345,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,[],[f2761,f2740,f2805]) ).
tff(f4783,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,[],[f4166,f2740,f2805,f2726]) ).
tff(f5089,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_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(forward_demodulation,[],[f4783,f4163]) ).
tff(f5090,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_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(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,[],[f5089,f2674]) ).
tff(f5091,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)))),
inference(forward_demodulation,[],[f5090,f4345]) ).
tff(f5093,definition,
( spl83_1
<=> hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)))) ),
introduced(definition,[new_symbols(definition,[spl83_1])],[avatar_definition]) ).
tff(f5095,plain,
( ~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))))
| spl83_1 ),
inference(avatar_component_clause,[],[f5093]) ).
tff(f5096,plain,
~ spl83_1,
inference(avatar_split_clause,[],[f5091,f5093]) ).
tff(f7604,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls)))),
inference(forward_demodulation,[],[f4169,f3030]) ).
tff(f7785,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls))),
inference(forward_demodulation,[],[f7604,f2738]) ).
tff(f7872,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t))),
inference(forward_demodulation,[],[f7785,f4163]) ).
tff(f7924,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls)),hAPP_int_int(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(forward_demodulation,[],[f7872,f4170]) ).
tff(f7970,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)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),pls))),
inference(forward_demodulation,[],[f7924,f4163]) ).
tff(f7998,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)),hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_int_int(times_times_int(m),pls)))),
inference(forward_demodulation,[],[f7970,f2525]) ).
tff(f8017,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)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(m),pls)),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))))),
inference(forward_demodulation,[],[f7998,f2516]) ).
tff(f8031,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)),hAPP_int_int(times_times_int(m),hAPP_int_int(times_times_int(pls),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f8017,f2525]) ).
tff(f8038,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)),hAPP_int_int(times_times_int(pls),hAPP_int_int(times_times_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))))))),
inference(forward_demodulation,[],[f8031,f2920]) ).
tff(f8044,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(forward_demodulation,[],[f8038,f2601]) ).
tff(f8049,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_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(forward_demodulation,[],[f8044,f4163]) ).
tff(f8053,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_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(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,[],[f8049,f2674]) ).
tff(f8057,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)))),
inference(forward_demodulation,[],[f8053,f4345]) ).
tff(f8061,plain,
( $false
| spl83_1 ),
inference(forward_subsumption_resolution,[],[f8057,f5095]) ).
tff(f8062,plain,
spl83_1,
inference(avatar_contradiction_clause,[],[f8061]) ).
cnf(s1,plain,
~ spl83_1,
inference(sat_conversion,[],[f5096]) ).
cnf(s201,plain,
spl83_1,
inference(sat_conversion,[],[f8062]) ).
cnf(s202,plain,
$false,
inference(rat,[],[s1,s201]) ).
tff(f8166,plain,
$false,
inference(avatar_sat_refutation,[],[s202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 21:41:49 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 5.31/1.79 % (3781771)Detected formulas, will run a generic FOF schedule.
% 5.31/1.79 % (3781778)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=4033259631:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.31/1.79 % (3781782)dis-21_1_sil=8000:lcm=predicate:random_seed=1683281891: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)
% 5.31/1.79 % (3781776)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=482759829:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.31/1.79 % (3781780)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=53545499:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.31/1.79 % (3781781)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1294705515:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.31/1.79 % (3781777)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=3750828073:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.31/1.79 % (3781779)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3350954020:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.31/1.79 % (3781782)Instruction limit reached!
% 5.31/1.79 % (3781782)------------------------------
% 5.31/1.79 % (3781782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781782)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781782)Termination reason: Instruction limit
% 5.31/1.79 % (3781782)Termination phase: Property scanning
% 5.31/1.79 % (3781782)Time elapsed: 0.054 s
% 5.31/1.79 % (3781782)Peak memory usage: 88 MB
% 5.31/1.79 % (3781782)Instructions burned: 129 (million)
% 5.31/1.79 % (3781779)Instruction limit reached!
% 5.31/1.79 % (3781779)------------------------------
% 5.31/1.79 % (3781779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781779)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781779)Termination reason: Instruction limit
% 5.31/1.79 % (3781779)Termination phase: Saturation
% 5.31/1.79 % (3781779)Time elapsed: 0.059 s
% 5.31/1.79 % (3781779)Peak memory usage: 90 MB
% 5.31/1.79 % (3781779)Instructions burned: 110 (million)
% 5.31/1.79 % (3781781)Instruction limit reached!
% 5.31/1.79 % (3781781)------------------------------
% 5.31/1.79 % (3781781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781781)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781781)Termination reason: Instruction limit
% 5.31/1.79 % (3781781)Termination phase: Saturation
% 5.31/1.79 % (3781781)Time elapsed: 0.064 s
% 5.31/1.79 % (3781781)Peak memory usage: 90 MB
% 5.31/1.79 % (3781781)Instructions burned: 139 (million)
% 5.31/1.79 % (3781780)Instruction limit reached!
% 5.31/1.79 % (3781780)------------------------------
% 5.31/1.79 % (3781780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781780)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781780)Termination reason: Instruction limit
% 5.31/1.79 % (3781780)Termination phase: Saturation
% 5.31/1.79 % (3781780)Time elapsed: 0.066 s
% 5.31/1.79 % (3781780)Peak memory usage: 90 MB
% 5.31/1.79 % (3781780)Instructions burned: 120 (million)
% 5.31/1.79 % (3781790)lrs+10_1_sil=8000:sp=occurrence:random_seed=2866449455:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.31/1.79 % (3781792)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3701313711:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.31/1.79 % (3781793)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=786007970:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.31/1.79 % (3781791)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2189089051:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.31/1.79 % (3781791)Instruction limit reached!
% 5.31/1.79 % (3781791)------------------------------
% 5.31/1.79 % (3781791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781791)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781791)Termination reason: Instruction limit
% 5.31/1.79 % (3781791)Termination phase: Saturation
% 5.31/1.79 % (3781791)Time elapsed: 0.089 s
% 5.31/1.79 % (3781791)Peak memory usage: 91 MB
% 5.31/1.79 % (3781791)Instructions burned: 158 (million)
% 5.31/1.79 % (3781793)Instruction limit reached!
% 5.31/1.79 % (3781793)------------------------------
% 5.31/1.79 % (3781793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781793)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781793)Termination reason: Instruction limit
% 5.31/1.79 % (3781793)Termination phase: Saturation
% 5.31/1.79 % (3781793)Time elapsed: 0.142 s
% 5.31/1.79 % (3781793)Peak memory usage: 92 MB
% 5.31/1.79 % (3781793)Instructions burned: 250 (million)
% 5.31/1.79 % (3781790)Instruction limit reached!
% 5.31/1.79 % (3781790)------------------------------
% 5.31/1.79 % (3781790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781790)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781790)Termination reason: Instruction limit
% 5.31/1.79 % (3781790)Termination phase: Saturation
% 5.31/1.79 % (3781790)Time elapsed: 0.166 s
% 5.31/1.79 % (3781790)Peak memory usage: 92 MB
% 5.31/1.79 % (3781790)Instructions burned: 285 (million)
% 5.31/1.79 % (3781792)Instruction limit reached!
% 5.31/1.79 % (3781792)------------------------------
% 5.31/1.79 % (3781792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781792)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781792)Termination reason: Instruction limit
% 5.31/1.79 % (3781792)Termination phase: Saturation
% 5.31/1.79 % (3781792)Time elapsed: 0.187 s
% 5.31/1.79 % (3781792)Peak memory usage: 92 MB
% 5.31/1.79 % (3781792)Instructions burned: 326 (million)
% 5.31/1.79 % (3781798)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1153279727:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.31/1.79 % (3781799)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3835876813:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.31/1.79 % (3781778)First to succeed.
% 5.31/1.79 % (3781778)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3781771"
% 5.31/1.79 % (3781800)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=539860562:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.31/1.79 % (3781801)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1572541280:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.31/1.79 % (3781800)Instruction limit reached!
% 5.31/1.79 % (3781800)------------------------------
% 5.31/1.79 % (3781800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781800)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781800)Termination reason: Instruction limit
% 5.31/1.79 % (3781800)Termination phase: Saturation
% 5.31/1.79 % (3781800)Time elapsed: 0.055 s
% 5.31/1.79 % (3781800)Peak memory usage: 90 MB
% 5.31/1.79 % (3781800)Instructions burned: 114 (million)
% 5.31/1.79 % (3781798)Instruction limit reached!
% 5.31/1.79 % (3781798)------------------------------
% 5.31/1.79 % (3781798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781798)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781798)Termination reason: Instruction limit
% 5.31/1.79 % (3781798)Termination phase: Saturation
% 5.31/1.79 % (3781798)Time elapsed: 0.154 s
% 5.31/1.79 % (3781798)Peak memory usage: 92 MB
% 5.31/1.79 % (3781798)Instructions burned: 294 (million)
% 5.31/1.79 % (3781801)Instruction limit reached!
% 5.31/1.79 % (3781801)------------------------------
% 5.31/1.79 % (3781801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.79 % (3781801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.79 % (3781801)CaDiCaL version: 2.1.3
% 5.31/1.79 % (3781801)Termination reason: Instruction limit
% 5.31/1.79 % (3781801)Termination phase: Property scanning
% 5.31/1.79 % (3781801)Time elapsed: 0.056 s
% 5.31/1.79 % (3781801)Peak memory usage: 88 MB
% 5.31/1.79 % (3781801)Instructions burned: 128 (million)
% 5.31/1.79 % (3781778)Refutation found. Thanks to Tanya!
% 5.31/1.79 % SZS status Theorem for theBenchmark
% 5.31/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 6.73/1.89 % (3781778)------------------------------
% 6.73/1.89 % (3781778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.73/1.89 % (3781778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.89 % (3781778)CaDiCaL version: 2.1.3
% 6.73/1.89 % (3781778)Termination reason: Refutation
% 6.73/1.89 % (3781778)Time elapsed: 0.571 s
% 6.73/1.89 % (3781778)Peak memory usage: 139 MB
% 6.73/1.89 % (3781778)Instructions burned: 1716 (million)
% 6.73/1.89 % (3781778)------------------------------
% 6.73/1.89 % (3781778)------------------------------
% 6.73/1.89 % (3781771)Success in time 0.943 s
% 6.73/1.89 % Vampire exiting
%------------------------------------------------------------------------------