%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925_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 : n004.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 12:17:33 PM UTC 2026
% Result : Theorem 2.89s 1.35s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 35 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 9 |; 5 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 85 ( 85 usr; 35 con; 0-3 aty)
% Number of variables : 24 ( 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(type_def_9,type,
fun_int_bool: $tType ).
tff(type_def_10,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_11,type,
fun_nat_bool: $tType ).
tff(type_def_12,type,
fun_nat_int: $tType ).
tff(type_def_13,type,
fun_nat_nat: $tType ).
tff(type_def_14,type,
fun_nat_real: $tType ).
tff(type_def_15,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_16,type,
fun_real_bool: $tType ).
tff(type_def_17,type,
fun_re413263731l_bool: $tType ).
tff(func_def_0,type,
abs_abs_int: int > int ).
tff(func_def_1,type,
abs_abs_real: real > real ).
tff(func_def_2,type,
minus_minus_int: ( int * int ) > int ).
tff(func_def_3,type,
minus_minus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
minus_minus_real: ( real * real ) > real ).
tff(func_def_5,type,
one_one_int: int ).
tff(func_def_6,type,
one_one_nat: nat ).
tff(func_def_7,type,
one_one_real: real ).
tff(func_def_8,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_9,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_10,type,
plus_plus_real: ( real * real ) > real ).
tff(func_def_11,type,
times_times_int: ( int * int ) > int ).
tff(func_def_12,type,
times_times_nat: ( nat * nat ) > nat ).
tff(func_def_13,type,
times_times_real: ( real * real ) > real ).
tff(func_def_14,type,
zero_zero_int: int ).
tff(func_def_15,type,
zero_zero_nat: nat ).
tff(func_def_16,type,
zero_zero_real: real ).
tff(func_def_17,type,
if_int: ( bool * int * int ) > int ).
tff(func_def_18,type,
if_nat: ( bool * nat * nat ) > nat ).
tff(func_def_19,type,
zcong: ( int * int ) > fun_int_bool ).
tff(func_def_20,type,
zprime: fun_int_bool ).
tff(func_def_21,type,
bit0: int > int ).
tff(func_def_22,type,
bit1: int > int ).
tff(func_def_23,type,
min: int ).
tff(func_def_24,type,
pls: int ).
tff(func_def_25,type,
nat_1: int > nat ).
tff(func_def_26,type,
number_number_of_int: int > int ).
tff(func_def_27,type,
number_number_of_nat: int > nat ).
tff(func_def_28,type,
number267125858f_real: int > real ).
tff(func_def_29,type,
succ: int > int ).
tff(func_def_30,type,
semiri1621563631at_int: fun_nat_int ).
tff(func_def_31,type,
semiri984289939at_nat: fun_nat_nat ).
tff(func_def_32,type,
semiri132038758t_real: fun_nat_real ).
tff(func_def_33,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_34,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_35,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_36,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_37,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_38,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_39,type,
power_power_int: int > fun_nat_int ).
tff(func_def_40,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_41,type,
power_power_real: real > fun_nat_real ).
tff(func_def_42,type,
legendre: ( int * int ) > int ).
tff(func_def_43,type,
quadRes: int > fun_int_bool ).
tff(func_def_44,type,
dvd_dvd_int: fun_int_fun_int_bool ).
tff(func_def_45,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(func_def_46,type,
twoSqu820444569sum2sq: fun_int_bool ).
tff(func_def_47,type,
fFalse: bool ).
tff(func_def_48,type,
fTrue: bool ).
tff(func_def_49,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_50,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_51,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_52,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_53,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_54,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_55,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_56,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_57,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_58,type,
m: int ).
tff(func_def_59,type,
m1: int ).
tff(func_def_60,type,
n: nat ).
tff(func_def_61,type,
s1: int ).
tff(func_def_62,type,
s: int ).
tff(func_def_63,type,
t: int ).
tff(func_def_64,type,
tn: nat ).
tff(func_def_65,type,
x: int ).
tff(func_def_66,type,
y: int ).
tff(func_def_67,type,
sK2: ( fun_int_bool * int ) > int ).
tff(func_def_68,type,
sK3: ( fun_int_bool * int ) > int ).
tff(func_def_69,type,
sK4: ( int * int ) > nat ).
tff(func_def_70,type,
sK5: fun_int_bool > nat ).
tff(func_def_71,type,
sK6: fun_int_bool > int ).
tff(func_def_72,type,
sK7: fun_int_bool > int ).
tff(func_def_73,type,
sK8: fun_int_bool > nat ).
tff(func_def_74,type,
sK9: int > nat ).
tff(func_def_75,type,
sK10: int ).
tff(func_def_76,type,
sK11: int ).
tff(func_def_77,type,
sK12: ( nat * nat ) > nat ).
tff(func_def_78,type,
sK13: ( nat * nat ) > nat ).
tff(func_def_79,type,
sK14: int ).
tff(func_def_80,type,
sK15: ( int * int * int ) > int ).
tff(func_def_81,type,
sK16: ( fun_int_bool * int ) > int ).
tff(func_def_82,type,
sK17: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_83,type,
sK18: ( fun_nat_bool * nat * nat ) > nat ).
tff(func_def_84,type,
sK19: ( nat * fun_nat_bool ) > nat ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( bool * int * bool ) > $o ).
tff(pred_def_3,type,
sP1: ( int * bool * bool ) > $o ).
tff(f99,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
tff(f104,axiom,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
tff(f129,axiom,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
tff(f270,axiom,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(X0,one_one_int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_less__add__one) ).
tff(f285,axiom,
! [X0: int,X1: nat] :
( ( hAPP_nat_int(power_power_int(X0),X1) = zero_zero_int )
<=> ( ( X0 = zero_zero_int )
& ( X1 != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_power__eq__0__iff) ).
tff(f288,axiom,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
tff(f350,axiom,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f1205,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f1206,negated_conjecture,
( ( ~ hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f1205]) ).
tff(f1207,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f1206]) ).
tff(f1684,plain,
! [X0: int,X1: nat] :
( ( ( hAPP_nat_int(power_power_int(X0),X1) = zero_zero_int )
| ( zero_zero_int != X0 )
| ( zero_zero_nat = X1 ) )
& ( ( ( X0 = zero_zero_int )
& ( X1 != zero_zero_nat ) )
| ( zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ) ),
inference(nnf_transformation,[],[f285]) ).
tff(f1685,plain,
! [X0: int,X1: nat] :
( ( ( hAPP_nat_int(power_power_int(X0),X1) = zero_zero_int )
| ( zero_zero_int != X0 )
| ( zero_zero_nat = X1 ) )
& ( ( ( X0 = zero_zero_int )
& ( X1 != zero_zero_nat ) )
| ( zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ) ),
inference(flattening,[],[f1684]) ).
tff(f1857,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1207]) ).
tff(f1886,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(X0,one_one_int))),
inference(cnf_transformation,[],[f270]) ).
tff(f1896,plain,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(cnf_transformation,[],[f129]) ).
tff(f1960,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f350]) ).
tff(f2019,plain,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
inference(cnf_transformation,[],[f104]) ).
tff(f2068,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f99]) ).
tff(f2124,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f288]) ).
tff(f2174,plain,
! [X0: int,X1: nat] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ),
inference(cnf_transformation,[],[f1685]) ).
tff(f2857,plain,
pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(definition_unfolding,[],[f1857,f2068,f2019,f1896]) ).
tff(f3003,plain,
! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f2124,f2068]) ).
tff(f3023,plain,
! [X0: int,X1: nat] :
( ( pls != hAPP_nat_int(power_power_int(X0),X1) )
| ( pls = X0 ) ),
inference(definition_unfolding,[],[f2174,f2068,f2068]) ).
tff(f3480,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(one_one_int,X0))),
inference(superposition,[],[f1886,f1960]) ).
tff(f3630,plain,
( ( pls != pls )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls ) ),
inference(superposition,[],[f3023,f2857]) ).
tff(f3633,plain,
plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(trivial_inequality_removal,[],[f3630]) ).
tff(f3636,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,n)),pls)),
inference(superposition,[],[f3480,f3633]) ).
tff(f3643,plain,
$false,
inference(forward_subsumption_resolution,[],[f3636,f3003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:43:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.89/1.35 % (3903114)Detected formulas, will run a generic FOF schedule.
% 2.89/1.35 % (3903119)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=3403585164:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.89/1.35 % (3903125)dis-21_1_sil=8000:lcm=predicate:random_seed=3509096734: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)
% 2.89/1.35 % (3903123)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2283283558:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.89/1.35 % (3903124)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3298514293:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.89/1.35 % (3903122)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=754570764:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.89/1.35 % (3903120)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=516590231:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.89/1.35 % (3903121)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=1453271103:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.89/1.35 % (3903123)First to succeed.
% 2.89/1.35 % (3903123)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3903114"
% 2.89/1.35 % (3903125)Instruction limit reached!
% 2.89/1.35 % (3903125)------------------------------
% 2.89/1.35 % (3903125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.35 % (3903125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.35 % (3903125)CaDiCaL version: 2.1.3
% 2.89/1.35 % (3903125)Termination reason: Instruction limit
% 2.89/1.35 % (3903125)Termination phase: Saturation
% 2.89/1.35 % (3903125)Time elapsed: 0.058 s
% 2.89/1.35 % (3903125)Peak memory usage: 90 MB
% 2.89/1.35 % (3903125)Instructions burned: 130 (million)
% 2.89/1.35 % (3903122)Instruction limit reached!
% 2.89/1.35 % (3903122)------------------------------
% 2.89/1.35 % (3903122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.35 % (3903122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.35 % (3903122)CaDiCaL version: 2.1.3
% 2.89/1.35 % (3903122)Termination reason: Instruction limit
% 2.89/1.35 % (3903122)Termination phase: Saturation
% 2.89/1.35 % (3903122)Time elapsed: 0.055 s
% 2.89/1.35 % (3903122)Peak memory usage: 90 MB
% 2.89/1.35 % (3903122)Instructions burned: 109 (million)
% 2.89/1.35 % (3903124)Also succeeded, but the first one will report.
% 2.89/1.35 % (3903134)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3577467734:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.89/1.35 % (3903133)lrs+10_1_sil=8000:sp=occurrence:random_seed=3689391566:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.89/1.35 % (3903134)Also succeeded, but the first one will report.
% 2.89/1.35 % (3903133)Also succeeded, but the first one will report.
% 2.89/1.35 % (3903123)Refutation found. Thanks to Tanya!
% 2.89/1.35 % SZS status Theorem for theBenchmark
% 2.89/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.45 % (3903123)------------------------------
% 3.71/1.45 % (3903123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.45 % (3903123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.45 % (3903123)CaDiCaL version: 2.1.3
% 3.71/1.45 % (3903123)Termination reason: Refutation
% 3.71/1.45 % (3903123)Time elapsed: 0.038 s
% 3.71/1.45 % (3903123)Peak memory usage: 90 MB
% 3.71/1.45 % (3903123)Instructions burned: 74 (million)
% 3.71/1.45 % (3903123)------------------------------
% 3.71/1.45 % (3903123)------------------------------
% 3.71/1.45 % (3903114)Success in time 0.501 s
% 3.71/1.45 % Vampire exiting
%------------------------------------------------------------------------------