%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925_2 : 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 : n012.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 3.21s 1.19s
% Output : Refutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 16 ( 15 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 70 ( 70 usr; 22 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?; 19 :)
% 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_int: $tType ).
tff(type_def_11,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_12,type,
fun_nat_bool: $tType ).
tff(type_def_13,type,
fun_nat_int: $tType ).
tff(type_def_14,type,
fun_nat_nat: $tType ).
tff(type_def_15,type,
fun_nat_real: $tType ).
tff(type_def_16,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_17,type,
fun_real_bool: $tType ).
tff(type_def_18,type,
fun_real_real: $tType ).
tff(type_def_19,type,
fun_re413263731l_bool: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
one_one_real: real ).
tff(func_def_3,type,
plus_plus_int: int > fun_int_int ).
tff(func_def_4,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_5,type,
plus_plus_real: real > fun_real_real ).
tff(func_def_6,type,
times_times_int: ( int * int ) > int ).
tff(func_def_7,type,
zero_zero_int: int ).
tff(func_def_8,type,
zero_zero_nat: nat ).
tff(func_def_9,type,
zero_zero_real: real ).
tff(func_def_10,type,
if_nat: ( bool * nat ) > fun_nat_nat ).
tff(func_def_11,type,
bit0: int > int ).
tff(func_def_12,type,
bit1: int > int ).
tff(func_def_13,type,
pls: int ).
tff(func_def_14,type,
number_number_of_int: int > int ).
tff(func_def_15,type,
number_number_of_nat: int > nat ).
tff(func_def_16,type,
number267125858f_real: int > real ).
tff(func_def_17,type,
succ: int > int ).
tff(func_def_18,type,
semiri1621563631at_int: fun_nat_int ).
tff(func_def_19,type,
semiri984289939at_nat: fun_nat_nat ).
tff(func_def_20,type,
semiri132038758t_real: fun_nat_real ).
tff(func_def_21,type,
sqrt: real > real ).
tff(func_def_22,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_23,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_24,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_25,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_26,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_27,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_28,type,
power_power_int: int > fun_nat_int ).
tff(func_def_29,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_30,type,
power_power_real: real > fun_nat_real ).
tff(func_def_31,type,
fFalse: bool ).
tff(func_def_32,type,
fTrue: bool ).
tff(func_def_33,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_34,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(func_def_35,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_36,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_37,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_38,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_39,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_40,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_41,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_42,type,
hAPP_real_real: ( fun_real_real * real ) > real ).
tff(func_def_43,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_44,type,
m1: int ).
tff(func_def_45,type,
n: nat ).
tff(func_def_46,type,
t: int ).
tff(func_def_47,type,
tn: nat ).
tff(func_def_48,type,
sK2: ( fun_int_bool * int ) > int ).
tff(func_def_49,type,
sK3: int > nat ).
tff(func_def_50,type,
sK4: ( nat * nat ) > nat ).
tff(func_def_51,type,
sK5: ( real * nat ) > real ).
tff(func_def_52,type,
sK6: ( real * nat ) > real ).
tff(func_def_53,type,
sK7: fun_int_bool > int ).
tff(func_def_54,type,
sK8: fun_int_bool > nat ).
tff(func_def_55,type,
sK9: fun_int_bool > nat ).
tff(func_def_56,type,
sK10: fun_int_bool > int ).
tff(func_def_57,type,
sK11: ( int * int ) > nat ).
tff(func_def_58,type,
sK12: int > nat ).
tff(func_def_59,type,
sK13: int > nat ).
tff(func_def_60,type,
sK14: ( nat * nat ) > nat ).
tff(func_def_61,type,
sK15: ( nat * fun_nat_bool ) > nat ).
tff(func_def_62,type,
sK16: int > nat ).
tff(func_def_63,type,
sK17: fun_nat_nat > nat ).
tff(func_def_64,type,
sK18: fun_nat_nat > nat ).
tff(func_def_65,type,
sK19: ( fun_int_bool * int ) > int ).
tff(func_def_66,type,
sK20: ( nat * fun_nat_bool ) > nat ).
tff(func_def_67,type,
sK21: fun_nat_nat > nat ).
tff(func_def_68,type,
sK22: fun_nat_nat > nat ).
tff(func_def_69,type,
sK23: ( real * real ) > real ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( int * bool * bool ) > $o ).
tff(pred_def_3,type,
sP1: ( bool * int * bool ) > $o ).
tff(f84,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_83_int__less__0__conv) ).
tff(f177,axiom,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
tff(f232,axiom,
! [X0: nat,X1: int] :
( ( X1 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
tff(f271,axiom,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_less__add__one) ).
tff(f574,axiom,
! [X0: int] : ( succ(X0) = hAPP_int_int(plus_plus_int(X0),one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_succ__def) ).
tff(f584,axiom,
! [X0: int] : ( number_number_of_int(succ(X0)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_number__of__succ) ).
tff(f703,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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(f704,negated_conjecture,
( ( ~ hAPP_nat_int(power_power_int(hAPP_int_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)],[f703]) ).
tff(f707,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f704]) ).
tff(f756,plain,
! [X0: nat,X1: int] :
( ( hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[],[f232]) ).
tff(f1512,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,[],[f84]) ).
tff(f1636,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f177]) ).
tff(f1726,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f756]) ).
tff(f1768,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
inference(cnf_transformation,[],[f271]) ).
tff(f2185,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(X0),one_one_int) = succ(X0) ),
inference(cnf_transformation,[],[f574]) ).
tff(f2195,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = number_number_of_int(succ(X0)) ),
inference(cnf_transformation,[],[f584]) ).
tff(f2367,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f707]) ).
tff(f2640,plain,
( ( zero_zero_int != zero_zero_int )
| ( zero_zero_int = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(superposition,[],[f1726,f2367]) ).
tff(f2645,plain,
zero_zero_int = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),
inference(trivial_inequality_removal,[],[f2640]) ).
tff(f2652,plain,
! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),succ(X0))),
inference(forward_demodulation,[],[f1768,f2185]) ).
tff(f2669,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X0)) = succ(X0) ),
inference(forward_demodulation,[],[f2195,f1636]) ).
tff(f2670,plain,
! [X0: int] : ( hAPP_int_int(plus_plus_int(one_one_int),X0) = succ(X0) ),
inference(forward_demodulation,[],[f2669,f1636]) ).
tff(f2671,plain,
zero_zero_int = succ(hAPP_nat_int(semiri1621563631at_int,n)),
inference(superposition,[],[f2670,f2645]) ).
tff(f2689,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,n)),zero_zero_int)),
inference(superposition,[],[f2652,f2671]) ).
tff(f2690,plain,
$false,
inference(forward_subsumption_resolution,[],[f2689,f1512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.35 % Computer : n012.cluster.edu
% 0.04/0.35 % Model : x86_64 x86_64
% 0.04/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.35 % Memory : 8046.5625MB
% 0.04/0.35 % OS : Linux 6.8.0-71-generic
% 0.04/0.35 % CPULimit : 300
% 0.04/0.35 % WCLimit : 300
% 0.04/0.35 % DateTime : Sun Sep 27 21:41:19 UTC 2026
% 0.04/0.35 % CPUTime :
% 0.04/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.38 Running first-order theorem proving
% 0.04/0.38 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
% 3.21/1.19 % (2773043)Detected formulas, will run a generic FOF schedule.
% 3.21/1.19 % (2773056)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1349824416:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.21/1.19 % (2773056)First to succeed.
% 3.21/1.19 % (2773056)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2773043"
% 3.21/1.19 % (2773054)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3874881413:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.21/1.19 % (2773057)dis-21_1_sil=8000:lcm=predicate:random_seed=3949119352: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)
% 3.21/1.19 % (2773052)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=4123797684:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.21/1.19 % (2773055)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=754549705:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.21/1.19 % (2773053)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=420599048:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.21/1.19 % (2773051)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=3064616590:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.21/1.19 % (2773054)Also succeeded, but the first one will report.
% 3.21/1.19 % (2773055)Also succeeded, but the first one will report.
% 3.21/1.19 % (2773057)Instruction limit reached!
% 3.21/1.19 % (2773057)------------------------------
% 3.21/1.19 % (2773057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.19 % (2773057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.19 % (2773057)CaDiCaL version: 2.1.3
% 3.21/1.19 % (2773057)Termination reason: Instruction limit
% 3.21/1.19 % (2773057)Termination phase: Saturation
% 3.21/1.19 % (2773057)Time elapsed: 0.066 s
% 3.21/1.19 % (2773057)Peak memory usage: 90 MB
% 3.21/1.19 % (2773057)Instructions burned: 130 (million)
% 3.21/1.19 % (2773056)Refutation found. Thanks to Tanya!
% 3.21/1.19 % SZS status Theorem for theBenchmark
% 3.21/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.21/1.19 % (2773056)------------------------------
% 3.21/1.19 % (2773056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.19 % (2773056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.19 % (2773056)CaDiCaL version: 2.1.3
% 3.21/1.19 % (2773056)Termination reason: Refutation
% 3.21/1.19 % (2773056)Time elapsed: 0.022 s
% 3.21/1.19 % (2773056)Peak memory usage: 90 MB
% 3.21/1.19 % (2773056)Instructions burned: 76 (million)
% 3.21/1.19 % (2773056)------------------------------
% 3.21/1.19 % (2773056)------------------------------
% 3.21/1.19 % (2773043)Success in time 0.423 s
% 3.21/1.19 % Vampire exiting
%------------------------------------------------------------------------------