%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:26:09 PM UTC 2026
% Result : Theorem 0.64s 0.57s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 70 ( 70 usr; 22 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% 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,
sK0: ( fun_int_bool * int ) > int ).
tff(func_def_49,type,
sK1: int > nat ).
tff(func_def_50,type,
sK2: ( nat * nat ) > nat ).
tff(func_def_51,type,
sK3: ( real * nat ) > real ).
tff(func_def_52,type,
sK4: ( real * nat ) > real ).
tff(func_def_53,type,
sK5: fun_int_bool > int ).
tff(func_def_54,type,
sK6: fun_int_bool > nat ).
tff(func_def_55,type,
sK7: fun_int_bool > int ).
tff(func_def_56,type,
sK8: fun_int_bool > nat ).
tff(func_def_57,type,
sK9: ( int * int ) > nat ).
tff(func_def_58,type,
sK10: int > nat ).
tff(func_def_59,type,
sK11: int > nat ).
tff(func_def_60,type,
sK12: ( nat * nat ) > nat ).
tff(func_def_61,type,
sK13: ( nat * fun_nat_bool ) > nat ).
tff(func_def_62,type,
sK14: int > nat ).
tff(func_def_63,type,
sK15: fun_nat_nat > nat ).
tff(func_def_64,type,
sK16: fun_nat_nat > nat ).
tff(func_def_65,type,
sK17: ( fun_int_bool * int ) > int ).
tff(func_def_66,type,
sK18: ( nat * fun_nat_bool ) > nat ).
tff(func_def_67,type,
sK19: fun_nat_nat > nat ).
tff(func_def_68,type,
sK20: fun_nat_nat > nat ).
tff(func_def_69,type,
sK21: ( real * real ) > real ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(f1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f49,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I2_J) ).
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) = hAPP_int_int(plus_plus_int(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
tff(f129,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_128_Bit1__def) ).
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(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(f1128,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f1]) ).
tff(f1191,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(cnf_transformation,[],[f49]) ).
tff(f1271,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f99]) ).
tff(f1276,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f104]) ).
tff(f1307,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,[],[f129]) ).
tff(f1453,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int = X1 )
| ( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) ) ),
inference(cnf_transformation,[],[f756]) ).
tff(f2068,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(f2069,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f1128,f1271]) ).
tff(f2217,plain,
! [X0: nat,X1: int] :
( ( pls != hAPP_nat_int(power_power_int(X1),X0) )
| ( pls = X1 ) ),
inference(definition_unfolding,[],[f1453,f1271,f1271]) ).
tff(f2382,plain,
pls = 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(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,[],[f2068,f1271,f1276,f1307]) ).
tff(f2870,plain,
( ( pls != pls )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls ) ),
inference(superposition,[],[f2217,f2382]) ).
tff(f2873,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(trivial_inequality_removal,[],[f2870]) ).
tff(f4127,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(forward_demodulation,[],[f2069,f2873]) ).
tff(f4128,plain,
$false,
inference(forward_subsumption_resolution,[],[f4127,f1191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n026.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 21:44:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.57 % (3235569)Will run a generic schedule for satisfiability detection.
% 0.64/0.57 % (3235577)dis+10_1_sil=32000:sp=arity:random_seed=2194454870:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.57 % (3235575)% WARNING: option uhcvi not known.
% 0.64/0.57 % (3235574)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2510176425_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.57 % (3235575)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=87559673:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.57 % (3235576)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=661167005:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.57 % (3235578)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=460244610:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.57 % (3235579)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1465363877:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.57 % (3235580)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=74770697:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.57 % (3235577)Instruction limit reached!
% 0.64/0.57 % (3235577)------------------------------
% 0.64/0.57 % (3235577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.57 % (3235577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.57 % (3235577)CaDiCaL version: 2.1.3
% 0.64/0.57 % (3235577)Termination reason: Instruction limit
% 0.64/0.57 % (3235577)Termination phase: Saturation
% 0.64/0.57 % (3235577)Time elapsed: 0.027 s
% 0.64/0.57 % (3235577)Peak memory usage: 13 MB
% 0.64/0.57 % (3235577)Instructions burned: 104 (million)
% 0.64/0.57 % (3235588)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3579487161:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.64/0.57 % (3235578)Instruction limit reached!
% 0.64/0.57 % (3235578)------------------------------
% 0.64/0.57 % (3235578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.57 % (3235578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.57 % (3235578)CaDiCaL version: 2.1.3
% 0.64/0.57 % (3235578)Termination reason: Instruction limit
% 0.64/0.57 % (3235578)Termination phase: Saturation
% 0.64/0.57 % (3235578)Time elapsed: 0.056 s
% 0.64/0.57 % (3235578)Peak memory usage: 13 MB
% 0.64/0.57 % (3235578)Instructions burned: 118 (million)
% 0.64/0.57 % (3235575) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3235569-3235575"...
% 0.64/0.57 % (3235575)...printing done.
% 0.64/0.57 % (3235575)Refutation found. Thanks to Tanya!
% 0.64/0.57 % SZS status Theorem for theBenchmark
% 0.64/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.57 % (3235575)------------------------------
% 0.64/0.57 % (3235575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.57 % (3235575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.57 % (3235575)CaDiCaL version: 2.1.3
% 0.64/0.57 % (3235575)Termination reason: Refutation
% 0.64/0.57 % (3235575)Time elapsed: 0.066 s
% 0.64/0.57 % (3235575)Peak memory usage: 14 MB
% 0.64/0.57 % (3235575)Instructions burned: 118 (million)
% 0.64/0.57 % (3235569)Success in time 0.137 s
% 0.64/0.57 % Vampire exiting
%------------------------------------------------------------------------------