%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN004_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:26:54 PM UTC 2026
% Result : Theorem 0.22s 0.57s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_9,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m: int ).
tff(func_def_13,type,
m1: int ).
tff(func_def_14,type,
n: nat ).
tff(func_def_15,type,
t: int ).
tff(func_def_16,type,
v: int ).
tff(func_def_17,type,
w: int ).
tff(func_def_18,type,
x: int ).
tff(func_def_19,type,
y: int ).
tff(func_def_20,type,
sK0: int ).
tff(func_def_21,type,
sK1: int ).
tff(func_def_22,type,
sK2: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord581940658strict:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
zprime: int > $o ).
tff(pred_def_14,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_15,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_17,type,
pp: bool > $o ).
tff(f1,axiom,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_m1) ).
tff(f2,axiom,
plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_xy) ).
tff(f55,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_nat__1__add__1) ).
tff(f118,conjecture,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) = times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f119,negated_conjecture,
( ( ~ times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ) = times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
tff(f120,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) != times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(flattening,[],[f119]) ).
tff(f214,plain,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),
inference(cnf_transformation,[],[f1]) ).
tff(f215,plain,
plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f2]) ).
tff(f283,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f55]) ).
tff(f371,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) != times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(cnf_transformation,[],[f120]) ).
tff(f381,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,power_power(int,x,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,y,plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f215,f283]) ).
tff(f382,plain,
times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,w,plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f214,f283]) ).
tff(f494,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,w,plus_plus(nat,one_one(nat),one_one(nat))))) != times_times(int,plus_plus(int,power_power(int,x,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,y,plus_plus(nat,one_one(nat),one_one(nat)))),plus_plus(int,power_power(int,v,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,w,plus_plus(nat,one_one(nat),one_one(nat))))),
inference(superposition,[],[f371,f283]) ).
tff(f495,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)) != times_times(int,plus_plus(int,power_power(int,x,plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,y,plus_plus(nat,one_one(nat),one_one(nat)))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),
inference(forward_demodulation,[],[f494,f382]) ).
tff(f496,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)) != times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),
inference(forward_demodulation,[],[f495,f381]) ).
tff(f497,plain,
$false,
inference(trivial_inequality_removal,[],[f496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN004_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 21:49:45 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.49 Running first-order model finding
% 0.22/0.49 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
% 0.22/0.57 % (2431893)Will run a generic schedule for satisfiability detection.
% 0.22/0.57 % (2431900)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=456772571:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.57 % (2431901)dis+10_1_sil=32000:sp=arity:random_seed=2652154998:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.57 % (2431899)% WARNING: option uhcvi not known.
% 0.22/0.57 % (2431898)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=787544749_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.57 % (2431902)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1017061229:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.57 % (2431903)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=124577910:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.57 % (2431899)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1300560621:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.57 % (2431904)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=117871140:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.57 % Exception at run slice level
% 0.22/0.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.57 % (2431903) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2431893-2431903"...
% 0.22/0.57 % (2431903)...printing done.
% 0.22/0.57 % (2431903)Refutation found. Thanks to Tanya!
% 0.22/0.57 % SZS status Theorem for theBenchmark
% 0.22/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.57 % (2431903)------------------------------
% 0.22/0.57 % (2431903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.57 % (2431903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.57 % (2431903)CaDiCaL version: 2.1.3
% 0.22/0.57 % (2431903)Termination reason: Refutation
% 0.22/0.57 % (2431903)Time elapsed: 0.018 s
% 0.22/0.57 % (2431903)Peak memory usage: 12 MB
% 0.22/0.57 % (2431903)Instructions burned: 18 (million)
% 0.22/0.57 % (2431893)Success in time 0.066 s
% 0.22/0.57 % Vampire exiting
%------------------------------------------------------------------------------