%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM940_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 : n017.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 12:26:15 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 7 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 10 ( 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 : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% 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,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
min: int ).
tff(func_def_8,type,
pls: int ).
tff(func_def_9,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_10,type,
legendre: ( int * int ) > int ).
tff(func_def_11,type,
fFalse: bool ).
tff(func_def_12,type,
fTrue: bool ).
tff(func_def_13,type,
m: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_14,type,
zprime: int > $o ).
tff(pred_def_15,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_17,type,
pp: bool > $o ).
tff(f1,axiom,
~ ( dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__0964_A_K_Am_A_L_A1_Advd_A1_A_124_A4_A_K_Am_A_L_A1_Advd_A2_A_061_061_062_AFalse_096) ).
tff(f2,axiom,
( ( legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = one_one(int) )
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_A_124_A4_A_K_Am_A_L_A1_Advd_A1_A_124_A4_A_K_Am_A_L_A1_Advd_A2_096) ).
tff(f52,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Bit0__def) ).
tff(f61,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Bit1__def) ).
tff(f117,conjecture,
legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f118,negated_conjecture,
( ( ~ legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) = one_one(int) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
tff(f119,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f118]) ).
tff(f123,plain,
( ~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))
& ~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,bit0(bit1(pls)))) ),
inference(ennf_transformation,[],[f1]) ).
tff(f198,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f123]) ).
tff(f199,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
inference(cnf_transformation,[],[f123]) ).
tff(f200,plain,
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) )
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,bit0(bit1(pls)))) ),
inference(cnf_transformation,[],[f2]) ).
tff(f260,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f269,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f61]) ).
tff(f339,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f119]) ).
tff(f340,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int)),one_one(int)),
inference(definition_unfolding,[],[f199,f260,f260,f269]) ).
tff(f341,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int)),number_number_of(int,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,[],[f198,f260,f260,f269,f260,f269]) ).
tff(f342,plain,
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int))) )
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int)),one_one(int))
| dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int)),number_number_of(int,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,[],[f200,f260,f260,f269,f260,f260,f269,f260,f260,f269,f260,f269]) ).
tff(f398,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int))),
inference(definition_unfolding,[],[f339,f260,f260,f269]) ).
tff(f419,plain,
$false,
inference(global_subsumption,[],[f340,f341,f342,f398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM940_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n017.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 21:41:36 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.19/0.49 % (2965065)Will run a generic schedule for satisfiability detection.
% 0.19/0.49 % (2965070)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=884477608_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.49 % Exception at run slice level
% 0.19/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.49 % (2965071)% WARNING: option uhcvi not known.
% 0.19/0.49 % (2965071)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2850157497:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.49 % (2965072)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2822332895:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.49 % (2965073)dis+10_1_sil=32000:sp=arity:random_seed=1931908919:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.49 % (2965074)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2333925994:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.49 % (2965075)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1995234648:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.49 % (2965076)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1250540884:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.49 % (2965078)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=544007500:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.49 % (2965072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2965065-2965072"...
% 0.19/0.49 % Exception at run slice level
% 0.19/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.49 % (2965072)...printing done.
% 0.19/0.49 % (2965075) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2965065-2965075"...
% 0.19/0.49 % (2965074) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2965065-2965074"...
% 0.19/0.49 % (2965072)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (2965072)------------------------------
% 0.19/0.49 % (2965072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.49 % (2965072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.49 % (2965072)CaDiCaL version: 2.1.3
% 0.19/0.49 % (2965072)Termination reason: Refutation
% 0.19/0.49 % (2965072)Time elapsed: 0.006 s
% 0.19/0.49 % (2965072)Peak memory usage: 11 MB
% 0.19/0.49 % (2965072)Instructions burned: 10 (million)
% 0.19/0.49 % (2965065)Success in time 0.053 s
% 0.19/0.49 % Vampire exiting
%------------------------------------------------------------------------------