%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM940_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:17:39 PM UTC 2026
% Result : Theorem 2.28s 1.18s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 19 |; 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 : 8 ( 8 !; 0 ?; 8 :)
% 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/sandbox2/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/sandbox2/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(f47,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_number__of__is__id) ).
tff(f50,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_add__Pls__right) ).
tff(f52,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(f128,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(f160,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(f164,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f61]) ).
tff(f171,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f50]) ).
tff(f176,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f211,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f47]) ).
tff(f213,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(f215,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,[],[f128]) ).
tff(f216,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,[],[f128]) ).
tff(f250,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,[],[f160,f176,f176,f164]) ).
tff(f284,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,[],[f213,f176,f176,f164,f176,f176,f164,f176,f176,f164,f176,f164]) ).
tff(f286,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,[],[f216,f176,f176,f164]) ).
tff(f287,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,[],[f215,f176,f176,f164,f176,f164]) ).
tff(f311,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(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(forward_demodulation,[],[f250,f211]) ).
tff(f312,plain,
one_one(int) != legendre(min,plus_plus(int,times_times(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(forward_demodulation,[],[f311,f211]) ).
tff(f314,plain,
one_one(int) != legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),one_one(int))),
inference(superposition,[],[f312,f171]) ).
tff(f315,plain,
one_one(int) != legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int))),
inference(forward_demodulation,[],[f314,f171]) ).
tff(f3153,plain,
~ dvd_dvd(int,plus_plus(int,times_times(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(forward_demodulation,[],[f286,f211]) ).
tff(f3154,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f3153,f171]) ).
tff(f3155,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f3154,f171]) ).
tff(f3231,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)),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(forward_demodulation,[],[f287,f211]) ).
tff(f3232,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),m),one_one(int)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),
inference(forward_demodulation,[],[f3231,f171]) ).
tff(f3233,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),m),one_one(int)),plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f3232,f171]) ).
tff(f3234,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f3233,f211]) ).
tff(f3266,plain,
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(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(forward_demodulation,[],[f284,f211]) ).
tff(f3267,plain,
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),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(forward_demodulation,[],[f3266,f171]) ).
tff(f3268,plain,
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),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(forward_demodulation,[],[f3267,f171]) ).
tff(f3269,plain,
( ( one_one(int) = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),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(forward_demodulation,[],[f3268,f211]) ).
tff(f3270,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))
| 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(forward_subsumption_resolution,[],[f3269,f315]) ).
tff(f3271,plain,
( dvd_dvd(int,plus_plus(int,times_times(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(forward_demodulation,[],[f3270,f211]) ).
tff(f3272,plain,
( dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),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(forward_demodulation,[],[f3271,f171]) ).
tff(f3273,plain,
( dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),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(forward_demodulation,[],[f3272,f171]) ).
tff(f3274,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(forward_subsumption_resolution,[],[f3273,f3155]) ).
tff(f3275,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)),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(forward_demodulation,[],[f3274,f211]) ).
tff(f3276,plain,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),m),one_one(int)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),
inference(forward_demodulation,[],[f3275,f171]) ).
tff(f3277,plain,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),m),one_one(int)),plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f3276,f171]) ).
tff(f3278,plain,
dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f3277,f211]) ).
tff(f3279,plain,
$false,
inference(forward_subsumption_resolution,[],[f3278,f3234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM940_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.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 21:49:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.28/1.18 % (2036782)Detected formulas, will run a generic FOF schedule.
% 2.28/1.18 % (2036791)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2966639403:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.28/1.18 % (2036791)First to succeed.
% 2.28/1.18 % (2036791)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2036782"
% 2.28/1.18 % (2036787)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=2706605161:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.28/1.18 % (2036789)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=3197860144:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.28/1.18 % (2036793)dis-21_1_sil=8000:lcm=predicate:random_seed=2061178649: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)
% 2.28/1.18 % (2036790)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1405287931:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.28/1.18 % (2036788)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=4035675741:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.28/1.18 % (2036792)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4219554992:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.28/1.18 % (2036790)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.28/1.18 % (2036789)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.28/1.18 % (2036792)Also succeeded, but the first one will report.
% 2.28/1.18 % (2036793)Instruction limit reached!
% 2.28/1.18 % (2036793)------------------------------
% 2.28/1.18 % (2036793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.18 % (2036793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.18 % (2036793)CaDiCaL version: 2.1.3
% 2.28/1.18 % (2036793)Termination reason: Instruction limit
% 2.28/1.18 % (2036793)Termination phase: Saturation
% 2.28/1.18 % (2036793)Time elapsed: 0.054 s
% 2.28/1.18 % (2036793)Peak memory usage: 90 MB
% 2.28/1.18 % (2036793)Instructions burned: 132 (million)
% 2.28/1.18 % (2036790)Instruction limit reached!
% 2.28/1.18 % (2036790)------------------------------
% 2.28/1.18 % (2036790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.18 % (2036790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.18 % (2036790)CaDiCaL version: 2.1.3
% 2.28/1.18 % (2036790)Termination reason: Instruction limit
% 2.28/1.18 % (2036790)Termination phase: Saturation
% 2.28/1.18 % (2036790)Time elapsed: 0.064 s
% 2.28/1.18 % (2036790)Peak memory usage: 89 MB
% 2.28/1.18 % (2036790)Instructions burned: 110 (million)
% 2.28/1.18 % (2036791)Refutation found. Thanks to Tanya!
% 2.28/1.18 % SZS status Theorem for theBenchmark
% 2.28/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.87/1.38 % (2036791)------------------------------
% 2.87/1.38 % (2036791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.38 % (2036791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.38 % (2036791)CaDiCaL version: 2.1.3
% 2.87/1.38 % (2036791)Termination reason: Refutation
% 2.87/1.38 % (2036791)Time elapsed: 0.032 s
% 2.87/1.38 % (2036791)Peak memory usage: 89 MB
% 2.87/1.38 % (2036791)Instructions burned: 107 (million)
% 2.87/1.38 % (2036791)------------------------------
% 2.87/1.38 % (2036791)------------------------------
% 2.87/1.38 % (2036782)Success in time 0.331 s
% 2.87/1.38 % Vampire exiting
%------------------------------------------------------------------------------