%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM952_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:26:17 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?; 26 :)
% 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,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
min: int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > 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(func_def_14,type,
s: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zprime: int > $o ).
tff(pred_def_10,type,
quadRes: ( int * int ) > $o ).
tff(pred_def_11,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(f1,axiom,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(f2,axiom,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
tff(f28,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__Bit0__Bit0) ).
tff(f52,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_nat__1__add__1) ).
tff(f65,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Numeral1__eq1__nat) ).
tff(f70,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_number__of__is__id) ).
tff(f78,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__Pls__right) ).
tff(f79,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__Pls) ).
tff(f80,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Bit0__def) ).
tff(f82,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_int__distrib_I1_J) ).
tff(f84,axiom,
! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_plus__numeral__code_I9_J) ).
tff(f89,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Bit1__def) ).
tff(f113,conjecture,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
inference(flattening,[],[f114]) ).
tff(f178,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(cnf_transformation,[],[f1]) ).
tff(f179,plain,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))),
inference(cnf_transformation,[],[f2]) ).
tff(f209,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f28]) ).
tff(f234,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f52]) ).
tff(f247,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(cnf_transformation,[],[f65]) ).
tff(f253,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f70]) ).
tff(f266,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f78]) ).
tff(f267,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f79]) ).
tff(f268,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f270,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f82]) ).
tff(f272,plain,
! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f84]) ).
tff(f277,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f89]) ).
tff(f303,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
inference(cnf_transformation,[],[f115]) ).
tff(f304,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,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)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,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)))),one_one(int)),
inference(definition_unfolding,[],[f178,f268,f277,f268,f277]) ).
tff(f305,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)),minus_minus(int,power_power(int,s,number_number_of(nat,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)))),number_number_of(int,min))),
inference(definition_unfolding,[],[f179,f268,f268,f277,f268,f277]) ).
tff(f332,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ),
inference(definition_unfolding,[],[f209,f268,f268,f268]) ).
tff(f347,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,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,[],[f234,f268,f277]) ).
tff(f353,plain,
one_one(nat) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f247,f277]) ).
tff(f364,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,power_power(int,s,number_number_of(nat,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)))),one_one(int))),
inference(definition_unfolding,[],[f303,f268,f268,f277,f268,f277]) ).
tff(f369,plain,
one_one(nat) = number_number_of(nat,plus_plus(int,one_one(int),pls)),
inference(forward_demodulation,[],[f353,f266]) ).
tff(f373,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),
inference(forward_demodulation,[],[f347,f266]) ).
tff(f386,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)),minus_minus(int,power_power(int,s,number_number_of(nat,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)))),min)),
inference(forward_demodulation,[],[f305,f253]) ).
tff(f387,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int)),
inference(forward_demodulation,[],[f304,f266]) ).
tff(f392,plain,
one_one(nat) = number_number_of(nat,one_one(int)),
inference(forward_demodulation,[],[f369,f266]) ).
tff(f395,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls))),
inference(forward_demodulation,[],[f373,f332]) ).
tff(f408,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)),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),min)),
inference(forward_demodulation,[],[f386,f266]) ).
tff(f409,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls)))),one_one(int)),
inference(forward_demodulation,[],[f387,f332]) ).
tff(f416,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls)),
inference(forward_demodulation,[],[f395,f267]) ).
tff(f425,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),one_one(int)),plus_plus(int,pls,pls)),plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls)))),min)),
inference(forward_demodulation,[],[f408,f332]) ).
tff(f426,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls))),one_one(int)),
inference(forward_demodulation,[],[f409,f267]) ).
tff(f433,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f416,f266]) ).
tff(f442,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),one_one(int)),pls),plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls))),min)),
inference(forward_demodulation,[],[f425,f267]) ).
tff(f443,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int)),
inference(forward_demodulation,[],[f426,f266]) ).
tff(f446,plain,
number_number_of(nat,plus_plus(int,one_one(int),one_one(int))) = plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int))),
inference(forward_demodulation,[],[f433,f392]) ).
tff(f451,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)),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),min)),
inference(forward_demodulation,[],[f442,f266]) ).
tff(f452,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int)) = minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),min),
inference(forward_demodulation,[],[f443,f253]) ).
tff(f459,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)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f451,f446]) ).
tff(f460,plain,
minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min) = plus_plus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),one_one(int)),
inference(forward_demodulation,[],[f452,f446]) ).
tff(f467,plain,
dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),number_number_of(int,plus_plus(int,one_one(int),one_one(int)))),m),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f459,f272]) ).
tff(f474,plain,
dvd_dvd(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),m),times_times(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),m)),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f467,f270]) ).
tff(f481,plain,
dvd_dvd(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,number_number_of(int,one_one(int)),number_number_of(int,one_one(int))),m),times_times(int,plus_plus(int,number_number_of(int,one_one(int)),number_number_of(int,one_one(int))),m)),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f474,f272]) ).
tff(f487,plain,
dvd_dvd(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m))),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f481,f270]) ).
tff(f492,plain,
dvd_dvd(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,one_one(int),m)),plus_plus(int,times_times(int,one_one(int),m),times_times(int,one_one(int),m))),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f487,f253]) ).
tff(f548,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)),plus_plus(int,power_power(int,s,number_number_of(nat,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)))),one_one(int))),
inference(superposition,[],[f364,f253]) ).
tff(f553,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)),plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int))),
inference(forward_demodulation,[],[f548,f266]) ).
tff(f556,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls)),plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,pls,pls)))),one_one(int))),
inference(forward_demodulation,[],[f553,f332]) ).
tff(f559,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls),plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls)),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),pls))),one_one(int))),
inference(forward_demodulation,[],[f556,f267]) ).
tff(f562,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,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int))),
inference(forward_demodulation,[],[f559,f266]) ).
tff(f565,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,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),one_one(int))),
inference(forward_demodulation,[],[f562,f446]) ).
tff(f568,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)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f565,f460]) ).
tff(f571,plain,
~ dvd_dvd(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),m),times_times(int,plus_plus(int,one_one(int),one_one(int)),m)),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f568,f270]) ).
tff(f574,plain,
~ dvd_dvd(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,one_one(int),m)),plus_plus(int,times_times(int,one_one(int),m),times_times(int,one_one(int),m))),one_one(int)),minus_minus(int,power_power(int,s,plus_plus(nat,number_number_of(nat,one_one(int)),number_number_of(nat,one_one(int)))),min)),
inference(forward_demodulation,[],[f571,f270]) ).
tff(f577,plain,
$false,
inference(forward_subsumption_resolution,[],[f574,f492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM952_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:50:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.46 % (3917892)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (3917902)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3133866923:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (3917898)% WARNING: option uhcvi not known.
% 0.17/0.46 % (3917902) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3917892-3917902"...
% 0.17/0.46 % (3917898)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=955999212:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (3917897)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2221938544_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (3917899)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1002634625:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (3917900)dis+10_1_sil=32000:sp=arity:random_seed=1396193437:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (3917903)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2984917924:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (3917901)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2412857155:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (3917902)...printing done.
% 0.17/0.46 % (3917902)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (3917902)------------------------------
% 0.17/0.46 % (3917902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (3917902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (3917902)CaDiCaL version: 2.1.3
% 0.17/0.46 % (3917902)Termination reason: Refutation
% 0.17/0.46 % (3917902)Time elapsed: 0.007 s
% 0.17/0.46 % (3917902)Peak memory usage: 12 MB
% 0.17/0.46 % (3917902)Instructions burned: 23 (million)
% 0.17/0.46 % (3917892)Success in time 0.043 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------