%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN008_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 : n003.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 12:26:55 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 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 : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 18 ( 18 !; 0 ?; 18 :)
% 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,
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,
m1: int ).
tff(func_def_13,type,
n: nat ).
tff(func_def_14,type,
r: int ).
tff(func_def_15,type,
sa: int ).
tff(func_def_16,type,
v: int ).
tff(func_def_17,type,
w: int ).
tff(func_def_18,type,
sK0: 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,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,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(f43,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_42_nat__1__add__1) ).
tff(f68,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_add__Pls__right) ).
tff(f70,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Bit0__def) ).
tff(f72,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_int__distrib_I2_J) ).
tff(f75,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,X2,minus_minus(int,X1,X0)) = minus_minus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_int__distrib_I4_J) ).
tff(f81,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Bit1__def) ).
tff(f114,conjecture,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),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)))))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f115,negated_conjecture,
( ( ~ plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),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)))))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))) ) = plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
tff(f116,plain,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),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)))))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f115]) ).
tff(f176,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(f223,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f43]) ).
tff(f252,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f68]) ).
tff(f254,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f70]) ).
tff(f256,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f259,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X2,minus_minus(int,X1,X0)) = minus_minus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(cnf_transformation,[],[f75]) ).
tff(f265,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
tff(f298,plain,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),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)))))),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f116]) ).
tff(f299,plain,
times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = plus_plus(int,power_power(int,v,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)))),power_power(int,w,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,[],[f176,f254,f265,f254,f265]) ).
tff(f335,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,[],[f223,f254,f265]) ).
tff(f360,plain,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),plus_plus(int,power_power(int,v,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)))),power_power(int,w,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(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)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),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))))) != plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),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)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),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,[],[f298,f254,f265,f254,f265,f254,f265,f254,f265,f254,f265,f254,f265]) ).
tff(f1041,plain,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))))),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))))) != plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))))),
inference(forward_demodulation,[],[f360,f252]) ).
tff(f1042,plain,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,w,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))) != plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,minus_minus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,w)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1041,f252]) ).
tff(f1043,plain,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,w,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))) != plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,r,v)),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1042,f259]) ).
tff(f1044,plain,
plus_plus(int,power_power(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,times_times(int,r,v),times_times(int,sa,w))),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,w,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))) != plus_plus(int,power_power(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,times_times(int,r,v),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1043,f256]) ).
tff(f1045,plain,
plus_plus(int,power_power(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,times_times(int,r,v),times_times(int,sa,w))),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,w,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))) != plus_plus(int,power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,plus_plus(int,times_times(int,r,v),times_times(int,sa,w)),m1)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1044,f256]) ).
tff(f1067,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,[],[f335,f252]) ).
tff(f1068,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,[],[f1067,f252]) ).
tff(f1087,plain,
plus_plus(int,power_power(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,times_times(int,r,v),times_times(int,sa,w))),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))))),plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),plus_plus(nat,one_one(nat),one_one(nat)))) != plus_plus(int,power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,plus_plus(int,times_times(int,r,v),times_times(int,sa,w)),m1)),plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(superposition,[],[f1045,f1068]) ).
tff(f1732,plain,
times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))))),
inference(forward_demodulation,[],[f299,f252]) ).
tff(f1733,plain,
times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),power_power(int,w,number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1732,f252]) ).
tff(f1734,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,[],[f1733,f1068]) ).
tff(f1895,plain,
plus_plus(int,power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,plus_plus(int,times_times(int,r,v),times_times(int,sa,w)),m1)),plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),plus_plus(nat,one_one(nat),one_one(nat)))) != plus_plus(int,power_power(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,times_times(int,r,v),times_times(int,sa,w))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f1087,f1734]) ).
tff(f1896,plain,
plus_plus(int,power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,plus_plus(int,times_times(int,r,v),times_times(int,sa,w)),m1)),plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),plus_plus(nat,one_one(nat),one_one(nat)))) != plus_plus(int,power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,plus_plus(int,times_times(int,r,v),times_times(int,sa,w)),m1)),plus_plus(nat,one_one(nat),one_one(nat))),power_power(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,r,w),times_times(int,sa,v))),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f1895,f256]) ).
tff(f1897,plain,
$false,
inference(trivial_inequality_removal,[],[f1896]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN008_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 21:51:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.18/0.48 % (948779)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (948787)dis+10_1_sil=32000:sp=arity:random_seed=271433069:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (948785)% WARNING: option uhcvi not known.
% 0.18/0.48 % (948784)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4283106455_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (948785)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=682176947:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (948786)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1847260164:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (948788)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3679253952:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (948790)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1528538355:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (948789)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1325993944:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % Exception at run slice level
% 0.18/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.48 % (948787) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-948779-948787"...
% 0.18/0.48 % (948787)...printing done.
% 0.18/0.48 % (948798)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=610879426:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.48 % (948787)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (948787)------------------------------
% 0.18/0.48 % (948787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (948787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (948787)CaDiCaL version: 2.1.3
% 0.18/0.48 % (948787)Termination reason: Refutation
% 0.18/0.48 % (948787)Time elapsed: 0.031 s
% 0.18/0.48 % (948787)Peak memory usage: 12 MB
% 0.18/0.48 % (948787)Instructions burned: 105 (million)
% 0.18/0.48 % (948779)Success in time 0.064 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------