%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM660^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 : Wed Sep 30 08:18:26 AM UTC 2026
% Result : Theorem 0.61s 0.42s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 66 unt; 0 typ; 2 def)
% Number of atoms : 487 ( 122 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 519 ( 15 ~; 7 |; 0 &; 430 @)
% ( 2 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 171 ( 167 usr; 9 con; 0-7 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 15 sgn 2 !; 0 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
is_of: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
eps: ( $i > $o ) > $i ).
thf(func_def_4,type,
in: $i > $i > $o ).
thf(func_def_5,type,
d_Subq: $i > $i > $o ).
thf(func_def_7,type,
union: $i > $i ).
thf(func_def_8,type,
power: $i > $i ).
thf(func_def_9,type,
repl: $i > ( $i > $i ) > $i ).
thf(func_def_10,type,
d_Union_closed: $i > $o ).
thf(func_def_11,type,
d_Power_closed: $i > $o ).
thf(func_def_12,type,
d_Repl_closed: $i > $o ).
thf(func_def_13,type,
d_ZF_closed: $i > $o ).
thf(func_def_14,type,
univof: $i > $i ).
thf(func_def_15,type,
if: $o > $i > $i > $i ).
thf(func_def_16,type,
nIn: $i > $i > $o ).
thf(func_def_17,type,
d_UPair: $i > $i > $i ).
thf(func_def_18,type,
d_Sing: $i > $i ).
thf(func_def_19,type,
binunion: $i > $i > $i ).
thf(func_def_20,type,
famunion: $i > ( $i > $i ) > $i ).
thf(func_def_21,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
d_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_23,type,
setminus: $i > $i > $i ).
thf(func_def_24,type,
d_In_rec_G: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_25,type,
d_In_rec: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_26,type,
ordsucc: $i > $i ).
thf(func_def_27,type,
nat_p: $i > $o ).
thf(func_def_29,type,
d_Inj1: $i > $i ).
thf(func_def_30,type,
d_Inj0: $i > $i ).
thf(func_def_31,type,
d_Unj: $i > $i ).
thf(func_def_32,type,
pair: $i > $i > $i ).
thf(func_def_33,type,
proj0: $i > $i ).
thf(func_def_34,type,
proj1: $i > $i ).
thf(func_def_35,type,
d_Sigma: $i > ( $i > $i ) > $i ).
thf(func_def_36,type,
setprod: $i > $i > $i ).
thf(func_def_37,type,
ap: $i > $i > $i ).
thf(func_def_38,type,
pair_p: $i > $o ).
thf(func_def_39,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_40,type,
imp: $o > $o > $o ).
thf(func_def_41,type,
d_not: $o > $o ).
thf(func_def_42,type,
wel: $o > $o ).
thf(func_def_43,type,
obvious: $o ).
thf(func_def_44,type,
l_ec: $o > $o > $o ).
thf(func_def_45,type,
d_and: $o > $o > $o ).
thf(func_def_46,type,
l_or: $o > $o > $o ).
thf(func_def_47,type,
orec: $o > $o > $o ).
thf(func_def_48,type,
l_iff: $o > $o > $o ).
thf(func_def_49,type,
all: $i > ( $i > $o ) > $o ).
thf(func_def_50,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(func_def_51,type,
l_some: $i > ( $i > $o ) > $o ).
thf(func_def_52,type,
or3: $o > $o > $o > $o ).
thf(func_def_53,type,
and3: $o > $o > $o > $o ).
thf(func_def_54,type,
ec3: $o > $o > $o > $o ).
thf(func_def_55,type,
orec3: $o > $o > $o > $o ).
thf(func_def_56,type,
e_is: $i > $i > $i > $o ).
thf(func_def_57,type,
amone: $i > ( $i > $o ) > $o ).
thf(func_def_58,type,
one: $i > ( $i > $o ) > $o ).
thf(func_def_59,type,
ind: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
injective: $i > $i > $i > $o ).
thf(func_def_61,type,
image: $i > $i > $i > $i > $o ).
thf(func_def_62,type,
tofs: $i > $i > $i > $i > $i ).
thf(func_def_63,type,
soft: $i > $i > $i > $i > $i ).
thf(func_def_64,type,
inverse: $i > $i > $i > $i ).
thf(func_def_65,type,
surjective: $i > $i > $i > $o ).
thf(func_def_66,type,
bijective: $i > $i > $i > $o ).
thf(func_def_67,type,
invf: $i > $i > $i > $i ).
thf(func_def_68,type,
inj_h: $i > $i > $i > $i > $i > $i ).
thf(func_def_69,type,
e_in: $i > ( $i > $o ) > $i > $i ).
thf(func_def_70,type,
out: $i > ( $i > $o ) > $i > $i ).
thf(func_def_71,type,
d_pair: $i > $i > $i > $i > $i ).
thf(func_def_72,type,
first: $i > $i > $i > $i ).
thf(func_def_73,type,
second: $i > $i > $i > $i ).
thf(func_def_74,type,
prop1: $o > $i > $i > $i > $i > $o ).
thf(func_def_75,type,
ite: $o > $i > $i > $i > $i ).
thf(func_def_76,type,
wissel_wa: $i > $i > $i > $i > $i ).
thf(func_def_77,type,
wissel_wb: $i > $i > $i > $i > $i ).
thf(func_def_78,type,
wissel: $i > $i > $i > $i ).
thf(func_def_79,type,
changef: $i > $i > $i > $i > $i > $i ).
thf(func_def_80,type,
r_ec: $o > $o > $o ).
thf(func_def_81,type,
esti: $i > $i > $i > $o ).
thf(func_def_82,type,
empty: $i > $i > $o ).
thf(func_def_83,type,
nonempty: $i > $i > $o ).
thf(func_def_84,type,
incl: $i > $i > $i > $o ).
thf(func_def_85,type,
st_disj: $i > $i > $i > $o ).
thf(func_def_86,type,
nissetprop: $i > $i > $i > $i > $o ).
thf(func_def_87,type,
unmore: $i > $i > $i > $i ).
thf(func_def_88,type,
ecelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
ecp: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_90,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_91,type,
ect: $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
ectset: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_93,type,
ectelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_94,type,
ecect: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_95,type,
fixfu: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_96,type,
d_10_prop1: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i > $o ).
thf(func_def_97,type,
prop2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $o ).
thf(func_def_98,type,
indeq: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_99,type,
fixfu2: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_100,type,
d_11_i: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_101,type,
indeq2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i ).
thf(func_def_103,type,
n_is: $i > $i > $o ).
thf(func_def_104,type,
nis: $i > $i > $o ).
thf(func_def_105,type,
n_in: $i > $i > $o ).
thf(func_def_106,type,
n_some: ( $i > $o ) > $o ).
thf(func_def_107,type,
n_all: ( $i > $o ) > $o ).
thf(func_def_108,type,
n_one: ( $i > $o ) > $o ).
thf(func_def_110,type,
cond1: $i > $o ).
thf(func_def_111,type,
cond2: $i > $o ).
thf(func_def_112,type,
i1_s: ( $i > $o ) > $i ).
thf(func_def_113,type,
d_22_prop1: $i > $o ).
thf(func_def_114,type,
d_23_prop1: $i > $o ).
thf(func_def_115,type,
d_24_prop1: $i > $o ).
thf(func_def_116,type,
d_24_prop2: $i > $i > $o ).
thf(func_def_117,type,
prop3: $i > $i > $i > $o ).
thf(func_def_118,type,
prop4: $i > $o ).
thf(func_def_119,type,
d_24_g: $i > $i ).
thf(func_def_120,type,
plus: $i > $i ).
thf(func_def_121,type,
n_pl: $i > $i > $i ).
thf(func_def_122,type,
d_25_prop1: $i > $i > $i > $o ).
thf(func_def_123,type,
d_26_prop1: $i > $i > $o ).
thf(func_def_124,type,
d_27_prop1: $i > $i > $o ).
thf(func_def_125,type,
d_28_prop1: $i > $i > $i > $o ).
thf(func_def_126,type,
diffprop: $i > $i > $i > $o ).
thf(func_def_127,type,
d_29_ii: $i > $i > $o ).
thf(func_def_128,type,
iii: $i > $i > $o ).
thf(func_def_129,type,
d_29_prop1: $i > $i > $o ).
thf(func_def_130,type,
moreis: $i > $i > $o ).
thf(func_def_131,type,
lessis: $i > $i > $o ).
thf(func_def_132,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_136,type,
vIMP: $o > $o > $o ).
thf(func_def_139,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_140,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_141,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_142,type,
vNOT: $o > $o ).
thf(func_def_143,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_144,type,
vOR: $o > $o > $o ).
thf(func_def_145,type,
vAND: $o > $o > $o ).
thf(func_def_146,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_147,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_148,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_149,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_150,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK1: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_152,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK3: $i > $i > $i > $i ).
thf(func_def_154,type,
sK4: $i > $i ).
thf(func_def_155,type,
sK5: $i > $i > $o ).
thf(func_def_156,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_158,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK9: $i > $i > $o ).
thf(func_def_160,type,
sK10: $i > $i > $o ).
thf(func_def_161,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_162,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK15: $i > $i > $o ).
thf(func_def_166,type,
sK16: $i > $i > $o ).
thf(func_def_169,type,
sK19: $i > $i > $i > $i ).
thf(f1,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(f2,axiom,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f74,axiom,
( ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) )
= imp ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(f81,axiom,
( ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) )
= l_or ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
thf(f91,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) )
= e_is ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(f157,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(f160,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(f203,axiom,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_diffprop) ).
thf(f205,axiom,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) )
= d_29_ii ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(f206,axiom,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii) ).
thf(f216,axiom,
( moreis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_moreis) ).
thf(f217,axiom,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lessis) ).
thf(f218,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).
thf(f219,negated_conjecture,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f218]) ).
thf(f315,plain,
( ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) )
= imp ),
inference(rectify,[],[f74]) ).
thf(f316,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f345,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f351,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f366,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f400,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f217]) ).
thf(f412,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f443,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( d_29_ii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f216]) ).
thf(f479,plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f480,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f479]) ).
thf(f485,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f533,plain,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( ( moreis @ X1 @ X3 )
=> ( lessis @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f219]) ).
thf(f534,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( moreis @ Y0 @ Y1 )
=> ( lessis @ Y1 @ Y0 ) ) ) )
!= $true ),
inference(fool_elimination,[],[f533]) ).
thf(f535,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f563,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( moreis @ Y0 @ Y1 )
=> ( lessis @ Y1 @ Y0 ) ) ) )
!= $true ),
inference(flattening,[],[f534]) ).
thf(f608,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f345]) ).
thf(f618,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f620,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(cnf_transformation,[],[f316]) ).
thf(f632,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f485]) ).
thf(f641,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f412]) ).
thf(f648,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f351]) ).
thf(f652,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f400]) ).
thf(f667,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f480]) ).
thf(f674,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f366]) ).
thf(f682,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( moreis @ Y0 @ Y1 )
=> ( lessis @ Y1 @ Y0 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f563]) ).
thf(f688,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( d_29_ii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f443]) ).
thf(f692,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f535]) ).
thf(f703,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f711,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f667,f692]) ).
thf(f713,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f703,f632]) ).
thf(f714,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( Y4 = Y5 )
@ nat
@ Y0
@ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(definition_unfolding,[],[f674,f713]) ).
thf(f715,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] :
( l_some @ nat
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] :
( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y2
@ ( n_pl @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f648,f618,f714]) ).
thf(f716,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] :
( l_some @ nat
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] :
( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y2
@ ( n_pl @ Y3 @ Y4 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f641,f618,f714]) ).
thf(f717,plain,
( l_or
= ( ^ [Y0: $o] :
( ^ [Y1: $o,Y2: $o] :
( Y1
=> Y2 )
@ ( d_not @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f608,f620]) ).
thf(f718,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ ( d_not @ Y2 ) )
@ ( ^ [Y2: $i,Y3: $i] :
( l_some @ nat
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] :
( ^ [Y7: $i,Y8: $i,Y9: $i] : ( Y8 = Y9 )
@ nat
@ Y4
@ ( n_pl @ Y5 @ Y6 ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] : ( Y3 = Y4 )
@ nat
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f652,f717,f716,f713]) ).
thf(f719,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ ( d_not @ Y2 ) )
@ ( ^ [Y2: $i,Y3: $i] :
( l_some @ nat
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] :
( ^ [Y7: $i,Y8: $i,Y9: $i] : ( Y8 = Y9 )
@ nat
@ Y4
@ ( n_pl @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] : ( Y3 = Y4 )
@ nat
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f688,f717,f715,f713]) ).
thf(f773,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $o] :
( ^ [Y5: $o,Y6: $o] :
( Y5
=> Y6 )
@ ( d_not @ Y4 ) )
@ ( ^ [Y4: $i,Y5: $i] :
( l_some @ nat
@ ( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ^ [Y9: $i,Y10: $i,Y11: $i] : ( Y10 = Y11 )
@ nat
@ Y6
@ ( n_pl @ Y7 @ Y8 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( Y5 = Y6 )
@ nat
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
=> ( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $o] :
( ^ [Y5: $o,Y6: $o] :
( Y5
=> Y6 )
@ ( d_not @ Y4 ) )
@ ( ^ [Y4: $i,Y5: $i] :
( l_some @ nat
@ ( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ^ [Y9: $i,Y10: $i,Y11: $i] : ( Y10 = Y11 )
@ nat
@ Y6
@ ( n_pl @ Y7 @ Y8 ) )
@ Y5
@ Y4 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( Y5 = Y6 )
@ nat
@ Y2
@ Y3 ) )
@ Y1
@ Y0 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f682,f711,f711,f719,f718]) ).
thf(f1139,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( Y0 = Y1 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f773]) ).
thf(f1140,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( Y0 = Y1 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( Y1 = Y0 ) ) ) ) ) )
@ sK17 ) ),
inference(sigma_proxy_clausification,[],[f1139]) ).
thf(f1141,plain,
( $false
= ( ( in @ sK17 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y1: $i] :
( sK17
= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( sK17 = Y0 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y1: $i] :
( sK17
= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( Y0 = sK17 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1140]) ).
thf(f1142,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y1: $i] :
( sK17
= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( sK17 = Y0 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y1: $i] :
( sK17
= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( Y0 = sK17 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1141]) ).
thf(f1144,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y1: $i] :
( sK17
= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( sK17 = Y0 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y1: $i] :
( sK17
= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( Y0 = sK17 ) ) ) )
@ sK18 ) ),
inference(sigma_proxy_clausification,[],[f1142]) ).
thf(f1145,plain,
( $false
= ( ( in @ sK18 @ nat )
=> ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
=> ( sK17 = sK18 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
=> ( sK18 = sK17 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1144]) ).
thf(f1146,plain,
( $false
= ( ( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
=> ( sK17 = sK18 ) )
=> ( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
=> ( sK18 = sK17 ) ) ) ),
inference(imp_proxy_clausification,[],[f1145]) ).
thf(f1148,plain,
( $false
= ( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
=> ( sK18 = sK17 ) ) ),
inference(imp_proxy_clausification,[],[f1146]) ).
thf(f1149,plain,
( $true
= ( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
=> ( sK17 = sK18 ) ) ),
inference(imp_proxy_clausification,[],[f1146]) ).
thf(f1150,plain,
( ( $false
= ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) ) )
| ( ( sK17 = sK18 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1149]) ).
thf(f1151,plain,
( ( $false
= ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) ) )
| ( sK17 = sK18 ) ),
inference(equality_proxy_clausification,[],[f1150]) ).
thf(f1152,plain,
( $false
= ( sK18 = sK17 ) ),
inference(imp_proxy_clausification,[],[f1148]) ).
thf(f1153,plain,
( ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f1148]) ).
thf(f1154,plain,
sK17 != sK18,
inference(equality_proxy_clausification,[],[f1152]) ).
thf(f1185,definition,
( spl20_1
<=> ( $false
= ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f1187,plain,
( ( $false
= ( d_not
@ ( l_some @ nat
@ ^ [Y0: $i] :
( sK17
= ( n_pl @ sK18 @ Y0 ) ) ) ) )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f1185]) ).
thf(f1189,definition,
( spl20_2
<=> ( sK17 = sK18 ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f1192,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f1151,f1189,f1185]) ).
thf(f1193,plain,
~ spl20_2,
inference(avatar_split_clause,[],[f1154,f1189]) ).
thf(f1207,plain,
( ( $false = $true )
| ~ spl20_1 ),
inference(forward_demodulation,[],[f1153,f1187]) ).
thf(f1208,plain,
( $false
| ~ spl20_1 ),
inference(trivial_inequality_removal,[],[f1207]) ).
thf(f1209,plain,
~ spl20_1,
inference(avatar_contradiction_clause,[],[f1208]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f1192]) ).
cnf(s2,plain,
~ spl20_2,
inference(sat_conversion,[],[f1193]) ).
cnf(s3,plain,
~ spl20_1,
inference(sat_conversion,[],[f1209]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f1210,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM660^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:35:42 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.39 % (532992)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.39 % (533011)lrs+10_16_si=on:nwc=1.5:random_seed=3717571554:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.39 % (533016)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.39 % (533016)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.61/0.39 % (533011)Instruction limit reached!
% 0.61/0.39 % (533011)------------------------------
% 0.61/0.39 % (533011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (533011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (533011)CaDiCaL version: 2.1.3
% 0.61/0.39 % (533011)Termination reason: Instruction limit
% 0.61/0.39 % (533011)Termination phase: Property scanning
% 0.61/0.39 % (533011)Time elapsed: 0.005 s
% 0.61/0.39 % (533011)Peak memory usage: 10 MB
% 0.61/0.39 % (533011)Instructions burned: 20 (million)
% 0.61/0.39 % (533010)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3436777415:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.39 % (533012)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=320999275:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.39 % (533015)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3132002055:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.39 % (533016)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=892844654:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.39 % (533013)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2287465451:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.61/0.39 % (533014)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2054104279:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.39 % (533012)Instruction limit reached!
% 0.61/0.39 % (533012)------------------------------
% 0.61/0.39 % (533012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (533012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (533012)CaDiCaL version: 2.1.3
% 0.61/0.39 % (533012)Termination reason: Instruction limit
% 0.61/0.39 % (533012)Termination phase: shuffling
% 0.61/0.39 % (533012)Time elapsed: 0.002 s
% 0.61/0.39 % (533012)Peak memory usage: 10 MB
% 0.61/0.39 % (533012)Instructions burned: 3 (million)
% 0.61/0.39 % (533021)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3381167225:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (533021)Instruction limit reached!
% 0.61/0.39 % (533021)------------------------------
% 0.61/0.39 % (533021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (533021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (533021)CaDiCaL version: 2.1.3
% 0.61/0.39 % (533021)Termination reason: Instruction limit
% 0.61/0.39 % (533021)Termination phase: shuffling
% 0.61/0.39 % (533021)Time elapsed: 0.001 s
% 0.61/0.39 % (533021)Peak memory usage: 10 MB
% 0.61/0.39 % (533021)Instructions burned: 3 (million)
% 0.61/0.39 % (533014)Instruction limit reached!
% 0.61/0.39 % (533014)------------------------------
% 0.61/0.39 % (533014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (533014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (533014)CaDiCaL version: 2.1.3
% 0.61/0.39 % (533014)Termination reason: Instruction limit
% 0.61/0.39 % (533014)Termination phase: Property scanning
% 0.61/0.39 % (533014)Time elapsed: 0.012 s
% 0.61/0.39 % (533014)Peak memory usage: 10 MB
% 0.61/0.39 % (533014)Instructions burned: 26 (million)
% 0.61/0.39 % (533034)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.39 % (533034)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=939649804:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.42 % (533029)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=795153287:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.42 % (533034)Instruction limit reached!
% 0.61/0.42 % (533034)------------------------------
% 0.61/0.42 % (533034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533034)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533034)Termination reason: Instruction limit
% 0.61/0.42 % (533034)Termination phase: shuffling
% 0.61/0.42 % (533034)Time elapsed: 0.002 s
% 0.61/0.42 % (533034)Peak memory usage: 10 MB
% 0.61/0.42 % (533034)Instructions burned: 11 (million)
% 0.61/0.42 % (533029)Instruction limit reached!
% 0.61/0.42 % (533029)------------------------------
% 0.61/0.42 % (533029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533029)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533029)Termination reason: Instruction limit
% 0.61/0.42 % (533029)Termination phase: shuffling
% 0.61/0.42 % (533029)Time elapsed: 0.005 s
% 0.61/0.42 % (533029)Peak memory usage: 10 MB
% 0.61/0.42 % (533029)Instructions burned: 8 (million)
% 0.61/0.42 % (533035)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3909388877:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.42 % (533042)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.61/0.42 % (533042)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.42 % (533015)Instruction limit reached!
% 0.61/0.42 % (533015)------------------------------
% 0.61/0.42 % (533015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533015)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533015)Termination reason: Instruction limit
% 0.61/0.42 % (533015)Termination phase: Function definition elimination
% 0.61/0.42 % (533015)Time elapsed: 0.033 s
% 0.61/0.42 % (533015)Peak memory usage: 11 MB
% 0.61/0.42 % (533015)Instructions burned: 75 (million)
% 0.61/0.42 % (533042)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4274463054:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.42 % (533035)Instruction limit reached!
% 0.61/0.42 % (533035)------------------------------
% 0.61/0.42 % (533035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533035)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533035)Termination reason: Instruction limit
% 0.61/0.42 % (533035)Termination phase: shuffling
% 0.61/0.42 % (533035)Time elapsed: 0.006 s
% 0.61/0.42 % (533035)Peak memory usage: 10 MB
% 0.61/0.42 % (533035)Instructions burned: 13 (million)
% 0.61/0.42 % (533010)Instruction limit reached!
% 0.61/0.42 % (533010)------------------------------
% 0.61/0.42 % (533010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533010)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533010)Termination reason: Instruction limit
% 0.61/0.42 % (533010)Termination phase: Function definition elimination
% 0.61/0.42 % (533010)Time elapsed: 0.038 s
% 0.61/0.42 % (533010)Peak memory usage: 11 MB
% 0.61/0.42 % (533010)Instructions burned: 89 (million)
% 0.61/0.42 % (533042)Instruction limit reached!
% 0.61/0.42 % (533042)------------------------------
% 0.61/0.42 % (533042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533042)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533042)Termination reason: Instruction limit
% 0.61/0.42 % (533042)Termination phase: Property scanning
% 0.61/0.42 % (533042)Time elapsed: 0.007 s
% 0.61/0.42 % (533042)Peak memory usage: 10 MB
% 0.61/0.42 % (533042)Instructions burned: 32 (million)
% 0.61/0.42 % (533052)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.42 % (533056)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=248456758:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.61/0.42 % (533052)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=4162569005:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.42 % (533053)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3278640729:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.42 % (533052)Instruction limit reached!
% 0.61/0.42 % (533052)------------------------------
% 0.61/0.42 % (533052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533052)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533052)Termination reason: Instruction limit
% 0.61/0.42 % (533052)Termination phase: shuffling
% 0.61/0.42 % (533052)Time elapsed: 0.002 s
% 0.61/0.42 % (533052)Peak memory usage: 10 MB
% 0.61/0.42 % (533052)Instructions burned: 4 (million)
% 0.61/0.42 % (533045)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1009380522:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.42 % (533049)lrs+10_1_si=on:cs=on:random_seed=102701611:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.42 % (533016)Instruction limit reached!
% 0.61/0.42 % (533016)------------------------------
% 0.61/0.42 % (533016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533056)Refutation not found, incomplete strategy
% 0.61/0.42 % (533056)------------------------------
% 0.61/0.42 % (533056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533056)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533016)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533056)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.42 % (533056)Time elapsed: 0.010 s
% 0.61/0.42 % (533056)Peak memory usage: 13 MB
% 0.61/0.42 % (533056)Instructions burned: 40 (million)
% 0.61/0.42 % (533016)Termination reason: Instruction limit
% 0.61/0.42 % (533016)Termination phase: Function definition elimination
% 0.61/0.42 % (533016)Time elapsed: 0.065 s
% 0.61/0.42 % (533016)Peak memory usage: 11 MB
% 0.61/0.42 % (533016)Instructions burned: 159 (million)
% 0.61/0.42 % (533056)------------------------------
% 0.61/0.42 % (533056)------------------------------
% 0.61/0.42 % (533049)Instruction limit reached!
% 0.61/0.42 % (533049)------------------------------
% 0.61/0.42 % (533049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533049)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533049)Termination reason: Instruction limit
% 0.61/0.42 % (533049)Termination phase: shuffling
% 0.61/0.42 % (533049)Time elapsed: 0.004 s
% 0.61/0.42 % (533049)Peak memory usage: 10 MB
% 0.61/0.42 % (533049)Instructions burned: 9 (million)
% 0.61/0.42 % (533073)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3114311905:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.42 % (533053)Instruction limit reached!
% 0.61/0.42 % (533053)------------------------------
% 0.61/0.42 % (533053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533053)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533053)Termination reason: Instruction limit
% 0.61/0.42 % (533053)Termination phase: Saturation
% 0.61/0.42 % (533053)Time elapsed: 0.018 s
% 0.61/0.42 % (533053)Peak memory usage: 11 MB
% 0.61/0.42 % (533053)Instructions burned: 40 (million)
% 0.61/0.42 % (533067)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2580923185:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.42 % (533072)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2902850956:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.42 % (533075)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3053235653:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.42 % (533067)Instruction limit reached!
% 0.61/0.42 % (533067)------------------------------
% 0.61/0.42 % (533067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533067)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533067)Termination reason: Instruction limit
% 0.61/0.42 % (533067)Termination phase: Property scanning
% 0.61/0.42 % (533067)Time elapsed: 0.012 s
% 0.61/0.42 % (533067)Peak memory usage: 10 MB
% 0.61/0.42 % (533067)Instructions burned: 25 (million)
% 0.61/0.42 % (533072)Instruction limit reached!
% 0.61/0.42 % (533072)------------------------------
% 0.61/0.42 % (533072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533072)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533072)Termination reason: Instruction limit
% 0.61/0.42 % (533072)Termination phase: shuffling
% 0.61/0.42 % (533072)Time elapsed: 0.007 s
% 0.61/0.42 % (533072)Peak memory usage: 10 MB
% 0.61/0.42 % (533072)Instructions burned: 16 (million)
% 0.61/0.42 % (533075)Instruction limit reached!
% 0.61/0.42 % (533075)------------------------------
% 0.61/0.42 % (533075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533075)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533075)Termination reason: Instruction limit
% 0.61/0.42 % (533075)Termination phase: shuffling
% 0.61/0.42 % (533075)Time elapsed: 0.006 s
% 0.61/0.42 % (533075)Peak memory usage: 10 MB
% 0.61/0.42 % (533075)Instructions burned: 14 (million)
% 0.61/0.42 % (533081)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3947218963:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.61/0.42 % (533045)Instruction limit reached!
% 0.61/0.42 % (533045)------------------------------
% 0.61/0.42 % (533045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533045)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533045)Termination reason: Instruction limit
% 0.61/0.42 % (533045)Termination phase: Function definition elimination
% 0.61/0.42 % (533045)Time elapsed: 0.037 s
% 0.61/0.42 % (533045)Peak memory usage: 11 MB
% 0.61/0.42 % (533045)Instructions burned: 87 (million)
% 0.61/0.42 % (533081)Instruction limit reached!
% 0.61/0.42 % (533081)------------------------------
% 0.61/0.42 % (533081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533081)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533081)Termination reason: Instruction limit
% 0.61/0.42 % (533081)Termination phase: shuffling
% 0.61/0.42 % (533081)Time elapsed: 0.002 s
% 0.61/0.42 % (533081)Peak memory usage: 10 MB
% 0.61/0.42 % (533081)Instructions burned: 3 (million)
% 0.61/0.42 % (533073) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-532992-533073"...
% 0.61/0.42 % (533073)...printing done.
% 0.61/0.42 % (533073)Refutation found. Thanks to Tanya!
% 0.61/0.42 % SZS status Theorem for theBenchmark
% 0.61/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.61/0.42 % (533073)------------------------------
% 0.61/0.42 % (533073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (533073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (533073)CaDiCaL version: 2.1.3
% 0.61/0.42 % (533073)Termination reason: Refutation
% 0.61/0.42 % (533073)Time elapsed: 0.027 s
% 0.61/0.42 % (533073)Peak memory usage: 14 MB
% 0.61/0.42 % (533073)Instructions burned: 112 (million)
% 0.61/0.42 % (532992)Success in time 0.16 s
% 0.61/0.42 % Vampire exiting
%------------------------------------------------------------------------------