%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM640^4 : 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 : n018.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 08:18:21 AM UTC 2026
% Result : Theorem 0.65s 0.44s
% Output : Refutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 336 ( 75 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 502 ( 9 ~; 11 |; 0 &; 438 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 165 ( 161 usr; 7 con; 0-7 aty)
% ( 17 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 134 ( 121 ^; 13 !; 0 ?; 134 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_125,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vIMP: $o > $o > $o ).
thf(func_def_130,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_131,type,
vAND: $o > $o > $o ).
thf(func_def_132,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_134,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_136,type,
vNOT: $o > $o ).
thf(func_def_137,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
vOR: $o > $o > $o ).
thf(func_def_140,type,
sK0: ( $i > $i ) > $i > ( $i > $i ) > $i ).
thf(func_def_141,type,
sK1: $i > $i > $i > $i ).
thf(func_def_142,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_143,type,
sK3: $i > $i ).
thf(func_def_144,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_145,type,
sK5: $i > $i > $i ).
thf(func_def_146,type,
sK6: $i > $i > $o ).
thf(func_def_147,type,
sK7: $i > $i > $o ).
thf(func_def_148,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_149,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK11: $i > $i > $o ).
thf(func_def_152,type,
sK12: $i > $i > $o ).
thf(func_def_153,type,
sK13: $i > $i > $o ).
thf(func_def_154,type,
sK14: $i > $i > $o ).
thf(func_def_155,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK16: $i > $i > $i ).
thf(func_def_157,type,
sK17: $i > $i > $o ).
thf(func_def_158,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_161,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_162,type,
sK22: $i > $i > $i > $i ).
thf(func_def_165,type,
sK25: ( $i > $o ) > $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,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
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(f187,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ ( ordsucc @ X1 ) ) @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4b) ).
thf(f191,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @ ( n_pl @ X0 @ ( ordsucc @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4f) ).
thf(f192,negated_conjecture,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @ ( n_pl @ X0 @ ( ordsucc @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f191]) ).
thf(f417,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] : ( n_is @ ( n_pl @ X1 @ ( ordsucc @ X3 ) ) @ ( ordsucc @ ( n_pl @ X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f187]) ).
thf(f418,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f417]) ).
thf(f447,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f470,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f473,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f474,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f473]) ).
thf(f487,plain,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X1 @ X3 ) ) @ ( n_pl @ X1 @ ( ordsucc @ X3 ) ) ) ) ),
inference(rectify,[],[f192]) ).
thf(f488,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) @ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f487]) ).
thf(f492,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) @ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) ) ) )
!= $true ),
inference(flattening,[],[f488]) ).
thf(f561,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f470]) ).
thf(f572,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f418]) ).
thf(f594,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) @ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f492]) ).
thf(f614,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f474]) ).
thf(f627,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f636,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f447]) ).
thf(f666,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,[],[f614,f561]) ).
thf(f669,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f627,f636]) ).
thf(f688,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: $i] : ( Y3 = Y4 )
@ nat
@ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) )
@ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f572,f666,f666,f669]) ).
thf(f695,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: $i] : ( Y3 = Y4 )
@ nat
@ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) )
@ ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f594,f666,f666,f669]) ).
thf(f910,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ ( ordsucc @ Y1 ) )
= ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f688]) ).
thf(f911,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ ( ordsucc @ Y1 ) )
= ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f910]) ).
thf(f912,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ ( ordsucc @ Y0 ) )
= ( ordsucc @ ( n_pl @ X1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f911]) ).
thf(f913,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ ( ordsucc @ Y0 ) )
= ( ordsucc @ ( n_pl @ X1 @ Y0 ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f912]) ).
thf(f914,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ ( ordsucc @ Y0 ) )
= ( ordsucc @ ( n_pl @ X1 @ Y0 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f913]) ).
thf(f915,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ( in @ X2 @ nat )
=> ( ( n_pl @ X1 @ ( ordsucc @ X2 ) )
= ( ordsucc @ ( n_pl @ X1 @ X2 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f914]) ).
thf(f916,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ nat ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ( n_pl @ X1 @ ( ordsucc @ X2 ) )
= ( ordsucc @ ( n_pl @ X1 @ X2 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f915]) ).
thf(f917,plain,
! [X2: $i,X1: $i] :
( ( ( ordsucc @ ( n_pl @ X1 @ X2 ) )
= ( n_pl @ X1 @ ( ordsucc @ X2 ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X2 @ nat ) ) ),
inference(equality_proxy_clausification,[],[f916]) ).
thf(f1045,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ordsucc @ ( n_pl @ Y0 @ Y1 ) )
= ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f695]) ).
thf(f1046,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ordsucc @ ( n_pl @ Y0 @ Y1 ) )
= ( n_pl @ Y0 @ ( ordsucc @ Y1 ) ) ) ) ) )
@ sK23 )
= $false ),
inference(sigma_proxy_clausification,[],[f1045]) ).
thf(f1047,plain,
( ( ( in @ sK23 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK23 @ Y0 ) )
= ( n_pl @ sK23 @ ( ordsucc @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1046]) ).
thf(f1048,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK23 @ Y0 ) )
= ( n_pl @ sK23 @ ( ordsucc @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1047]) ).
thf(f1049,plain,
( $true
= ( in @ sK23 @ nat ) ),
inference(imp_proxy_clausification,[],[f1047]) ).
thf(f1050,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK23 @ Y0 ) )
= ( n_pl @ sK23 @ ( ordsucc @ Y0 ) ) ) )
@ sK24 )
= $false ),
inference(sigma_proxy_clausification,[],[f1048]) ).
thf(f1051,plain,
( ( ( in @ sK24 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK23 @ sK24 ) )
= ( n_pl @ sK23 @ ( ordsucc @ sK24 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1050]) ).
thf(f1052,plain,
( ( ( ordsucc @ ( n_pl @ sK23 @ sK24 ) )
= ( n_pl @ sK23 @ ( ordsucc @ sK24 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1051]) ).
thf(f1053,plain,
( ( in @ sK24 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1051]) ).
thf(f1054,plain,
( ( ordsucc @ ( n_pl @ sK23 @ sK24 ) )
!= ( n_pl @ sK23 @ ( ordsucc @ sK24 ) ) ),
inference(equality_proxy_clausification,[],[f1052]) ).
thf(f1155,plain,
( ( ( in @ sK24 @ nat )
= $false )
| ( ( ordsucc @ ( n_pl @ sK23 @ sK24 ) )
!= ( ordsucc @ ( n_pl @ sK23 @ sK24 ) ) )
| ( $false
= ( in @ sK23 @ nat ) ) ),
inference(superposition,[],[f1054,f917]) ).
thf(f1158,plain,
( ( ( in @ sK24 @ nat )
= $false )
| ( $false
= ( in @ sK23 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1155]) ).
thf(f1159,plain,
( ( $false
= ( in @ sK23 @ nat ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f1158,f1053]) ).
thf(f1160,plain,
( $false
= ( in @ sK23 @ nat ) ),
inference(trivial_inequality_removal,[],[f1159]) ).
thf(f1172,plain,
$false = $true,
inference(superposition,[],[f1049,f1160]) ).
thf(f1173,plain,
$false,
inference(trivial_inequality_removal,[],[f1172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM640^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:20:41 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.26 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
% 0.65/0.40 % (1620)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.65/0.40 % (1632)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2386125431:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.65/0.40 % (1630)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=138765699:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.65/0.40 % (1631)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=383581415: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)
% 0.65/0.40 % (1632)Instruction limit reached!
% 0.65/0.40 % (1632)------------------------------
% 0.65/0.40 % (1632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.40 % (1632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.40 % (1632)CaDiCaL version: 2.1.3
% 0.65/0.40 % (1632)Termination reason: Instruction limit
% 0.65/0.40 % (1632)Termination phase: shuffling
% 0.65/0.40 % (1632)Time elapsed: 0.006 s
% 0.65/0.40 % (1632)Peak memory usage: 10 MB
% 0.65/0.40 % (1632)Instructions burned: 26 (million)
% 0.65/0.40 % (1627)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3678637973:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.65/0.40 % (1630)Instruction limit reached!
% 0.65/0.40 % (1630)------------------------------
% 0.65/0.40 % (1630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.40 % (1630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.40 % (1630)CaDiCaL version: 2.1.3
% 0.65/0.40 % (1630)Termination reason: Instruction limit
% 0.65/0.40 % (1630)Termination phase: shuffling
% 0.65/0.40 % (1630)Time elapsed: 0.003 s
% 0.65/0.40 % (1630)Peak memory usage: 10 MB
% 0.65/0.40 % (1630)Instructions burned: 5 (million)
% 0.65/0.40 % (1628)lrs+10_16_si=on:nwc=1.5:random_seed=4168397309:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.65/0.40 % (1639)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=265253775:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.40 % (1634)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.65/0.40 % (1634)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
% 0.65/0.40 % (1639)Instruction limit reached!
% 0.65/0.40 % (1639)------------------------------
% 0.65/0.40 % (1639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.40 % (1639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.40 % (1639)CaDiCaL version: 2.1.3
% 0.65/0.40 % (1639)Termination reason: Instruction limit
% 0.65/0.40 % (1639)Termination phase: shuffling
% 0.65/0.40 % (1639)Time elapsed: 0.001 s
% 0.65/0.40 % (1639)Peak memory usage: 10 MB
% 0.65/0.40 % (1639)Instructions burned: 3 (million)
% 0.65/0.40 % (1633)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3482094107:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.65/0.40 % (1634)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=347282603:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.65/0.40 % (1640)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1334869063:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.65/0.40 % (1628)Instruction limit reached!
% 0.65/0.40 % (1628)------------------------------
% 0.65/0.40 % (1628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.40 % (1628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.40 % (1628)CaDiCaL version: 2.1.3
% 0.65/0.40 % (1628)Termination reason: Instruction limit
% 0.65/0.40 % (1628)Termination phase: Property scanning
% 0.65/0.40 % (1628)Time elapsed: 0.016 s
% 0.65/0.40 % (1628)Peak memory usage: 10 MB
% 0.65/0.40 % (1628)Instructions burned: 18 (million)
% 0.65/0.40 % (1643)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (1640)Instruction limit reached!
% 0.65/0.44 % (1640)------------------------------
% 0.65/0.44 % (1640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1643)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=664505176:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.65/0.44 % (1640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1640)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1640)Termination reason: Instruction limit
% 0.65/0.44 % (1640)Termination phase: shuffling
% 0.65/0.44 % (1640)Time elapsed: 0.003 s
% 0.65/0.44 % (1640)Peak memory usage: 10 MB
% 0.65/0.44 % (1640)Instructions burned: 6 (million)
% 0.65/0.44 % (1643)Instruction limit reached!
% 0.65/0.44 % (1643)------------------------------
% 0.65/0.44 % (1643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1643)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1643)Termination reason: Instruction limit
% 0.65/0.44 % (1643)Termination phase: shuffling
% 0.65/0.44 % (1643)Time elapsed: 0.003 s
% 0.65/0.44 % (1643)Peak memory usage: 10 MB
% 0.65/0.44 % (1643)Instructions burned: 12 (million)
% 0.65/0.44 % (1649)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
% 0.65/0.44 % (1649)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (1650)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=1164036571:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.65/0.44 % (1647)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=49916648:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.65/0.44 % (1649)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2062868378:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.65/0.44 % (1627)Instruction limit reached!
% 0.65/0.44 % (1627)------------------------------
% 0.65/0.44 % (1627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1627)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1627)Termination reason: Instruction limit
% 0.65/0.44 % (1627)Termination phase: Function definition elimination
% 0.65/0.44 % (1627)Time elapsed: 0.043 s
% 0.65/0.44 % (1627)Peak memory usage: 11 MB
% 0.65/0.44 % (1627)Instructions burned: 89 (million)
% 0.65/0.44 % (1647)Instruction limit reached!
% 0.65/0.44 % (1647)------------------------------
% 0.65/0.44 % (1647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1647)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1647)Termination reason: Instruction limit
% 0.65/0.44 % (1647)Termination phase: shuffling
% 0.65/0.44 % (1647)Time elapsed: 0.006 s
% 0.65/0.44 % (1647)Peak memory usage: 10 MB
% 0.65/0.44 % (1647)Instructions burned: 13 (million)
% 0.65/0.44 % (1649)Instruction limit reached!
% 0.65/0.44 % (1649)------------------------------
% 0.65/0.44 % (1649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1649)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1649)Termination reason: Instruction limit
% 0.65/0.44 % (1649)Termination phase: Property scanning
% 0.65/0.44 % (1649)Time elapsed: 0.012 s
% 0.65/0.44 % (1649)Peak memory usage: 10 MB
% 0.65/0.44 % (1649)Instructions burned: 28 (million)
% 0.65/0.44 % (1650)Instruction limit reached!
% 0.65/0.44 % (1650)------------------------------
% 0.65/0.44 % (1650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1650)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1650)Termination reason: Instruction limit
% 0.65/0.44 % (1650)Termination phase: Function definition elimination
% 0.65/0.44 % (1650)Time elapsed: 0.019 s
% 0.65/0.44 % (1650)Peak memory usage: 10 MB
% 0.65/0.44 % (1650)Instructions burned: 88 (million)
% 0.65/0.44 % (1654)lrs+10_1_si=on:cs=on:random_seed=1927098038:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.65/0.44 % (1655)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.65/0.44 % (1657)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1669462557:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.65/0.44 % (1654)Instruction limit reached!
% 0.65/0.44 % (1654)------------------------------
% 0.65/0.44 % (1654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1654)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1654)Termination reason: Instruction limit
% 0.65/0.44 % (1654)Termination phase: shuffling
% 0.65/0.44 % (1654)Time elapsed: 0.005 s
% 0.65/0.44 % (1654)Peak memory usage: 10 MB
% 0.65/0.44 % (1654)Instructions burned: 9 (million)
% 0.65/0.44 % (1655)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=1106522130:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.44 % (1656)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=470059277:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.65/0.44 % (1655)Instruction limit reached!
% 0.65/0.44 % (1655)------------------------------
% 0.65/0.44 % (1655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1655)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1655)Termination reason: Instruction limit
% 0.65/0.44 % (1655)Termination phase: shuffling
% 0.65/0.44 % (1655)Time elapsed: 0.003 s
% 0.65/0.44 % (1655)Peak memory usage: 10 MB
% 0.65/0.44 % (1655)Instructions burned: 3 (million)
% 0.65/0.44 % (1657)Refutation not found, incomplete strategy
% 0.65/0.44 % (1657)------------------------------
% 0.65/0.44 % (1657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1657)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1657)Termination reason: Refutation not found, incomplete strategy
% 0.65/0.44 % (1657)Time elapsed: 0.009 s
% 0.65/0.44 % (1657)Peak memory usage: 12 MB
% 0.65/0.44 % (1657)Instructions burned: 34 (million)
% 0.65/0.44 % (1657)------------------------------
% 0.65/0.44 % (1657)------------------------------
% 0.65/0.44 % (1633)Instruction limit reached!
% 0.65/0.44 % (1633)------------------------------
% 0.65/0.44 % (1633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1633)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1633)Termination reason: Instruction limit
% 0.65/0.44 % (1633)Termination phase: Function definition elimination
% 0.65/0.44 % (1633)Time elapsed: 0.062 s
% 0.65/0.44 % (1633)Peak memory usage: 11 MB
% 0.65/0.44 % (1633)Instructions burned: 76 (million)
% 0.65/0.44 % (1634)Instruction limit reached!
% 0.65/0.44 % (1634)------------------------------
% 0.65/0.44 % (1634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1634)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1634)Termination reason: Instruction limit
% 0.65/0.44 % (1634)Termination phase: Property scanning
% 0.65/0.44 % (1634)Time elapsed: 0.066 s
% 0.65/0.44 % (1634)Peak memory usage: 12 MB
% 0.65/0.44 % (1634)Instructions burned: 157 (million)
% 0.65/0.44 % (1660)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3698926909:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.65/0.44 % (1656)Instruction limit reached!
% 0.65/0.44 % (1656)------------------------------
% 0.65/0.44 % (1656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1656)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1656)Termination reason: Instruction limit
% 0.65/0.44 % (1656)Termination phase: Saturation
% 0.65/0.44 % (1656)Time elapsed: 0.019 s
% 0.65/0.44 % (1656)Peak memory usage: 12 MB
% 0.65/0.44 % (1656)Instructions burned: 38 (million)
% 0.65/0.44 % (1664)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2032890044:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.65/0.44 % (1663)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1687058407:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.44 % (1665)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3332097260:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.44 % (1660)Instruction limit reached!
% 0.65/0.44 % (1660)------------------------------
% 0.65/0.44 % (1660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1660)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1660)Termination reason: Instruction limit
% 0.65/0.44 % (1660)Termination phase: SInE selection
% 0.65/0.44 % (1660)Time elapsed: 0.012 s
% 0.65/0.44 % (1660)Peak memory usage: 10 MB
% 0.65/0.44 % (1660)Instructions burned: 26 (million)
% 0.65/0.44 % (1665)Instruction limit reached!
% 0.65/0.44 % (1665)------------------------------
% 0.65/0.44 % (1665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1665)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1665)Termination reason: Instruction limit
% 0.65/0.44 % (1665)Termination phase: shuffling
% 0.65/0.44 % (1665)Time elapsed: 0.007 s
% 0.65/0.44 % (1665)Peak memory usage: 10 MB
% 0.65/0.44 % (1665)Instructions burned: 15 (million)
% 0.65/0.44 % (1663)Instruction limit reached!
% 0.65/0.44 % (1663)------------------------------
% 0.65/0.44 % (1663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1663)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1663)Termination reason: Instruction limit
% 0.65/0.44 % (1663)Termination phase: shuffling
% 0.65/0.44 % (1663)Time elapsed: 0.008 s
% 0.65/0.44 % (1663)Peak memory usage: 10 MB
% 0.65/0.44 % (1663)Instructions burned: 14 (million)
% 0.65/0.44 % (1666)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1668445148: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)
% 0.65/0.44 % (1668)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3535673761:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.65/0.44 % (1666)Instruction limit reached!
% 0.65/0.44 % (1666)------------------------------
% 0.65/0.44 % (1666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1666)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1666)Termination reason: Instruction limit
% 0.65/0.44 % (1666)Termination phase: shuffling
% 0.65/0.44 % (1666)Time elapsed: 0.003 s
% 0.65/0.44 % (1666)Peak memory usage: 10 MB
% 0.65/0.44 % (1666)Instructions burned: 3 (million)
% 0.65/0.44 % (1664) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1620-1664"...
% 0.65/0.44 % (1672)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1564369539:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.65/0.44 % (1664)...printing done.
% 0.65/0.44 % (1664)Refutation found. Thanks to Tanya!
% 0.65/0.44 % SZS status Theorem for theBenchmark
% 0.65/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.65/0.44 % (1664)------------------------------
% 0.65/0.44 % (1664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (1664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (1664)CaDiCaL version: 2.1.3
% 0.65/0.44 % (1664)Termination reason: Refutation
% 0.65/0.44 % (1664)Time elapsed: 0.027 s
% 0.65/0.44 % (1664)Peak memory usage: 13 MB
% 0.65/0.44 % (1664)Instructions burned: 108 (million)
% 0.65/0.44 % (1620)Success in time 0.168 s
% 0.65/0.44 % Vampire exiting
%------------------------------------------------------------------------------