%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM642^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 1.79s 0.61s
% Output : Refutation 1.79s
% 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 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 163 ( 159 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_124,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_127,type,
db2:
!>[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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vOR: $o > $o > $o ).
thf(func_def_134,type,
vAND: $o > $o > $o ).
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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_140,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_141,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_142,type,
sK2: $i > $i > $i > $i ).
thf(func_def_143,type,
sK3: $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_144,type,
sK4: $i > $i ).
thf(func_def_145,type,
sK5: $i > $i > $i ).
thf(func_def_146,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_147,type,
sK7: $i > $i > $o ).
thf(func_def_148,type,
sK8: $i > $i > $o ).
thf(func_def_149,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK10: $i > $i > $o ).
thf(func_def_151,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK13: $i > $i > $o ).
thf(func_def_154,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_155,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK17: $i > $i > $i > $i ).
thf(func_def_158,type,
sK18: $i > $i > $i ).
thf(func_def_159,type,
sK19: $i > $i > $o ).
thf(func_def_162,type,
sK22: $i > $i > $o ).
thf(func_def_163,type,
sK23: $i > $i > $o ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) )
= is_of ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f91,axiom,
( e_is
= ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(f157,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(f189,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ ( ordsucc @ X0 ) @ X1 ) @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4d) ).
thf(f193,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 @ ( ordsucc @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4h) ).
thf(f194,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 @ ( ordsucc @ X0 ) @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f193]) ).
thf(f200,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] : ( n_is @ ( n_pl @ ( ordsucc @ X1 ) @ X3 ) @ ( ordsucc @ ( n_pl @ X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f189]) ).
thf(f201,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ ( ordsucc @ Y0 ) @ Y1 ) @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f200]) ).
thf(f231,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f241,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f299,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f300,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f475,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 @ ( ordsucc @ X1 ) @ X3 ) ) ) ),
inference(rectify,[],[f194]) ).
thf(f476,plain,
( $true
!= ( 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 @ ( ordsucc @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f475]) ).
thf(f498,plain,
( $true
!= ( 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 @ ( ordsucc @ Y0 ) @ Y1 ) ) ) ) ),
inference(flattening,[],[f476]) ).
thf(f564,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f300]) ).
thf(f582,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f589,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f597,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ ( ordsucc @ Y0 ) @ Y1 ) @ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f201]) ).
thf(f603,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f241]) ).
thf(f649,plain,
( $true
!= ( 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 @ ( ordsucc @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f498]) ).
thf(f669,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,[],[f564,f589]) ).
thf(f674,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f582,f603]) ).
thf(f703,plain,
( $true
= ( ^ [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 @ ( ordsucc @ Y0 ) @ Y1 )
@ ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f597,f669,f669,f674]) ).
thf(f730,plain,
( $true
!= ( ^ [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 @ ( ordsucc @ Y0 ) @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f649,f669,f669,f674]) ).
thf(f1035,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ordsucc @ ( n_pl @ Y0 @ Y1 ) )
= ( n_pl @ ( ordsucc @ Y0 ) @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f730]) ).
thf(f1036,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ordsucc @ ( n_pl @ Y0 @ Y1 ) )
= ( n_pl @ ( ordsucc @ Y0 ) @ Y1 ) ) ) ) )
@ sK20 ) ),
inference(sigma_proxy_clausification,[],[f1035]) ).
thf(f1037,plain,
( ( ( in @ sK20 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK20 @ Y0 ) )
= ( n_pl @ ( ordsucc @ sK20 ) @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1036]) ).
thf(f1038,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK20 @ Y0 ) )
= ( n_pl @ ( ordsucc @ sK20 ) @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1037]) ).
thf(f1039,plain,
( $true
= ( in @ sK20 @ nat ) ),
inference(imp_proxy_clausification,[],[f1037]) ).
thf(f1040,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK20 @ Y0 ) )
= ( n_pl @ ( ordsucc @ sK20 ) @ Y0 ) ) )
@ sK21 )
= $false ),
inference(sigma_proxy_clausification,[],[f1038]) ).
thf(f1041,plain,
( ( ( in @ sK21 @ nat )
=> ( ( ordsucc @ ( n_pl @ sK20 @ sK21 ) )
= ( n_pl @ ( ordsucc @ sK20 ) @ sK21 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1040]) ).
thf(f1042,plain,
( ( ( ordsucc @ ( n_pl @ sK20 @ sK21 ) )
= ( n_pl @ ( ordsucc @ sK20 ) @ sK21 ) )
= $false ),
inference(imp_proxy_clausification,[],[f1041]) ).
thf(f1043,plain,
( $true
= ( in @ sK21 @ nat ) ),
inference(imp_proxy_clausification,[],[f1041]) ).
thf(f1044,plain,
( ( ordsucc @ ( n_pl @ sK20 @ sK21 ) )
!= ( n_pl @ ( ordsucc @ sK20 ) @ sK21 ) ),
inference(equality_proxy_clausification,[],[f1042]) ).
thf(f1083,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ ( ordsucc @ Y0 ) @ Y1 )
= ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f703]) ).
thf(f1084,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ ( ordsucc @ Y0 ) @ Y1 )
= ( ordsucc @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1083]) ).
thf(f1085,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ ( ordsucc @ X1 ) @ Y0 )
= ( ordsucc @ ( n_pl @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1084]) ).
thf(f1086,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ ( ordsucc @ X1 ) @ Y0 )
= ( ordsucc @ ( n_pl @ X1 @ Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1085]) ).
thf(f1087,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ ( ordsucc @ X1 ) @ Y0 )
= ( ordsucc @ ( n_pl @ X1 @ Y0 ) ) ) )
@ X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1086]) ).
thf(f1088,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ nat )
=> ( ( n_pl @ ( ordsucc @ X1 ) @ X2 )
= ( ordsucc @ ( n_pl @ X1 @ X2 ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1087]) ).
thf(f1089,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( n_pl @ ( ordsucc @ X1 ) @ X2 )
= ( ordsucc @ ( n_pl @ X1 @ X2 ) ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1088]) ).
thf(f1090,plain,
! [X2: $i,X1: $i] :
( ( ( ordsucc @ ( n_pl @ X1 @ X2 ) )
= ( n_pl @ ( ordsucc @ X1 ) @ X2 ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(equality_proxy_clausification,[],[f1089]) ).
thf(f1173,plain,
( ( ( in @ sK21 @ nat )
= $false )
| ( ( in @ sK20 @ nat )
= $false )
| ( ( ordsucc @ ( n_pl @ sK20 @ sK21 ) )
!= ( ordsucc @ ( n_pl @ sK20 @ sK21 ) ) ) ),
inference(superposition,[],[f1044,f1090]) ).
thf(f1174,plain,
( ( ( in @ sK21 @ nat )
= $false )
| ( ( in @ sK20 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1173]) ).
thf(f1179,plain,
( ( $true = $false )
| ( ( in @ sK20 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1174,f1043]) ).
thf(f1180,plain,
( ( in @ sK20 @ nat )
= $false ),
inference(trivial_inequality_removal,[],[f1179]) ).
thf(f1183,plain,
$true = $false,
inference(superposition,[],[f1039,f1180]) ).
thf(f1185,plain,
$false,
inference(trivial_inequality_removal,[],[f1183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM642^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.20 % Computer : n019.cluster.edu
% 0.13/0.20 % Model : x86_64 x86_64
% 0.13/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.20 % Memory : 8046.5625MB
% 0.13/0.20 % OS : Linux 6.8.0-71-generic
% 0.13/0.20 % CPULimit : 300
% 0.13/0.20 % WCLimit : 300
% 0.13/0.20 % DateTime : Tue Sep 29 12:24:48 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.24 Running higher-order theorem proving
% 0.26/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/0.50 % (683899)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.05/0.50 % (683904)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1250218756:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.05/0.50 % (683905)lrs+10_16_si=on:nwc=1.5:random_seed=931777441:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.05/0.50 % (683909)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3518907092:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.05/0.50 % (683910)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.05/0.50 % (683910)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
% 1.05/0.50 % (683906)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=925956912:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.05/0.50 % (683907)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=2080866394: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)
% 1.05/0.50 % (683906)Instruction limit reached!
% 1.05/0.50 % (683906)------------------------------
% 1.05/0.50 % (683906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (683906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (683906)CaDiCaL version: 2.1.3
% 1.05/0.50 % (683906)Termination reason: Instruction limit
% 1.05/0.50 % (683906)Termination phase: shuffling
% 1.05/0.50 % (683906)Time elapsed: 0.004 s
% 1.05/0.50 % (683906)Peak memory usage: 10 MB
% 1.05/0.50 % (683906)Instructions burned: 3 (million)
% 1.05/0.50 % (683908)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3991408098:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.05/0.50 % (683905)Instruction limit reached!
% 1.05/0.50 % (683905)------------------------------
% 1.05/0.50 % (683905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (683905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (683905)CaDiCaL version: 2.1.3
% 1.05/0.50 % (683905)Termination reason: Instruction limit
% 1.05/0.50 % (683905)Termination phase: Property scanning
% 1.05/0.50 % (683910)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=1696098240:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.05/0.50 % (683905)Time elapsed: 0.015 s
% 1.05/0.50 % (683905)Peak memory usage: 10 MB
% 1.05/0.50 % (683905)Instructions burned: 18 (million)
% 1.05/0.50 % (683904)Instruction limit reached!
% 1.05/0.50 % (683904)------------------------------
% 1.05/0.50 % (683904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (683904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (683904)CaDiCaL version: 2.1.3
% 1.05/0.50 % (683904)Termination reason: Instruction limit
% 1.05/0.50 % (683904)Termination phase: Function definition elimination
% 1.05/0.50 % (683904)Time elapsed: 0.033 s
% 1.05/0.50 % (683904)Peak memory usage: 10 MB
% 1.05/0.50 % (683904)Instructions burned: 88 (million)
% 1.05/0.50 % (683908)Instruction limit reached!
% 1.05/0.50 % (683908)------------------------------
% 1.05/0.50 % (683908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (683908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (683908)CaDiCaL version: 2.1.3
% 1.05/0.50 % (683908)Termination reason: Instruction limit
% 1.05/0.50 % (683908)Termination phase: Preprocessing 3
% 1.05/0.50 % (683908)Time elapsed: 0.023 s
% 1.05/0.50 % (683908)Peak memory usage: 10 MB
% 1.05/0.50 % (683908)Instructions burned: 27 (million)
% 1.05/0.50 % (683918)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1009466916:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.05/0.50 % (683919)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3933401233:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.05/0.55 % (683918)Instruction limit reached!
% 1.05/0.55 % (683918)------------------------------
% 1.05/0.55 % (683918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.55 % (683918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.55 % (683918)CaDiCaL version: 2.1.3
% 1.05/0.55 % (683918)Termination reason: Instruction limit
% 1.05/0.55 % (683918)Termination phase: shuffling
% 1.05/0.55 % (683918)Time elapsed: 0.003 s
% 1.05/0.55 % (683918)Peak memory usage: 10 MB
% 1.05/0.55 % (683918)Instructions burned: 3 (million)
% 1.05/0.55 % (683919)Instruction limit reached!
% 1.05/0.55 % (683919)------------------------------
% 1.05/0.55 % (683919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.55 % (683919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.55 % (683919)CaDiCaL version: 2.1.3
% 1.05/0.55 % (683919)Termination reason: Instruction limit
% 1.05/0.55 % (683919)Termination phase: shuffling
% 1.05/0.55 % (683919)Time elapsed: 0.005 s
% 1.05/0.55 % (683919)Peak memory usage: 10 MB
% 1.05/0.55 % (683919)Instructions burned: 6 (million)
% 1.05/0.55 % (683909)Instruction limit reached!
% 1.05/0.55 % (683909)------------------------------
% 1.05/0.55 % (683909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.55 % (683909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.55 % (683909)CaDiCaL version: 2.1.3
% 1.05/0.55 % (683909)Termination reason: Instruction limit
% 1.05/0.55 % (683909)Termination phase: Function definition elimination
% 1.05/0.55 % (683909)Time elapsed: 0.055 s
% 1.05/0.55 % (683909)Peak memory usage: 11 MB
% 1.05/0.55 % (683909)Instructions burned: 76 (million)
% 1.05/0.55 % (683920)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.55 % (683920)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2227266597:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.05/0.55 % (683920)Instruction limit reached!
% 1.05/0.55 % (683920)------------------------------
% 1.05/0.55 % (683920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.55 % (683920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.55 % (683920)CaDiCaL version: 2.1.3
% 1.05/0.55 % (683920)Termination reason: Instruction limit
% 1.05/0.55 % (683920)Termination phase: shuffling
% 1.05/0.55 % (683920)Time elapsed: 0.006 s
% 1.05/0.55 % (683920)Peak memory usage: 9 MB
% 1.05/0.55 % (683920)Instructions burned: 7 (million)
% 1.05/0.55 % (683921)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1262253245:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.05/0.55 % (683924)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
% 1.05/0.55 % (683924)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.55 % (683924)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3241052593:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.05/0.55 % (683925)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=3021337222:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.05/0.55 % (683921)Instruction limit reached!
% 1.05/0.55 % (683921)------------------------------
% 1.05/0.55 % (683921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.55 % (683921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.55 % (683921)CaDiCaL version: 2.1.3
% 1.05/0.55 % (683921)Termination reason: Instruction limit
% 1.05/0.55 % (683921)Termination phase: Property scanning
% 1.05/0.55 % (683921)Time elapsed: 0.014 s
% 1.05/0.55 % (683921)Peak memory usage: 10 MB
% 1.05/0.55 % (683921)Instructions burned: 16 (million)
% 1.05/0.55 % (683924)Instruction limit reached!
% 1.05/0.55 % (683924)------------------------------
% 1.05/0.55 % (683924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.55 % (683924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (683924)CaDiCaL version: 2.1.3
% 1.79/0.59 % (683924)Termination reason: Instruction limit
% 1.79/0.59 % (683924)Termination phase: Property scanning
% 1.79/0.59 % (683924)Time elapsed: 0.013 s
% 1.79/0.59 % (683924)Peak memory usage: 11 MB
% 1.79/0.59 % (683924)Instructions burned: 31 (million)
% 1.79/0.59 % (683926)lrs+10_1_si=on:cs=on:random_seed=464115523:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.79/0.59 % (683929)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.79/0.59 % (683926)Instruction limit reached!
% 1.79/0.59 % (683926)------------------------------
% 1.79/0.59 % (683926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (683926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (683926)CaDiCaL version: 2.1.3
% 1.79/0.59 % (683926)Termination reason: Instruction limit
% 1.79/0.59 % (683926)Termination phase: shuffling
% 1.79/0.59 % (683926)Time elapsed: 0.008 s
% 1.79/0.59 % (683926)Peak memory usage: 10 MB
% 1.79/0.59 % (683926)Instructions burned: 8 (million)
% 1.79/0.59 % (683933)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3112170782:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.79/0.59 % (683929)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=3493366859:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.79/0.59 % (683929)Instruction limit reached!
% 1.79/0.59 % (683929)------------------------------
% 1.79/0.59 % (683929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (683929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (683929)CaDiCaL version: 2.1.3
% 1.79/0.59 % (683929)Termination reason: Instruction limit
% 1.79/0.59 % (683929)Termination phase: shuffling
% 1.79/0.59 % (683929)Time elapsed: 0.003 s
% 1.79/0.59 % (683929)Peak memory usage: 10 MB
% 1.79/0.59 % (683929)Instructions burned: 3 (million)
% 1.79/0.59 % (683910)Instruction limit reached!
% 1.79/0.59 % (683910)------------------------------
% 1.79/0.59 % (683910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (683910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (683910)CaDiCaL version: 2.1.3
% 1.79/0.59 % (683910)Termination reason: Instruction limit
% 1.79/0.59 % (683910)Termination phase: Property scanning
% 1.79/0.59 % (683910)Time elapsed: 0.107 s
% 1.79/0.59 % (683910)Peak memory usage: 11 MB
% 1.79/0.59 % (683910)Instructions burned: 158 (million)
% 1.79/0.59 % (683934)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3514822505:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.79/0.59 % (683933)Instruction limit reached!
% 1.79/0.59 % (683933)------------------------------
% 1.79/0.59 % (683933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (683933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (683933)CaDiCaL version: 2.1.3
% 1.79/0.59 % (683933)Termination reason: Instruction limit
% 1.79/0.59 % (683933)Termination phase: Saturation
% 1.79/0.59 % (683933)Time elapsed: 0.018 s
% 1.79/0.59 % (683933)Peak memory usage: 12 MB
% 1.79/0.59 % (683933)Instructions burned: 39 (million)
% 1.79/0.59 % (683936)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=251220985:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.79/0.59 % (683925)Instruction limit reached!
% 1.79/0.59 % (683925)------------------------------
% 1.79/0.59 % (683925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (683925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (683925)CaDiCaL version: 2.1.3
% 1.79/0.59 % (683925)Termination reason: Instruction limit
% 1.79/0.59 % (683925)Termination phase: Function definition elimination
% 1.79/0.59 % (683925)Time elapsed: 0.061 s
% 1.79/0.59 % (683925)Peak memory usage: 10 MB
% 1.79/0.59 % (683925)Instructions burned: 86 (million)
% 1.79/0.59 % (683939)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2584769614:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.79/0.61 % (683942)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=627100282:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.79/0.61 % (683934)Refutation not found, incomplete strategy
% 1.79/0.61 % (683934)------------------------------
% 1.79/0.61 % (683934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683942)Instruction limit reached!
% 1.79/0.61 % (683942)------------------------------
% 1.79/0.61 % (683942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683934)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683934)Termination reason: Refutation not found, incomplete strategy
% 1.79/0.61 % (683934)Time elapsed: 0.030 s
% 1.79/0.61 % (683942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683934)Peak memory usage: 13 MB
% 1.79/0.61 % (683934)Instructions burned: 36 (million)
% 1.79/0.61 % (683942)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683942)Termination reason: Instruction limit
% 1.79/0.61 % (683942)Termination phase: shuffling
% 1.79/0.61 % (683942)Time elapsed: 0.007 s
% 1.79/0.61 % (683942)Peak memory usage: 10 MB
% 1.79/0.61 % (683942)Instructions burned: 15 (million)
% 1.79/0.61 % (683941)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3411304004:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.79/0.61 % (683934)------------------------------
% 1.79/0.61 % (683934)------------------------------
% 1.79/0.61 % (683939)Instruction limit reached!
% 1.79/0.61 % (683939)------------------------------
% 1.79/0.61 % (683939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683939)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683939)Termination reason: Instruction limit
% 1.79/0.61 % (683939)Termination phase: shuffling
% 1.79/0.61 % (683939)Time elapsed: 0.012 s
% 1.79/0.61 % (683939)Peak memory usage: 10 MB
% 1.79/0.61 % (683939)Instructions burned: 14 (million)
% 1.79/0.61 % (683936)Instruction limit reached!
% 1.79/0.61 % (683936)------------------------------
% 1.79/0.61 % (683936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683936)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683936)Termination reason: Instruction limit
% 1.79/0.61 % (683936)Termination phase: Property scanning
% 1.79/0.61 % (683936)Time elapsed: 0.025 s
% 1.79/0.61 % (683936)Peak memory usage: 10 MB
% 1.79/0.61 % (683936)Instructions burned: 25 (million)
% 1.79/0.61 % (683944)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=434647831: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)
% 1.79/0.61 % (683944)Instruction limit reached!
% 1.79/0.61 % (683944)------------------------------
% 1.79/0.61 % (683944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683944)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683944)Termination reason: Instruction limit
% 1.79/0.61 % (683944)Termination phase: shuffling
% 1.79/0.61 % (683944)Time elapsed: 0.002 s
% 1.79/0.61 % (683944)Peak memory usage: 10 MB
% 1.79/0.61 % (683944)Instructions burned: 4 (million)
% 1.79/0.61 % (683948)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3342902329:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 1.79/0.61 % (683949)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2204032626:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.79/0.61 % (683950)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3003915844:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 1.79/0.61 % (683952)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.79/0.61 % (683952)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.79/0.61 % (683948)Instruction limit reached!
% 1.79/0.61 % (683948)------------------------------
% 1.79/0.61 % (683948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683948)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683948)Termination reason: Instruction limit
% 1.79/0.61 % (683948)Termination phase: Property scanning
% 1.79/0.61 % (683948)Time elapsed: 0.012 s
% 1.79/0.61 % (683948)Peak memory usage: 10 MB
% 1.79/0.61 % (683948)Instructions burned: 26 (million)
% 1.79/0.61 % (683953)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.79/0.61 % (683949)Instruction limit reached!
% 1.79/0.61 % (683949)------------------------------
% 1.79/0.61 % (683949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683949)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683949)Termination reason: Instruction limit
% 1.79/0.61 % (683949)Termination phase: Property scanning
% 1.79/0.61 % (683949)Time elapsed: 0.012 s
% 1.79/0.61 % (683949)Peak memory usage: 10 MB
% 1.79/0.61 % (683949)Instructions burned: 24 (million)
% 1.79/0.61 % (683952)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1791096883:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 1.79/0.61 % (683953)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=295054837:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.79/0.61 % (683953)Instruction limit reached!
% 1.79/0.61 % (683953)------------------------------
% 1.79/0.61 % (683953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683953)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683953)Termination reason: Instruction limit
% 1.79/0.61 % (683953)Termination phase: shuffling
% 1.79/0.61 % (683953)Time elapsed: 0.007 s
% 1.79/0.61 % (683953)Peak memory usage: 10 MB
% 1.79/0.61 % (683953)Instructions burned: 8 (million)
% 1.79/0.61 % (683952)Instruction limit reached!
% 1.79/0.61 % (683952)------------------------------
% 1.79/0.61 % (683952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683952)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683952)Termination reason: Instruction limit
% 1.79/0.61 % (683952)Termination phase: shuffling
% 1.79/0.61 % (683952)Time elapsed: 0.012 s
% 1.79/0.61 % (683952)Peak memory usage: 10 MB
% 1.79/0.61 % (683952)Instructions burned: 14 (million)
% 1.79/0.61 % (683958)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4030209337:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.79/0.61 % (683958)Instruction limit reached!
% 1.79/0.61 % (683958)------------------------------
% 1.79/0.61 % (683958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683958)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683958)Termination reason: Instruction limit
% 1.79/0.61 % (683958)Termination phase: shuffling
% 1.79/0.61 % (683958)Time elapsed: 0.003 s
% 1.79/0.61 % (683958)Peak memory usage: 10 MB
% 1.79/0.61 % (683958)Instructions burned: 7 (million)
% 1.79/0.61 % (683957)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2937281679:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.79/0.61 % (683962)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3995255708:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.79/0.61 % (683964)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=427423296:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.79/0.61 % (683950)Instruction limit reached!
% 1.79/0.61 % (683950)------------------------------
% 1.79/0.61 % (683950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683950)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683950)Termination reason: Instruction limit
% 1.79/0.61 % (683950)Termination phase: Saturation
% 1.79/0.61 % (683950)Time elapsed: 0.050 s
% 1.79/0.61 % (683950)Peak memory usage: 12 MB
% 1.79/0.61 % (683950)Instructions burned: 60 (million)
% 1.79/0.61 % (683961)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4095942555:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.79/0.61 % (683962)Instruction limit reached!
% 1.79/0.61 % (683962)------------------------------
% 1.79/0.61 % (683962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683962)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683962)Termination reason: Instruction limit
% 1.79/0.61 % (683962)Termination phase: SInE selection
% 1.79/0.61 % (683962)Time elapsed: 0.013 s
% 1.79/0.61 % (683962)Peak memory usage: 10 MB
% 1.79/0.61 % (683962)Instructions burned: 28 (million)
% 1.79/0.61 % (683941) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-683899-683941"...
% 1.79/0.61 % (683941)...printing done.
% 1.79/0.61 % (683941)Refutation found. Thanks to Tanya!
% 1.79/0.61 % SZS status Theorem for theBenchmark
% 1.79/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.79/0.61 % (683941)------------------------------
% 1.79/0.61 % (683941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.61 % (683941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.61 % (683941)CaDiCaL version: 2.1.3
% 1.79/0.61 % (683941)Termination reason: Refutation
% 1.79/0.61 % (683941)Time elapsed: 0.089 s
% 1.79/0.61 % (683941)Peak memory usage: 13 MB
% 1.79/0.61 % (683941)Instructions burned: 110 (million)
% 1.79/0.61 % (683899)Success in time 0.304 s
% 1.79/0.61 % Vampire exiting
%------------------------------------------------------------------------------