%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM666^4 : 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 : n012.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 08:18:28 AM UTC 2026
% Result : Theorem 3.38s 0.76s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of formulae : 148 ( 89 unt; 0 typ; 2 def)
% Number of atoms : 1725 ( 425 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 1966 ( 29 ~; 117 |; 0 &;1541 @)
% ( 2 <=>; 229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 191 ( 187 usr; 10 con; 0-7 aty)
% ( 48 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 645 ( 22 sgn 69 !; 0 ?; 645 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_134,type,
vIMP: $o > $o > $o ).
thf(func_def_135,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_140,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_141,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_144,type,
vAND: $o > $o > $o ).
thf(func_def_145,type,
vOR: $o > $o > $o ).
thf(func_def_146,type,
vNOT: $o > $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,
sP0: ( $i > $o ) > $o ).
thf(func_def_151,type,
sP1: $i > ( $i > $i ) > $i > $o ).
thf(func_def_152,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_154,type,
sK4: $i > $i ).
thf(func_def_155,type,
sK5: $i > $i > $i > $i ).
thf(func_def_156,type,
sK6: $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_157,type,
sK7: ( $i > $i ) > $i > ( $i > $i ) > $i ).
thf(func_def_158,type,
sK8: $i > $i > $o ).
thf(func_def_159,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK10: $i > $i > $i > $i ).
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 > $i > $o ).
thf(func_def_164,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_168,type,
sK18: $i > $i > $o ).
thf(func_def_169,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_172,type,
sK22: $i > $i > $o ).
thf(func_def_173,type,
sK23: $i > $i > $o ).
thf(func_def_175,type,
sK25: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_176,type,
sK26: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_177,type,
sK27: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_178,type,
sK28: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_179,type,
sK29: ( $i > $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_180,type,
sK30: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_181,type,
sK31: $i > $i ).
thf(func_def_182,type,
sK32: $i > $i ).
thf(func_def_183,type,
sK33: $i > $i ).
thf(func_def_184,type,
sK34: $i > $i ).
thf(func_def_185,type,
sK35: $i > $i ).
thf(func_def_186,type,
sK36: $i > $i ).
thf(func_def_187,type,
sK37: $i > $i ).
thf(func_def_188,type,
sK38: $i > $i ).
thf(func_def_189,type,
sK39: $i > $i > $i ).
thf(func_def_190,type,
sK40: $i > $i ).
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,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f74,axiom,
( ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) )
= imp ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(f75,axiom,
( ( ^ [X0: $o] : ( imp @ X0 @ $false ) )
= d_not ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(f81,axiom,
( ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) )
= l_or ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
thf(f91,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) )
= e_is ),
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(f160,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',def_diffprop) ).
thf(f205,axiom,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(f206,axiom,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) )
= iii ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',def_lessis) ).
thf(f228,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( iii @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(f229,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( lessis @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(f232,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( ( moreis @ X1 @ X2 )
=> ( d_29_ii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16d) ).
thf(f233,negated_conjecture,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( ( moreis @ X1 @ X2 )
=> ( d_29_ii @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f232]) ).
thf(f247,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f269,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f217]) ).
thf(f282,plain,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X5: $i] :
( ( d_29_ii @ X1 @ X3 )
=> ( ( moreis @ X3 @ X5 )
=> ( d_29_ii @ X1 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f233]) ).
thf(f283,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( ( moreis @ Y1 @ Y2 )
=> ( d_29_ii @ Y0 @ Y2 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f282]) ).
thf(f284,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f338,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f341,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X5: $i] :
( ( lessis @ X1 @ X3 )
=> ( ( iii @ X3 @ X5 )
=> ( iii @ X1 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f229]) ).
thf(f342,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( lessis @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f341]) ).
thf(f365,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( d_29_ii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f216]) ).
thf(f389,plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f390,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f389]) ).
thf(f408,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f437,plain,
( ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) )
= imp ),
inference(rectify,[],[f74]) ).
thf(f438,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(fool_elimination,[],[f437]) ).
thf(f445,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f458,plain,
( ( ^ [X0: $o] : ( imp @ X0 @ $false ) )
= d_not ),
inference(rectify,[],[f75]) ).
thf(f459,plain,
( d_not
= ( ^ [Y0: $o] : ( imp @ Y0 @ $false ) ) ),
inference(fool_elimination,[],[f458]) ).
thf(f475,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X5: $i] :
( ( iii @ X1 @ X3 )
=> ( ( iii @ X3 @ X5 )
=> ( iii @ X1 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f228]) ).
thf(f476,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f475]) ).
thf(f594,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f605,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( ( moreis @ Y1 @ Y2 )
=> ( d_29_ii @ Y0 @ Y2 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f283]) ).
thf(f677,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( d_29_ii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f365]) ).
thf(f678,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f594]) ).
thf(f697,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f338]) ).
thf(f712,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f269]) ).
thf(f720,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f408]) ).
thf(f732,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f736,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f739,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(cnf_transformation,[],[f438]) ).
thf(f748,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f284]) ).
thf(f749,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( ( moreis @ Y1 @ Y2 )
=> ( d_29_ii @ Y0 @ Y2 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f605]) ).
thf(f754,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f445]) ).
thf(f779,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f476]) ).
thf(f788,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f390]) ).
thf(f790,plain,
( d_not
= ( ^ [Y0: $o] : ( imp @ Y0 @ $false ) ) ),
inference(cnf_transformation,[],[f459]) ).
thf(f798,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f813,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( lessis @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f342]) ).
thf(f817,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f736,f697]) ).
thf(f818,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,[],[f720,f817]) ).
thf(f819,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,[],[f798,f732,f818]) ).
thf(f820,plain,
( d_not
= ( ^ [Y0: $o] :
( ^ [Y1: $o,Y2: $o] :
( Y1
=> Y2 )
@ Y0
@ $false ) ) ),
inference(definition_unfolding,[],[f790,f739]) ).
thf(f821,plain,
( l_or
= ( ^ [Y0: $o] :
( ^ [Y1: $o,Y2: $o] :
( Y1
=> Y2 )
@ ( ^ [Y1: $o] :
( ^ [Y2: $o,Y3: $o] :
( Y2
=> Y3 )
@ Y1
@ $false )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f678,f739,f820]) ).
thf(f823,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,[],[f754,f732,f818]) ).
thf(f825,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ ( ^ [Y3: $o] :
( ^ [Y4: $o,Y5: $o] :
( Y4
=> Y5 )
@ Y3
@ $false )
@ 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,[],[f677,f821,f823,f817]) ).
thf(f826,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ ( ^ [Y3: $o] :
( ^ [Y4: $o,Y5: $o] :
( Y4
=> Y5 )
@ Y3
@ $false )
@ 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,[],[f712,f821,f819,f817]) ).
thf(f838,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,[],[f788,f748]) ).
thf(f892,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 > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y3
@ Y4 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y3: $i,Y4: $i] :
( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ ( ^ [Y6: $o] :
( ^ [Y7: $o,Y8: $o] :
( Y7
=> Y8 )
@ Y6
@ $false )
@ Y5 ) )
@ ( ^ [Y5: $i,Y6: $i] :
( l_some @ nat
@ ( ^ [Y7: $i,Y8: $i,Y9: $i] :
( ^ [Y10: $i,Y11: $i,Y12: $i] : ( Y11 = Y12 )
@ nat
@ Y7
@ ( n_pl @ Y8 @ Y9 ) )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 )
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y3
@ Y4 ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y3
@ Y4 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f749,f838,f838,f838,f823,f825,f823]) ).
thf(f908,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 > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f779,f838,f838,f838,f819,f819,f819]) ).
thf(f927,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 > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i] :
( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ ( ^ [Y6: $o] :
( ^ [Y7: $o,Y8: $o] :
( Y7
=> Y8 )
@ Y6
@ $false )
@ Y5 ) )
@ ( ^ [Y5: $i,Y6: $i] :
( l_some @ nat
@ ( ^ [Y7: $i,Y8: $i,Y9: $i] :
( ^ [Y10: $i,Y11: $i,Y12: $i] : ( Y11 = Y12 )
@ nat
@ Y7
@ ( n_pl @ Y8 @ Y9 ) )
@ Y6
@ Y5 ) )
@ Y3
@ Y4 )
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y3
@ Y4 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f813,f838,f838,f838,f826,f819,f819]) ).
thf(f950,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f908]) ).
thf(f951,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f950]) ).
thf(f952,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f951]) ).
thf(f953,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f952]) ).
thf(f954,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f953]) ).
thf(f955,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f954]) ).
thf(f956,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f955]) ).
thf(f957,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) )
@ X3 ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f956]) ).
thf(f958,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X3 @ nat )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) )
= $true )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f957]) ).
thf(f959,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ nat ) )
| ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) )
= $true )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f958]) ).
thf(f960,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ nat ) )
| ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f959]) ).
thf(f961,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f960]) ).
thf(f1158,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f927]) ).
thf(f1159,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1158]) ).
thf(f1160,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1159]) ).
thf(f1161,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1160]) ).
thf(f1162,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1161]) ).
thf(f1163,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1162]) ).
thf(f1164,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1163]) ).
thf(f1165,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) )
@ X3 )
= $true )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1164]) ).
thf(f1166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X3 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1165]) ).
thf(f1167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1166]) ).
thf(f1168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1167]) ).
thf(f1169,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1168]) ).
thf(f1170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( X1 = X2 )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
= $false )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $false
= ( in @ X3 @ nat ) ) ),
inference(imp_proxy_clausification,[],[f1169]) ).
thf(f1174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
= $false )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1170]) ).
thf(f1348,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y2 @ Y3 ) ) )
=> $false )
=> ( Y1 = Y2 ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f892]) ).
thf(f1349,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y2 @ Y3 ) ) )
=> $false )
=> ( Y1 = Y2 ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK15 ) ),
inference(sigma_proxy_clausification,[],[f1348]) ).
thf(f1350,plain,
( $false
= ( ( in @ sK15 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( sK15
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( sK15
= ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1349]) ).
thf(f1351,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( sK15
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( sK15
= ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1350]) ).
thf(f1352,plain,
( ( in @ sK15 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1350]) ).
thf(f1353,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( sK15
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( sK15
= ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK16 ) ),
inference(sigma_proxy_clausification,[],[f1351]) ).
thf(f1354,plain,
( ( ( in @ sK16 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK15
= ( n_pl @ sK16 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK16
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( sK16 = Y0 ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( sK15
= ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1353]) ).
thf(f1355,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK15
= ( n_pl @ sK16 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK16
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( sK16 = Y0 ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( sK15
= ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1354]) ).
thf(f1356,plain,
( $true
= ( in @ sK16 @ nat ) ),
inference(imp_proxy_clausification,[],[f1354]) ).
thf(f1357,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK15
= ( n_pl @ sK16 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK16
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( sK16 = Y0 ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( sK15
= ( n_pl @ Y0 @ Y1 ) ) ) ) ) )
@ sK17 )
= $false ),
inference(sigma_proxy_clausification,[],[f1355]) ).
thf(f1358,plain,
( $false
= ( ( in @ sK17 @ nat )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK16 @ Y0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) )
=> $false )
=> ( sK16 = sK17 ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK17 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1357]) ).
thf(f1359,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK16 @ Y0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) )
=> $false )
=> ( sK16 = sK17 ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK17 @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1358]) ).
thf(f1360,plain,
( $true
= ( in @ sK17 @ nat ) ),
inference(imp_proxy_clausification,[],[f1358]) ).
thf(f1361,plain,
( $false
= ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) )
=> $false )
=> ( sK16 = sK17 ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK17 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1359]) ).
thf(f1362,plain,
( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK16 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1359]) ).
thf(f1363,plain,
( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK17 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1361]) ).
thf(f1364,plain,
( $true
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) )
=> $false )
=> ( sK16 = sK17 ) ) ),
inference(imp_proxy_clausification,[],[f1361]) ).
thf(f1365,plain,
( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) )
=> $false )
= $false )
| ( $true
= ( sK16 = sK17 ) ) ),
inference(imp_proxy_clausification,[],[f1364]) ).
thf(f1367,plain,
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( $true
= ( sK16 = sK17 ) ) ),
inference(imp_proxy_clausification,[],[f1365]) ).
thf(f1368,plain,
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( sK17 = sK16 ) ),
inference(equality_proxy_clausification,[],[f1367]) ).
thf(f1700,definition,
( spl24_1
<=> ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
thf(f1702,plain,
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f1700]) ).
thf(f1704,definition,
( spl24_2
<=> ( sK17 = sK16 ) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
thf(f1706,plain,
( ( sK17 = sK16 )
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f1704]) ).
thf(f1707,plain,
( spl24_1
| spl24_2 ),
inference(avatar_split_clause,[],[f1368,f1704,f1700]) ).
thf(f2014,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ sK15 @ nat )
= $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f1363,f961]) ).
thf(f2019,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( ( in @ sK15 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f2014]) ).
thf(f2031,plain,
! [X0: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( ( in @ sK15 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f2019,f1360]) ).
thf(f2032,plain,
! [X0: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( ( in @ sK15 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f2031]) ).
thf(f2043,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(forward_demodulation,[],[f2032,f1352]) ).
thf(f2044,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f2043]) ).
thf(f2059,plain,
( ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) )
| ( $false
= ( in @ sK16 @ nat ) ) ),
inference(constrained_superposition,[],[f2044,f1362]) ).
thf(f2066,plain,
( ( $false
= ( in @ sK16 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f2059]) ).
thf(f2076,plain,
( ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) ) ),
inference(forward_demodulation,[],[f2066,f1356]) ).
thf(f2077,plain,
( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK16
= ( n_pl @ sK17 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f2076]) ).
thf(f2098,plain,
( ( $true = $false )
| ~ spl24_1 ),
inference(constrained_superposition,[],[f1702,f2077]) ).
thf(f2104,plain,
( $false
| ~ spl24_1 ),
inference(trivial_inequality_removal,[],[f2098]) ).
thf(f2105,plain,
~ spl24_1,
inference(avatar_contradiction_clause,[],[f2104]) ).
thf(f2718,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $true = $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( ( in @ sK15 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( sK17 != X0 ) ),
inference(constrained_superposition,[],[f1363,f1174]) ).
thf(f2745,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ sK15 @ nat )
= $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( sK17 != X0 ) ),
inference(trivial_inequality_removal,[],[f2718]) ).
thf(f2782,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( in @ X0 @ nat )
= $false )
| ( sK17 != X0 )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( in @ sK17 @ nat ) ) ),
inference(forward_demodulation,[],[f2745,f1352]) ).
thf(f2783,plain,
! [X0: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( sK17 != X0 )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f2782]) ).
thf(f2812,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( sK17 != X0 )
| ( ( in @ X0 @ nat )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f2783,f1360]) ).
thf(f2813,plain,
! [X0: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( sK17 != X0 )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f2812]) ).
thf(f2826,plain,
( ! [X0: $i] :
( ( sK16 != X0 )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false ) )
| ~ spl24_2 ),
inference(forward_demodulation,[],[f2813,f1706]) ).
thf(f2830,plain,
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK15
= ( n_pl @ sK16 @ Y0 ) ) ) )
| ( $false
= ( in @ sK16 @ nat ) )
| ~ spl24_2 ),
inference(equality_resolution,[],[f2826]) ).
thf(f2831,plain,
( ( $true = $false )
| ( $false
= ( in @ sK16 @ nat ) )
| ~ spl24_2 ),
inference(forward_demodulation,[],[f2830,f1362]) ).
thf(f2832,plain,
( ( $false
= ( in @ sK16 @ nat ) )
| ~ spl24_2 ),
inference(trivial_inequality_removal,[],[f2831]) ).
thf(f2833,plain,
( ( $true = $false )
| ~ spl24_2 ),
inference(constrained_superposition,[],[f2832,f1356]) ).
thf(f2841,plain,
( $false
| ~ spl24_2 ),
inference(trivial_inequality_removal,[],[f2833]) ).
thf(f2842,plain,
~ spl24_2,
inference(avatar_contradiction_clause,[],[f2841]) ).
cnf(s1,plain,
( spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f1707]) ).
cnf(s14,plain,
~ spl24_1,
inference(sat_conversion,[],[f2105]) ).
cnf(s18,plain,
~ spl24_2,
inference(sat_conversion,[],[f2842]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s14]) ).
thf(f2843,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM666^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 12:32:49 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running higher-order theorem proving
% 0.09/0.16 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
% 0.48/0.28 % (35663)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.28 % (35668)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1174829145:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.28 % (35674)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.28 % (35674)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
% 0.48/0.28 % (35669)lrs+10_16_si=on:nwc=1.5:random_seed=1874149442:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.28 % (35670)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3560417192:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.28 % (35674)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=1561255527:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.28 % (35673)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4100727503:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.28 % (35671)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=1702040343: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)
% 0.48/0.28 % (35672)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=662258415:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.28 % (35670)Instruction limit reached!
% 0.48/0.28 % (35670)------------------------------
% 0.48/0.28 % (35670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.28 % (35670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.28 % (35670)CaDiCaL version: 2.1.3
% 0.48/0.28 % (35670)Termination reason: Instruction limit
% 0.48/0.28 % (35670)Termination phase: shuffling
% 0.48/0.28 % (35670)Time elapsed: 0.002 s
% 0.48/0.28 % (35670)Peak memory usage: 10 MB
% 0.48/0.28 % (35670)Instructions burned: 4 (million)
% 0.48/0.28 % (35669)Instruction limit reached!
% 0.48/0.28 % (35669)------------------------------
% 0.48/0.28 % (35669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.28 % (35669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.28 % (35669)CaDiCaL version: 2.1.3
% 0.48/0.28 % (35669)Termination reason: Instruction limit
% 0.48/0.28 % (35669)Termination phase: shuffling
% 0.48/0.28 % (35669)Time elapsed: 0.008 s
% 0.48/0.28 % (35669)Peak memory usage: 10 MB
% 0.48/0.28 % (35669)Instructions burned: 18 (million)
% 0.48/0.28 % (35672)Instruction limit reached!
% 0.48/0.28 % (35672)------------------------------
% 0.48/0.28 % (35672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.28 % (35672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.28 % (35672)CaDiCaL version: 2.1.3
% 0.48/0.28 % (35672)Termination reason: Instruction limit
% 0.48/0.28 % (35672)Termination phase: Property scanning
% 0.48/0.28 % (35672)Time elapsed: 0.010 s
% 0.48/0.28 % (35672)Peak memory usage: 10 MB
% 0.48/0.28 % (35672)Instructions burned: 24 (million)
% 0.48/0.28 % (35683)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3857385218:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.28 % (35683)Instruction limit reached!
% 0.48/0.28 % (35683)------------------------------
% 0.48/0.28 % (35683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.28 % (35683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.28 % (35683)CaDiCaL version: 2.1.3
% 0.48/0.28 % (35683)Termination reason: Instruction limit
% 0.48/0.28 % (35683)Termination phase: shuffling
% 0.48/0.28 % (35683)Time elapsed: 0.002 s
% 0.48/0.28 % (35683)Peak memory usage: 10 MB
% 0.48/0.28 % (35683)Instructions burned: 4 (million)
% 0.48/0.28 % (35668)Instruction limit reached!
% 0.48/0.28 % (35668)------------------------------
% 0.48/0.28 % (35668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.28 % (35668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.31 % (35668)CaDiCaL version: 2.1.3
% 0.48/0.31 % (35668)Termination reason: Instruction limit
% 0.48/0.31 % (35668)Termination phase: Function definition elimination
% 0.48/0.31 % (35668)Time elapsed: 0.029 s
% 0.48/0.31 % (35668)Peak memory usage: 11 MB
% 0.48/0.31 % (35668)Instructions burned: 89 (million)
% 0.48/0.31 % (35687)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.31 % (35684)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=513802162:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.31 % (35687)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1563413479:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.31 % (35684)Instruction limit reached!
% 0.48/0.31 % (35684)------------------------------
% 0.48/0.31 % (35684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.31 % (35684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.31 % (35684)CaDiCaL version: 2.1.3
% 0.48/0.31 % (35684)Termination reason: Instruction limit
% 0.48/0.31 % (35684)Termination phase: shuffling
% 0.48/0.31 % (35684)Time elapsed: 0.004 s
% 0.48/0.31 % (35684)Peak memory usage: 10 MB
% 0.48/0.31 % (35684)Instructions burned: 8 (million)
% 0.48/0.31 % (35673)Instruction limit reached!
% 0.48/0.31 % (35673)------------------------------
% 0.48/0.31 % (35673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.31 % (35673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.31 % (35673)CaDiCaL version: 2.1.3
% 0.48/0.31 % (35673)Termination reason: Instruction limit
% 0.48/0.31 % (35673)Termination phase: Function definition elimination
% 0.48/0.31 % (35673)Time elapsed: 0.030 s
% 0.48/0.31 % (35673)Peak memory usage: 11 MB
% 0.48/0.31 % (35673)Instructions burned: 75 (million)
% 0.48/0.31 % (35687)Instruction limit reached!
% 0.48/0.31 % (35687)------------------------------
% 0.48/0.31 % (35687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.31 % (35687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.31 % (35687)CaDiCaL version: 2.1.3
% 0.48/0.31 % (35687)Termination reason: Instruction limit
% 0.48/0.31 % (35687)Termination phase: shuffling
% 0.48/0.31 % (35687)Time elapsed: 0.005 s
% 0.48/0.31 % (35687)Peak memory usage: 10 MB
% 0.48/0.31 % (35687)Instructions burned: 10 (million)
% 0.48/0.31 % (35689)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=433593304:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.31 % (35691)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
% 0.48/0.31 % (35691)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.31 % (35691)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1983305585:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.31 % (35696)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.48/0.31 % (35689)Instruction limit reached!
% 0.48/0.31 % (35689)------------------------------
% 0.48/0.31 % (35689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.31 % (35689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.31 % (35689)CaDiCaL version: 2.1.3
% 0.48/0.31 % (35689)Termination reason: Instruction limit
% 0.48/0.31 % (35689)Termination phase: shuffling
% 0.48/0.31 % (35689)Time elapsed: 0.006 s
% 0.48/0.31 % (35689)Peak memory usage: 10 MB
% 0.48/0.31 % (35689)Instructions burned: 14 (million)
% 0.48/0.31 % (35696)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=2303734061:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.31 % (35694)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=3716393067:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.48/0.33 % (35695)lrs+10_1_si=on:cs=on:random_seed=1429058523:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.48/0.33 % (35696)Instruction limit reached!
% 0.48/0.33 % (35696)------------------------------
% 0.48/0.33 % (35696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (35696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (35696)CaDiCaL version: 2.1.3
% 0.48/0.33 % (35696)Termination reason: Instruction limit
% 0.48/0.33 % (35696)Termination phase: shuffling
% 0.48/0.33 % (35696)Time elapsed: 0.002 s
% 0.48/0.33 % (35696)Peak memory usage: 10 MB
% 0.48/0.33 % (35696)Instructions burned: 4 (million)
% 0.48/0.33 % (35695)Instruction limit reached!
% 0.48/0.33 % (35695)------------------------------
% 0.48/0.33 % (35695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (35695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (35695)CaDiCaL version: 2.1.3
% 0.48/0.33 % (35695)Termination reason: Instruction limit
% 0.48/0.33 % (35695)Termination phase: shuffling
% 0.48/0.33 % (35695)Time elapsed: 0.004 s
% 0.48/0.33 % (35695)Peak memory usage: 10 MB
% 0.48/0.33 % (35695)Instructions burned: 9 (million)
% 0.48/0.33 % (35699)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4255354304:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.48/0.33 % (35691)Instruction limit reached!
% 0.48/0.33 % (35691)------------------------------
% 0.48/0.33 % (35691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (35691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (35691)CaDiCaL version: 2.1.3
% 0.48/0.33 % (35691)Termination reason: Instruction limit
% 0.48/0.33 % (35691)Termination phase: Property scanning
% 0.48/0.33 % (35691)Time elapsed: 0.012 s
% 0.48/0.33 % (35691)Peak memory usage: 10 MB
% 0.48/0.33 % (35691)Instructions burned: 29 (million)
% 0.48/0.33 % (35674)Instruction limit reached!
% 0.48/0.33 % (35674)------------------------------
% 0.48/0.33 % (35674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (35674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (35674)CaDiCaL version: 2.1.3
% 0.48/0.33 % (35674)Termination reason: Instruction limit
% 0.48/0.33 % (35674)Termination phase: Function definition elimination
% 0.48/0.33 % (35674)Time elapsed: 0.054 s
% 0.48/0.33 % (35674)Peak memory usage: 11 MB
% 0.48/0.33 % (35674)Instructions burned: 158 (million)
% 0.48/0.33 % (35699)Instruction limit reached!
% 0.48/0.33 % (35699)------------------------------
% 0.48/0.33 % (35699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (35699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (35699)CaDiCaL version: 2.1.3
% 0.48/0.33 % (35699)Termination reason: Instruction limit
% 0.48/0.33 % (35699)Termination phase: Property scanning
% 0.48/0.33 % (35699)Time elapsed: 0.010 s
% 0.48/0.33 % (35699)Peak memory usage: 11 MB
% 0.48/0.33 % (35699)Instructions burned: 39 (million)
% 0.48/0.33 % (35703)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=707105337:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.48/0.33 % (35704)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=740369758:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.48/0.33 % (35706)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4028974820:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.48/0.33 % (35707)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2960632299:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.48/0.33 % (35708)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1034468714:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.48/0.33 % (35706)Instruction limit reached!
% 0.48/0.33 % (35706)------------------------------
% 0.48/0.33 % (35706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (35706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (35706)CaDiCaL version: 2.1.3
% 0.48/0.33 % (35706)Termination reason: Instruction limit
% 1.23/0.40 % (35706)Termination phase: shuffling
% 1.23/0.40 % (35706)Time elapsed: 0.006 s
% 1.23/0.40 % (35706)Peak memory usage: 10 MB
% 1.23/0.40 % (35706)Instructions burned: 14 (million)
% 1.23/0.40 % (35694)Instruction limit reached!
% 1.23/0.40 % (35694)------------------------------
% 1.23/0.40 % (35694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.40 % (35694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.40 % (35694)CaDiCaL version: 2.1.3
% 1.23/0.40 % (35694)Termination reason: Instruction limit
% 1.23/0.40 % (35694)Termination phase: Function definition elimination
% 1.23/0.40 % (35694)Time elapsed: 0.034 s
% 1.23/0.40 % (35694)Peak memory usage: 11 MB
% 1.23/0.40 % (35694)Instructions burned: 89 (million)
% 1.23/0.40 % (35704)Instruction limit reached!
% 1.23/0.40 % (35704)------------------------------
% 1.23/0.40 % (35704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.40 % (35704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.40 % (35704)CaDiCaL version: 2.1.3
% 1.23/0.40 % (35704)Termination reason: Instruction limit
% 1.23/0.40 % (35704)Termination phase: Property scanning
% 1.23/0.40 % (35704)Time elapsed: 0.011 s
% 1.23/0.40 % (35704)Peak memory usage: 10 MB
% 1.23/0.40 % (35704)Instructions burned: 25 (million)
% 1.23/0.40 % (35708)Instruction limit reached!
% 1.23/0.40 % (35708)------------------------------
% 1.23/0.40 % (35708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.40 % (35708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.40 % (35708)CaDiCaL version: 2.1.3
% 1.23/0.40 % (35708)Termination reason: Instruction limit
% 1.23/0.40 % (35708)Termination phase: shuffling
% 1.23/0.40 % (35708)Time elapsed: 0.007 s
% 1.23/0.40 % (35708)Peak memory usage: 10 MB
% 1.23/0.40 % (35708)Instructions burned: 16 (million)
% 1.23/0.40 % (35703)Refutation not found, incomplete strategy
% 1.23/0.40 % (35703)------------------------------
% 1.23/0.40 % (35703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.40 % (35703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.40 % (35703)CaDiCaL version: 2.1.3
% 1.23/0.40 % (35703)Termination reason: Refutation not found, incomplete strategy
% 1.23/0.40 % (35703)Time elapsed: 0.021 s
% 1.23/0.40 % (35703)Peak memory usage: 13 MB
% 1.23/0.40 % (35703)Instructions burned: 49 (million)
% 1.23/0.40 % (35703)------------------------------
% 1.23/0.40 % (35703)------------------------------
% 1.23/0.40 % (35714)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=184359776: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)
% 1.23/0.40 % (35715)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3865256611:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.23/0.40 % (35714)Instruction limit reached!
% 1.23/0.40 % (35714)------------------------------
% 1.23/0.40 % (35714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.40 % (35714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.40 % (35714)CaDiCaL version: 2.1.3
% 1.23/0.40 % (35714)Termination reason: Instruction limit
% 1.23/0.40 % (35714)Termination phase: shuffling
% 1.23/0.40 % (35714)Time elapsed: 0.002 s
% 1.23/0.40 % (35714)Peak memory usage: 10 MB
% 1.23/0.40 % (35714)Instructions burned: 4 (million)
% 1.23/0.40 % (35716)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1965471133:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.23/0.40 % (35717)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1108012261:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.23/0.40 % (35718)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
% 1.23/0.40 % (35718)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.23/0.40 % (35718)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=796979115:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.23/0.40 % (35718)Instruction limit reached!
% 1.23/0.40 % (35718)------------------------------
% 1.84/0.44 % (35718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.44 % (35718)CaDiCaL version: 2.1.3
% 1.84/0.44 % (35718)Termination reason: Instruction limit
% 1.84/0.44 % (35718)Termination phase: shuffling
% 1.84/0.44 % (35718)Time elapsed: 0.004 s
% 1.84/0.44 % (35718)Peak memory usage: 10 MB
% 1.84/0.44 % (35718)Instructions burned: 18 (million)
% 1.84/0.44 % (35715)Instruction limit reached!
% 1.84/0.44 % (35715)------------------------------
% 1.84/0.44 % (35715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.44 % (35715)CaDiCaL version: 2.1.3
% 1.84/0.44 % (35715)Termination reason: Instruction limit
% 1.84/0.44 % (35715)Termination phase: Property scanning
% 1.84/0.44 % (35715)Time elapsed: 0.011 s
% 1.84/0.44 % (35715)Peak memory usage: 10 MB
% 1.84/0.44 % (35715)Instructions burned: 26 (million)
% 1.84/0.44 % (35716)Instruction limit reached!
% 1.84/0.44 % (35716)------------------------------
% 1.84/0.44 % (35716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.44 % (35716)CaDiCaL version: 2.1.3
% 1.84/0.44 % (35716)Termination reason: Instruction limit
% 1.84/0.44 % (35716)Termination phase: Property scanning
% 1.84/0.44 % (35716)Time elapsed: 0.010 s
% 1.84/0.44 % (35716)Peak memory usage: 10 MB
% 1.84/0.44 % (35716)Instructions burned: 24 (million)
% 1.84/0.44 % (35721)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.84/0.44 % (35721)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=720858100:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.84/0.44 % (35721)Instruction limit reached!
% 1.84/0.44 % (35721)------------------------------
% 1.84/0.44 % (35721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.44 % (35721)CaDiCaL version: 2.1.3
% 1.84/0.44 % (35721)Termination reason: Instruction limit
% 1.84/0.44 % (35721)Termination phase: shuffling
% 1.84/0.44 % (35721)Time elapsed: 0.004 s
% 1.84/0.44 % (35721)Peak memory usage: 10 MB
% 1.84/0.44 % (35721)Instructions burned: 9 (million)
% 1.84/0.44 % (35725)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=896186853:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.84/0.44 % (35726)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2675151506:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.84/0.44 % (35727)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3486826401:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.84/0.44 % (35717)Instruction limit reached!
% 1.84/0.44 % (35717)------------------------------
% 1.84/0.44 % (35717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.44 % (35717)CaDiCaL version: 2.1.3
% 1.84/0.44 % (35717)Termination reason: Instruction limit
% 1.84/0.44 % (35717)Termination phase: Property scanning
% 1.84/0.44 % (35717)Time elapsed: 0.026 s
% 1.84/0.44 % (35717)Peak memory usage: 11 MB
% 1.84/0.44 % (35717)Instructions burned: 61 (million)
% 1.84/0.44 % (35725)Instruction limit reached!
% 1.84/0.44 % (35725)------------------------------
% 1.84/0.44 % (35725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.44 % (35725)CaDiCaL version: 2.1.3
% 1.84/0.44 % (35725)Termination reason: Instruction limit
% 1.84/0.44 % (35725)Termination phase: Property scanning
% 1.84/0.44 % (35725)Time elapsed: 0.007 s
% 1.84/0.44 % (35725)Peak memory usage: 10 MB
% 1.84/0.44 % (35725)Instructions burned: 32 (million)
% 1.84/0.44 % (35726)Instruction limit reached!
% 1.84/0.44 % (35726)------------------------------
% 1.84/0.44 % (35726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.44 % (35726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.50 % (35726)CaDiCaL version: 2.1.3
% 1.84/0.50 % (35726)Termination reason: Instruction limit
% 1.84/0.50 % (35726)Termination phase: shuffling
% 1.84/0.50 % (35726)Time elapsed: 0.004 s
% 1.84/0.50 % (35726)Peak memory usage: 10 MB
% 1.84/0.50 % (35726)Instructions burned: 10 (million)
% 1.84/0.50 % (35729)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4239261149:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.84/0.50 % (35727)Instruction limit reached!
% 1.84/0.50 % (35727)------------------------------
% 1.84/0.50 % (35727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.50 % (35727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.50 % (35727)CaDiCaL version: 2.1.3
% 1.84/0.50 % (35727)Termination reason: Instruction limit
% 1.84/0.50 % (35727)Termination phase: Property scanning
% 1.84/0.50 % (35727)Time elapsed: 0.011 s
% 1.84/0.50 % (35727)Peak memory usage: 10 MB
% 1.84/0.50 % (35727)Instructions burned: 26 (million)
% 1.84/0.50 % (35733)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1396120410:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.84/0.50 % (35729)Instruction limit reached!
% 1.84/0.50 % (35729)------------------------------
% 1.84/0.50 % (35729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.50 % (35729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.50 % (35729)CaDiCaL version: 2.1.3
% 1.84/0.50 % (35729)Termination reason: Instruction limit
% 1.84/0.50 % (35729)Termination phase: Property scanning
% 1.84/0.50 % (35729)Time elapsed: 0.009 s
% 1.84/0.50 % (35729)Peak memory usage: 10 MB
% 1.84/0.50 % (35729)Instructions burned: 21 (million)
% 1.84/0.50 % (35734)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1316084587:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.84/0.50 % (35735)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2559117680:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.84/0.50 % (35737)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1047412233:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.84/0.50 % (35739)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.84/0.50 % (35739)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2369155444:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.84/0.50 % (35739)Instruction limit reached!
% 1.84/0.50 % (35739)------------------------------
% 1.84/0.50 % (35739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.50 % (35739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.50 % (35739)CaDiCaL version: 2.1.3
% 1.84/0.50 % (35739)Termination reason: Instruction limit
% 1.84/0.50 % (35739)Termination phase: shuffling
% 1.84/0.50 % (35739)Time elapsed: 0.004 s
% 1.84/0.50 % (35739)Peak memory usage: 10 MB
% 1.84/0.50 % (35739)Instructions burned: 9 (million)
% 1.84/0.50 % (35737)Instruction limit reached!
% 1.84/0.50 % (35737)------------------------------
% 1.84/0.50 % (35737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.50 % (35737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.50 % (35737)CaDiCaL version: 2.1.3
% 1.84/0.50 % (35737)Termination reason: Instruction limit
% 1.84/0.50 % (35737)Termination phase: Property scanning
% 1.84/0.50 % (35737)Time elapsed: 0.019 s
% 1.84/0.50 % (35737)Peak memory usage: 10 MB
% 1.84/0.50 % (35737)Instructions burned: 43 (million)
% 1.84/0.50 % (35744)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2945570421:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 1.84/0.50 % (35746)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3023391868:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.84/0.50 % (35734)Instruction limit reached!
% 1.84/0.50 % (35734)------------------------------
% 1.84/0.50 % (35734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35734)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35734)Termination reason: Instruction limit
% 2.52/0.56 % (35734)Termination phase: Function definition elimination
% 2.52/0.56 % (35734)Time elapsed: 0.050 s
% 2.52/0.56 % (35734)Peak memory usage: 11 MB
% 2.52/0.56 % (35734)Instructions burned: 144 (million)
% 2.52/0.56 % (35753)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.52/0.56 % (35753)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1542812156:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.52/0.56 % (35707)Instruction limit reached!
% 2.52/0.56 % (35707)------------------------------
% 2.52/0.56 % (35707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35707)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35707)Termination reason: Instruction limit
% 2.52/0.56 % (35707)Termination phase: Saturation
% 2.52/0.56 % (35707)Time elapsed: 0.145 s
% 2.52/0.56 % (35707)Peak memory usage: 15 MB
% 2.52/0.56 % (35707)Instructions burned: 328 (million)
% 2.52/0.56 % (35753)Instruction limit reached!
% 2.52/0.56 % (35753)------------------------------
% 2.52/0.56 % (35753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35753)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35753)Termination reason: Instruction limit
% 2.52/0.56 % (35753)Termination phase: shuffling
% 2.52/0.56 % (35753)Time elapsed: 0.003 s
% 2.52/0.56 % (35753)Peak memory usage: 10 MB
% 2.52/0.56 % (35753)Instructions burned: 6 (million)
% 2.52/0.56 % (35746)Refutation not found, incomplete strategy
% 2.52/0.56 % (35746)------------------------------
% 2.52/0.56 % (35746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35746)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35746)Termination reason: Refutation not found, incomplete strategy
% 2.52/0.56 % (35746)Time elapsed: 0.034 s
% 2.52/0.56 % (35746)Peak memory usage: 13 MB
% 2.52/0.56 % (35746)Instructions burned: 78 (million)
% 2.52/0.56 % (35746)------------------------------
% 2.52/0.56 % (35746)------------------------------
% 2.52/0.56 % (35735)Instruction limit reached!
% 2.52/0.56 % (35735)------------------------------
% 2.52/0.56 % (35735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35735)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35735)Termination reason: Instruction limit
% 2.52/0.56 % (35735)Termination phase: Saturation
% 2.52/0.56 % (35735)Time elapsed: 0.082 s
% 2.52/0.56 % (35735)Peak memory usage: 14 MB
% 2.52/0.56 % (35735)Instructions burned: 196 (million)
% 2.52/0.56 % (35756)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1360163646:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.52/0.56 % (35757)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3650802095:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.52/0.56 % (35757)Instruction limit reached!
% 2.52/0.56 % (35757)------------------------------
% 2.52/0.56 % (35757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35757)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35757)Termination reason: Instruction limit
% 2.52/0.56 % (35757)Termination phase: shuffling
% 2.52/0.56 % (35757)Time elapsed: 0.009 s
% 2.52/0.56 % (35757)Peak memory usage: 10 MB
% 2.52/0.56 % (35757)Instructions burned: 19 (million)
% 2.52/0.56 % (35756)Instruction limit reached!
% 2.52/0.56 % (35756)------------------------------
% 2.52/0.56 % (35756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.56 % (35756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.56 % (35756)CaDiCaL version: 2.1.3
% 2.52/0.56 % (35756)Termination reason: Instruction limit
% 2.52/0.56 % (35756)Termination phase: Property scanning
% 2.52/0.56 % (35756)Time elapsed: 0.009 s
% 2.52/0.56 % (35756)Peak memory usage: 10 MB
% 2.52/0.62 % (35756)Instructions burned: 22 (million)
% 2.52/0.62 % (35758)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1436796547:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.52/0.62 % (35759)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3355380203:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.52/0.62 % (35744)Instruction limit reached!
% 2.52/0.62 % (35744)------------------------------
% 2.52/0.62 % (35744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.62 % (35744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.62 % (35744)CaDiCaL version: 2.1.3
% 2.52/0.62 % (35744)Termination reason: Instruction limit
% 2.52/0.62 % (35744)Termination phase: Saturation
% 2.52/0.62 % (35744)Time elapsed: 0.073 s
% 2.52/0.62 % (35744)Peak memory usage: 13 MB
% 2.52/0.62 % (35744)Instructions burned: 183 (million)
% 2.52/0.62 % (35764)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1679148839:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.52/0.62 % (35763)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2005540059:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.52/0.62 % (35766)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2983458354:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2997 on theBenchmark for (2997ds/21Mi)
% 2.52/0.62 % (35766)Instruction limit reached!
% 2.52/0.62 % (35766)------------------------------
% 2.52/0.62 % (35766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.62 % (35766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.62 % (35766)CaDiCaL version: 2.1.3
% 2.52/0.62 % (35766)Termination reason: Instruction limit
% 2.52/0.62 % (35766)Termination phase: Property scanning
% 2.52/0.62 % (35766)Time elapsed: 0.010 s
% 2.52/0.62 % (35766)Peak memory usage: 10 MB
% 2.52/0.62 % (35766)Instructions burned: 22 (million)
% 2.52/0.62 % (35671)Instruction limit reached!
% 2.52/0.62 % (35671)------------------------------
% 2.52/0.62 % (35671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.62 % (35671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.62 % (35671)CaDiCaL version: 2.1.3
% 2.52/0.62 % (35671)Termination reason: Instruction limit
% 2.52/0.62 % (35671)Termination phase: Saturation
% 2.52/0.62 % (35671)Time elapsed: 0.283 s
% 2.52/0.62 % (35671)Peak memory usage: 17 MB
% 2.52/0.62 % (35671)Instructions burned: 636 (million)
% 2.52/0.62 % (35763)Instruction limit reached!
% 2.52/0.62 % (35763)------------------------------
% 2.52/0.62 % (35763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.62 % (35763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.62 % (35763)CaDiCaL version: 2.1.3
% 2.52/0.62 % (35763)Termination reason: Instruction limit
% 2.52/0.62 % (35763)Termination phase: SInE selection
% 2.52/0.62 % (35763)Time elapsed: 0.020 s
% 2.52/0.62 % (35763)Peak memory usage: 11 MB
% 2.52/0.62 % (35763)Instructions burned: 46 (million)
% 2.52/0.62 % (35764)Refutation not found, incomplete strategy
% 2.52/0.62 % (35764)------------------------------
% 2.52/0.62 % (35764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.62 % (35764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.62 % (35764)CaDiCaL version: 2.1.3
% 2.52/0.62 % (35764)Termination reason: Refutation not found, incomplete strategy
% 2.52/0.62 % (35764)Time elapsed: 0.027 s
% 2.52/0.62 % (35764)Peak memory usage: 13 MB
% 2.52/0.62 % (35764)Instructions burned: 84 (million)
% 2.52/0.62 % (35764)------------------------------
% 2.52/0.62 % (35764)------------------------------
% 2.52/0.62 % (35770)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.52/0.62 % (35770)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3189802564:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.38/0.75 % (35771)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2478641946:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.38/0.75 % (35772)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3237318944:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.38/0.75 % (35771)Instruction limit reached!
% 3.38/0.75 % (35771)------------------------------
% 3.38/0.75 % (35771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.75 % (35771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.75 % (35771)CaDiCaL version: 2.1.3
% 3.38/0.75 % (35771)Termination reason: Instruction limit
% 3.38/0.75 % (35771)Termination phase: shuffling
% 3.38/0.75 % (35771)Time elapsed: 0.006 s
% 3.38/0.75 % (35771)Peak memory usage: 10 MB
% 3.38/0.75 % (35771)Instructions burned: 14 (million)
% 3.38/0.75 % (35773)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3452971132:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.38/0.75 % (35773)Instruction limit reached!
% 3.38/0.75 % (35773)------------------------------
% 3.38/0.75 % (35773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.75 % (35773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.75 % (35773)CaDiCaL version: 2.1.3
% 3.38/0.75 % (35773)Termination reason: Instruction limit
% 3.38/0.75 % (35773)Termination phase: Function definition elimination
% 3.38/0.75 % (35773)Time elapsed: 0.013 s
% 3.38/0.75 % (35773)Peak memory usage: 11 MB
% 3.38/0.75 % (35773)Instructions burned: 54 (million)
% 3.38/0.75 % (35780)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2854380032:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.38/0.75 % (35772)Instruction limit reached!
% 3.38/0.75 % (35772)------------------------------
% 3.38/0.75 % (35772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.75 % (35772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.75 % (35772)CaDiCaL version: 2.1.3
% 3.38/0.75 % (35772)Termination reason: Instruction limit
% 3.38/0.75 % (35772)Termination phase: Function definition elimination
% 3.38/0.75 % (35772)Time elapsed: 0.028 s
% 3.38/0.75 % (35772)Peak memory usage: 11 MB
% 3.38/0.75 % (35772)Instructions burned: 67 (million)
% 3.38/0.75 % (35780)Instruction limit reached!
% 3.38/0.75 % (35780)------------------------------
% 3.38/0.75 % (35780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.75 % (35780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.75 % (35780)CaDiCaL version: 2.1.3
% 3.38/0.75 % (35780)Termination reason: Instruction limit
% 3.38/0.75 % (35780)Termination phase: Property scanning
% 3.38/0.75 % (35780)Time elapsed: 0.014 s
% 3.38/0.75 % (35780)Peak memory usage: 10 MB
% 3.38/0.75 % (35780)Instructions burned: 33 (million)
% 3.38/0.75 % (35781)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3518018370:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 3.38/0.75 % (35758)Instruction limit reached!
% 3.38/0.75 % (35758)------------------------------
% 3.38/0.75 % (35758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.75 % (35758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.75 % (35758)CaDiCaL version: 2.1.3
% 3.38/0.75 % (35758)Termination reason: Instruction limit
% 3.38/0.75 % (35758)Termination phase: Function definition elimination
% 3.38/0.75 % (35758)Time elapsed: 0.099 s
% 3.38/0.75 % (35758)Peak memory usage: 11 MB
% 3.38/0.75 % (35758)Instructions burned: 319 (million)
% 3.38/0.75 % (35783)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=536297961:cond=on:i=34:hud=10:nm=10:rtra=on_2996 on theBenchmark for (2996ds/34Mi)
% 3.38/0.75 % (35786)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.38/0.75 % (35784)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3627481381:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2996 on theBenchmark for (2996ds/67Mi)
% 3.38/0.75 % (35786)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=319712610:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2996 on theBenchmark for (2996ds/180Mi)
% 3.38/0.76 % (35770)Instruction limit reached!
% 3.38/0.76 % (35770)------------------------------
% 3.38/0.76 % (35770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35770)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35770)Termination reason: Instruction limit
% 3.38/0.76 % (35770)Termination phase: Function definition elimination
% 3.38/0.76 % (35770)Time elapsed: 0.066 s
% 3.38/0.76 % (35770)Peak memory usage: 11 MB
% 3.38/0.76 % (35770)Instructions burned: 201 (million)
% 3.38/0.76 % (35783)Instruction limit reached!
% 3.38/0.76 % (35783)------------------------------
% 3.38/0.76 % (35783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35783)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35783)Termination reason: Instruction limit
% 3.38/0.76 % (35783)Termination phase: Property scanning
% 3.38/0.76 % (35783)Time elapsed: 0.017 s
% 3.38/0.76 % (35783)Peak memory usage: 10 MB
% 3.38/0.76 % (35783)Instructions burned: 41 (million)
% 3.38/0.76 % (35790)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1907187919:st=2:i=246:sd=3:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/246Mi)
% 3.38/0.76 % (35784)Instruction limit reached!
% 3.38/0.76 % (35784)------------------------------
% 3.38/0.76 % (35784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35784)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35784)Termination reason: Instruction limit
% 3.38/0.76 % (35784)Termination phase: Function definition elimination
% 3.38/0.76 % (35784)Time elapsed: 0.027 s
% 3.38/0.76 % (35784)Peak memory usage: 11 MB
% 3.38/0.76 % (35784)Instructions burned: 67 (million)
% 3.38/0.76 % (35791)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2797908890:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.38/0.76 % (35793)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2647889373:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.38/0.76 % (35786)Instruction limit reached!
% 3.38/0.76 % (35786)------------------------------
% 3.38/0.76 % (35786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35786)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35786)Termination reason: Instruction limit
% 3.38/0.76 % (35786)Termination phase: Function definition elimination
% 3.38/0.76 % (35786)Time elapsed: 0.046 s
% 3.38/0.76 % (35786)Peak memory usage: 11 MB
% 3.38/0.76 % (35786)Instructions burned: 181 (million)
% 3.38/0.76 % (35793)Refutation not found, incomplete strategy
% 3.38/0.76 % (35793)------------------------------
% 3.38/0.76 % (35793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35793)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35793)Termination reason: Refutation not found, incomplete strategy
% 3.38/0.76 % (35793)Time elapsed: 0.011 s
% 3.38/0.76 % (35793)Peak memory usage: 13 MB
% 3.38/0.76 % (35793)Instructions burned: 45 (million)
% 3.38/0.76 % (35793)------------------------------
% 3.38/0.76 % (35793)------------------------------
% 3.38/0.76 % (35781)Instruction limit reached!
% 3.38/0.76 % (35781)------------------------------
% 3.38/0.76 % (35781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35781)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35781)Termination reason: Instruction limit
% 3.38/0.76 % (35781)Termination phase: Saturation
% 3.38/0.76 % (35781)Time elapsed: 0.066 s
% 3.38/0.76 % (35781)Peak memory usage: 13 MB
% 3.38/0.76 % (35781)Instructions burned: 137 (million)
% 3.38/0.76 % (35797)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3023237266:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/515Mi)
% 3.38/0.76 % (35790)Refutation not found, incomplete strategy
% 3.38/0.76 % (35790)------------------------------
% 3.38/0.76 % (35790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35790)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35790)Termination reason: Refutation not found, incomplete strategy
% 3.38/0.76 % (35790)Time elapsed: 0.035 s
% 3.38/0.76 % (35790)Peak memory usage: 13 MB
% 3.38/0.76 % (35790)Instructions burned: 81 (million)
% 3.38/0.76 % (35790)------------------------------
% 3.38/0.76 % (35790)------------------------------
% 3.38/0.76 % (35796)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3291100526:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 3.38/0.76 % (35791)Instruction limit reached!
% 3.38/0.76 % (35791)------------------------------
% 3.38/0.76 % (35791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35791)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35791)Termination reason: Instruction limit
% 3.38/0.76 % (35791)Termination phase: Function definition elimination
% 3.38/0.76 % (35791)Time elapsed: 0.037 s
% 3.38/0.76 % (35791)Peak memory usage: 11 MB
% 3.38/0.76 % (35791)Instructions burned: 97 (million)
% 3.38/0.76 % (35798)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1200782641:st=1.5:i=130:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/130Mi)
% 3.38/0.76 % (35800)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3283152264:i=44:ep=R:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/44Mi)
% 3.38/0.76 % (35803)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=825218632:s2a=on:i=571:nm=16:rtra=on_2995 on theBenchmark for (2995ds/571Mi)
% 3.38/0.76 % (35800)Instruction limit reached!
% 3.38/0.76 % (35800)------------------------------
% 3.38/0.76 % (35800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35800)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35800)Termination reason: Instruction limit
% 3.38/0.76 % (35800)Termination phase: Property scanning
% 3.38/0.76 % (35800)Time elapsed: 0.019 s
% 3.38/0.76 % (35800)Peak memory usage: 11 MB
% 3.38/0.76 % (35800)Instructions burned: 44 (million)
% 3.38/0.76 % (35806)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2017110770:i=450:rtra=on:ixr=off:ntd=on_2995 on theBenchmark for (2995ds/450Mi)
% 3.38/0.76 % (35798)Instruction limit reached!
% 3.38/0.76 % (35798)------------------------------
% 3.38/0.76 % (35798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35798)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35798)Termination reason: Instruction limit
% 3.38/0.76 % (35798)Termination phase: Saturation
% 3.38/0.76 % (35798)Time elapsed: 0.057 s
% 3.38/0.76 % (35798)Peak memory usage: 13 MB
% 3.38/0.76 % (35798)Instructions burned: 131 (million)
% 3.38/0.76 % (35811)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1055261169:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 3.38/0.76 % (35811)Instruction limit reached!
% 3.38/0.76 % (35811)------------------------------
% 3.38/0.76 % (35811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35811)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35811)Termination reason: Instruction limit
% 3.38/0.76 % (35811)Termination phase: Function definition elimination
% 3.38/0.76 % (35811)Time elapsed: 0.023 s
% 3.38/0.76 % (35811)Peak memory usage: 11 MB
% 3.38/0.76 % (35811)Instructions burned: 98 (million)
% 3.38/0.76 % (35816)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=2761460003:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2994 on theBenchmark for (2994ds/65Mi)
% 3.38/0.76 % (35797) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-35663-35797"...
% 3.38/0.76 % (35816)Instruction limit reached!
% 3.38/0.76 % (35816)------------------------------
% 3.38/0.76 % (35816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35816)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35816)Termination reason: Instruction limit
% 3.38/0.76 % (35816)Termination phase: Function definition elimination
% 3.38/0.76 % (35816)Time elapsed: 0.017 s
% 3.38/0.76 % (35816)Peak memory usage: 11 MB
% 3.38/0.76 % (35816)Instructions burned: 67 (million)
% 3.38/0.76 % (35797)...printing done.
% 3.38/0.76 % (35797)Refutation found. Thanks to Tanya!
% 3.38/0.76 % SZS status Theorem for theBenchmark
% 3.38/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/0.76 % (35797)------------------------------
% 3.38/0.76 % (35797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.38/0.76 % (35797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/0.76 % (35797)CaDiCaL version: 2.1.3
% 3.38/0.76 % (35797)Termination reason: Refutation
% 3.38/0.76 % (35797)Time elapsed: 0.132 s
% 3.38/0.76 % (35797)Peak memory usage: 15 MB
% 3.38/0.76 % (35797)Instructions burned: 394 (million)
% 3.38/0.76 % (35663)Success in time 0.589 s
% 3.38/0.76 % Vampire exiting
%------------------------------------------------------------------------------