%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM663^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:18:27 AM UTC 2026
% Result : Theorem 3.62s 0.99s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 20
% Syntax : Number of formulae : 194 ( 92 unt; 0 typ; 4 def)
% Number of atoms : 2373 ( 610 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 2475 ( 103 ~; 267 |; 0 &;1800 @)
% ( 4 <=>; 254 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 188 ( 184 usr; 12 con; 0-7 aty)
% ( 47 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 780 ( 74 sgn 114 !; 0 ?; 780 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
is_of: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
eps: ( $i > $o ) > $i ).
thf(func_def_4,type,
in: $i > $i > $o ).
thf(func_def_5,type,
d_Subq: $i > $i > $o ).
thf(func_def_7,type,
union: $i > $i ).
thf(func_def_8,type,
power: $i > $i ).
thf(func_def_9,type,
repl: $i > ( $i > $i ) > $i ).
thf(func_def_10,type,
d_Union_closed: $i > $o ).
thf(func_def_11,type,
d_Power_closed: $i > $o ).
thf(func_def_12,type,
d_Repl_closed: $i > $o ).
thf(func_def_13,type,
d_ZF_closed: $i > $o ).
thf(func_def_14,type,
univof: $i > $i ).
thf(func_def_15,type,
if: $o > $i > $i > $i ).
thf(func_def_16,type,
nIn: $i > $i > $o ).
thf(func_def_17,type,
d_UPair: $i > $i > $i ).
thf(func_def_18,type,
d_Sing: $i > $i ).
thf(func_def_19,type,
binunion: $i > $i > $i ).
thf(func_def_20,type,
famunion: $i > ( $i > $i ) > $i ).
thf(func_def_21,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
d_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_23,type,
setminus: $i > $i > $i ).
thf(func_def_24,type,
d_In_rec_G: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_25,type,
d_In_rec: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_26,type,
ordsucc: $i > $i ).
thf(func_def_27,type,
nat_p: $i > $o ).
thf(func_def_29,type,
d_Inj1: $i > $i ).
thf(func_def_30,type,
d_Inj0: $i > $i ).
thf(func_def_31,type,
d_Unj: $i > $i ).
thf(func_def_32,type,
pair: $i > $i > $i ).
thf(func_def_33,type,
proj0: $i > $i ).
thf(func_def_34,type,
proj1: $i > $i ).
thf(func_def_35,type,
d_Sigma: $i > ( $i > $i ) > $i ).
thf(func_def_36,type,
setprod: $i > $i > $i ).
thf(func_def_37,type,
ap: $i > $i > $i ).
thf(func_def_38,type,
pair_p: $i > $o ).
thf(func_def_39,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_40,type,
imp: $o > $o > $o ).
thf(func_def_41,type,
d_not: $o > $o ).
thf(func_def_42,type,
wel: $o > $o ).
thf(func_def_43,type,
obvious: $o ).
thf(func_def_44,type,
l_ec: $o > $o > $o ).
thf(func_def_45,type,
d_and: $o > $o > $o ).
thf(func_def_46,type,
l_or: $o > $o > $o ).
thf(func_def_47,type,
orec: $o > $o > $o ).
thf(func_def_48,type,
l_iff: $o > $o > $o ).
thf(func_def_49,type,
all: $i > ( $i > $o ) > $o ).
thf(func_def_50,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(func_def_51,type,
l_some: $i > ( $i > $o ) > $o ).
thf(func_def_52,type,
or3: $o > $o > $o > $o ).
thf(func_def_53,type,
and3: $o > $o > $o > $o ).
thf(func_def_54,type,
ec3: $o > $o > $o > $o ).
thf(func_def_55,type,
orec3: $o > $o > $o > $o ).
thf(func_def_56,type,
e_is: $i > $i > $i > $o ).
thf(func_def_57,type,
amone: $i > ( $i > $o ) > $o ).
thf(func_def_58,type,
one: $i > ( $i > $o ) > $o ).
thf(func_def_59,type,
ind: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
injective: $i > $i > $i > $o ).
thf(func_def_61,type,
image: $i > $i > $i > $i > $o ).
thf(func_def_62,type,
tofs: $i > $i > $i > $i > $i ).
thf(func_def_63,type,
soft: $i > $i > $i > $i > $i ).
thf(func_def_64,type,
inverse: $i > $i > $i > $i ).
thf(func_def_65,type,
surjective: $i > $i > $i > $o ).
thf(func_def_66,type,
bijective: $i > $i > $i > $o ).
thf(func_def_67,type,
invf: $i > $i > $i > $i ).
thf(func_def_68,type,
inj_h: $i > $i > $i > $i > $i > $i ).
thf(func_def_69,type,
e_in: $i > ( $i > $o ) > $i > $i ).
thf(func_def_70,type,
out: $i > ( $i > $o ) > $i > $i ).
thf(func_def_71,type,
d_pair: $i > $i > $i > $i > $i ).
thf(func_def_72,type,
first: $i > $i > $i > $i ).
thf(func_def_73,type,
second: $i > $i > $i > $i ).
thf(func_def_74,type,
prop1: $o > $i > $i > $i > $i > $o ).
thf(func_def_75,type,
ite: $o > $i > $i > $i > $i ).
thf(func_def_76,type,
wissel_wa: $i > $i > $i > $i > $i ).
thf(func_def_77,type,
wissel_wb: $i > $i > $i > $i > $i ).
thf(func_def_78,type,
wissel: $i > $i > $i > $i ).
thf(func_def_79,type,
changef: $i > $i > $i > $i > $i > $i ).
thf(func_def_80,type,
r_ec: $o > $o > $o ).
thf(func_def_81,type,
esti: $i > $i > $i > $o ).
thf(func_def_82,type,
empty: $i > $i > $o ).
thf(func_def_83,type,
nonempty: $i > $i > $o ).
thf(func_def_84,type,
incl: $i > $i > $i > $o ).
thf(func_def_85,type,
st_disj: $i > $i > $i > $o ).
thf(func_def_86,type,
nissetprop: $i > $i > $i > $i > $o ).
thf(func_def_87,type,
unmore: $i > $i > $i > $i ).
thf(func_def_88,type,
ecelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
ecp: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_90,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_91,type,
ect: $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
ectset: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_93,type,
ectelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_94,type,
ecect: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_95,type,
fixfu: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_96,type,
d_10_prop1: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i > $o ).
thf(func_def_97,type,
prop2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $o ).
thf(func_def_98,type,
indeq: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_99,type,
fixfu2: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_100,type,
d_11_i: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_101,type,
indeq2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i ).
thf(func_def_103,type,
n_is: $i > $i > $o ).
thf(func_def_104,type,
nis: $i > $i > $o ).
thf(func_def_105,type,
n_in: $i > $i > $o ).
thf(func_def_106,type,
n_some: ( $i > $o ) > $o ).
thf(func_def_107,type,
n_all: ( $i > $o ) > $o ).
thf(func_def_108,type,
n_one: ( $i > $o ) > $o ).
thf(func_def_110,type,
cond1: $i > $o ).
thf(func_def_111,type,
cond2: $i > $o ).
thf(func_def_112,type,
i1_s: ( $i > $o ) > $i ).
thf(func_def_113,type,
d_22_prop1: $i > $o ).
thf(func_def_114,type,
d_23_prop1: $i > $o ).
thf(func_def_115,type,
d_24_prop1: $i > $o ).
thf(func_def_116,type,
d_24_prop2: $i > $i > $o ).
thf(func_def_117,type,
prop3: $i > $i > $i > $o ).
thf(func_def_118,type,
prop4: $i > $o ).
thf(func_def_119,type,
d_24_g: $i > $i ).
thf(func_def_120,type,
plus: $i > $i ).
thf(func_def_121,type,
n_pl: $i > $i > $i ).
thf(func_def_122,type,
d_25_prop1: $i > $i > $i > $o ).
thf(func_def_123,type,
d_26_prop1: $i > $i > $o ).
thf(func_def_124,type,
d_27_prop1: $i > $i > $o ).
thf(func_def_125,type,
d_28_prop1: $i > $i > $i > $o ).
thf(func_def_126,type,
diffprop: $i > $i > $i > $o ).
thf(func_def_127,type,
d_29_ii: $i > $i > $o ).
thf(func_def_128,type,
iii: $i > $i > $o ).
thf(func_def_129,type,
d_29_prop1: $i > $i > $o ).
thf(func_def_130,type,
moreis: $i > $i > $o ).
thf(func_def_131,type,
lessis: $i > $i > $o ).
thf(func_def_132,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_139,type,
vIMP: $o > $o > $o ).
thf(func_def_140,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_141,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_142,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_144,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_145,type,
vAND: $o > $o > $o ).
thf(func_def_146,type,
vOR: $o > $o > $o ).
thf(func_def_147,type,
vNOT: $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 > $i ).
thf(func_def_153,type,
sK3: ( $i > $i ) > $i > ( $i > $i ) > $i ).
thf(func_def_154,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_155,type,
sK5: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_156,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK7: $i > $i > $i > $i ).
thf(func_def_161,type,
sK11: $i > $i > $o ).
thf(func_def_162,type,
sK12: $i > $i > $o ).
thf(func_def_163,type,
sK13: $i > $i > $o ).
thf(func_def_164,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_166,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_167,type,
sK17: $i > $i > $o ).
thf(func_def_168,type,
sK18: ( $i > $o ) > $i ).
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 > $i > $i > $i ).
thf(func_def_172,type,
sK22: $i > $i > $o ).
thf(func_def_173,type,
sK23: ( $i > $o ) > $i ).
thf(func_def_174,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK26: $i > $i ).
thf(func_def_177,type,
sK27: $i > $i ).
thf(func_def_178,type,
sK28: $i > $i ).
thf(func_def_179,type,
sK29: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_180,type,
sK30: $i > $i ).
thf(func_def_181,type,
sK31: $i > $i ).
thf(func_def_182,type,
sK32: $i > $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(f1,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f74,axiom,
( ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) )
= imp ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(f75,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(f81,axiom,
( ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) )
= l_or ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
thf(f91,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) )
= e_is ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(f157,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(f160,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(f203,axiom,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_diffprop) ).
thf(f205,axiom,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) )
= d_29_ii ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(f206,axiom,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii) ).
thf(f217,axiom,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lessis) ).
thf(f222,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_not @ ( d_29_ii @ X0 @ X1 ) )
=> ( lessis @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10e) ).
thf(f224,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10g) ).
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/sandbox/benchmark/theBenchmark.p',satz15) ).
thf(f229,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] :
( ( lessis @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(f230,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] :
( ( lessis @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f229]) ).
thf(f241,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f255,plain,
( ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) )
= imp ),
inference(rectify,[],[f74]) ).
thf(f256,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(fool_elimination,[],[f255]) ).
thf(f287,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f289,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,[],[f230]) ).
thf(f290,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,[],[f289]) ).
thf(f295,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f217]) ).
thf(f317,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( ( d_not @ ( d_29_ii @ X1 @ X3 ) )
=> ( lessis @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f222]) ).
thf(f318,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( d_not @ ( d_29_ii @ Y0 @ Y1 ) )
=> ( lessis @ Y0 @ Y1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f317]) ).
thf(f341,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f366,plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(rectify,[],[f75]) ).
thf(f367,plain,
( d_not
= ( ^ [Y0: $o] : ( imp @ Y0 @ $false ) ) ),
inference(fool_elimination,[],[f366]) ).
thf(f387,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f390,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f391,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f390]) ).
thf(f452,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f496,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( ( d_29_ii @ X1 @ X3 )
=> ( d_not @ ( lessis @ X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f224]) ).
thf(f497,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( d_not @ ( lessis @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f496]) ).
thf(f555,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f581,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(f582,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,[],[f581]) ).
thf(f596,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(flattening,[],[f290]) ).
thf(f675,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f241]) ).
thf(f687,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f287]) ).
thf(f690,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f555]) ).
thf(f697,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f452]) ).
thf(f699,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(cnf_transformation,[],[f256]) ).
thf(f703,plain,
( d_not
= ( ^ [Y0: $o] : ( imp @ Y0 @ $false ) ) ),
inference(cnf_transformation,[],[f367]) ).
thf(f728,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( d_not @ ( lessis @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f497]) ).
thf(f735,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f387]) ).
thf(f740,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,[],[f582]) ).
thf(f745,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f341]) ).
thf(f765,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( d_not @ ( d_29_ii @ Y0 @ Y1 ) )
=> ( lessis @ Y0 @ Y1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f318]) ).
thf(f769,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f776,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f295]) ).
thf(f785,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,[],[f596]) ).
thf(f786,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f796,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f391]) ).
thf(f803,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f786,f697]) ).
thf(f804,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,[],[f690,f803]) ).
thf(f805,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,[],[f735,f769,f804]) ).
thf(f806,plain,
( d_not
= ( ^ [Y0: $o] :
( ^ [Y1: $o,Y2: $o] :
( Y1
=> Y2 )
@ Y0
@ $false ) ) ),
inference(definition_unfolding,[],[f703,f699]) ).
thf(f807,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,[],[f745,f699,f806]) ).
thf(f809,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,[],[f687,f769,f804]) ).
thf(f812,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,[],[f776,f807,f805,f803]) ).
thf(f824,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,[],[f796,f675]) ).
thf(f873,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( 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: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ Y2
@ $false )
@ ( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $o] :
( ^ [Y5: $o,Y6: $o] :
( Y5
=> Y6 )
@ ( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ Y5
@ $false )
@ Y4 ) )
@ ( ^ [Y4: $i,Y5: $i] :
( l_some @ nat
@ ( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ^ [Y9: $i,Y10: $i,Y11: $i] : ( Y10 = Y11 )
@ nat
@ Y6
@ ( n_pl @ Y7 @ Y8 ) )
@ Y5
@ Y4 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( Y5 = Y6 )
@ nat
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f728,f824,f824,f809,f806,f812]) ).
thf(f881,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i > $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 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f740,f824,f824,f824,f805,f805,f805]) ).
thf(f891,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: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ Y2
@ $false )
@ ( ^ [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: $o] :
( ^ [Y5: $o,Y6: $o] :
( Y5
=> Y6 )
@ ( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ Y5
@ $false )
@ Y4 ) )
@ ( ^ [Y4: $i,Y5: $i] :
( l_some @ nat
@ ( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ^ [Y9: $i,Y10: $i,Y11: $i] : ( Y10 = Y11 )
@ nat
@ Y6
@ ( n_pl @ Y7 @ Y8 ) )
@ Y5
@ Y4 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( Y5 = Y6 )
@ nat
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f765,f824,f824,f806,f809,f812]) ).
thf(f900,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i > $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 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f785,f824,f824,f824,f812,f805,f805]) ).
thf(f918,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f891]) ).
thf(f919,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f918]) ).
thf(f920,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f919]) ).
thf(f921,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f920]) ).
thf(f922,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) ) ) )
@ X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f921]) ).
thf(f923,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f922]) ).
thf(f924,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f923]) ).
thf(f925,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f924]) ).
thf(f927,plain,
! [X2: $i,X1: $i] :
( ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f925]) ).
thf(f928,plain,
! [X2: $i,X1: $i] :
( ( ( X1 = X2 )
= $true )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f927]) ).
thf(f929,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false ) )
| ( X1 = X2 )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(equality_proxy_clausification,[],[f928]) ).
thf(f931,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 = X2 )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f929]) ).
thf(f952,plain,
( ( !! @ $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 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f900]) ).
thf(f953,plain,
( ( ^ [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 ) ) ) ) ) ) ) ) ) )
@ sK8 )
= $false ),
inference(sigma_proxy_clausification,[],[f952]) ).
thf(f954,plain,
( ( ( in @ sK8 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ sK8 @ Y2 ) ) )
=> $false )
=> ( sK8 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ sK8 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f953]) ).
thf(f955,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ sK8 @ Y2 ) ) )
=> $false )
=> ( sK8 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ sK8 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f954]) ).
thf(f956,plain,
( ( in @ sK8 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f954]) ).
thf(f957,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ sK8 @ Y2 ) ) )
=> $false )
=> ( sK8 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ sK8 @ Y2 ) ) ) ) ) ) ) )
@ sK9 )
= $false ),
inference(sigma_proxy_clausification,[],[f955]) ).
thf(f958,plain,
( ( ( in @ sK9 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK9
= ( n_pl @ sK8 @ Y1 ) ) )
=> $false )
=> ( sK8 = sK9 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ sK9 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ sK8 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f957]) ).
thf(f959,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK9
= ( n_pl @ sK8 @ Y1 ) ) )
=> $false )
=> ( sK8 = sK9 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ sK9 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ sK8 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f958]) ).
thf(f960,plain,
( $true
= ( in @ sK9 @ nat ) ),
inference(imp_proxy_clausification,[],[f958]) ).
thf(f961,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK9
= ( n_pl @ sK8 @ Y1 ) ) )
=> $false )
=> ( sK8 = sK9 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ sK9 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ sK8 @ Y1 ) ) ) ) ) )
@ sK10 )
= $false ),
inference(sigma_proxy_clausification,[],[f959]) ).
thf(f962,plain,
( ( ( in @ sK10 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) )
=> $false )
=> ( sK8 = sK9 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK9 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK8 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f961]) ).
thf(f963,plain,
( ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) )
=> $false )
=> ( sK8 = sK9 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK9 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK8 @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f962]) ).
thf(f964,plain,
( ( in @ sK10 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f962]) ).
thf(f965,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK9 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK8 @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f963]) ).
thf(f966,plain,
( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) )
=> $false )
=> ( sK8 = sK9 ) )
= $true ),
inference(imp_proxy_clausification,[],[f963]) ).
thf(f967,plain,
( ( ( sK8 = sK9 )
= $true )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) )
=> $false ) ) ),
inference(imp_proxy_clausification,[],[f966]) ).
thf(f968,plain,
( ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) )
=> $false ) )
| ( sK8 = sK9 ) ),
inference(equality_proxy_clausification,[],[f967]) ).
thf(f970,plain,
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) )
| ( sK8 = sK9 ) ),
inference(imp_proxy_clausification,[],[f968]) ).
thf(f971,plain,
( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK8 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f965]) ).
thf(f972,plain,
( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ sK9 @ Y0 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f965]) ).
thf(f1223,plain,
( ( !! @ $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 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f881]) ).
thf(f1224,plain,
! [X1: $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 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1223]) ).
thf(f1225,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,[],[f1224]) ).
thf(f1226,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( !! @ $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 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1225]) ).
thf(f1227,plain,
! [X2: $i,X1: $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 ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1226]) ).
thf(f1228,plain,
! [X2: $i,X1: $i] :
( ( ( ( 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 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1227]) ).
thf(f1229,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( !! @ $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 ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1228]) ).
thf(f1230,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ 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 @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1229]) ).
thf(f1231,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $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 ) ),
inference(beta-eta_normalization,[],[f1230]) ).
thf(f1232,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( 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 @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1231]) ).
thf(f1233,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ nat )
= $false )
| ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1232]) ).
thf(f1234,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1233]) ).
thf(f1441,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> $false ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f873]) ).
thf(f1442,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> $false ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1441]) ).
thf(f1443,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> $false ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1442]) ).
thf(f1444,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> $false ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1443]) ).
thf(f1445,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> $false ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1444]) ).
thf(f1446,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ( in @ X2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> $false ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1445]) ).
thf(f1447,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> $false ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1446]) ).
thf(f1448,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> $false )
= $true ) ),
inference(imp_proxy_clausification,[],[f1447]) ).
thf(f1449,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1448]) ).
thf(f1450,plain,
! [X2: $i,X1: $i] :
( ( ( X1 = X2 )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $true = $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1449]) ).
thf(f1455,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $true = $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1450]) ).
thf(f1456,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 != X2 ) ),
inference(trivial_inequality_removal,[],[f1455]) ).
thf(f1639,definition,
( spl25_1
<=> ( sK8 = sK9 ) ),
introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).
thf(f1641,plain,
( ( sK8 = sK9 )
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f1639]) ).
thf(f1643,definition,
( spl25_2
<=> ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
thf(f1645,plain,
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) )
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f1643]) ).
thf(f1646,plain,
( spl25_1
| spl25_2 ),
inference(avatar_split_clause,[],[f970,f1643,f1639]) ).
thf(f1723,plain,
! [X0: $i] :
( ( ( in @ sK10 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ sK8 @ nat )
= $false )
| ( $true = $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK8 @ Y0 ) ) )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ X0 @ Y0 ) ) )
= $false ) ),
inference(constrained_superposition,[],[f971,f1234]) ).
thf(f1727,plain,
! [X0: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK8 @ Y0 ) ) )
= $false )
| ( ( in @ sK8 @ nat )
= $false )
| ( ( in @ sK10 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ X0 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1723]) ).
thf(f1731,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK8 @ Y0 ) ) )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ X0 @ Y0 ) ) )
= $false )
| ( ( in @ sK10 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1727,f956]) ).
thf(f1732,plain,
! [X0: $i] :
( ( ( in @ sK10 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ X0 @ Y0 ) ) )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK8 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1731]) ).
thf(f1735,plain,
! [X0: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ X0 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( $true = $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK8 @ Y0 ) ) )
= $false ) ),
inference(forward_demodulation,[],[f1732,f964]) ).
thf(f1736,plain,
! [X0: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK10
= ( n_pl @ X0 @ Y0 ) ) )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK8 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1735]) ).
thf(f1751,plain,
( ( $true = $false )
| ( ( in @ sK9 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) ) ),
inference(constrained_superposition,[],[f972,f1736]) ).
thf(f1755,plain,
( ( ( in @ sK9 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f1751]) ).
thf(f1792,plain,
( ( ( in @ sK9 @ nat )
= $false )
| ( sK10 != sK9 )
| ( ( in @ sK10 @ nat )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f972,f1456]) ).
thf(f1793,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X2 != X3 )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( $true = $false )
| ( ( in @ X4 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X4
= ( n_pl @ X1 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X3 ) )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ X4 @ Y0 ) ) )
= $false ) ),
inference(constrained_superposition,[],[f1234,f1456]) ).
thf(f1795,plain,
( ( sK10 != sK9 )
| ( ( in @ sK9 @ nat )
= $false )
| ( ( in @ sK10 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1792]) ).
thf(f1796,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X4
= ( n_pl @ X1 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X4 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ X4 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X3 ) )
| ( X2 != X3 ) ),
inference(trivial_inequality_removal,[],[f1793]) ).
thf(f1801,plain,
( ( sK10 != sK8 )
| ( ( in @ sK10 @ nat )
= $false )
| ( ( in @ sK9 @ nat )
= $false )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f1795,f1641]) ).
thf(f1803,plain,
( ( $true = $false )
| ( ( in @ sK9 @ nat )
= $false )
| ( sK10 != sK8 )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f1801,f964]) ).
thf(f1804,plain,
( ( ( in @ sK9 @ nat )
= $false )
| ( sK10 != sK8 )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f1803]) ).
thf(f1806,plain,
( ( ( in @ sK8 @ nat )
= $false )
| ( sK10 != sK8 )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f1804,f1641]) ).
thf(f1809,plain,
( ( $true = $false )
| ( sK10 != sK8 )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f1806,f956]) ).
thf(f1810,plain,
( ( sK10 != sK8 )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f1809]) ).
thf(f2057,plain,
( ( ( in @ sK8 @ nat )
= $false )
| ( sK10 = sK8 )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true )
| ( $true = $false )
| ( ( in @ sK10 @ nat )
= $false ) ),
inference(constrained_superposition,[],[f971,f931]) ).
thf(f2091,plain,
( ( ( in @ sK8 @ nat )
= $false )
| ( sK10 = sK8 )
| ( ( in @ sK10 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f2057]) ).
thf(f2124,plain,
( ( ( in @ sK8 @ nat )
= $false )
| ( ( in @ sK10 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true )
| ~ spl25_1 ),
inference(forward_subsumption_resolution,[],[f2091,f1810]) ).
thf(f2143,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true )
| ( ( in @ sK10 @ nat )
= $false )
| ( $true = $false )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2124,f956]) ).
thf(f2144,plain,
( ( ( in @ sK10 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2143]) ).
thf(f2158,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true )
| ( $true = $false )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2144,f964]) ).
thf(f2159,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $true )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2158]) ).
thf(f2411,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ sK9 @ nat )
= $false )
| ( X0 != X1 )
| ( $true = $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( ( in @ sK10 @ nat )
= $false ) ),
inference(constrained_superposition,[],[f972,f1796]) ).
thf(f2424,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( X0 != X1 )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ sK10 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ sK9 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f2411]) ).
thf(f2436,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( ( in @ sK9 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( X0 != X1 )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f2424,f964]) ).
thf(f2437,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( X0 != X1 )
| ( ( in @ sK9 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f2436]) ).
thf(f2448,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( X0 != X1 )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ sK8 @ nat )
= $false ) )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2437,f1641]) ).
thf(f2452,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( X0 != X1 )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2448,f956]) ).
thf(f2453,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK9 ) )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X0 != X1 )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2452]) ).
thf(f2460,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( sK9 != X1 )
| ( ( in @ sK9 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) )
| ( ( in @ X1 @ nat )
= $false ) )
| ~ spl25_1 ),
inference(equality_resolution,[],[f2453]) ).
thf(f2463,plain,
( ! [X0: $i,X1: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ sK9 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( sK8 != X1 )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) ) )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2460,f1641]) ).
thf(f2464,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( sK8 != X1 )
| ( ( in @ sK8 @ nat )
= $false ) )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2463,f1641]) ).
thf(f2465,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true = $false )
| ( sK8 != X1 )
| ( ( in @ X0 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) ) )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2464,f956]) ).
thf(f2466,plain,
( ! [X0: $i,X1: $i] :
( ( sK8 != X1 )
| ( ( in @ X1 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) ) )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2465]) ).
thf(f2467,plain,
( ! [X0: $i] :
( ( ( in @ sK8 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK8 ) ) )
| ~ spl25_1 ),
inference(equality_resolution,[],[f2466]) ).
thf(f2468,plain,
( ! [X0: $i] :
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( $true = $false )
| ( ( in @ X0 @ nat )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK8 ) ) )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2467,f956]) ).
thf(f2469,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK8 ) )
| ( ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ X0 @ nat )
= $false ) )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2468]) ).
thf(f2471,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK8
= ( n_pl @ sK10 @ Y0 ) ) )
= $false )
| ( ( in @ sK8 @ nat )
= $false )
| ~ spl25_1 ),
inference(equality_resolution,[],[f2469]) ).
thf(f2473,plain,
( ( ( in @ sK8 @ nat )
= $false )
| ( $true = $false )
| ~ spl25_1 ),
inference(forward_demodulation,[],[f2471,f2159]) ).
thf(f2474,plain,
( ( ( in @ sK8 @ nat )
= $false )
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2473]) ).
thf(f2476,plain,
( ( $true = $false )
| ~ spl25_1 ),
inference(constrained_superposition,[],[f2474,f956]) ).
thf(f2483,plain,
( $false
| ~ spl25_1 ),
inference(trivial_inequality_removal,[],[f2476]) ).
thf(f2484,plain,
~ spl25_1,
inference(avatar_contradiction_clause,[],[f2483]) ).
thf(f2488,definition,
( spl25_21
<=> ( ( in @ sK9 @ nat )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl25_21])],[avatar_definition]) ).
thf(f2490,plain,
( ( ( in @ sK9 @ nat )
= $false )
| ~ spl25_21 ),
inference(avatar_component_clause,[],[f2488]) ).
thf(f2492,definition,
( spl25_22
<=> ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_22])],[avatar_definition]) ).
thf(f2494,plain,
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK9
= ( n_pl @ sK8 @ Y0 ) ) ) )
| ~ spl25_22 ),
inference(avatar_component_clause,[],[f2492]) ).
thf(f2515,plain,
( spl25_22
| spl25_21 ),
inference(avatar_split_clause,[],[f1755,f2488,f2492]) ).
thf(f2562,plain,
( ( $true = $false )
| ~ spl25_21 ),
inference(constrained_superposition,[],[f960,f2490]) ).
thf(f2568,plain,
( $false
| ~ spl25_21 ),
inference(trivial_inequality_removal,[],[f2562]) ).
thf(f2569,plain,
~ spl25_21,
inference(avatar_contradiction_clause,[],[f2568]) ).
thf(f2828,plain,
( ( $true = $false )
| ~ spl25_2
| ~ spl25_22 ),
inference(constrained_superposition,[],[f2494,f1645]) ).
thf(f2839,plain,
( $false
| ~ spl25_2
| ~ spl25_22 ),
inference(trivial_inequality_removal,[],[f2828]) ).
thf(f2840,plain,
( ~ spl25_2
| ~ spl25_22 ),
inference(avatar_contradiction_clause,[],[f2839]) ).
cnf(s1,plain,
( spl25_1
| spl25_2 ),
inference(sat_conversion,[],[f1646]) ).
cnf(s28,plain,
~ spl25_1,
inference(sat_conversion,[],[f2484]) ).
cnf(s33,plain,
( spl25_21
| spl25_22 ),
inference(sat_conversion,[],[f2515]) ).
cnf(s45,plain,
~ spl25_21,
inference(sat_conversion,[],[f2569]) ).
cnf(s53,plain,
( ~ spl25_2
| ~ spl25_22 ),
inference(sat_conversion,[],[f2840]) ).
cnf(s61,plain,
spl25_22,
inference(rat,[],[s33,s45]) ).
cnf(s62,plain,
~ spl25_2,
inference(rat,[],[s53,s61]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s1,s62,s28]) ).
thf(f2862,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM663^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:36:33 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.65/0.41 % (3457527)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.65/0.41 % (3457539)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1359904003:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.65/0.41 % (3457545)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.65/0.41 % (3457545)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.65/0.41 % (3457540)lrs+10_16_si=on:nwc=1.5:random_seed=1094066878:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.65/0.41 % (3457543)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3179667547:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.65/0.41 % (3457542)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=1690550256:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.65/0.41 % (3457544)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1292772252:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.65/0.41 % (3457545)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=3720703642:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.65/0.41 % (3457541)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2307568296:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.65/0.41 % (3457540)Instruction limit reached!
% 0.65/0.41 % (3457540)------------------------------
% 0.65/0.41 % (3457540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.41 % (3457540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.41 % (3457540)CaDiCaL version: 2.1.3
% 0.65/0.41 % (3457540)Termination reason: Instruction limit
% 0.65/0.41 % (3457540)Termination phase: shuffling
% 0.65/0.41 % (3457540)Time elapsed: 0.011 s
% 0.65/0.41 % (3457540)Peak memory usage: 10 MB
% 0.65/0.41 % (3457540)Instructions burned: 20 (million)
% 0.65/0.41 % (3457541)Instruction limit reached!
% 0.65/0.41 % (3457541)------------------------------
% 0.65/0.41 % (3457541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.41 % (3457543)Instruction limit reached!
% 0.65/0.41 % (3457543)------------------------------
% 0.65/0.41 % (3457543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.41 % (3457541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.41 % (3457541)CaDiCaL version: 2.1.3
% 0.65/0.41 % (3457541)Termination reason: Instruction limit
% 0.65/0.41 % (3457541)Termination phase: shuffling
% 0.65/0.41 % (3457543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.41 % (3457541)Time elapsed: 0.004 s
% 0.65/0.41 % (3457541)Peak memory usage: 10 MB
% 0.65/0.41 % (3457541)Instructions burned: 3 (million)
% 0.65/0.41 % (3457543)CaDiCaL version: 2.1.3
% 0.65/0.41 % (3457543)Termination reason: Instruction limit
% 0.65/0.41 % (3457543)Termination phase: Property scanning
% 0.65/0.41 % (3457543)Time elapsed: 0.013 s
% 0.65/0.41 % (3457543)Peak memory usage: 10 MB
% 0.65/0.41 % (3457543)Instructions burned: 24 (million)
% 0.65/0.41 % (3457539)Instruction limit reached!
% 0.65/0.41 % (3457539)------------------------------
% 0.65/0.41 % (3457539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.41 % (3457539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.41 % (3457539)CaDiCaL version: 2.1.3
% 0.65/0.41 % (3457539)Termination reason: Instruction limit
% 0.65/0.41 % (3457539)Termination phase: Function definition elimination
% 0.65/0.41 % (3457539)Time elapsed: 0.022 s
% 0.65/0.41 % (3457539)Peak memory usage: 11 MB
% 0.65/0.41 % (3457539)Instructions burned: 90 (million)
% 0.65/0.41 % (3457564)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.41 % (3457564)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2987529027:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.65/0.44 % (3457564)Instruction limit reached!
% 0.65/0.44 % (3457564)------------------------------
% 0.65/0.44 % (3457564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (3457564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (3457564)CaDiCaL version: 2.1.3
% 0.65/0.44 % (3457564)Termination reason: Instruction limit
% 0.65/0.44 % (3457564)Termination phase: shuffling
% 0.65/0.44 % (3457564)Time elapsed: 0.003 s
% 0.65/0.44 % (3457564)Peak memory usage: 10 MB
% 0.65/0.44 % (3457564)Instructions burned: 11 (million)
% 0.65/0.44 % (3457574)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.65/0.44 % (3457574)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (3457574)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2844015643:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.65/0.44 % (3457561)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=138494531:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.44 % (3457561)Instruction limit reached!
% 0.65/0.44 % (3457561)------------------------------
% 0.65/0.44 % (3457561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (3457561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (3457561)CaDiCaL version: 2.1.3
% 0.65/0.44 % (3457561)Termination reason: Instruction limit
% 0.65/0.44 % (3457561)Termination phase: shuffling
% 0.65/0.44 % (3457561)Time elapsed: 0.002 s
% 0.65/0.44 % (3457561)Peak memory usage: 10 MB
% 0.65/0.44 % (3457561)Instructions burned: 3 (million)
% 0.65/0.44 % (3457572)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2697953031:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.65/0.44 % (3457574)Instruction limit reached!
% 0.65/0.44 % (3457574)------------------------------
% 0.65/0.44 % (3457574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (3457574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (3457574)CaDiCaL version: 2.1.3
% 0.65/0.44 % (3457574)Termination reason: Instruction limit
% 0.65/0.44 % (3457574)Termination phase: Property scanning
% 0.65/0.44 % (3457574)Time elapsed: 0.009 s
% 0.65/0.44 % (3457574)Peak memory usage: 10 MB
% 0.65/0.44 % (3457574)Instructions burned: 33 (million)
% 0.65/0.44 % (3457563)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=543070121:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.65/0.44 % (3457572)Instruction limit reached!
% 0.65/0.44 % (3457572)------------------------------
% 0.65/0.44 % (3457572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (3457572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (3457572)CaDiCaL version: 2.1.3
% 0.65/0.44 % (3457572)Termination reason: Instruction limit
% 0.65/0.44 % (3457572)Termination phase: shuffling
% 0.65/0.44 % (3457572)Time elapsed: 0.007 s
% 0.65/0.44 % (3457572)Peak memory usage: 10 MB
% 0.65/0.44 % (3457572)Instructions burned: 14 (million)
% 0.65/0.44 % (3457563)Instruction limit reached!
% 0.65/0.44 % (3457563)------------------------------
% 0.65/0.44 % (3457563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (3457563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (3457563)CaDiCaL version: 2.1.3
% 0.65/0.44 % (3457563)Termination reason: Instruction limit
% 0.65/0.44 % (3457563)Termination phase: shuffling
% 0.65/0.44 % (3457563)Time elapsed: 0.003 s
% 0.65/0.44 % (3457563)Peak memory usage: 10 MB
% 0.65/0.44 % (3457563)Instructions burned: 6 (million)
% 0.65/0.44 % (3457581)lrs+10_1_si=on:cs=on:random_seed=1565967245:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.65/0.44 % (3457544)Instruction limit reached!
% 0.65/0.44 % (3457544)------------------------------
% 0.65/0.44 % (3457544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (3457544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.47 % (3457544)CaDiCaL version: 2.1.3
% 0.65/0.47 % (3457544)Termination reason: Instruction limit
% 0.65/0.47 % (3457544)Termination phase: Function definition elimination
% 0.65/0.47 % (3457544)Time elapsed: 0.063 s
% 0.65/0.47 % (3457544)Peak memory usage: 11 MB
% 0.65/0.47 % (3457544)Instructions burned: 76 (million)
% 0.65/0.47 % (3457581)Instruction limit reached!
% 0.65/0.47 % (3457581)------------------------------
% 0.65/0.47 % (3457581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.47 % (3457581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.47 % (3457581)CaDiCaL version: 2.1.3
% 0.65/0.47 % (3457581)Termination reason: Instruction limit
% 0.65/0.47 % (3457581)Termination phase: shuffling
% 0.65/0.47 % (3457581)Time elapsed: 0.003 s
% 0.65/0.47 % (3457581)Peak memory usage: 10 MB
% 0.65/0.47 % (3457581)Instructions burned: 12 (million)
% 0.65/0.47 % (3457579)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=2490317050:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.65/0.47 % (3457583)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.65/0.47 % (3457545)Instruction limit reached!
% 0.65/0.47 % (3457545)------------------------------
% 0.65/0.47 % (3457545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.47 % (3457545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.47 % (3457545)CaDiCaL version: 2.1.3
% 0.65/0.47 % (3457545)Termination reason: Instruction limit
% 0.65/0.47 % (3457545)Termination phase: Function definition elimination
% 0.65/0.47 % (3457545)Time elapsed: 0.072 s
% 0.65/0.47 % (3457545)Peak memory usage: 11 MB
% 0.65/0.47 % (3457545)Instructions burned: 158 (million)
% 0.65/0.47 % (3457583)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=2232400237:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.47 % (3457587)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1293926720:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.65/0.47 % (3457584)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=634960733:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.65/0.47 % (3457583)Instruction limit reached!
% 0.65/0.47 % (3457583)------------------------------
% 0.65/0.47 % (3457583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.47 % (3457583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.47 % (3457583)CaDiCaL version: 2.1.3
% 0.65/0.47 % (3457583)Termination reason: Instruction limit
% 0.65/0.47 % (3457583)Termination phase: shuffling
% 0.65/0.47 % (3457583)Time elapsed: 0.002 s
% 0.65/0.47 % (3457583)Peak memory usage: 10 MB
% 0.65/0.47 % (3457583)Instructions burned: 4 (million)
% 0.65/0.47 % (3457586)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=324260580:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.65/0.47 % (3457587)Instruction limit reached!
% 0.65/0.47 % (3457587)------------------------------
% 0.65/0.47 % (3457587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.47 % (3457587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.47 % (3457587)CaDiCaL version: 2.1.3
% 0.65/0.47 % (3457587)Termination reason: Instruction limit
% 0.65/0.47 % (3457587)Termination phase: Property scanning
% 0.65/0.47 % (3457587)Time elapsed: 0.006 s
% 0.65/0.47 % (3457587)Peak memory usage: 10 MB
% 0.65/0.47 % (3457587)Instructions burned: 27 (million)
% 0.65/0.47 % (3457589)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1723310689:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.47 % (3457595)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1494847695:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.47 % (3457584)Instruction limit reached!
% 0.65/0.47 % (3457584)------------------------------
% 0.65/0.47 % (3457584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457584)CaDiCaL version: 2.1.3
% 1.43/0.51 % (3457584)Termination reason: Instruction limit
% 1.43/0.51 % (3457584)Termination phase: Saturation
% 1.43/0.51 % (3457584)Time elapsed: 0.018 s
% 1.43/0.51 % (3457584)Peak memory usage: 12 MB
% 1.43/0.51 % (3457584)Instructions burned: 39 (million)
% 1.43/0.51 % (3457593)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1115009809:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.43/0.51 % (3457595)Instruction limit reached!
% 1.43/0.51 % (3457595)------------------------------
% 1.43/0.51 % (3457595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457595)CaDiCaL version: 2.1.3
% 1.43/0.51 % (3457595)Termination reason: Instruction limit
% 1.43/0.51 % (3457595)Termination phase: shuffling
% 1.43/0.51 % (3457595)Time elapsed: 0.004 s
% 1.43/0.51 % (3457595)Peak memory usage: 10 MB
% 1.43/0.51 % (3457595)Instructions burned: 19 (million)
% 1.43/0.51 % (3457589)Instruction limit reached!
% 1.43/0.51 % (3457589)------------------------------
% 1.43/0.51 % (3457589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457589)CaDiCaL version: 2.1.3
% 1.43/0.51 % (3457589)Termination reason: Instruction limit
% 1.43/0.51 % (3457589)Termination phase: shuffling
% 1.43/0.51 % (3457589)Time elapsed: 0.006 s
% 1.43/0.51 % (3457589)Peak memory usage: 10 MB
% 1.43/0.51 % (3457589)Instructions burned: 14 (million)
% 1.43/0.51 % (3457579)Instruction limit reached!
% 1.43/0.51 % (3457579)------------------------------
% 1.43/0.51 % (3457579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457579)CaDiCaL version: 2.1.3
% 1.43/0.51 % (3457579)Termination reason: Instruction limit
% 1.43/0.51 % (3457579)Termination phase: Function definition elimination
% 1.43/0.51 % (3457579)Time elapsed: 0.036 s
% 1.43/0.51 % (3457579)Peak memory usage: 11 MB
% 1.43/0.51 % (3457579)Instructions burned: 87 (million)
% 1.43/0.51 % (3457586)Refutation not found, incomplete strategy
% 1.43/0.51 % (3457586)------------------------------
% 1.43/0.51 % (3457586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457586)CaDiCaL version: 2.1.3
% 1.43/0.51 % (3457586)Termination reason: Refutation not found, incomplete strategy
% 1.43/0.51 % (3457586)Time elapsed: 0.022 s
% 1.43/0.51 % (3457586)Peak memory usage: 13 MB
% 1.43/0.51 % (3457586)Instructions burned: 48 (million)
% 1.43/0.51 % (3457586)------------------------------
% 1.43/0.51 % (3457586)------------------------------
% 1.43/0.51 % (3457600)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2196317284:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.43/0.51 % (3457600)Instruction limit reached!
% 1.43/0.51 % (3457600)------------------------------
% 1.43/0.51 % (3457600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457600)CaDiCaL version: 2.1.3
% 1.43/0.51 % (3457600)Termination reason: Instruction limit
% 1.43/0.51 % (3457600)Termination phase: Property scanning
% 1.43/0.51 % (3457600)Time elapsed: 0.006 s
% 1.43/0.51 % (3457600)Peak memory usage: 10 MB
% 1.43/0.51 % (3457600)Instructions burned: 27 (million)
% 1.43/0.51 % (3457599)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1388393701: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)
% 1.43/0.51 % (3457601)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3280926551:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.43/0.51 % (3457599)Instruction limit reached!
% 1.43/0.51 % (3457599)------------------------------
% 1.43/0.51 % (3457599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.51 % (3457599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.51 % (3457599)CaDiCaL version: 2.1.3
% 2.12/0.60 % (3457599)Termination reason: Instruction limit
% 2.12/0.60 % (3457599)Termination phase: shuffling
% 2.12/0.60 % (3457599)Time elapsed: 0.003 s
% 2.12/0.60 % (3457599)Peak memory usage: 10 MB
% 2.12/0.60 % (3457599)Instructions burned: 5 (million)
% 2.12/0.60 % (3457603)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
% 2.12/0.60 % (3457603)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.12/0.60 % (3457605)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.12/0.60 % (3457602)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1901404780:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.12/0.60 % (3457605)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=1399884705:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.12/0.60 % (3457603)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=944669245:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.12/0.60 % (3457605)Instruction limit reached!
% 2.12/0.60 % (3457605)------------------------------
% 2.12/0.60 % (3457605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.60 % (3457605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.60 % (3457605)CaDiCaL version: 2.1.3
% 2.12/0.60 % (3457605)Termination reason: Instruction limit
% 2.12/0.60 % (3457605)Termination phase: shuffling
% 2.12/0.60 % (3457605)Time elapsed: 0.002 s
% 2.12/0.60 % (3457605)Peak memory usage: 10 MB
% 2.12/0.60 % (3457605)Instructions burned: 8 (million)
% 2.12/0.60 % (3457601)Instruction limit reached!
% 2.12/0.60 % (3457601)------------------------------
% 2.12/0.60 % (3457601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.60 % (3457601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.60 % (3457601)CaDiCaL version: 2.1.3
% 2.12/0.60 % (3457601)Termination reason: Instruction limit
% 2.12/0.60 % (3457601)Termination phase: Property scanning
% 2.12/0.60 % (3457601)Time elapsed: 0.012 s
% 2.12/0.60 % (3457601)Peak memory usage: 10 MB
% 2.12/0.60 % (3457601)Instructions burned: 26 (million)
% 2.12/0.60 % (3457603)Instruction limit reached!
% 2.12/0.60 % (3457603)------------------------------
% 2.12/0.60 % (3457603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.60 % (3457603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.60 % (3457603)CaDiCaL version: 2.1.3
% 2.12/0.60 % (3457603)Termination reason: Instruction limit
% 2.12/0.60 % (3457603)Termination phase: shuffling
% 2.12/0.60 % (3457603)Time elapsed: 0.008 s
% 2.12/0.60 % (3457603)Peak memory usage: 10 MB
% 2.12/0.60 % (3457603)Instructions burned: 19 (million)
% 2.12/0.60 % (3457608)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=2171847029:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.12/0.60 % (3457612)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3153546412:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.12/0.60 % (3457612)Instruction limit reached!
% 2.12/0.60 % (3457612)------------------------------
% 2.12/0.60 % (3457612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.60 % (3457612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.60 % (3457612)CaDiCaL version: 2.1.3
% 2.12/0.60 % (3457612)Termination reason: Instruction limit
% 2.12/0.60 % (3457612)Termination phase: shuffling
% 2.12/0.60 % (3457612)Time elapsed: 0.002 s
% 2.12/0.60 % (3457612)Peak memory usage: 10 MB
% 2.12/0.60 % (3457612)Instructions burned: 11 (million)
% 2.12/0.60 % (3457613)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2188741631:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.12/0.60 % (3457602)Instruction limit reached!
% 2.12/0.60 % (3457602)------------------------------
% 2.12/0.60 % (3457602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.66 % (3457602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.66 % (3457602)CaDiCaL version: 2.1.3
% 2.33/0.66 % (3457602)Termination reason: Instruction limit
% 2.33/0.66 % (3457602)Termination phase: Property scanning
% 2.33/0.66 % (3457602)Time elapsed: 0.026 s
% 2.33/0.66 % (3457602)Peak memory usage: 11 MB
% 2.33/0.66 % (3457602)Instructions burned: 62 (million)
% 2.33/0.66 % (3457614)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2995445795:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.33/0.66 % (3457617)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=724660329:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.33/0.66 % (3457608)Instruction limit reached!
% 2.33/0.66 % (3457608)------------------------------
% 2.33/0.66 % (3457608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.66 % (3457608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.66 % (3457608)CaDiCaL version: 2.1.3
% 2.33/0.66 % (3457608)Termination reason: Instruction limit
% 2.33/0.66 % (3457608)Termination phase: Property scanning
% 2.33/0.66 % (3457608)Time elapsed: 0.016 s
% 2.33/0.66 % (3457608)Peak memory usage: 10 MB
% 2.33/0.66 % (3457608)Instructions burned: 36 (million)
% 2.33/0.66 % (3457613)Instruction limit reached!
% 2.33/0.66 % (3457613)------------------------------
% 2.33/0.66 % (3457613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.66 % (3457613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.66 % (3457613)CaDiCaL version: 2.1.3
% 2.33/0.66 % (3457613)Termination reason: Instruction limit
% 2.33/0.66 % (3457613)Termination phase: Property scanning
% 2.33/0.66 % (3457613)Time elapsed: 0.011 s
% 2.33/0.66 % (3457613)Peak memory usage: 10 MB
% 2.33/0.66 % (3457613)Instructions burned: 23 (million)
% 2.33/0.66 % (3457614)Instruction limit reached!
% 2.33/0.66 % (3457614)------------------------------
% 2.33/0.66 % (3457614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.66 % (3457614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.66 % (3457614)CaDiCaL version: 2.1.3
% 2.33/0.66 % (3457614)Termination reason: Instruction limit
% 2.33/0.66 % (3457614)Termination phase: Property scanning
% 2.33/0.66 % (3457614)Time elapsed: 0.010 s
% 2.33/0.66 % (3457614)Peak memory usage: 10 MB
% 2.33/0.66 % (3457614)Instructions burned: 21 (million)
% 2.33/0.66 % (3457619)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1978600185:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.33/0.66 % (3457622)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3789796058:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.33/0.66 % (3457624)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.33/0.66 % (3457623)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3177931720:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.33/0.66 % (3457624)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2115927402:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.33/0.66 % (3457624)Instruction limit reached!
% 2.33/0.66 % (3457624)------------------------------
% 2.33/0.66 % (3457624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.66 % (3457624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.66 % (3457624)CaDiCaL version: 2.1.3
% 2.33/0.66 % (3457624)Termination reason: Instruction limit
% 2.33/0.66 % (3457624)Termination phase: shuffling
% 2.33/0.66 % (3457624)Time elapsed: 0.004 s
% 2.33/0.66 % (3457624)Peak memory usage: 10 MB
% 2.33/0.66 % (3457624)Instructions burned: 8 (million)
% 2.33/0.66 % (3457623)Instruction limit reached!
% 2.33/0.66 % (3457623)------------------------------
% 2.33/0.66 % (3457623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.66 % (3457623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.66 % (3457623)CaDiCaL version: 2.1.3
% 2.33/0.66 % (3457623)Termination reason: Instruction limit
% 2.33/0.66 % (3457623)Termination phase: Property scanning
% 2.62/0.72 % (3457623)Time elapsed: 0.019 s
% 2.62/0.72 % (3457623)Peak memory usage: 11 MB
% 2.62/0.72 % (3457623)Instructions burned: 43 (million)
% 2.62/0.72 % (3457629)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=727025247:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.62/0.72 % (3457630)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=3281114721: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)
% 2.62/0.72 % (3457619)Instruction limit reached!
% 2.62/0.72 % (3457619)------------------------------
% 2.62/0.72 % (3457619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.72 % (3457619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.72 % (3457619)CaDiCaL version: 2.1.3
% 2.62/0.72 % (3457619)Termination reason: Instruction limit
% 2.62/0.72 % (3457619)Termination phase: Function definition elimination
% 2.62/0.72 % (3457619)Time elapsed: 0.061 s
% 2.62/0.72 % (3457619)Peak memory usage: 11 MB
% 2.62/0.72 % (3457619)Instructions burned: 144 (million)
% 2.62/0.72 % (3457638)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.62/0.72 % (3457630)Refutation not found, incomplete strategy
% 2.62/0.72 % (3457630)------------------------------
% 2.62/0.72 % (3457630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.72 % (3457630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.72 % (3457630)CaDiCaL version: 2.1.3
% 2.62/0.72 % (3457638)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=863863713:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.62/0.72 % (3457630)Termination reason: Refutation not found, incomplete strategy
% 2.62/0.72 % (3457630)Time elapsed: 0.033 s
% 2.62/0.72 % (3457630)Peak memory usage: 13 MB
% 2.62/0.72 % (3457630)Instructions burned: 74 (million)
% 2.62/0.72 % (3457630)------------------------------
% 2.62/0.72 % (3457630)------------------------------
% 2.62/0.72 % (3457638)Instruction limit reached!
% 2.62/0.72 % (3457638)------------------------------
% 2.62/0.72 % (3457638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.72 % (3457638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.72 % (3457638)CaDiCaL version: 2.1.3
% 2.62/0.72 % (3457638)Termination reason: Instruction limit
% 2.62/0.72 % (3457638)Termination phase: shuffling
% 2.62/0.72 % (3457638)Time elapsed: 0.004 s
% 2.62/0.72 % (3457638)Peak memory usage: 10 MB
% 2.62/0.72 % (3457638)Instructions burned: 7 (million)
% 2.62/0.72 % (3457593)Instruction limit reached!
% 2.62/0.72 % (3457593)------------------------------
% 2.62/0.72 % (3457593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.72 % (3457593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.72 % (3457593)CaDiCaL version: 2.1.3
% 2.62/0.72 % (3457593)Termination reason: Instruction limit
% 2.62/0.72 % (3457593)Termination phase: Saturation
% 2.62/0.72 % (3457593)Time elapsed: 0.164 s
% 2.62/0.72 % (3457593)Peak memory usage: 14 MB
% 2.62/0.72 % (3457593)Instructions burned: 327 (million)
% 2.62/0.72 % (3457622)Instruction limit reached!
% 2.62/0.72 % (3457622)------------------------------
% 2.62/0.72 % (3457622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.72 % (3457622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.72 % (3457622)CaDiCaL version: 2.1.3
% 2.62/0.72 % (3457622)Termination reason: Instruction limit
% 2.62/0.72 % (3457622)Termination phase: Saturation
% 2.62/0.72 % (3457622)Time elapsed: 0.096 s
% 2.62/0.72 % (3457622)Peak memory usage: 14 MB
% 2.62/0.72 % (3457622)Instructions burned: 194 (million)
% 2.62/0.72 % (3457645)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2535800164:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.62/0.72 % (3457647)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3256900912:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.62/0.72 % (3457650)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=3311425139:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.62/0.78 % (3457645)Instruction limit reached!
% 2.62/0.78 % (3457645)------------------------------
% 2.62/0.78 % (3457645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.78 % (3457645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.78 % (3457645)CaDiCaL version: 2.1.3
% 2.62/0.78 % (3457645)Termination reason: Instruction limit
% 2.62/0.78 % (3457645)Termination phase: Property scanning
% 2.62/0.78 % (3457645)Time elapsed: 0.010 s
% 2.62/0.78 % (3457645)Peak memory usage: 10 MB
% 2.62/0.78 % (3457645)Instructions burned: 23 (million)
% 2.62/0.78 % (3457647)Instruction limit reached!
% 2.62/0.78 % (3457647)------------------------------
% 2.62/0.78 % (3457647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.78 % (3457647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.78 % (3457647)CaDiCaL version: 2.1.3
% 2.62/0.78 % (3457647)Termination reason: Instruction limit
% 2.62/0.78 % (3457647)Termination phase: Property scanning
% 2.62/0.78 % (3457647)Time elapsed: 0.011 s
% 2.62/0.78 % (3457647)Peak memory usage: 10 MB
% 2.62/0.78 % (3457647)Instructions burned: 23 (million)
% 2.62/0.78 % (3457653)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=1931989065:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.62/0.78 % (3457629)Instruction limit reached!
% 2.62/0.78 % (3457629)------------------------------
% 2.62/0.78 % (3457629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.78 % (3457629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.78 % (3457629)CaDiCaL version: 2.1.3
% 2.62/0.78 % (3457629)Termination reason: Instruction limit
% 2.62/0.78 % (3457629)Termination phase: Saturation
% 2.62/0.78 % (3457629)Time elapsed: 0.090 s
% 2.62/0.78 % (3457629)Peak memory usage: 14 MB
% 2.62/0.78 % (3457629)Instructions burned: 182 (million)
% 2.62/0.78 % (3457660)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=2322628184:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.62/0.78 % (3457662)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1833427560:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.62/0.78 % (3457666)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3440970606:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.62/0.78 % (3457660)Instruction limit reached!
% 2.62/0.78 % (3457660)------------------------------
% 2.62/0.78 % (3457660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.78 % (3457660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.78 % (3457660)CaDiCaL version: 2.1.3
% 2.62/0.78 % (3457660)Termination reason: Instruction limit
% 2.62/0.78 % (3457660)Termination phase: SInE selection
% 2.62/0.78 % (3457660)Time elapsed: 0.020 s
% 2.62/0.78 % (3457660)Peak memory usage: 10 MB
% 2.62/0.78 % (3457660)Instructions burned: 46 (million)
% 2.62/0.78 % (3457666)Instruction limit reached!
% 2.62/0.78 % (3457666)------------------------------
% 2.62/0.78 % (3457666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.78 % (3457666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.78 % (3457666)CaDiCaL version: 2.1.3
% 2.62/0.78 % (3457666)Termination reason: Instruction limit
% 2.62/0.78 % (3457666)Termination phase: Property scanning
% 2.62/0.78 % (3457666)Time elapsed: 0.010 s
% 2.62/0.78 % (3457666)Peak memory usage: 10 MB
% 2.62/0.78 % (3457666)Instructions burned: 23 (million)
% 2.62/0.78 % (3457675)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.62/0.78 % (3457675)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=4268563136:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.62/0.78 % (3457662)Refutation not found, incomplete strategy
% 2.62/0.78 % (3457662)------------------------------
% 3.35/0.85 % (3457662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.85 % (3457662)CaDiCaL version: 2.1.3
% 3.35/0.85 % (3457662)Termination reason: Refutation not found, incomplete strategy
% 3.35/0.85 % (3457662)Time elapsed: 0.038 s
% 3.35/0.85 % (3457662)Peak memory usage: 13 MB
% 3.35/0.85 % (3457662)Instructions burned: 82 (million)
% 3.35/0.85 % (3457676)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3970556649:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.35/0.85 % (3457662)------------------------------
% 3.35/0.85 % (3457662)------------------------------
% 3.35/0.85 % (3457676)Instruction limit reached!
% 3.35/0.85 % (3457676)------------------------------
% 3.35/0.85 % (3457676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.85 % (3457676)CaDiCaL version: 2.1.3
% 3.35/0.85 % (3457676)Termination reason: Instruction limit
% 3.35/0.85 % (3457676)Termination phase: shuffling
% 3.35/0.85 % (3457676)Time elapsed: 0.006 s
% 3.35/0.85 % (3457676)Peak memory usage: 10 MB
% 3.35/0.85 % (3457676)Instructions burned: 14 (million)
% 3.35/0.85 % (3457686)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=2826530300:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.35/0.85 % (3457688)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2149680851:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.35/0.85 % (3457542)Instruction limit reached!
% 3.35/0.85 % (3457542)------------------------------
% 3.35/0.85 % (3457542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.85 % (3457542)CaDiCaL version: 2.1.3
% 3.35/0.85 % (3457542)Termination reason: Instruction limit
% 3.35/0.85 % (3457542)Termination phase: Saturation
% 3.35/0.85 % (3457542)Time elapsed: 0.370 s
% 3.35/0.85 % (3457542)Peak memory usage: 17 MB
% 3.35/0.85 % (3457542)Instructions burned: 635 (million)
% 3.35/0.85 % (3457696)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1440984353:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.35/0.85 % (3457688)Instruction limit reached!
% 3.35/0.85 % (3457688)------------------------------
% 3.35/0.85 % (3457688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.85 % (3457688)CaDiCaL version: 2.1.3
% 3.35/0.85 % (3457688)Termination reason: Instruction limit
% 3.35/0.85 % (3457688)Termination phase: Function definition elimination
% 3.35/0.85 % (3457688)Time elapsed: 0.023 s
% 3.35/0.85 % (3457688)Peak memory usage: 11 MB
% 3.35/0.85 % (3457688)Instructions burned: 53 (million)
% 3.35/0.85 % (3457686)Instruction limit reached!
% 3.35/0.85 % (3457686)------------------------------
% 3.35/0.85 % (3457686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.85 % (3457686)CaDiCaL version: 2.1.3
% 3.35/0.85 % (3457686)Termination reason: Instruction limit
% 3.35/0.85 % (3457686)Termination phase: Function definition elimination
% 3.35/0.85 % (3457686)Time elapsed: 0.030 s
% 3.35/0.85 % (3457686)Peak memory usage: 11 MB
% 3.35/0.85 % (3457686)Instructions burned: 68 (million)
% 3.35/0.85 % (3457617)Instruction limit reached!
% 3.35/0.85 % (3457617)------------------------------
% 3.35/0.85 % (3457617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.85 % (3457617)CaDiCaL version: 2.1.3
% 3.35/0.85 % (3457617)Termination reason: Instruction limit
% 3.35/0.85 % (3457617)Termination phase: Property scanning
% 3.35/0.85 % (3457617)Time elapsed: 0.250 s
% 3.35/0.85 % (3457617)Peak memory usage: 11 MB
% 3.35/0.85 % (3457617)Instructions burned: 1242 (million)
% 3.35/0.85 % (3457696)Instruction limit reached!
% 3.35/0.85 % (3457696)------------------------------
% 3.35/0.85 % (3457696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.85 % (3457696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457696)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457696)Termination reason: Instruction limit
% 3.62/0.99 % (3457696)Termination phase: Property scanning
% 3.62/0.99 % (3457696)Time elapsed: 0.014 s
% 3.62/0.99 % (3457696)Peak memory usage: 10 MB
% 3.62/0.99 % (3457696)Instructions burned: 32 (million)
% 3.62/0.99 % (3457650)Instruction limit reached!
% 3.62/0.99 % (3457650)------------------------------
% 3.62/0.99 % (3457650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457650)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457650)Termination reason: Instruction limit
% 3.62/0.99 % (3457650)Termination phase: Property scanning
% 3.62/0.99 % (3457650)Time elapsed: 0.123 s
% 3.62/0.99 % (3457650)Peak memory usage: 11 MB
% 3.62/0.99 % (3457650)Instructions burned: 316 (million)
% 3.62/0.99 % (3457701)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4209546826:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.62/0.99 % (3457703)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=876669632:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.62/0.99 % (3457706)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3550982461:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.62/0.99 % (3457675)Instruction limit reached!
% 3.62/0.99 % (3457675)------------------------------
% 3.62/0.99 % (3457675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457675)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457675)Termination reason: Instruction limit
% 3.62/0.99 % (3457675)Termination phase: Function definition elimination
% 3.62/0.99 % (3457675)Time elapsed: 0.080 s
% 3.62/0.99 % (3457675)Peak memory usage: 11 MB
% 3.62/0.99 % (3457675)Instructions burned: 201 (million)
% 3.62/0.99 % (3457708)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.62/0.99 % (3457708)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1079534473:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.62/0.99 % (3457709)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3861334159:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.62/0.99 % (3457703)Instruction limit reached!
% 3.62/0.99 % (3457703)------------------------------
% 3.62/0.99 % (3457703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457703)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457703)Termination reason: Instruction limit
% 3.62/0.99 % (3457703)Termination phase: Property scanning
% 3.62/0.99 % (3457703)Time elapsed: 0.015 s
% 3.62/0.99 % (3457703)Peak memory usage: 10 MB
% 3.62/0.99 % (3457703)Instructions burned: 35 (million)
% 3.62/0.99 % (3457706)Instruction limit reached!
% 3.62/0.99 % (3457706)------------------------------
% 3.62/0.99 % (3457706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457706)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457706)Termination reason: Instruction limit
% 3.62/0.99 % (3457706)Termination phase: Function definition elimination
% 3.62/0.99 % (3457706)Time elapsed: 0.016 s
% 3.62/0.99 % (3457706)Peak memory usage: 11 MB
% 3.62/0.99 % (3457706)Instructions burned: 71 (million)
% 3.62/0.99 % (3457717)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1124878551:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.62/0.99 % (3457724)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=420374414:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 3.62/0.99 % (3457721)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=326961467:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.62/0.99 % (3457709)Refutation not found, incomplete strategy
% 3.62/0.99 % (3457709)------------------------------
% 3.62/0.99 % (3457709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457709)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457709)Termination reason: Refutation not found, incomplete strategy
% 3.62/0.99 % (3457709)Time elapsed: 0.038 s
% 3.62/0.99 % (3457709)Peak memory usage: 13 MB
% 3.62/0.99 % (3457709)Instructions burned: 80 (million)
% 3.62/0.99 % (3457709)------------------------------
% 3.62/0.99 % (3457709)------------------------------
% 3.62/0.99 % (3457721)Refutation not found, incomplete strategy
% 3.62/0.99 % (3457721)------------------------------
% 3.62/0.99 % (3457721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457721)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457721)Termination reason: Refutation not found, incomplete strategy
% 3.62/0.99 % (3457721)Time elapsed: 0.020 s
% 3.62/0.99 % (3457721)Peak memory usage: 13 MB
% 3.62/0.99 % (3457721)Instructions burned: 42 (million)
% 3.62/0.99 % (3457721)------------------------------
% 3.62/0.99 % (3457721)------------------------------
% 3.62/0.99 % (3457717)Instruction limit reached!
% 3.62/0.99 % (3457717)------------------------------
% 3.62/0.99 % (3457717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457717)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457717)Termination reason: Instruction limit
% 3.62/0.99 % (3457717)Termination phase: Function definition elimination
% 3.62/0.99 % (3457717)Time elapsed: 0.040 s
% 3.62/0.99 % (3457717)Peak memory usage: 11 MB
% 3.62/0.99 % (3457717)Instructions burned: 97 (million)
% 3.62/0.99 % (3457701)Instruction limit reached!
% 3.62/0.99 % (3457701)------------------------------
% 3.62/0.99 % (3457701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457701)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457701)Termination reason: Instruction limit
% 3.62/0.99 % (3457701)Termination phase: Saturation
% 3.62/0.99 % (3457701)Time elapsed: 0.071 s
% 3.62/0.99 % (3457701)Peak memory usage: 13 MB
% 3.62/0.99 % (3457701)Instructions burned: 137 (million)
% 3.62/0.99 % (3457736)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=299221270:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 3.62/0.99 % (3457737)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=460298822:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 3.62/0.99 % (3457708)Instruction limit reached!
% 3.62/0.99 % (3457708)------------------------------
% 3.62/0.99 % (3457708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457708)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457708)Termination reason: Instruction limit
% 3.62/0.99 % (3457708)Termination phase: Function definition elimination
% 3.62/0.99 % (3457708)Time elapsed: 0.073 s
% 3.62/0.99 % (3457708)Peak memory usage: 11 MB
% 3.62/0.99 % (3457708)Instructions burned: 182 (million)
% 3.62/0.99 % (3457743)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3486740989:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 3.62/0.99 % (3457744)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2846009419:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 3.62/0.99 % (3457748)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=843949850:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 3.62/0.99 % (3457743)Instruction limit reached!
% 3.62/0.99 % (3457743)------------------------------
% 3.62/0.99 % (3457743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457743)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457743)Termination reason: Instruction limit
% 3.62/0.99 % (3457743)Termination phase: Property scanning
% 3.62/0.99 % (3457743)Time elapsed: 0.019 s
% 3.62/0.99 % (3457743)Peak memory usage: 11 MB
% 3.62/0.99 % (3457743)Instructions burned: 44 (million)
% 3.62/0.99 % (3457758)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1211791959:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 3.62/0.99 % (3457737)Instruction limit reached!
% 3.62/0.99 % (3457737)------------------------------
% 3.62/0.99 % (3457737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457737)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457737)Termination reason: Instruction limit
% 3.62/0.99 % (3457737)Termination phase: Saturation
% 3.62/0.99 % (3457737)Time elapsed: 0.061 s
% 3.62/0.99 % (3457737)Peak memory usage: 13 MB
% 3.62/0.99 % (3457737)Instructions burned: 131 (million)
% 3.62/0.99 % (3457763)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=3850121917:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2994 on theBenchmark for (2994ds/65Mi)
% 3.62/0.99 % (3457758)Instruction limit reached!
% 3.62/0.99 % (3457758)------------------------------
% 3.62/0.99 % (3457758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457758)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457758)Termination reason: Instruction limit
% 3.62/0.99 % (3457758)Termination phase: Function definition elimination
% 3.62/0.99 % (3457758)Time elapsed: 0.040 s
% 3.62/0.99 % (3457758)Peak memory usage: 11 MB
% 3.62/0.99 % (3457758)Instructions burned: 97 (million)
% 3.62/0.99 % (3457763)Instruction limit reached!
% 3.62/0.99 % (3457763)------------------------------
% 3.62/0.99 % (3457763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457763)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457763)Termination reason: Instruction limit
% 3.62/0.99 % (3457763)Termination phase: Function definition elimination
% 3.62/0.99 % (3457763)Time elapsed: 0.028 s
% 3.62/0.99 % (3457763)Peak memory usage: 11 MB
% 3.62/0.99 % (3457763)Instructions burned: 65 (million)
% 3.62/0.99 % (3457773)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=934411563:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 3.62/0.99 % (3457778)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=1178188589:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 3.62/0.99 % (3457773)Instruction limit reached!
% 3.62/0.99 % (3457773)------------------------------
% 3.62/0.99 % (3457773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457773)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457773)Termination reason: Instruction limit
% 3.62/0.99 % (3457773)Termination phase: Function definition elimination
% 3.62/0.99 % (3457773)Time elapsed: 0.044 s
% 3.62/0.99 % (3457773)Peak memory usage: 11 MB
% 3.62/0.99 % (3457773)Instructions burned: 106 (million)
% 3.62/0.99 % (3457787)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=676132373:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 3.62/0.99 % (3457736) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3457527-3457736"...
% 3.62/0.99 % (3457724)Instruction limit reached!
% 3.62/0.99 % (3457724)------------------------------
% 3.62/0.99 % (3457724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457724)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457724)Termination reason: Instruction limit
% 3.62/0.99 % (3457724)Termination phase: Saturation
% 3.62/0.99 % (3457724)Time elapsed: 0.229 s
% 3.62/0.99 % (3457724)Peak memory usage: 16 MB
% 3.62/0.99 % (3457724)Instructions burned: 876 (million)
% 3.62/0.99 % (3457736)...printing done.
% 3.62/0.99 % (3457736)Refutation found. Thanks to Tanya!
% 3.62/0.99 % SZS status Theorem for theBenchmark
% 3.62/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/0.99 % (3457736)------------------------------
% 3.62/0.99 % (3457736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.99 % (3457736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.99 % (3457736)CaDiCaL version: 2.1.3
% 3.62/0.99 % (3457736)Termination reason: Refutation
% 3.62/0.99 % (3457736)Time elapsed: 0.188 s
% 3.62/0.99 % (3457736)Peak memory usage: 15 MB
% 3.62/0.99 % (3457736)Instructions burned: 404 (million)
% 3.62/0.99 % (3457527)Success in time 0.717 s
% 3.62/0.99 % Vampire exiting
%------------------------------------------------------------------------------