%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM681^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:18:31 AM UTC 2026
% Result : Theorem 0.66s 0.44s
% Output : Refutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 8
% Syntax : Number of formulae : 108 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 1163 ( 294 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 1476 ( 25 ~; 110 |; 0 &;1160 @)
% ( 0 <=>; 126 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 170 ( 166 usr; 8 con; 0-7 aty)
% ( 55 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 372 ( 283 ^; 89 !; 0 ?; 372 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
is_of: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
eps: ( $i > $o ) > $i ).
thf(func_def_4,type,
in: $i > $i > $o ).
thf(func_def_5,type,
d_Subq: $i > $i > $o ).
thf(func_def_7,type,
union: $i > $i ).
thf(func_def_8,type,
power: $i > $i ).
thf(func_def_9,type,
repl: $i > ( $i > $i ) > $i ).
thf(func_def_10,type,
d_Union_closed: $i > $o ).
thf(func_def_11,type,
d_Power_closed: $i > $o ).
thf(func_def_12,type,
d_Repl_closed: $i > $o ).
thf(func_def_13,type,
d_ZF_closed: $i > $o ).
thf(func_def_14,type,
univof: $i > $i ).
thf(func_def_15,type,
if: $o > $i > $i > $i ).
thf(func_def_16,type,
nIn: $i > $i > $o ).
thf(func_def_17,type,
d_UPair: $i > $i > $i ).
thf(func_def_18,type,
d_Sing: $i > $i ).
thf(func_def_19,type,
binunion: $i > $i > $i ).
thf(func_def_20,type,
famunion: $i > ( $i > $i ) > $i ).
thf(func_def_21,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
d_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_23,type,
setminus: $i > $i > $i ).
thf(func_def_24,type,
d_In_rec_G: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_25,type,
d_In_rec: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_26,type,
ordsucc: $i > $i ).
thf(func_def_27,type,
nat_p: $i > $o ).
thf(func_def_29,type,
d_Inj1: $i > $i ).
thf(func_def_30,type,
d_Inj0: $i > $i ).
thf(func_def_31,type,
d_Unj: $i > $i ).
thf(func_def_32,type,
pair: $i > $i > $i ).
thf(func_def_33,type,
proj0: $i > $i ).
thf(func_def_34,type,
proj1: $i > $i ).
thf(func_def_35,type,
d_Sigma: $i > ( $i > $i ) > $i ).
thf(func_def_36,type,
setprod: $i > $i > $i ).
thf(func_def_37,type,
ap: $i > $i > $i ).
thf(func_def_38,type,
pair_p: $i > $o ).
thf(func_def_39,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_40,type,
imp: $o > $o > $o ).
thf(func_def_41,type,
d_not: $o > $o ).
thf(func_def_42,type,
wel: $o > $o ).
thf(func_def_43,type,
obvious: $o ).
thf(func_def_44,type,
l_ec: $o > $o > $o ).
thf(func_def_45,type,
d_and: $o > $o > $o ).
thf(func_def_46,type,
l_or: $o > $o > $o ).
thf(func_def_47,type,
orec: $o > $o > $o ).
thf(func_def_48,type,
l_iff: $o > $o > $o ).
thf(func_def_49,type,
all: $i > ( $i > $o ) > $o ).
thf(func_def_50,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(func_def_51,type,
l_some: $i > ( $i > $o ) > $o ).
thf(func_def_52,type,
or3: $o > $o > $o > $o ).
thf(func_def_53,type,
and3: $o > $o > $o > $o ).
thf(func_def_54,type,
ec3: $o > $o > $o > $o ).
thf(func_def_55,type,
orec3: $o > $o > $o > $o ).
thf(func_def_56,type,
e_is: $i > $i > $i > $o ).
thf(func_def_57,type,
amone: $i > ( $i > $o ) > $o ).
thf(func_def_58,type,
one: $i > ( $i > $o ) > $o ).
thf(func_def_59,type,
ind: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
injective: $i > $i > $i > $o ).
thf(func_def_61,type,
image: $i > $i > $i > $i > $o ).
thf(func_def_62,type,
tofs: $i > $i > $i > $i > $i ).
thf(func_def_63,type,
soft: $i > $i > $i > $i > $i ).
thf(func_def_64,type,
inverse: $i > $i > $i > $i ).
thf(func_def_65,type,
surjective: $i > $i > $i > $o ).
thf(func_def_66,type,
bijective: $i > $i > $i > $o ).
thf(func_def_67,type,
invf: $i > $i > $i > $i ).
thf(func_def_68,type,
inj_h: $i > $i > $i > $i > $i > $i ).
thf(func_def_69,type,
e_in: $i > ( $i > $o ) > $i > $i ).
thf(func_def_70,type,
out: $i > ( $i > $o ) > $i > $i ).
thf(func_def_71,type,
d_pair: $i > $i > $i > $i > $i ).
thf(func_def_72,type,
first: $i > $i > $i > $i ).
thf(func_def_73,type,
second: $i > $i > $i > $i ).
thf(func_def_74,type,
prop1: $o > $i > $i > $i > $i > $o ).
thf(func_def_75,type,
ite: $o > $i > $i > $i > $i ).
thf(func_def_76,type,
wissel_wa: $i > $i > $i > $i > $i ).
thf(func_def_77,type,
wissel_wb: $i > $i > $i > $i > $i ).
thf(func_def_78,type,
wissel: $i > $i > $i > $i ).
thf(func_def_79,type,
changef: $i > $i > $i > $i > $i > $i ).
thf(func_def_80,type,
r_ec: $o > $o > $o ).
thf(func_def_81,type,
esti: $i > $i > $i > $o ).
thf(func_def_82,type,
empty: $i > $i > $o ).
thf(func_def_83,type,
nonempty: $i > $i > $o ).
thf(func_def_84,type,
incl: $i > $i > $i > $o ).
thf(func_def_85,type,
st_disj: $i > $i > $i > $o ).
thf(func_def_86,type,
nissetprop: $i > $i > $i > $i > $o ).
thf(func_def_87,type,
unmore: $i > $i > $i > $i ).
thf(func_def_88,type,
ecelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
ecp: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_90,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_91,type,
ect: $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
ectset: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_93,type,
ectelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_94,type,
ecect: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_95,type,
fixfu: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_96,type,
d_10_prop1: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i > $o ).
thf(func_def_97,type,
prop2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $o ).
thf(func_def_98,type,
indeq: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_99,type,
fixfu2: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_100,type,
d_11_i: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_101,type,
indeq2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i ).
thf(func_def_103,type,
n_is: $i > $i > $o ).
thf(func_def_104,type,
nis: $i > $i > $o ).
thf(func_def_105,type,
n_in: $i > $i > $o ).
thf(func_def_106,type,
n_some: ( $i > $o ) > $o ).
thf(func_def_107,type,
n_all: ( $i > $o ) > $o ).
thf(func_def_108,type,
n_one: ( $i > $o ) > $o ).
thf(func_def_110,type,
cond1: $i > $o ).
thf(func_def_111,type,
cond2: $i > $o ).
thf(func_def_112,type,
i1_s: ( $i > $o ) > $i ).
thf(func_def_113,type,
d_22_prop1: $i > $o ).
thf(func_def_114,type,
d_23_prop1: $i > $o ).
thf(func_def_115,type,
d_24_prop1: $i > $o ).
thf(func_def_116,type,
d_24_prop2: $i > $i > $o ).
thf(func_def_117,type,
prop3: $i > $i > $i > $o ).
thf(func_def_118,type,
prop4: $i > $o ).
thf(func_def_119,type,
d_24_g: $i > $i ).
thf(func_def_120,type,
plus: $i > $i ).
thf(func_def_121,type,
n_pl: $i > $i > $i ).
thf(func_def_122,type,
d_25_prop1: $i > $i > $i > $o ).
thf(func_def_123,type,
d_26_prop1: $i > $i > $o ).
thf(func_def_124,type,
d_27_prop1: $i > $i > $o ).
thf(func_def_125,type,
d_28_prop1: $i > $i > $i > $o ).
thf(func_def_126,type,
diffprop: $i > $i > $i > $o ).
thf(func_def_127,type,
d_29_ii: $i > $i > $o ).
thf(func_def_128,type,
iii: $i > $i > $o ).
thf(func_def_129,type,
d_29_prop1: $i > $i > $o ).
thf(func_def_130,type,
moreis: $i > $i > $o ).
thf(func_def_131,type,
lessis: $i > $i > $o ).
thf(func_def_132,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_136,type,
vIMP: $o > $o > $o ).
thf(func_def_139,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_140,type,
vAND: $o > $o > $o ).
thf(func_def_141,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_142,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_144,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_145,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_146,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_147,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_148,type,
vNOT: $o > $o ).
thf(func_def_149,type,
vOR: $o > $o > $o ).
thf(func_def_150,type,
sK0: $i > $i > $i > $i ).
thf(func_def_151,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK2: $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_153,type,
sK3: $i > $i ).
thf(func_def_154,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_155,type,
sK5: $i > $i > $i > $i ).
thf(func_def_156,type,
sK6: $i > $i > $o ).
thf(func_def_157,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_158,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK10: $i > $i > $o ).
thf(func_def_161,type,
sK11: $i > $i > $o ).
thf(func_def_162,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK13: $i > $i > $o ).
thf(func_def_164,type,
sK14: $i > $i > $o ).
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 > $o ) > $i ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) )
= is_of ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f91,axiom,
( e_is
= ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(f157,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(f197,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(f202,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] :
( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) )
=> ( n_is @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz8a) ).
thf(f242,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] :
( ( n_is @ X0 @ X1 )
=> ( n_is @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19e) ).
thf(f253,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] :
( ( n_is @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) )
=> ( n_is @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20b) ).
thf(f254,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] :
( ( n_is @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) )
=> ( n_is @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f253]) ).
thf(f366,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f404,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] :
( ( n_is @ X1 @ X3 )
=> ( n_is @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f242]) ).
thf(f405,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ Y0 @ Y1 )
=> ( n_is @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f404]) ).
thf(f430,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] :
( ( n_is @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X1 @ X5 ) )
=> ( n_is @ X3 @ X5 ) ) ) ) ),
inference(rectify,[],[f202]) ).
thf(f431,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ ( n_pl @ Y0 @ Y1 ) @ ( n_pl @ Y0 @ Y2 ) )
=> ( n_is @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f430]) ).
thf(f484,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] : ( n_is @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f197]) ).
thf(f485,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ Y0 @ Y1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f484]) ).
thf(f516,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f517,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f516]) ).
thf(f518,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] :
( ( n_is @ ( n_pl @ X1 @ X5 ) @ ( n_pl @ X3 @ X5 ) )
=> ( n_is @ X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f254]) ).
thf(f519,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) )
=> ( n_is @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f518]) ).
thf(f546,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f668,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) )
=> ( n_is @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(flattening,[],[f519]) ).
thf(f704,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) )
=> ( n_is @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f668]) ).
thf(f719,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ Y0 @ Y1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f485]) ).
thf(f720,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ ( n_pl @ Y0 @ Y1 ) @ ( n_pl @ Y0 @ Y2 ) )
=> ( n_is @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f431]) ).
thf(f753,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f366]) ).
thf(f768,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f517]) ).
thf(f780,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( n_is @ Y0 @ Y1 )
=> ( n_is @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f405]) ).
thf(f789,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f792,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f546]) ).
thf(f807,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,[],[f768,f792]) ).
thf(f809,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f789,f753]) ).
thf(f823,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: $i] : ( Y4 = Y5 )
@ nat
@ ( n_pl @ Y0 @ Y2 )
@ ( n_pl @ Y1 @ Y2 ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( Y4 = Y5 )
@ nat
@ Y0
@ Y1 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f704,f807,f807,f807,f809,f809]) ).
thf(f836,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( Y3 = Y4 )
@ nat
@ ( n_pl @ Y0 @ Y1 )
@ ( n_pl @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f719,f807,f807,f809]) ).
thf(f837,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: $i] : ( Y4 = Y5 )
@ nat
@ ( n_pl @ Y0 @ Y1 )
@ ( n_pl @ Y0 @ Y2 ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( Y4 = Y5 )
@ nat
@ Y1
@ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f720,f807,f807,f807,f809,f809]) ).
thf(f882,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: $i] : ( Y4 = Y5 )
@ nat
@ Y0
@ Y1 )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( Y4 = Y5 )
@ nat
@ ( n_pl @ Y2 @ Y0 )
@ ( n_pl @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f780,f807,f807,f807,f809,f809]) ).
thf(f1104,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( Y0 = Y1 )
=> ( ( n_pl @ Y2 @ Y0 )
= ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f882]) ).
thf(f1105,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( Y0 = Y1 )
=> ( ( n_pl @ Y2 @ Y0 )
= ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1104]) ).
thf(f1106,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( X1 = Y0 )
=> ( ( n_pl @ Y1 @ X1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1105]) ).
thf(f1107,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( X1 = Y0 )
=> ( ( n_pl @ Y1 @ X1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1106]) ).
thf(f1108,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( X1 = Y0 )
=> ( ( n_pl @ Y1 @ X1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) ) )
@ X2 )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1107]) ).
thf(f1109,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( X1 = X2 )
=> ( ( n_pl @ Y0 @ X1 )
= ( n_pl @ Y0 @ X2 ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1108]) ).
thf(f1110,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( X1 = X2 )
=> ( ( n_pl @ Y0 @ X1 )
= ( n_pl @ Y0 @ X2 ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1109]) ).
thf(f1111,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( X1 = X2 )
=> ( ( n_pl @ Y0 @ X1 )
= ( n_pl @ Y0 @ X2 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1110]) ).
thf(f1112,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X3 @ nat )
=> ( ( X1 = X2 )
=> ( ( n_pl @ X3 @ X1 )
= ( n_pl @ X3 @ X2 ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1111]) ).
thf(f1113,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ( X1 = X2 )
=> ( ( n_pl @ X3 @ X1 )
= ( n_pl @ X3 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1112]) ).
thf(f1114,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ nat )
= $false )
| ( $false
= ( X1 = X2 ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ( n_pl @ X3 @ X1 )
= ( n_pl @ X3 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1113]) ).
thf(f1115,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( X1 != X2 )
| ( ( ( n_pl @ X3 @ X1 )
= ( n_pl @ X3 @ X2 ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f1114]) ).
thf(f1116,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( n_pl @ X3 @ X1 )
= ( n_pl @ X3 @ X2 ) )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1115]) ).
thf(f1142,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y0 @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f837]) ).
thf(f1143,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y0 @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1142]) ).
thf(f1144,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ X1 @ Y1 ) )
=> ( Y0 = Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1143]) ).
thf(f1145,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ X1 @ Y1 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1144]) ).
thf(f1146,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ X1 @ Y1 ) )
=> ( Y0 = Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1145]) ).
thf(f1147,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ Y0 ) )
=> ( X2 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1146]) ).
thf(f1148,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ Y0 ) )
=> ( X2 = Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1147]) ).
thf(f1149,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ Y0 ) )
=> ( X2 = Y0 ) ) )
@ X3 )
= $true )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1148]) ).
thf(f1150,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( ( in @ X3 @ nat )
=> ( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ X3 ) )
=> ( X2 = X3 ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1149]) ).
thf(f1151,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ nat )
= $false )
| ( $true
= ( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ X3 ) )
=> ( X2 = X3 ) ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1150]) ).
thf(f1152,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( X2 = X3 )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( $false
= ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f1151]) ).
thf(f1153,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X1 @ X3 ) ) )
| ( X2 = X3 )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(equality_proxy_clausification,[],[f1152]) ).
thf(f1154,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( n_pl @ X1 @ X2 )
!= ( n_pl @ X1 @ X3 ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( X2 = X3 )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(equality_proxy_clausification,[],[f1153]) ).
thf(f1426,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f836]) ).
thf(f1427,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1426]) ).
thf(f1428,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1427]) ).
thf(f1429,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ Y0 @ X1 ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1428]) ).
thf(f1430,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ Y0 @ X1 ) ) )
@ X2 )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1429]) ).
thf(f1431,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ nat )
=> ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X2 @ X1 ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1430]) ).
thf(f1432,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X2 @ X1 ) )
= $true )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1431]) ).
thf(f1433,plain,
! [X2: $i,X1: $i] :
( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X2 @ X1 ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(equality_proxy_clausification,[],[f1432]) ).
thf(f1584,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( n_pl @ Y0 @ Y2 )
= ( n_pl @ Y1 @ Y2 ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f823]) ).
thf(f1585,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( n_pl @ Y0 @ Y2 )
= ( n_pl @ Y1 @ Y2 ) )
=> ( Y0 = Y1 ) ) ) ) ) ) )
@ sK18 ) ),
inference(sigma_proxy_clausification,[],[f1584]) ).
thf(f1586,plain,
( ( ( in @ sK18 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( n_pl @ sK18 @ Y1 )
= ( n_pl @ Y0 @ Y1 ) )
=> ( sK18 = Y0 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1585]) ).
thf(f1587,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( n_pl @ sK18 @ Y1 )
= ( n_pl @ Y0 @ Y1 ) )
=> ( sK18 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1586]) ).
thf(f1588,plain,
( ( in @ sK18 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1586]) ).
thf(f1589,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( n_pl @ sK18 @ Y1 )
= ( n_pl @ Y0 @ Y1 ) )
=> ( sK18 = Y0 ) ) ) ) )
@ sK19 )
= $false ),
inference(sigma_proxy_clausification,[],[f1587]) ).
thf(f1590,plain,
( $false
= ( ( in @ sK19 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( n_pl @ sK18 @ Y0 )
= ( n_pl @ sK19 @ Y0 ) )
=> ( sK18 = sK19 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1589]) ).
thf(f1591,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( n_pl @ sK18 @ Y0 )
= ( n_pl @ sK19 @ Y0 ) )
=> ( sK18 = sK19 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1590]) ).
thf(f1592,plain,
( ( in @ sK19 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1590]) ).
thf(f1593,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( n_pl @ sK18 @ Y0 )
= ( n_pl @ sK19 @ Y0 ) )
=> ( sK18 = sK19 ) ) )
@ sK20 ) ),
inference(sigma_proxy_clausification,[],[f1591]) ).
thf(f1594,plain,
( $false
= ( ( in @ sK20 @ nat )
=> ( ( ( n_pl @ sK18 @ sK20 )
= ( n_pl @ sK19 @ sK20 ) )
=> ( sK18 = sK19 ) ) ) ),
inference(beta-eta_normalization,[],[f1593]) ).
thf(f1595,plain,
( $false
= ( ( ( n_pl @ sK18 @ sK20 )
= ( n_pl @ sK19 @ sK20 ) )
=> ( sK18 = sK19 ) ) ),
inference(imp_proxy_clausification,[],[f1594]) ).
thf(f1596,plain,
( ( in @ sK20 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1594]) ).
thf(f1597,plain,
( $false
= ( sK18 = sK19 ) ),
inference(imp_proxy_clausification,[],[f1595]) ).
thf(f1598,plain,
( ( ( n_pl @ sK18 @ sK20 )
= ( n_pl @ sK19 @ sK20 ) )
= $true ),
inference(imp_proxy_clausification,[],[f1595]) ).
thf(f1599,plain,
( ( n_pl @ sK19 @ sK20 )
= ( n_pl @ sK18 @ sK20 ) ),
inference(equality_proxy_clausification,[],[f1598]) ).
thf(f1600,plain,
sK18 != sK19,
inference(equality_proxy_clausification,[],[f1597]) ).
thf(f1616,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( X0 != X2 )
| ( ( in @ X0 @ nat )
= $false )
| ( ( n_pl @ X0 @ X1 )
= ( n_pl @ X1 @ X2 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(superposition,[],[f1116,f1433]) ).
thf(f1628,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( n_pl @ X0 @ X1 )
= ( n_pl @ X1 @ X2 ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false )
| ( X0 != X2 ) ),
inference(duplicate_literal_removal,[],[f1616]) ).
thf(f1668,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( n_pl @ X0 @ X1 )
!= ( n_pl @ X1 @ X2 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X0 = X2 )
| ( ( in @ X0 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(superposition,[],[f1154,f1433]) ).
thf(f1670,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( n_pl @ X0 @ X1 )
!= ( n_pl @ X1 @ X2 ) )
| ( ( in @ X1 @ nat )
= $false )
| ( X0 = X2 )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(duplicate_literal_removal,[],[f1668]) ).
thf(f1864,plain,
! [X0: $i] :
( ( sK20 != X0 )
| ( ( n_pl @ X0 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( in @ sK19 @ nat ) )
| ( $false
= ( in @ sK20 @ nat ) ) ),
inference(superposition,[],[f1628,f1599]) ).
thf(f1937,plain,
! [X0: $i] :
( ( $false
= ( in @ sK20 @ nat ) )
| ( $false = $true )
| ( ( n_pl @ X0 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) )
| ( sK20 != X0 )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1864,f1592]) ).
thf(f1938,plain,
! [X0: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( sK20 != X0 )
| ( ( n_pl @ X0 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) )
| ( $false
= ( in @ sK20 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1937]) ).
thf(f1945,plain,
! [X0: $i] :
( ( ( n_pl @ X0 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) )
| ( sK20 != X0 )
| ( $false = $true )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1938,f1596]) ).
thf(f1946,plain,
! [X0: $i] :
( ( sK20 != X0 )
| ( ( in @ X0 @ nat )
= $false )
| ( ( n_pl @ X0 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) ) ),
inference(trivial_inequality_removal,[],[f1945]) ).
thf(f1953,plain,
( ( $false
= ( in @ sK20 @ nat ) )
| ( ( n_pl @ sK20 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) ) ),
inference(equality_resolution,[],[f1946]) ).
thf(f1955,plain,
( ( $false = $true )
| ( ( n_pl @ sK20 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) ) ),
inference(forward_demodulation,[],[f1953,f1596]) ).
thf(f1956,plain,
( ( n_pl @ sK20 @ sK19 )
= ( n_pl @ sK18 @ sK20 ) ),
inference(trivial_inequality_removal,[],[f1955]) ).
thf(f2026,plain,
! [X0: $i] :
( ( $false
= ( in @ sK20 @ nat ) )
| ( ( n_pl @ X0 @ sK20 )
!= ( n_pl @ sK18 @ sK20 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( sK19 = X0 )
| ( $false
= ( in @ sK19 @ nat ) ) ),
inference(superposition,[],[f1670,f1956]) ).
thf(f2047,plain,
! [X0: $i] :
( ( ( n_pl @ X0 @ sK20 )
!= ( n_pl @ sK18 @ sK20 ) )
| ( $false
= ( in @ sK19 @ nat ) )
| ( ( in @ X0 @ nat )
= $false )
| ( sK19 = X0 )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f2026,f1596]) ).
thf(f2048,plain,
! [X0: $i] :
( ( sK19 = X0 )
| ( ( n_pl @ X0 @ sK20 )
!= ( n_pl @ sK18 @ sK20 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( in @ sK19 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f2047]) ).
thf(f2051,plain,
! [X0: $i] :
( ( ( in @ X0 @ nat )
= $false )
| ( ( n_pl @ X0 @ sK20 )
!= ( n_pl @ sK18 @ sK20 ) )
| ( sK19 = X0 )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f2048,f1592]) ).
thf(f2052,plain,
! [X0: $i] :
( ( ( n_pl @ X0 @ sK20 )
!= ( n_pl @ sK18 @ sK20 ) )
| ( ( in @ X0 @ nat )
= $false )
| ( sK19 = X0 ) ),
inference(trivial_inequality_removal,[],[f2051]) ).
thf(f2160,plain,
( ( ( in @ sK18 @ nat )
= $false )
| ( sK18 = sK19 ) ),
inference(equality_resolution,[],[f2052]) ).
thf(f2181,plain,
( ( in @ sK18 @ nat )
= $false ),
inference(forward_subsumption_resolution,[],[f2160,f1600]) ).
thf(f2205,plain,
$false = $true,
inference(superposition,[],[f1588,f2181]) ).
thf(f2206,plain,
$false,
inference(trivial_inequality_removal,[],[f2205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM681^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:40:22 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.66/0.38 % (1217374)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.66/0.38 % (1217379)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2316980751:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.66/0.38 % (1217385)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.66/0.38 % (1217385)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
% 0.66/0.38 % (1217380)lrs+10_16_si=on:nwc=1.5:random_seed=518462522:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.66/0.38 % (1217381)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=47638557:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.66/0.38 % (1217384)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=950942862:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.66/0.38 % (1217383)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2946908928:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.66/0.38 % (1217382)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=3052439242: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)
% 0.66/0.38 % (1217385)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=3630913212:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.66/0.38 % (1217381)Instruction limit reached!
% 0.66/0.38 % (1217381)------------------------------
% 0.66/0.38 % (1217381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1217381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1217381)CaDiCaL version: 2.1.3
% 0.66/0.38 % (1217381)Termination reason: Instruction limit
% 0.66/0.38 % (1217381)Termination phase: shuffling
% 0.66/0.38 % (1217381)Time elapsed: 0.003 s
% 0.66/0.38 % (1217381)Peak memory usage: 10 MB
% 0.66/0.38 % (1217381)Instructions burned: 5 (million)
% 0.66/0.38 % (1217380)Instruction limit reached!
% 0.66/0.38 % (1217380)------------------------------
% 0.66/0.38 % (1217380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1217380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1217380)CaDiCaL version: 2.1.3
% 0.66/0.38 % (1217380)Termination reason: Instruction limit
% 0.66/0.38 % (1217380)Termination phase: shuffling
% 0.66/0.38 % (1217380)Time elapsed: 0.008 s
% 0.66/0.38 % (1217380)Peak memory usage: 10 MB
% 0.66/0.38 % (1217380)Instructions burned: 18 (million)
% 0.66/0.38 % (1217379)Instruction limit reached!
% 0.66/0.38 % (1217379)------------------------------
% 0.66/0.38 % (1217379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1217383)Instruction limit reached!
% 0.66/0.38 % (1217383)------------------------------
% 0.66/0.38 % (1217383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1217383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1217379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1217383)CaDiCaL version: 2.1.3
% 0.66/0.38 % (1217379)CaDiCaL version: 2.1.3
% 0.66/0.38 % (1217379)Termination reason: Instruction limit
% 0.66/0.38 % (1217379)Termination phase: Function definition elimination
% 0.66/0.38 % (1217383)Termination reason: Instruction limit
% 0.66/0.38 % (1217383)Termination phase: Property scanning
% 0.66/0.38 % (1217379)Time elapsed: 0.020 s
% 0.66/0.38 % (1217383)Time elapsed: 0.011 s
% 0.66/0.38 % (1217379)Peak memory usage: 11 MB
% 0.66/0.38 % (1217383)Peak memory usage: 10 MB
% 0.66/0.38 % (1217379)Instructions burned: 90 (million)
% 0.66/0.38 % (1217383)Instructions burned: 26 (million)
% 0.66/0.38 % (1217395)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.38 % (1217393)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4152491319:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.42 % (1217395)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3999101877:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.66/0.42 % (1217395)Instruction limit reached!
% 0.66/0.42 % (1217395)------------------------------
% 0.66/0.42 % (1217395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (1217395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (1217395)CaDiCaL version: 2.1.3
% 0.66/0.42 % (1217395)Termination reason: Instruction limit
% 0.66/0.42 % (1217395)Termination phase: shuffling
% 0.66/0.42 % (1217395)Time elapsed: 0.002 s
% 0.66/0.42 % (1217395)Peak memory usage: 10 MB
% 0.66/0.42 % (1217395)Instructions burned: 10 (million)
% 0.66/0.42 % (1217393)Instruction limit reached!
% 0.66/0.42 % (1217393)------------------------------
% 0.66/0.42 % (1217393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (1217393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (1217393)CaDiCaL version: 2.1.3
% 0.66/0.42 % (1217393)Termination reason: Instruction limit
% 0.66/0.42 % (1217393)Termination phase: shuffling
% 0.66/0.42 % (1217393)Time elapsed: 0.003 s
% 0.66/0.42 % (1217393)Peak memory usage: 10 MB
% 0.66/0.42 % (1217393)Instructions burned: 7 (million)
% 0.66/0.42 % (1217396)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=79370035:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.66/0.42 % (1217399)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
% 0.66/0.42 % (1217399)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.42 % (1217384)Instruction limit reached!
% 0.66/0.42 % (1217384)------------------------------
% 0.66/0.42 % (1217384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (1217384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (1217384)CaDiCaL version: 2.1.3
% 0.66/0.42 % (1217384)Termination reason: Instruction limit
% 0.66/0.42 % (1217384)Termination phase: Function definition elimination
% 0.66/0.42 % (1217384)Time elapsed: 0.033 s
% 0.66/0.42 % (1217384)Peak memory usage: 11 MB
% 0.66/0.42 % (1217384)Instructions burned: 76 (million)
% 0.66/0.42 % (1217394)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2899030011:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.66/0.42 % (1217399)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2356142412:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.66/0.42 % (1217394)Instruction limit reached!
% 0.66/0.42 % (1217394)------------------------------
% 0.66/0.42 % (1217394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (1217394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (1217394)CaDiCaL version: 2.1.3
% 0.66/0.42 % (1217394)Termination reason: Instruction limit
% 0.66/0.42 % (1217394)Termination phase: shuffling
% 0.66/0.42 % (1217394)Time elapsed: 0.003 s
% 0.66/0.42 % (1217394)Peak memory usage: 10 MB
% 0.66/0.42 % (1217394)Instructions burned: 6 (million)
% 0.66/0.42 % (1217396)Instruction limit reached!
% 0.66/0.42 % (1217396)------------------------------
% 0.66/0.42 % (1217396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (1217396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (1217396)CaDiCaL version: 2.1.3
% 0.66/0.42 % (1217396)Termination reason: Instruction limit
% 0.66/0.42 % (1217396)Termination phase: shuffling
% 0.66/0.42 % (1217396)Time elapsed: 0.006 s
% 0.66/0.42 % (1217396)Peak memory usage: 10 MB
% 0.66/0.42 % (1217396)Instructions burned: 14 (million)
% 0.66/0.42 % (1217399)Instruction limit reached!
% 0.66/0.42 % (1217399)------------------------------
% 0.66/0.42 % (1217399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (1217399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (1217399)CaDiCaL version: 2.1.3
% 0.66/0.42 % (1217399)Termination reason: Instruction limit
% 0.66/0.44 % (1217399)Termination phase: Property scanning
% 0.66/0.44 % (1217399)Time elapsed: 0.006 s
% 0.66/0.44 % (1217399)Peak memory usage: 10 MB
% 0.66/0.44 % (1217399)Instructions burned: 29 (million)
% 0.66/0.44 % (1217400)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=1797534327:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.66/0.44 % (1217407)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4023321769:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.66/0.44 % (1217403)lrs+10_1_si=on:cs=on:random_seed=1368212683:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.66/0.44 % (1217406)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1371177361:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.66/0.44 % (1217403)Instruction limit reached!
% 0.66/0.44 % (1217403)------------------------------
% 0.66/0.44 % (1217403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217403)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217403)Termination reason: Instruction limit
% 0.66/0.44 % (1217403)Termination phase: shuffling
% 0.66/0.44 % (1217403)Time elapsed: 0.004 s
% 0.66/0.44 % (1217403)Peak memory usage: 10 MB
% 0.66/0.44 % (1217403)Instructions burned: 9 (million)
% 0.66/0.44 % (1217385)Instruction limit reached!
% 0.66/0.44 % (1217385)------------------------------
% 0.66/0.44 % (1217385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217385)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217385)Termination reason: Instruction limit
% 0.66/0.44 % (1217385)Termination phase: Function definition elimination
% 0.66/0.44 % (1217385)Time elapsed: 0.064 s
% 0.66/0.44 % (1217385)Peak memory usage: 11 MB
% 0.66/0.44 % (1217385)Instructions burned: 158 (million)
% 0.66/0.44 % (1217407)Refutation not found, incomplete strategy
% 0.66/0.44 % (1217407)------------------------------
% 0.66/0.44 % (1217407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217407)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217407)Termination reason: Refutation not found, incomplete strategy
% 0.66/0.44 % (1217407)Time elapsed: 0.013 s
% 0.66/0.44 % (1217407)Peak memory usage: 13 MB
% 0.66/0.44 % (1217407)Instructions burned: 56 (million)
% 0.66/0.44 % (1217405)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.66/0.44 % (1217407)------------------------------
% 0.66/0.44 % (1217407)------------------------------
% 0.66/0.44 % (1217405)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=644699034:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.44 % (1217405)Instruction limit reached!
% 0.66/0.44 % (1217405)------------------------------
% 0.66/0.44 % (1217405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217405)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217405)Termination reason: Instruction limit
% 0.66/0.44 % (1217405)Termination phase: shuffling
% 0.66/0.44 % (1217405)Time elapsed: 0.003 s
% 0.66/0.44 % (1217405)Peak memory usage: 10 MB
% 0.66/0.44 % (1217405)Instructions burned: 7 (million)
% 0.66/0.44 % (1217406)Instruction limit reached!
% 0.66/0.44 % (1217406)------------------------------
% 0.66/0.44 % (1217406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217406)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217406)Termination reason: Instruction limit
% 0.66/0.44 % (1217406)Termination phase: Property scanning
% 0.66/0.44 % (1217406)Time elapsed: 0.017 s
% 0.66/0.44 % (1217406)Peak memory usage: 10 MB
% 0.66/0.44 % (1217406)Instructions burned: 40 (million)
% 0.66/0.44 % (1217414)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=547656920:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.66/0.44 % (1217412)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3114017245:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.66/0.44 % (1217400)Instruction limit reached!
% 0.66/0.44 % (1217400)------------------------------
% 0.66/0.44 % (1217400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217400)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217400)Termination reason: Instruction limit
% 0.66/0.44 % (1217400)Termination phase: Function definition elimination
% 0.66/0.44 % (1217400)Time elapsed: 0.037 s
% 0.66/0.44 % (1217400)Peak memory usage: 11 MB
% 0.66/0.44 % (1217400)Instructions burned: 88 (million)
% 0.66/0.44 % (1217413)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=125307541:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.44 % (1217412)Instruction limit reached!
% 0.66/0.44 % (1217412)------------------------------
% 0.66/0.44 % (1217412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217412)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217412)Termination reason: Instruction limit
% 0.66/0.44 % (1217412)Termination phase: Property scanning
% 0.66/0.44 % (1217412)Time elapsed: 0.011 s
% 0.66/0.44 % (1217412)Peak memory usage: 10 MB
% 0.66/0.44 % (1217412)Instructions burned: 26 (million)
% 0.66/0.44 % (1217413)Instruction limit reached!
% 0.66/0.44 % (1217413)------------------------------
% 0.66/0.44 % (1217413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217413)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217413)Termination reason: Instruction limit
% 0.66/0.44 % (1217413)Termination phase: shuffling
% 0.66/0.44 % (1217413)Time elapsed: 0.007 s
% 0.66/0.44 % (1217413)Peak memory usage: 10 MB
% 0.66/0.44 % (1217413)Instructions burned: 16 (million)
% 0.66/0.44 % (1217416)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=91326637:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.44 % (1217417)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1250839968:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.66/0.44 % (1217417)Instruction limit reached!
% 0.66/0.44 % (1217417)------------------------------
% 0.66/0.44 % (1217417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217417)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217417)Termination reason: Instruction limit
% 0.66/0.44 % (1217417)Termination phase: shuffling
% 0.66/0.44 % (1217417)Time elapsed: 0.004 s
% 0.66/0.44 % (1217417)Peak memory usage: 10 MB
% 0.66/0.44 % (1217417)Instructions burned: 8 (million)
% 0.66/0.44 % (1217420)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=975182315:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.66/0.44 % (1217416)Instruction limit reached!
% 0.66/0.44 % (1217416)------------------------------
% 0.66/0.44 % (1217416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217416)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217416)Termination reason: Instruction limit
% 0.66/0.44 % (1217416)Termination phase: shuffling
% 0.66/0.44 % (1217416)Time elapsed: 0.007 s
% 0.66/0.44 % (1217416)Peak memory usage: 10 MB
% 0.66/0.44 % (1217416)Instructions burned: 15 (million)
% 0.66/0.44 % (1217422)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1512731114:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.66/0.44 % (1217423)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1988832685:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.66/0.44 % (1217420)Instruction limit reached!
% 0.66/0.44 % (1217420)------------------------------
% 0.66/0.44 % (1217420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217420)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217420)Termination reason: Instruction limit
% 0.66/0.44 % (1217420)Termination phase: Property scanning
% 0.66/0.44 % (1217420)Time elapsed: 0.012 s
% 0.66/0.44 % (1217420)Peak memory usage: 10 MB
% 0.66/0.44 % (1217420)Instructions burned: 28 (million)
% 0.66/0.44 % (1217426)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
% 0.66/0.44 % (1217426)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.66/0.44 % (1217428)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.66/0.44 % (1217426)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=1343200677:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.44 % (1217428)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=3201128865:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.66/0.44 % (1217422)Instruction limit reached!
% 0.66/0.44 % (1217422)------------------------------
% 0.66/0.44 % (1217422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217422)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217422)Termination reason: Instruction limit
% 0.66/0.44 % (1217422)Termination phase: Property scanning
% 0.66/0.44 % (1217422)Time elapsed: 0.011 s
% 0.66/0.44 % (1217422)Peak memory usage: 10 MB
% 0.66/0.44 % (1217422)Instructions burned: 25 (million)
% 0.66/0.44 % (1217428)Instruction limit reached!
% 0.66/0.44 % (1217428)------------------------------
% 0.66/0.44 % (1217428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217428)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217428)Termination reason: Instruction limit
% 0.66/0.44 % (1217428)Termination phase: shuffling
% 0.66/0.44 % (1217428)Time elapsed: 0.004 s
% 0.66/0.44 % (1217428)Peak memory usage: 10 MB
% 0.66/0.44 % (1217428)Instructions burned: 9 (million)
% 0.66/0.44 % (1217426)Instruction limit reached!
% 0.66/0.44 % (1217426)------------------------------
% 0.66/0.44 % (1217426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217426)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217426)Termination reason: Instruction limit
% 0.66/0.44 % (1217426)Termination phase: shuffling
% 0.66/0.44 % (1217426)Time elapsed: 0.007 s
% 0.66/0.44 % (1217426)Peak memory usage: 10 MB
% 0.66/0.44 % (1217426)Instructions burned: 16 (million)
% 0.66/0.44 % (1217414) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1217374-1217414"...
% 0.66/0.44 % (1217414)...printing done.
% 0.66/0.44 % (1217414)Refutation found. Thanks to Tanya!
% 0.66/0.44 % SZS status Theorem for theBenchmark
% 0.66/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.66/0.44 % (1217414)------------------------------
% 0.66/0.44 % (1217414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (1217414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (1217414)CaDiCaL version: 2.1.3
% 0.66/0.44 % (1217414)Termination reason: Refutation
% 0.66/0.44 % (1217414)Time elapsed: 0.050 s
% 0.66/0.44 % (1217414)Peak memory usage: 14 MB
% 0.66/0.44 % (1217414)Instructions burned: 216 (million)
% 0.66/0.44 % (1217374)Success in time 0.176 s
% 0.66/0.44 % Vampire exiting
%------------------------------------------------------------------------------