%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM721^4 : 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 : n003.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 08:18:40 AM UTC 2026
% Result : Theorem 1.19s 0.48s
% Output : Refutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 80 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 1242 ( 143 equ; 0 cnn)
% Maximal formula atoms : 15 ( 15 avg)
% Number of connectives : 1587 ( 7 ~; 69 |; 0 &;1305 @)
% ( 0 <=>; 151 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 179 ( 175 usr; 9 con; 0-7 aty)
% ( 55 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 277 ( 237 ^; 40 !; 0 ?; 277 :)
% 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,
lbprop: ( $i > $o ) > $i > $i > $o ).
thf(func_def_133,type,
n_lb: ( $i > $o ) > $i > $o ).
thf(func_def_134,type,
min: ( $i > $o ) > $i > $o ).
thf(func_def_135,type,
d_428_prop1: $i > $i > $o ).
thf(func_def_136,type,
d_428_prop2: $i > $i > $o ).
thf(func_def_137,type,
d_428_prop4: $i > $o ).
thf(func_def_139,type,
d_428_g: $i > $i ).
thf(func_def_140,type,
times: $i > $i ).
thf(func_def_141,type,
n_ts: $i > $i > $i ).
thf(func_def_142,type,
d_429_prop1: $i > $i > $o ).
thf(func_def_143,type,
d_430_prop1: $i > $i > $i > $o ).
thf(func_def_144,type,
d_431_prop1: $i > $i > $i > $o ).
thf(func_def_145,type,
vAND: $o > $o > $o ).
thf(func_def_146,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_147,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_148,type,
vIMP: $o > $o > $o ).
thf(func_def_151,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_152,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_153,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_154,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_155,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_156,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_157,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_158,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_159,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_160,type,
vNOT: $o > $o ).
thf(func_def_161,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_162,type,
vOR: $o > $o > $o ).
thf(func_def_163,type,
sK0: $i > $i ).
thf(func_def_164,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK8: $i > $i > $o ).
thf(func_def_172,type,
sK9: $i > $i > $o ).
thf(func_def_173,type,
sK10: $i > $i > $o ).
thf(func_def_174,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_175,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK13: $i > $i > $o ).
thf(func_def_177,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_178,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_179,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_180,type,
sK17: $i > $i > $o ).
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(f160,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
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,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) )
= iii ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii) ).
thf(f322,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] :
( all_of
@ ^ [X3: $i] : ( in @ X3 @ nat )
@ ^ [X3: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( ( d_29_ii @ X2 @ X3 )
=> ( d_29_ii @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34) ).
thf(f323,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] :
( all_of
@ ^ [X3: $i] : ( in @ X3 @ nat )
@ ^ [X3: $i] :
( ( iii @ X0 @ X1 )
=> ( ( iii @ X2 @ X3 )
=> ( iii @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34a) ).
thf(f324,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] :
( all_of
@ ^ [X3: $i] : ( in @ X3 @ nat )
@ ^ [X3: $i] :
( ( iii @ X0 @ X1 )
=> ( ( iii @ X2 @ X3 )
=> ( iii @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f323]) ).
thf(f403,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f619,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f714,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] :
( all_of
@ ^ [X6: $i] : ( in @ X6 @ nat )
@ ^ [X7: $i] :
( ( iii @ X1 @ X3 )
=> ( ( iii @ X5 @ X7 )
=> ( iii @ ( n_ts @ X1 @ X5 ) @ ( n_ts @ X3 @ X7 ) ) ) ) ) ) ) ),
inference(rectify,[],[f324]) ).
thf(f715,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] :
( all_of
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y2 @ Y3 )
=> ( iii @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f714]) ).
thf(f718,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] :
( all_of
@ ^ [X6: $i] : ( in @ X6 @ nat )
@ ^ [X7: $i] :
( ( d_29_ii @ X1 @ X3 )
=> ( ( d_29_ii @ X5 @ X7 )
=> ( d_29_ii @ ( n_ts @ X1 @ X5 ) @ ( n_ts @ X3 @ X7 ) ) ) ) ) ) ) ),
inference(rectify,[],[f322]) ).
thf(f719,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] :
( all_of
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y2 @ Y3 )
=> ( d_29_ii @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f718]) ).
thf(f830,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f836,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f837,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f836]) ).
thf(f870,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] :
( all_of
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y2 @ Y3 )
=> ( iii @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f715]) ).
thf(f903,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f403]) ).
thf(f910,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f619]) ).
thf(f923,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f935,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f837]) ).
thf(f966,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f830]) ).
thf(f1002,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] :
( all_of
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y2 @ Y3 )
=> ( d_29_ii @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f719]) ).
thf(f1003,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] :
( all_of
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y2 @ Y3 )
=> ( iii @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f870]) ).
thf(f1032,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,[],[f935,f903]) ).
thf(f1033,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f966,f923]) ).
thf(f1034,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( l_some @ nat @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f910,f923]) ).
thf(f1136,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 > $o,Y4: $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ^ [Y6: $i,Y7: $i > $o] : ( Y7 @ Y6 )
@ Y5
@ Y3 )
=> ( Y4 @ Y5 ) ) )
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i] : ( l_some @ nat @ ( diffprop @ Y4 @ Y5 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y4: $i,Y5: $i] : ( l_some @ nat @ ( diffprop @ Y4 @ Y5 ) )
@ Y2
@ Y3 )
=> ( ^ [Y4: $i,Y5: $i] : ( l_some @ nat @ ( diffprop @ Y4 @ Y5 ) )
@ ( n_ts @ Y0 @ Y2 )
@ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f1002,f1032,f1032,f1032,f1032,f1033,f1033,f1033]) ).
thf(f1137,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 > $o,Y4: $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ^ [Y6: $i,Y7: $i > $o] : ( Y7 @ Y6 )
@ Y5
@ Y3 )
=> ( Y4 @ Y5 ) ) )
@ ^ [Y3: $i] : ( in @ Y3 @ nat )
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i] : ( l_some @ nat @ ( diffprop @ Y5 @ Y4 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y4: $i,Y5: $i] : ( l_some @ nat @ ( diffprop @ Y5 @ Y4 ) )
@ Y2
@ Y3 )
=> ( ^ [Y4: $i,Y5: $i] : ( l_some @ nat @ ( diffprop @ Y5 @ Y4 ) )
@ ( n_ts @ Y0 @ Y2 )
@ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f1003,f1032,f1032,f1032,f1032,f1034,f1034,f1034]) ).
thf(f1225,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y0 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y3 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y1 @ Y3 ) @ ( n_ts @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f1137]) ).
thf(f1226,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y0 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y3 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y1 @ Y3 ) @ ( n_ts @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f1225]) ).
thf(f1227,plain,
( $false
= ( ( in @ sK3 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ sK3 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1226]) ).
thf(f1228,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ sK3 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1227]) ).
thf(f1229,plain,
( $true
= ( in @ sK3 @ nat ) ),
inference(imp_proxy_clausification,[],[f1227]) ).
thf(f1230,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ sK3 @ Y1 ) ) ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f1228]) ).
thf(f1231,plain,
( $false
= ( ( in @ sK4 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ Y1 ) @ ( n_ts @ sK3 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1230]) ).
thf(f1232,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ Y1 ) @ ( n_ts @ sK3 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1231]) ).
thf(f1233,plain,
( ( in @ sK4 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1231]) ).
thf(f1234,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ Y1 ) @ ( n_ts @ sK3 @ Y0 ) ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f1232]) ).
thf(f1235,plain,
( $false
= ( ( in @ sK5 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ sK5 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ Y0 ) @ ( n_ts @ sK3 @ sK5 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1234]) ).
thf(f1236,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ sK5 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ Y0 ) @ ( n_ts @ sK3 @ sK5 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1235]) ).
thf(f1237,plain,
( ( in @ sK5 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1235]) ).
thf(f1238,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ sK5 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ Y0 ) @ ( n_ts @ sK3 @ sK5 ) ) ) ) ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f1236]) ).
thf(f1239,plain,
( $false
= ( ( in @ sK6 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ sK6 ) @ ( n_ts @ sK3 @ sK5 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1238]) ).
thf(f1240,plain,
( $false
= ( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
=> ( ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ sK6 ) @ ( n_ts @ sK3 @ sK5 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1239]) ).
thf(f1241,plain,
( ( in @ sK6 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1239]) ).
thf(f1242,plain,
( $false
= ( ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ sK6 ) @ ( n_ts @ sK3 @ sK5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1240]) ).
thf(f1243,plain,
( ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) )
= $true ),
inference(imp_proxy_clausification,[],[f1240]) ).
thf(f1244,plain,
( ( l_some @ nat @ ( diffprop @ ( n_ts @ sK4 @ sK6 ) @ ( n_ts @ sK3 @ sK5 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1242]) ).
thf(f1245,plain,
( ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) )
= $true ),
inference(imp_proxy_clausification,[],[f1242]) ).
thf(f2011,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y3 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1136]) ).
thf(f2012,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y3 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ Y0 @ Y2 ) @ ( n_ts @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f2011]) ).
thf(f2013,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ Y0 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ Y1 ) @ ( n_ts @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f2012]) ).
thf(f2014,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ Y0 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ Y1 ) @ ( n_ts @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2013]) ).
thf(f2015,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ Y0 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ Y1 ) @ ( n_ts @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f2014]) ).
thf(f2016,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ Y0 ) @ ( n_ts @ X2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f2015]) ).
thf(f2017,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ Y0 ) @ ( n_ts @ X2 @ Y1 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f2016]) ).
thf(f2018,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ Y0 ) @ ( n_ts @ X2 @ Y1 ) ) ) ) ) ) ) )
@ X3 ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f2017]) ).
thf(f2019,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ( in @ X3 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ X3 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2018]) ).
thf(f2020,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ X3 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ Y0 ) ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f2019]) ).
thf(f2021,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ X3 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ Y0 ) ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2020]) ).
thf(f2022,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( ( ( in @ X4 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ X3 @ X4 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ X4 ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f2021]) ).
thf(f2023,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ nat ) )
| ( ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( ( l_some @ nat @ ( diffprop @ X3 @ X4 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ X4 ) ) ) ) )
= $true )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f2022]) ).
thf(f2024,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( l_some @ nat @ ( diffprop @ X3 @ X4 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ X4 ) ) ) ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ X1 @ X2 ) ) )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X4 @ nat ) ) ),
inference(imp_proxy_clausification,[],[f2023]) ).
thf(f2025,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X3 ) @ ( n_ts @ X2 @ X4 ) ) ) )
| ( ( l_some @ nat @ ( diffprop @ X3 @ X4 ) )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ X1 @ X2 ) ) )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X4 @ nat ) ) ),
inference(imp_proxy_clausification,[],[f2024]) ).
thf(f2802,plain,
( ( $false = $true )
| ( ( in @ sK4 @ nat )
= $false )
| ( ( in @ sK6 @ nat )
= $false )
| ( $false
= ( in @ sK5 @ nat ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) )
| ( $false
= ( in @ sK3 @ nat ) ) ),
inference(superposition,[],[f2025,f1244]) ).
thf(f2814,plain,
( ( $false
= ( l_some @ nat @ ( diffprop @ sK4 @ sK3 ) ) )
| ( $false
= ( in @ sK5 @ nat ) )
| ( ( in @ sK6 @ nat )
= $false )
| ( ( in @ sK4 @ nat )
= $false )
| ( $false
= ( in @ sK3 @ nat ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f2802]) ).
thf(f2818,plain,
( ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) )
| ( $false
= ( in @ sK3 @ nat ) )
| ( $false = $true )
| ( $false
= ( in @ sK5 @ nat ) )
| ( ( in @ sK6 @ nat )
= $false )
| ( ( in @ sK4 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f2814,f1243]) ).
thf(f2819,plain,
( ( ( in @ sK4 @ nat )
= $false )
| ( $false
= ( in @ sK3 @ nat ) )
| ( ( in @ sK6 @ nat )
= $false )
| ( $false
= ( in @ sK5 @ nat ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f2818]) ).
thf(f2822,plain,
( ( $false
= ( in @ sK3 @ nat ) )
| ( $false = $true )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) )
| ( $false
= ( in @ sK5 @ nat ) )
| ( ( in @ sK6 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f2819,f1233]) ).
thf(f2823,plain,
( ( $false
= ( in @ sK3 @ nat ) )
| ( $false
= ( in @ sK5 @ nat ) )
| ( ( in @ sK6 @ nat )
= $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f2822]) ).
thf(f2826,plain,
( ( ( in @ sK6 @ nat )
= $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) )
| ( $false = $true )
| ( $false
= ( in @ sK5 @ nat ) ) ),
inference(forward_demodulation,[],[f2823,f1229]) ).
thf(f2827,plain,
( ( ( in @ sK6 @ nat )
= $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) )
| ( $false
= ( in @ sK5 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f2826]) ).
thf(f2830,plain,
( ( $false
= ( in @ sK5 @ nat ) )
| ( $false = $true )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) ) ),
inference(forward_demodulation,[],[f2827,f1241]) ).
thf(f2831,plain,
( ( $false
= ( l_some @ nat @ ( diffprop @ sK6 @ sK5 ) ) )
| ( $false
= ( in @ sK5 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f2830]) ).
thf(f2834,plain,
( ( $false
= ( in @ sK5 @ nat ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f2831,f1245]) ).
thf(f2835,plain,
( $false
= ( in @ sK5 @ nat ) ),
inference(trivial_inequality_removal,[],[f2834]) ).
thf(f2848,plain,
$false = $true,
inference(superposition,[],[f2835,f1237]) ).
thf(f2851,plain,
$false,
inference(trivial_inequality_removal,[],[f2848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM721^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.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
% 0.09/0.19 % DateTime : Tue Sep 29 12:46:58 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.21/0.28 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
% 0.54/0.42 % (2453164)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.42 % (2453174)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1340881113:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.42 % (2453175)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.42 % (2453175)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
% 0.54/0.42 % (2453169)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2516307150:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.42 % (2453171)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1416285158:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.42 % (2453173)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=810664561:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.42 % (2453172)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=4235291054: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)
% 0.54/0.42 % (2453175)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=520951154:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.42 % (2453171)Instruction limit reached!
% 0.54/0.42 % (2453171)------------------------------
% 0.54/0.42 % (2453171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.42 % (2453171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.42 % (2453171)CaDiCaL version: 2.1.3
% 0.54/0.42 % (2453171)Termination reason: Instruction limit
% 0.54/0.42 % (2453171)Termination phase: shuffling
% 0.54/0.42 % (2453171)Time elapsed: 0.003 s
% 0.54/0.42 % (2453171)Peak memory usage: 10 MB
% 0.54/0.42 % (2453171)Instructions burned: 5 (million)
% 0.54/0.42 % (2453174)Instruction limit reached!
% 0.54/0.42 % (2453174)------------------------------
% 0.54/0.42 % (2453174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.42 % (2453174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.42 % (2453174)CaDiCaL version: 2.1.3
% 0.54/0.42 % (2453174)Termination reason: Instruction limit
% 0.54/0.42 % (2453174)Termination phase: Unused predicate definition removal
% 0.54/0.42 % (2453174)Time elapsed: 0.017 s
% 0.54/0.42 % (2453174)Peak memory usage: 11 MB
% 0.54/0.42 % (2453174)Instructions burned: 75 (million)
% 0.54/0.42 % (2453170)lrs+10_16_si=on:nwc=1.5:random_seed=2588692660:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.42 % (2453173)Instruction limit reached!
% 0.54/0.42 % (2453173)------------------------------
% 0.54/0.42 % (2453173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.42 % (2453173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.42 % (2453173)CaDiCaL version: 2.1.3
% 0.54/0.42 % (2453173)Termination reason: Instruction limit
% 0.54/0.42 % (2453173)Termination phase: shuffling
% 0.54/0.42 % (2453173)Time elapsed: 0.011 s
% 0.54/0.42 % (2453173)Peak memory usage: 10 MB
% 0.54/0.42 % (2453173)Instructions burned: 25 (million)
% 0.54/0.42 % (2453183)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3696780894:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.42 % (2453182)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4094018916:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.42 % (2453183)Instruction limit reached!
% 0.54/0.42 % (2453183)------------------------------
% 0.54/0.42 % (2453183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.42 % (2453183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.42 % (2453183)CaDiCaL version: 2.1.3
% 0.54/0.42 % (2453183)Termination reason: Instruction limit
% 0.54/0.42 % (2453183)Termination phase: shuffling
% 0.54/0.42 % (2453183)Time elapsed: 0.003 s
% 0.54/0.42 % (2453183)Peak memory usage: 10 MB
% 0.54/0.42 % (2453183)Instructions burned: 14 (million)
% 0.54/0.46 % (2453182)Instruction limit reached!
% 0.54/0.46 % (2453182)------------------------------
% 0.54/0.46 % (2453182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.46 % (2453182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.46 % (2453182)CaDiCaL version: 2.1.3
% 0.54/0.46 % (2453182)Termination reason: Instruction limit
% 0.54/0.46 % (2453182)Termination phase: shuffling
% 0.54/0.46 % (2453182)Time elapsed: 0.003 s
% 0.54/0.46 % (2453182)Peak memory usage: 10 MB
% 0.54/0.46 % (2453182)Instructions burned: 7 (million)
% 0.54/0.46 % (2453185)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.46 % (2453185)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2357463120:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.46 % (2453170)Instruction limit reached!
% 0.54/0.46 % (2453170)------------------------------
% 0.54/0.46 % (2453170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.46 % (2453170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.46 % (2453170)CaDiCaL version: 2.1.3
% 0.54/0.46 % (2453170)Termination reason: Instruction limit
% 0.54/0.46 % (2453170)Termination phase: shuffling
% 0.54/0.46 % (2453170)Time elapsed: 0.021 s
% 0.54/0.46 % (2453170)Peak memory usage: 10 MB
% 0.54/0.46 % (2453170)Instructions burned: 21 (million)
% 0.54/0.46 % (2453185)Instruction limit reached!
% 0.54/0.46 % (2453185)------------------------------
% 0.54/0.46 % (2453185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.46 % (2453185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.46 % (2453185)CaDiCaL version: 2.1.3
% 0.54/0.46 % (2453185)Termination reason: Instruction limit
% 0.54/0.46 % (2453185)Termination phase: shuffling
% 0.54/0.46 % (2453185)Time elapsed: 0.003 s
% 0.54/0.46 % (2453185)Peak memory usage: 10 MB
% 0.54/0.46 % (2453185)Instructions burned: 7 (million)
% 0.54/0.46 % (2453188)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1656234998:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.46 % (2453169)Instruction limit reached!
% 0.54/0.46 % (2453169)------------------------------
% 0.54/0.46 % (2453169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.46 % (2453169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.46 % (2453169)CaDiCaL version: 2.1.3
% 0.54/0.46 % (2453169)Termination reason: Instruction limit
% 0.54/0.46 % (2453169)Termination phase: Property scanning
% 0.54/0.46 % (2453169)Time elapsed: 0.038 s
% 0.54/0.46 % (2453169)Peak memory usage: 11 MB
% 0.54/0.46 % (2453169)Instructions burned: 89 (million)
% 0.54/0.46 % (2453189)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
% 0.54/0.46 % (2453189)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.46 % (2453191)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=657973683:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.46 % (2453188)Instruction limit reached!
% 0.54/0.46 % (2453188)------------------------------
% 0.54/0.46 % (2453188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.46 % (2453188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.46 % (2453188)CaDiCaL version: 2.1.3
% 0.54/0.46 % (2453188)Termination reason: Instruction limit
% 0.54/0.46 % (2453188)Termination phase: shuffling
% 0.54/0.46 % (2453188)Time elapsed: 0.006 s
% 0.54/0.46 % (2453188)Peak memory usage: 10 MB
% 0.54/0.46 % (2453188)Instructions burned: 14 (million)
% 0.54/0.46 % (2453189)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2315169994:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.46 % (2453192)lrs+10_1_si=on:cs=on:random_seed=3147788854:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.46 % (2453194)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.19/0.48 % (2453192)Instruction limit reached!
% 1.19/0.48 % (2453192)------------------------------
% 1.19/0.48 % (2453192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453192)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453192)Termination reason: Instruction limit
% 1.19/0.48 % (2453192)Termination phase: shuffling
% 1.19/0.48 % (2453192)Time elapsed: 0.004 s
% 1.19/0.48 % (2453192)Peak memory usage: 10 MB
% 1.19/0.48 % (2453192)Instructions burned: 10 (million)
% 1.19/0.48 % (2453194)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=421704230:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.19/0.48 % (2453189)Instruction limit reached!
% 1.19/0.48 % (2453189)------------------------------
% 1.19/0.48 % (2453189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453189)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453189)Termination reason: Instruction limit
% 1.19/0.48 % (2453189)Termination phase: shuffling
% 1.19/0.48 % (2453189)Time elapsed: 0.012 s
% 1.19/0.48 % (2453189)Peak memory usage: 10 MB
% 1.19/0.48 % (2453189)Instructions burned: 29 (million)
% 1.19/0.48 % (2453194)Instruction limit reached!
% 1.19/0.48 % (2453194)------------------------------
% 1.19/0.48 % (2453194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453194)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453194)Termination reason: Instruction limit
% 1.19/0.48 % (2453194)Termination phase: shuffling
% 1.19/0.48 % (2453194)Time elapsed: 0.003 s
% 1.19/0.48 % (2453194)Peak memory usage: 10 MB
% 1.19/0.48 % (2453194)Instructions burned: 6 (million)
% 1.19/0.48 % (2453191)Instruction limit reached!
% 1.19/0.48 % (2453191)------------------------------
% 1.19/0.48 % (2453191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453196)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=123328298:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.19/0.48 % (2453191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453191)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453191)Termination reason: Instruction limit
% 1.19/0.48 % (2453191)Termination phase: Function definition elimination
% 1.19/0.48 % (2453191)Time elapsed: 0.020 s
% 1.19/0.48 % (2453191)Peak memory usage: 11 MB
% 1.19/0.48 % (2453191)Instructions burned: 89 (million)
% 1.19/0.48 % (2453175)Instruction limit reached!
% 1.19/0.48 % (2453175)------------------------------
% 1.19/0.48 % (2453175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453175)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453175)Termination reason: Instruction limit
% 1.19/0.48 % (2453175)Termination phase: Function definition elimination
% 1.19/0.48 % (2453175)Time elapsed: 0.064 s
% 1.19/0.48 % (2453175)Peak memory usage: 12 MB
% 1.19/0.48 % (2453175)Instructions burned: 159 (million)
% 1.19/0.48 % (2453204)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3662875066:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.19/0.48 % (2453200)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2549211641:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.19/0.48 % (2453201)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=212489511:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.19/0.48 % (2453202)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=757579313:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.48 % (2453196)Instruction limit reached!
% 1.19/0.48 % (2453196)------------------------------
% 1.19/0.48 % (2453196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453196)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453196)Termination reason: Instruction limit
% 1.19/0.48 % (2453196)Termination phase: Property scanning
% 1.19/0.48 % (2453196)Time elapsed: 0.017 s
% 1.19/0.48 % (2453196)Peak memory usage: 11 MB
% 1.19/0.48 % (2453196)Instructions burned: 40 (million)
% 1.19/0.48 % (2453205)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=120143658:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.48 % (2453202)Instruction limit reached!
% 1.19/0.48 % (2453202)------------------------------
% 1.19/0.48 % (2453202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453202)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453202)Termination reason: Instruction limit
% 1.19/0.48 % (2453202)Termination phase: shuffling
% 1.19/0.48 % (2453202)Time elapsed: 0.007 s
% 1.19/0.48 % (2453202)Peak memory usage: 10 MB
% 1.19/0.48 % (2453202)Instructions burned: 16 (million)
% 1.19/0.48 % (2453201)Instruction limit reached!
% 1.19/0.48 % (2453201)------------------------------
% 1.19/0.48 % (2453201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453201)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453201)Termination reason: Instruction limit
% 1.19/0.48 % (2453201)Termination phase: shuffling
% 1.19/0.48 % (2453201)Time elapsed: 0.011 s
% 1.19/0.48 % (2453201)Peak memory usage: 10 MB
% 1.19/0.48 % (2453201)Instructions burned: 26 (million)
% 1.19/0.48 % (2453205)Instruction limit reached!
% 1.19/0.48 % (2453205)------------------------------
% 1.19/0.48 % (2453205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453205)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453205)Termination reason: Instruction limit
% 1.19/0.48 % (2453205)Termination phase: shuffling
% 1.19/0.48 % (2453205)Time elapsed: 0.007 s
% 1.19/0.48 % (2453205)Peak memory usage: 10 MB
% 1.19/0.48 % (2453205)Instructions burned: 15 (million)
% 1.19/0.48 % (2453210)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=361402584: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)
% 1.19/0.48 % (2453210)Instruction limit reached!
% 1.19/0.48 % (2453210)------------------------------
% 1.19/0.48 % (2453210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453210)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453210)Termination reason: Instruction limit
% 1.19/0.48 % (2453210)Termination phase: shuffling
% 1.19/0.48 % (2453210)Time elapsed: 0.002 s
% 1.19/0.48 % (2453210)Peak memory usage: 10 MB
% 1.19/0.48 % (2453210)Instructions burned: 4 (million)
% 1.19/0.48 % (2453212)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=65312124:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.19/0.48 % (2453213)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3182884631:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.19/0.48 % (2453214)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1790994277:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.19/0.48 % (2453200)Refutation not found, incomplete strategy
% 1.19/0.48 % (2453200)------------------------------
% 1.19/0.48 % (2453200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453200)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453200)Termination reason: Refutation not found, incomplete strategy
% 1.19/0.48 % (2453200)Time elapsed: 0.040 s
% 1.19/0.48 % (2453200)Peak memory usage: 13 MB
% 1.19/0.48 % (2453200)Instructions burned: 93 (million)
% 1.19/0.48 % (2453200)------------------------------
% 1.19/0.48 % (2453200)------------------------------
% 1.19/0.48 % (2453213)Instruction limit reached!
% 1.19/0.48 % (2453213)------------------------------
% 1.19/0.48 % (2453213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453213)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453213)Termination reason: Instruction limit
% 1.19/0.48 % (2453213)Termination phase: shuffling
% 1.19/0.48 % (2453213)Time elapsed: 0.010 s
% 1.19/0.48 % (2453213)Peak memory usage: 10 MB
% 1.19/0.48 % (2453213)Instructions burned: 23 (million)
% 1.19/0.48 % (2453216)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.19/0.48 % (2453216)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.19/0.48 % (2453220)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.19/0.48 % (2453212)Instruction limit reached!
% 1.19/0.48 % (2453212)------------------------------
% 1.19/0.48 % (2453212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453212)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453212)Termination reason: Instruction limit
% 1.19/0.48 % (2453212)Termination phase: shuffling
% 1.19/0.48 % (2453212)Time elapsed: 0.027 s
% 1.19/0.48 % (2453212)Peak memory usage: 10 MB
% 1.19/0.48 % (2453212)Instructions burned: 26 (million)
% 1.19/0.48 % (2453204) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2453164-2453204"...
% 1.19/0.48 % (2453214)Instruction limit reached!
% 1.19/0.48 % (2453214)------------------------------
% 1.19/0.48 % (2453214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453214)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453214)Termination reason: Instruction limit
% 1.19/0.48 % (2453214)Termination phase: Preprocessing 3
% 1.19/0.48 % (2453214)Time elapsed: 0.026 s
% 1.19/0.48 % (2453214)Peak memory usage: 11 MB
% 1.19/0.48 % (2453214)Instructions burned: 61 (million)
% 1.19/0.48 % (2453220)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=2471581522:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.19/0.48 % (2453221)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=4241045771:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.19/0.48 % (2453216)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=2075013859:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.48 % (2453204)...printing done.
% 1.19/0.48 % (2453204)Refutation found. Thanks to Tanya!
% 1.19/0.48 % SZS status Theorem for theBenchmark
% 1.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 1.19/0.48 % (2453204)------------------------------
% 1.19/0.48 % (2453204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (2453204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (2453204)CaDiCaL version: 2.1.3
% 1.19/0.48 % (2453204)Termination reason: Refutation
% 1.19/0.48 % (2453204)Time elapsed: 0.065 s
% 1.19/0.48 % (2453204)Peak memory usage: 14 MB
% 1.19/0.48 % (2453204)Instructions burned: 278 (million)
% 1.19/0.48 % (2453164)Success in time 0.195 s
% 1.19/0.48 % Vampire exiting
%------------------------------------------------------------------------------