%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM676^4 : 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 : n014.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 08:18:30 AM UTC 2026
% Result : Theorem 0.67s 0.51s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 895 ( 120 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 1158 ( 7 ~; 32 |; 0 &; 959 @)
% ( 0 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 169 ( 165 usr; 9 con; 0-7 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 237 ( 214 ^; 23 !; 0 ?; 237 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_133,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_135,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_137,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
vIMP: $o > $o > $o ).
thf(func_def_143,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_144,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_145,type,
vNOT: $o > $o ).
thf(func_def_146,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_147,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_148,type,
vOR: $o > $o > $o ).
thf(func_def_149,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_150,type,
sK0: $i > $i > $i > $i ).
thf(func_def_151,type,
sK1: $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_152,type,
sK2: ( $i > $o ) > $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 > $o ).
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 > $o ) > $i ).
thf(func_def_162,type,
sK12: $i > $i > $o ).
thf(func_def_163,type,
sK13: $i > $i > $o ).
thf(func_def_168,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_169,type,
sK19: $i > $i > $i > $i ).
thf(f1,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f91,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) )
= e_is ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(f157,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(f160,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(f205,axiom,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(f241,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] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19d) ).
thf(f244,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] :
( ( n_is @ X0 @ X1 )
=> ( ( d_29_ii @ X2 @ X3 )
=> ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19g) ).
thf(f245,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] :
( ( n_is @ X0 @ X1 )
=> ( ( d_29_ii @ X2 @ X3 )
=> ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f244]) ).
thf(f264,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] :
( ( n_is @ X1 @ X3 )
=> ( ( d_29_ii @ X5 @ X7 )
=> ( d_29_ii @ ( n_pl @ X1 @ X5 ) @ ( n_pl @ X3 @ X7 ) ) ) ) ) ) ) ),
inference(rectify,[],[f245]) ).
thf(f265,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] :
( ( n_is @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y2 @ Y3 )
=> ( d_29_ii @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f264]) ).
thf(f282,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f407,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f536,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X5: $i] :
( ( d_29_ii @ X1 @ X3 )
=> ( d_29_ii @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f241]) ).
thf(f537,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] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( d_29_ii @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f536]) ).
thf(f543,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f544,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f543]) ).
thf(f589,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f641,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] :
( ( n_is @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y2 @ Y3 )
=> ( d_29_ii @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f265]) ).
thf(f675,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] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( d_29_ii @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f537]) ).
thf(f693,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f544]) ).
thf(f721,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f589]) ).
thf(f723,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f407]) ).
thf(f728,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f768,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] :
( ( n_is @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y2 @ Y3 )
=> ( d_29_ii @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f641]) ).
thf(f769,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f282]) ).
thf(f773,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f776,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,[],[f693,f723]) ).
thf(f779,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f773,f721]) ).
thf(f783,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f769,f728]) ).
thf(f788,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i] : ( l_some @ nat @ ( diffprop @ Y3 @ Y4 ) )
@ Y0
@ Y1 )
=> ( ^ [Y3: $i,Y4: $i] : ( l_some @ nat @ ( diffprop @ Y3 @ Y4 ) )
@ ( n_pl @ Y2 @ Y0 )
@ ( n_pl @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f675,f776,f776,f776,f783,f783]) ).
thf(f859,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ^ [Y3: $i > $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,Y6: $i] : ( Y5 = Y6 )
@ nat
@ 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_pl @ Y0 @ Y2 )
@ ( n_pl @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f768,f776,f776,f776,f776,f779,f783,f783]) ).
thf(f1277,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f788]) ).
thf(f1278,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1277]) ).
thf(f1279,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ X1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1278]) ).
thf(f1280,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ X1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1279]) ).
thf(f1281,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ X1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) )
@ X2 )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1280]) ).
thf(f1282,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ X1 ) @ ( n_pl @ Y0 @ X2 ) ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1281]) ).
thf(f1283,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ X1 ) @ ( n_pl @ Y0 @ X2 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1282]) ).
thf(f1284,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ X1 ) @ ( n_pl @ Y0 @ X2 ) ) ) ) )
@ X3 ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1283]) ).
thf(f1285,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X3 @ X1 ) @ ( n_pl @ X3 @ X2 ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1284]) ).
thf(f1286,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X3 @ X1 ) @ ( n_pl @ X3 @ X2 ) ) ) )
= $true )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1285]) ).
thf(f1287,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X3 @ X1 ) @ ( n_pl @ X3 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1286]) ).
thf(f1354,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 )
=> ( ( Y0 = Y1 )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y3 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f859]) ).
thf(f1355,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( Y0 = Y1 )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y3 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ sK14 )
= $false ),
inference(sigma_proxy_clausification,[],[f1354]) ).
thf(f1356,plain,
( ( ( in @ sK14 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( sK14 = Y0 )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ Y1 ) @ ( n_pl @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1355]) ).
thf(f1357,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( sK14 = Y0 )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ Y1 ) @ ( n_pl @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1356]) ).
thf(f1358,plain,
( $true
= ( in @ sK14 @ nat ) ),
inference(imp_proxy_clausification,[],[f1356]) ).
thf(f1359,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( sK14 = Y0 )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ Y1 ) @ ( n_pl @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
@ sK15 )
= $false ),
inference(sigma_proxy_clausification,[],[f1357]) ).
thf(f1360,plain,
( ( ( in @ sK15 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ Y0 ) @ ( n_pl @ sK15 @ Y1 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1359]) ).
thf(f1361,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ Y0 ) @ ( n_pl @ sK15 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1360]) ).
thf(f1363,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ Y0 ) @ ( n_pl @ sK15 @ Y1 ) ) ) ) ) ) ) )
@ sK16 )
= $false ),
inference(sigma_proxy_clausification,[],[f1361]) ).
thf(f1364,plain,
( $false
= ( ( in @ sK16 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ sK16 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1363]) ).
thf(f1365,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ sK16 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1364]) ).
thf(f1366,plain,
( $true
= ( in @ sK16 @ nat ) ),
inference(imp_proxy_clausification,[],[f1364]) ).
thf(f1367,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ sK16 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ Y0 ) ) ) ) ) )
@ sK17 ) ),
inference(sigma_proxy_clausification,[],[f1365]) ).
thf(f1368,plain,
( ( ( in @ sK17 @ nat )
=> ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ sK17 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1367]) ).
thf(f1369,plain,
( $false
= ( ( sK14 = sK15 )
=> ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ sK17 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1368]) ).
thf(f1370,plain,
( $true
= ( in @ sK17 @ nat ) ),
inference(imp_proxy_clausification,[],[f1368]) ).
thf(f1371,plain,
( ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ sK17 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1369]) ).
thf(f1372,plain,
( $true
= ( sK14 = sK15 ) ),
inference(imp_proxy_clausification,[],[f1369]) ).
thf(f1373,plain,
sK14 = sK15,
inference(equality_proxy_clausification,[],[f1372]) ).
thf(f1374,plain,
( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK15 @ sK17 ) ) ) ),
inference(imp_proxy_clausification,[],[f1371]) ).
thf(f1375,plain,
( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
= $true ),
inference(imp_proxy_clausification,[],[f1371]) ).
thf(f1468,plain,
( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK16 ) @ ( n_pl @ sK14 @ sK17 ) ) ) ),
inference(forward_demodulation,[],[f1374,f1373]) ).
thf(f1759,plain,
( ( $false
= ( in @ sK17 @ nat ) )
| ( $false
= ( in @ sK16 @ nat ) )
| ( $false
= ( in @ sK14 @ nat ) )
| ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
= $false )
| ( $false = $true ) ),
inference(superposition,[],[f1468,f1287]) ).
thf(f1775,plain,
( ( $false
= ( in @ sK14 @ nat ) )
| ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
= $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( $false
= ( in @ sK16 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1759]) ).
thf(f1780,plain,
( ( $false
= ( in @ sK17 @ nat ) )
| ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
= $false )
| ( $false
= ( in @ sK16 @ nat ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f1775,f1358]) ).
thf(f1781,plain,
( ( ( l_some @ nat @ ( diffprop @ sK16 @ sK17 ) )
= $false )
| ( $false
= ( in @ sK17 @ nat ) )
| ( $false
= ( in @ sK16 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1780]) ).
thf(f1784,plain,
( ( $false = $true )
| ( $false
= ( in @ sK17 @ nat ) )
| ( $false
= ( in @ sK16 @ nat ) ) ),
inference(forward_demodulation,[],[f1781,f1375]) ).
thf(f1785,plain,
( ( $false
= ( in @ sK17 @ nat ) )
| ( $false
= ( in @ sK16 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1784]) ).
thf(f1788,plain,
( ( $false
= ( in @ sK16 @ nat ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f1785,f1370]) ).
thf(f1789,plain,
( $false
= ( in @ sK16 @ nat ) ),
inference(trivial_inequality_removal,[],[f1788]) ).
thf(f1792,plain,
$false = $true,
inference(superposition,[],[f1789,f1366]) ).
thf(f1795,plain,
$false,
inference(trivial_inequality_removal,[],[f1792]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM676^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n014.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 12:36:00 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.20/0.29 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
% 0.67/0.43 % (2591666)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.67/0.43 % (2591674)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=1192312432: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)
% 0.67/0.43 % (2591677)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.67/0.43 % (2591677)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
% 0.67/0.43 % (2591672)lrs+10_16_si=on:nwc=1.5:random_seed=149576379:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.67/0.43 % (2591673)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3772618916:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.67/0.43 % (2591676)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3030299516:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.67/0.43 % (2591675)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3044432976:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.67/0.43 % (2591677)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=813151269:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.67/0.43 % (2591673)Instruction limit reached!
% 0.67/0.43 % (2591673)------------------------------
% 0.67/0.43 % (2591673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (2591673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (2591673)CaDiCaL version: 2.1.3
% 0.67/0.43 % (2591673)Termination reason: Instruction limit
% 0.67/0.43 % (2591673)Termination phase: shuffling
% 0.67/0.43 % (2591673)Time elapsed: 0.002 s
% 0.67/0.43 % (2591673)Peak memory usage: 10 MB
% 0.67/0.43 % (2591673)Instructions burned: 4 (million)
% 0.67/0.43 % (2591672)Instruction limit reached!
% 0.67/0.43 % (2591672)------------------------------
% 0.67/0.43 % (2591672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (2591672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (2591672)CaDiCaL version: 2.1.3
% 0.67/0.43 % (2591672)Termination reason: Instruction limit
% 0.67/0.43 % (2591672)Termination phase: shuffling
% 0.67/0.43 % (2591672)Time elapsed: 0.008 s
% 0.67/0.43 % (2591672)Peak memory usage: 10 MB
% 0.67/0.43 % (2591672)Instructions burned: 18 (million)
% 0.67/0.43 % (2591671)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1081174259:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.67/0.43 % (2591675)Instruction limit reached!
% 0.67/0.43 % (2591675)------------------------------
% 0.67/0.43 % (2591675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (2591675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (2591675)CaDiCaL version: 2.1.3
% 0.67/0.43 % (2591675)Termination reason: Instruction limit
% 0.67/0.43 % (2591675)Termination phase: Property scanning
% 0.67/0.43 % (2591675)Time elapsed: 0.011 s
% 0.67/0.43 % (2591675)Peak memory usage: 10 MB
% 0.67/0.43 % (2591675)Instructions burned: 25 (million)
% 0.67/0.43 % (2591684)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=617963647:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.43 % (2591684)Instruction limit reached!
% 0.67/0.43 % (2591684)------------------------------
% 0.67/0.43 % (2591684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (2591684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (2591684)CaDiCaL version: 2.1.3
% 0.67/0.43 % (2591684)Termination reason: Instruction limit
% 0.67/0.43 % (2591684)Termination phase: shuffling
% 0.67/0.43 % (2591684)Time elapsed: 0.003 s
% 0.67/0.43 % (2591684)Peak memory usage: 10 MB
% 0.67/0.43 % (2591684)Instructions burned: 7 (million)
% 0.67/0.43 % (2591685)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3366212882:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.67/0.46 % (2591687)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.46 % (2591685)Instruction limit reached!
% 0.67/0.46 % (2591685)------------------------------
% 0.67/0.46 % (2591685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (2591685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (2591685)CaDiCaL version: 2.1.3
% 0.67/0.46 % (2591685)Termination reason: Instruction limit
% 0.67/0.46 % (2591685)Termination phase: shuffling
% 0.67/0.46 % (2591685)Time elapsed: 0.003 s
% 0.67/0.46 % (2591685)Peak memory usage: 10 MB
% 0.67/0.46 % (2591685)Instructions burned: 7 (million)
% 0.67/0.46 % (2591687)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3109254487:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.67/0.46 % (2591676)Instruction limit reached!
% 0.67/0.46 % (2591676)------------------------------
% 0.67/0.46 % (2591676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (2591676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (2591676)CaDiCaL version: 2.1.3
% 0.67/0.46 % (2591676)Termination reason: Instruction limit
% 0.67/0.46 % (2591676)Termination phase: Function definition elimination
% 0.67/0.46 % (2591676)Time elapsed: 0.033 s
% 0.67/0.46 % (2591676)Peak memory usage: 11 MB
% 0.67/0.46 % (2591676)Instructions burned: 75 (million)
% 0.67/0.46 % (2591687)Instruction limit reached!
% 0.67/0.46 % (2591687)------------------------------
% 0.67/0.46 % (2591687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (2591687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (2591687)CaDiCaL version: 2.1.3
% 0.67/0.46 % (2591687)Termination reason: Instruction limit
% 0.67/0.46 % (2591687)Termination phase: shuffling
% 0.67/0.46 % (2591687)Time elapsed: 0.004 s
% 0.67/0.46 % (2591687)Peak memory usage: 10 MB
% 0.67/0.46 % (2591687)Instructions burned: 8 (million)
% 0.67/0.46 % (2591691)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
% 0.67/0.46 % (2591691)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.46 % (2591690)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=13784655:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.67/0.46 % (2591691)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=524802374:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.67/0.46 % (2591693)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=2575716075:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.67/0.46 % (2591690)Instruction limit reached!
% 0.67/0.46 % (2591690)------------------------------
% 0.67/0.46 % (2591690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (2591690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (2591690)CaDiCaL version: 2.1.3
% 0.67/0.46 % (2591690)Termination reason: Instruction limit
% 0.67/0.46 % (2591690)Termination phase: shuffling
% 0.67/0.46 % (2591690)Time elapsed: 0.006 s
% 0.67/0.46 % (2591690)Peak memory usage: 10 MB
% 0.67/0.46 % (2591690)Instructions burned: 13 (million)
% 0.67/0.46 % (2591694)lrs+10_1_si=on:cs=on:random_seed=3921961930:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.67/0.46 % (2591694)Instruction limit reached!
% 0.67/0.46 % (2591694)------------------------------
% 0.67/0.46 % (2591694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (2591694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (2591694)CaDiCaL version: 2.1.3
% 0.67/0.46 % (2591694)Termination reason: Instruction limit
% 0.67/0.46 % (2591694)Termination phase: shuffling
% 0.67/0.46 % (2591694)Time elapsed: 0.004 s
% 0.67/0.46 % (2591694)Peak memory usage: 10 MB
% 0.67/0.46 % (2591694)Instructions burned: 10 (million)
% 0.67/0.46 % (2591691)Instruction limit reached!
% 0.67/0.51 % (2591691)------------------------------
% 0.67/0.51 % (2591691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591691)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591691)Termination reason: Instruction limit
% 0.67/0.51 % (2591691)Termination phase: Property scanning
% 0.67/0.51 % (2591691)Time elapsed: 0.012 s
% 0.67/0.51 % (2591691)Peak memory usage: 10 MB
% 0.67/0.51 % (2591691)Instructions burned: 28 (million)
% 0.67/0.51 % (2591677)Instruction limit reached!
% 0.67/0.51 % (2591677)------------------------------
% 0.67/0.51 % (2591677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591677)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591677)Termination reason: Instruction limit
% 0.67/0.51 % (2591677)Termination phase: Function definition elimination
% 0.67/0.51 % (2591677)Time elapsed: 0.064 s
% 0.67/0.51 % (2591677)Peak memory usage: 11 MB
% 0.67/0.51 % (2591677)Instructions burned: 158 (million)
% 0.67/0.51 % (2591698)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.67/0.51 % (2591698)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=158023856:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.51 % (2591671)Instruction limit reached!
% 0.67/0.51 % (2591671)------------------------------
% 0.67/0.51 % (2591671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591671)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591671)Termination reason: Instruction limit
% 0.67/0.51 % (2591671)Termination phase: Function definition elimination
% 0.67/0.51 % (2591671)Time elapsed: 0.061 s
% 0.67/0.51 % (2591671)Peak memory usage: 11 MB
% 0.67/0.51 % (2591671)Instructions burned: 89 (million)
% 0.67/0.51 % (2591698)Instruction limit reached!
% 0.67/0.51 % (2591698)------------------------------
% 0.67/0.51 % (2591698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591698)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591698)Termination reason: Instruction limit
% 0.67/0.51 % (2591698)Termination phase: shuffling
% 0.67/0.51 % (2591698)Time elapsed: 0.003 s
% 0.67/0.51 % (2591698)Peak memory usage: 10 MB
% 0.67/0.51 % (2591698)Instructions burned: 6 (million)
% 0.67/0.51 % (2591700)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2247391418:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.67/0.51 % (2591701)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=707073118:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.67/0.51 % (2591702)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=903387034:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.67/0.51 % (2591693)Instruction limit reached!
% 0.67/0.51 % (2591693)------------------------------
% 0.67/0.51 % (2591693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591693)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591693)Termination reason: Instruction limit
% 0.67/0.51 % (2591693)Termination phase: Function definition elimination
% 0.67/0.51 % (2591693)Time elapsed: 0.036 s
% 0.67/0.51 % (2591693)Peak memory usage: 11 MB
% 0.67/0.51 % (2591693)Instructions burned: 86 (million)
% 0.67/0.51 % (2591704)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4271863632:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.51 % (2591705)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=382657986:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.67/0.51 % (2591700)Instruction limit reached!
% 0.67/0.51 % (2591700)------------------------------
% 0.67/0.51 % (2591700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591700)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591700)Termination reason: Instruction limit
% 0.67/0.51 % (2591700)Termination phase: SInE selection
% 0.67/0.51 % (2591700)Time elapsed: 0.016 s
% 0.67/0.51 % (2591700)Peak memory usage: 10 MB
% 0.67/0.51 % (2591700)Instructions burned: 38 (million)
% 0.67/0.51 % (2591702)Instruction limit reached!
% 0.67/0.51 % (2591702)------------------------------
% 0.67/0.51 % (2591702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591702)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591702)Termination reason: Instruction limit
% 0.67/0.51 % (2591702)Termination phase: Property scanning
% 0.67/0.51 % (2591702)Time elapsed: 0.011 s
% 0.67/0.51 % (2591702)Peak memory usage: 10 MB
% 0.67/0.51 % (2591702)Instructions burned: 25 (million)
% 0.67/0.51 % (2591704)Instruction limit reached!
% 0.67/0.51 % (2591704)------------------------------
% 0.67/0.51 % (2591704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591704)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591704)Termination reason: Instruction limit
% 0.67/0.51 % (2591704)Termination phase: shuffling
% 0.67/0.51 % (2591704)Time elapsed: 0.006 s
% 0.67/0.51 % (2591704)Peak memory usage: 10 MB
% 0.67/0.51 % (2591704)Instructions burned: 14 (million)
% 0.67/0.51 % (2591701)Refutation not found, incomplete strategy
% 0.67/0.51 % (2591701)------------------------------
% 0.67/0.51 % (2591701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591701)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591701)Termination reason: Refutation not found, incomplete strategy
% 0.67/0.51 % (2591701)Time elapsed: 0.025 s
% 0.67/0.51 % (2591701)Peak memory usage: 13 MB
% 0.67/0.51 % (2591701)Instructions burned: 56 (million)
% 0.67/0.51 % (2591701)------------------------------
% 0.67/0.51 % (2591701)------------------------------
% 0.67/0.51 % (2591709)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3507994605:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.51 % (2591709)Instruction limit reached!
% 0.67/0.51 % (2591709)------------------------------
% 0.67/0.51 % (2591709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591709)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591709)Termination reason: Instruction limit
% 0.67/0.51 % (2591709)Termination phase: shuffling
% 0.67/0.51 % (2591709)Time elapsed: 0.006 s
% 0.67/0.51 % (2591709)Peak memory usage: 10 MB
% 0.67/0.51 % (2591709)Instructions burned: 15 (million)
% 0.67/0.51 % (2591712)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3786552229: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)
% 0.67/0.51 % (2591713)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=254526097:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.67/0.51 % (2591712)Instruction limit reached!
% 0.67/0.51 % (2591712)------------------------------
% 0.67/0.51 % (2591712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591712)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591712)Termination reason: Instruction limit
% 0.67/0.51 % (2591712)Termination phase: shuffling
% 0.67/0.51 % (2591712)Time elapsed: 0.001 s
% 0.67/0.51 % (2591712)Peak memory usage: 10 MB
% 0.67/0.51 % (2591712)Instructions burned: 2 (million)
% 0.67/0.51 % (2591714)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2149364537:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.67/0.51 % (2591716)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2117724520:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.67/0.51 % (2591713)Instruction limit reached!
% 0.67/0.51 % (2591713)------------------------------
% 0.67/0.51 % (2591713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591713)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591713)Termination reason: Instruction limit
% 0.67/0.51 % (2591713)Termination phase: Property scanning
% 0.67/0.51 % (2591713)Time elapsed: 0.012 s
% 0.67/0.51 % (2591713)Peak memory usage: 10 MB
% 0.67/0.51 % (2591713)Instructions burned: 27 (million)
% 0.67/0.51 % (2591719)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
% 0.67/0.51 % (2591719)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.67/0.51 % (2591720)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.67/0.51 % (2591714)Instruction limit reached!
% 0.67/0.51 % (2591714)------------------------------
% 0.67/0.51 % (2591714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591714)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591714)Termination reason: Instruction limit
% 0.67/0.51 % (2591714)Termination phase: Property scanning
% 0.67/0.51 % (2591714)Time elapsed: 0.016 s
% 0.67/0.51 % (2591714)Peak memory usage: 10 MB
% 0.67/0.51 % (2591714)Instructions burned: 23 (million)
% 0.67/0.51 % (2591719)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=3580421967:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.51 % (2591720)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=911653848:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.67/0.51 % (2591720)Instruction limit reached!
% 0.67/0.51 % (2591720)------------------------------
% 0.67/0.51 % (2591720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591720)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591720)Termination reason: Instruction limit
% 0.67/0.51 % (2591720)Termination phase: shuffling
% 0.67/0.51 % (2591720)Time elapsed: 0.004 s
% 0.67/0.51 % (2591720)Peak memory usage: 10 MB
% 0.67/0.51 % (2591720)Instructions burned: 10 (million)
% 0.67/0.51 % (2591719)Instruction limit reached!
% 0.67/0.51 % (2591719)------------------------------
% 0.67/0.51 % (2591719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591719)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591719)Termination reason: Instruction limit
% 0.67/0.51 % (2591719)Termination phase: shuffling
% 0.67/0.51 % (2591719)Time elapsed: 0.007 s
% 0.67/0.51 % (2591719)Peak memory usage: 10 MB
% 0.67/0.51 % (2591719)Instructions burned: 15 (million)
% 0.67/0.51 % (2591716)Instruction limit reached!
% 0.67/0.51 % (2591716)------------------------------
% 0.67/0.51 % (2591716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591716)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591716)Termination reason: Instruction limit
% 0.67/0.51 % (2591716)Termination phase: Property scanning
% 0.67/0.51 % (2591716)Time elapsed: 0.026 s
% 0.67/0.51 % (2591716)Peak memory usage: 11 MB
% 0.67/0.51 % (2591716)Instructions burned: 62 (million)
% 0.67/0.51 % (2591723)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=1162972014:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.67/0.51 % (2591728)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2765068502:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 0.67/0.51 % (2591727)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2200191281:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.67/0.51 % (2591728)Instruction limit reached!
% 0.67/0.51 % (2591728)------------------------------
% 0.67/0.51 % (2591728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2591666-2591705"...
% 0.67/0.51 % (2591728)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591728)Termination reason: Instruction limit
% 0.67/0.51 % (2591728)Termination phase: shuffling
% 0.67/0.51 % (2591728)Time elapsed: 0.009 s
% 0.67/0.51 % (2591728)Peak memory usage: 10 MB
% 0.67/0.51 % (2591728)Instructions burned: 22 (million)
% 0.67/0.51 % (2591727)Instruction limit reached!
% 0.67/0.51 % (2591727)------------------------------
% 0.67/0.51 % (2591727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591727)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591727)Termination reason: Instruction limit
% 0.67/0.51 % (2591727)Termination phase: Property scanning
% 0.67/0.51 % (2591727)Time elapsed: 0.010 s
% 0.67/0.51 % (2591727)Peak memory usage: 10 MB
% 0.67/0.51 % (2591727)Instructions burned: 23 (million)
% 0.67/0.51 % (2591674)Instruction limit reached!
% 0.67/0.51 % (2591674)------------------------------
% 0.67/0.51 % (2591674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2591674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2591674)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2591674)Termination reason: Instruction limit
% 0.67/0.51 % (2591674)Termination phase: Saturation
% 0.67/0.51 % (2591674)Time elapsed: 0.177 s
% 0.67/0.51 % (2591674)Peak memory usage: 17 MB
% 0.67/0.51 % (2591674)Instructions burned: 636 (million)
% 0.67/0.51 % (2591725)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2281212257:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.67/0.51 % (2591729)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=208958345:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 0.67/0.51 % (2591705)...printing done.
% 0.67/0.51 % (2591705)Refutation found. Thanks to Tanya!
% 0.67/0.51 % SZS status Theorem for theBenchmark
% 0.67/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.52 % (2591705)------------------------------
% 0.25/0.52 % (2591705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.52 % (2591705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.52 % (2591705)CaDiCaL version: 2.1.3
% 0.25/0.52 % (2591705)Termination reason: Refutation
% 0.25/0.52 % (2591705)Time elapsed: 0.078 s
% 0.25/0.52 % (2591705)Peak memory usage: 14 MB
% 0.25/0.52 % (2591705)Instructions burned: 175 (million)
% 0.25/0.52 % (2591666)Success in time 0.22 s
% 0.25/0.52 % Vampire exiting
%------------------------------------------------------------------------------