%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM673^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 2.20s 0.73s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 9
% Syntax : Number of formulae : 91 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 993 ( 146 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 1248 ( 7 ~; 51 |; 0 &;1060 @)
% ( 0 <=>; 90 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 169 ( 165 usr; 8 con; 0-7 aty)
% ( 40 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 255 ( 221 ^; 34 !; 0 ?; 255 :)
% 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_134,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_136,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_137,type,
vNOT: $o > $o ).
thf(func_def_138,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_139,type,
vIMP: $o > $o > $o ).
thf(func_def_140,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_141,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_144,type,
vOR: $o > $o > $o ).
thf(func_def_145,type,
vAND: $o > $o > $o ).
thf(func_def_146,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_147,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_148,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_149,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_150,type,
sK0: $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_151,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK2: $i > $i > $i > $i ).
thf(func_def_153,type,
sK3: $i > $i ).
thf(func_def_154,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_155,type,
sK5: $i > $i > $o ).
thf(func_def_156,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_158,type,
sK8: $i > $i > $o ).
thf(func_def_159,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_161,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK15: $i > $i > $o ).
thf(func_def_166,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_167,type,
sK17: $i > $i > $o ).
thf(func_def_168,type,
sK18: $i > $i > $i > $i ).
thf(func_def_169,type,
sK19: $i > $i > $o ).
thf(f1,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(f2,axiom,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f91,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( X1 = X2 ) )
= e_is ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(f157,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(f160,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(f197,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(f205,axiom,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) )
= d_29_ii ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(f238,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 @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(f241,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19d) ).
thf(f242,negated_conjecture,
~ ( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f241]) ).
thf(f321,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f382,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f432,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,[],[f242]) ).
thf(f433,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,[],[f432]) ).
thf(f442,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f554,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 @ X1 @ X5 ) @ ( n_pl @ X3 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f238]) ).
thf(f555,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( d_29_ii @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f554]) ).
thf(f615,plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f616,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f615]) ).
thf(f624,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] : ( n_is @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f197]) ).
thf(f625,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ Y0 @ Y1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f624]) ).
thf(f632,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(flattening,[],[f433]) ).
thf(f683,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] : ( n_is @ ( n_pl @ Y0 @ Y1 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f625]) ).
thf(f684,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f442]) ).
thf(f702,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f321]) ).
thf(f703,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f723,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f616]) ).
thf(f726,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,[],[f632]) ).
thf(f753,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f760,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f382]) ).
thf(f761,plain,
( ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( all_of
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( d_29_ii @ Y0 @ Y1 )
=> ( d_29_ii @ ( n_pl @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f555]) ).
thf(f771,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f702,f753]) ).
thf(f773,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,[],[f723,f684]) ).
thf(f776,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f703,f760]) ).
thf(f795,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( Y3 = Y4 )
@ nat
@ ( n_pl @ Y0 @ Y1 )
@ ( n_pl @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f683,f773,f773,f776]) ).
thf(f823,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i] : ( l_some @ nat @ ( diffprop @ Y3 @ Y4 ) )
@ Y0
@ Y1 )
=> ( ^ [Y3: $i,Y4: $i] : ( l_some @ nat @ ( diffprop @ Y3 @ Y4 ) )
@ ( n_pl @ Y2 @ Y0 )
@ ( n_pl @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f726,f773,f773,f773,f771,f771]) ).
thf(f849,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i > $o] : ( Y4 @ Y3 )
@ Y2
@ Y0 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i > $o] : ( Y5 @ Y4 )
@ Y3
@ Y1 )
=> ( Y2 @ Y3 ) ) )
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ^ [Y5: $i,Y6: $i > $o] : ( Y6 @ Y5 )
@ Y4
@ Y2 )
=> ( Y3 @ Y4 ) ) )
@ ^ [Y2: $i] : ( in @ Y2 @ nat )
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i] : ( l_some @ nat @ ( diffprop @ Y3 @ Y4 ) )
@ Y0
@ Y1 )
=> ( ^ [Y3: $i,Y4: $i] : ( l_some @ nat @ ( diffprop @ Y3 @ Y4 ) )
@ ( n_pl @ Y0 @ Y2 )
@ ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f761,f773,f773,f773,f771,f771]) ).
thf(f973,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f795]) ).
thf(f974,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f973]) ).
thf(f975,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f974]) ).
thf(f976,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ Y0 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f975]) ).
thf(f977,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X1 @ Y0 )
= ( n_pl @ Y0 @ X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f976]) ).
thf(f978,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ nat )
=> ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X2 @ X1 ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f977]) ).
thf(f979,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X2 @ X1 ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f978]) ).
thf(f980,plain,
! [X2: $i,X1: $i] :
( ( ( n_pl @ X1 @ X2 )
= ( n_pl @ X2 @ X1 ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(equality_proxy_clausification,[],[f979]) ).
thf(f1115,plain,
( $true
!= ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f823]) ).
thf(f1116,plain,
( $false
= ( ^ [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 ) ) ) ) ) ) ) ) )
@ sK12 ) ),
inference(sigma_proxy_clausification,[],[f1115]) ).
thf(f1117,plain,
( $false
= ( ( in @ sK12 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ sK12 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1116]) ).
thf(f1118,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ sK12 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1117]) ).
thf(f1119,plain,
( $true
= ( in @ sK12 @ nat ) ),
inference(imp_proxy_clausification,[],[f1117]) ).
thf(f1120,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ sK12 ) @ ( n_pl @ Y1 @ Y0 ) ) ) ) ) ) )
@ sK13 )
= $false ),
inference(sigma_proxy_clausification,[],[f1118]) ).
thf(f1121,plain,
( ( ( in @ sK13 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ sK12 ) @ ( n_pl @ Y0 @ sK13 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1120]) ).
thf(f1122,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ sK12 ) @ ( n_pl @ Y0 @ sK13 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1121]) ).
thf(f1123,plain,
( $true
= ( in @ sK13 @ nat ) ),
inference(imp_proxy_clausification,[],[f1121]) ).
thf(f1124,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ sK12 ) @ ( n_pl @ Y0 @ sK13 ) ) ) ) )
@ sK14 )
= $false ),
inference(sigma_proxy_clausification,[],[f1122]) ).
thf(f1125,plain,
( ( ( in @ sK14 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK12 ) @ ( n_pl @ sK14 @ sK13 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1124]) ).
thf(f1126,plain,
( $false
= ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK12 ) @ ( n_pl @ sK14 @ sK13 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1125]) ).
thf(f1127,plain,
( $true
= ( in @ sK14 @ nat ) ),
inference(imp_proxy_clausification,[],[f1125]) ).
thf(f1128,plain,
( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK14 @ sK12 ) @ ( n_pl @ sK14 @ sK13 ) ) ) ),
inference(imp_proxy_clausification,[],[f1126]) ).
thf(f1129,plain,
( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
= $true ),
inference(imp_proxy_clausification,[],[f1126]) ).
thf(f1218,plain,
( $true
= ( !! @ $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 @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f849]) ).
thf(f1219,plain,
! [X1: $i] :
( $true
= ( ^ [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 @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1218]) ).
thf(f1220,plain,
! [X1: $i] :
( $true
= ( ( 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 @ X1 @ Y1 ) @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1219]) ).
thf(f1221,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 @ X1 @ Y1 ) @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1220]) ).
thf(f1222,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 @ X1 @ Y1 ) @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) )
@ X2 )
= $true )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1221]) ).
thf(f1223,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ Y0 ) @ ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1222]) ).
thf(f1224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ Y0 ) @ ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1223]) ).
thf(f1225,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 @ X1 @ Y0 ) @ ( n_pl @ X2 @ Y0 ) ) ) ) )
@ X3 ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1224]) ).
thf(f1226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( ( in @ X3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X2 @ X3 ) ) ) ) )
= $true )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1225]) ).
thf(f1227,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X2 @ X3 ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1226]) ).
thf(f1228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X2 @ X3 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1227]) ).
thf(f1484,plain,
( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK14 @ sK13 ) ) )
= $false )
| ( ( in @ sK12 @ nat )
= $false )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(superposition,[],[f1128,f980]) ).
thf(f1486,plain,
( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK14 @ sK13 ) ) )
= $false )
| ( $false
= ( in @ sK14 @ nat ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1484,f1119]) ).
thf(f1487,plain,
( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK14 @ sK13 ) ) )
= $false )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1486]) ).
thf(f1494,plain,
( ( $true = $false )
| ( ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK14 @ sK13 ) ) )
= $false ) ),
inference(forward_demodulation,[],[f1487,f1127]) ).
thf(f1495,plain,
( ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK14 @ sK13 ) ) )
= $false ),
inference(trivial_inequality_removal,[],[f1494]) ).
thf(f1513,plain,
( ( $false
= ( in @ sK14 @ nat ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK13 @ sK14 ) ) ) )
| ( $false
= ( in @ sK13 @ nat ) ) ),
inference(superposition,[],[f1495,f980]) ).
thf(f1514,plain,
( ( $false
= ( in @ sK13 @ nat ) )
| ( $true = $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK13 @ sK14 ) ) ) ) ),
inference(forward_demodulation,[],[f1513,f1127]) ).
thf(f1515,plain,
( ( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK13 @ sK14 ) ) ) )
| ( $false
= ( in @ sK13 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1514]) ).
thf(f1518,plain,
( ( $true = $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK13 @ sK14 ) ) ) ) ),
inference(forward_demodulation,[],[f1515,f1123]) ).
thf(f1519,plain,
( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK12 @ sK14 ) @ ( n_pl @ sK13 @ sK14 ) ) ) ),
inference(trivial_inequality_removal,[],[f1518]) ).
thf(f1770,plain,
( ( $false
= ( in @ sK14 @ nat ) )
| ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
= $false )
| ( $true = $false )
| ( ( in @ sK12 @ nat )
= $false )
| ( $false
= ( in @ sK13 @ nat ) ) ),
inference(superposition,[],[f1228,f1519]) ).
thf(f1772,plain,
( ( ( l_some @ nat @ ( diffprop @ sK12 @ sK13 ) )
= $false )
| ( ( in @ sK12 @ nat )
= $false )
| ( $false
= ( in @ sK13 @ nat ) )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1770]) ).
thf(f1788,plain,
( ( ( in @ sK12 @ nat )
= $false )
| ( $true = $false )
| ( $false
= ( in @ sK13 @ nat ) )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(forward_demodulation,[],[f1772,f1129]) ).
thf(f1789,plain,
( ( $false
= ( in @ sK13 @ nat ) )
| ( ( in @ sK12 @ nat )
= $false )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1788]) ).
thf(f1792,plain,
( ( ( in @ sK12 @ nat )
= $false )
| ( $true = $false )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(forward_demodulation,[],[f1789,f1123]) ).
thf(f1793,plain,
( ( ( in @ sK12 @ nat )
= $false )
| ( $false
= ( in @ sK14 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1792]) ).
thf(f1796,plain,
( ( $false
= ( in @ sK14 @ nat ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1793,f1119]) ).
thf(f1797,plain,
( $false
= ( in @ sK14 @ nat ) ),
inference(trivial_inequality_removal,[],[f1796]) ).
thf(f1800,plain,
$true = $false,
inference(superposition,[],[f1797,f1127]) ).
thf(f1804,plain,
$false,
inference(trivial_inequality_removal,[],[f1800]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM673^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n010.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 12:35:18 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.37 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/0.57 % (2789919)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.79/0.57 % (2789926)lrs+10_16_si=on:nwc=1.5:random_seed=239953411:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.79/0.57 % (2789925)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=558976161:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.79/0.57 % (2789931)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.79/0.57 % (2789931)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
% 0.79/0.57 % (2789926)Instruction limit reached!
% 0.79/0.57 % (2789926)------------------------------
% 0.79/0.57 % (2789926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.57 % (2789926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.57 % (2789926)CaDiCaL version: 2.1.3
% 0.79/0.57 % (2789926)Termination reason: Instruction limit
% 0.79/0.57 % (2789926)Termination phase: shuffling
% 0.79/0.57 % (2789926)Time elapsed: 0.009 s
% 0.79/0.57 % (2789926)Peak memory usage: 10 MB
% 0.79/0.57 % (2789926)Instructions burned: 20 (million)
% 0.79/0.57 % (2789927)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=425568775:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.79/0.57 % (2789929)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3721359640:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.79/0.57 % (2789928)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=4103568401: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)
% 0.79/0.57 % (2789930)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2518428395:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.79/0.57 % (2789931)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=141848327:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.79/0.57 % (2789927)Instruction limit reached!
% 0.79/0.57 % (2789927)------------------------------
% 0.79/0.57 % (2789927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.57 % (2789927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.57 % (2789927)CaDiCaL version: 2.1.3
% 0.79/0.57 % (2789927)Termination reason: Instruction limit
% 0.79/0.57 % (2789927)Termination phase: shuffling
% 0.79/0.57 % (2789927)Time elapsed: 0.003 s
% 0.79/0.57 % (2789927)Peak memory usage: 10 MB
% 0.79/0.57 % (2789927)Instructions burned: 3 (million)
% 0.79/0.57 % (2789929)Instruction limit reached!
% 0.79/0.57 % (2789929)------------------------------
% 0.79/0.57 % (2789929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.57 % (2789929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.57 % (2789929)CaDiCaL version: 2.1.3
% 0.79/0.57 % (2789929)Termination reason: Instruction limit
% 0.79/0.57 % (2789929)Termination phase: Property scanning
% 0.79/0.57 % (2789929)Time elapsed: 0.020 s
% 0.79/0.57 % (2789929)Peak memory usage: 10 MB
% 0.79/0.57 % (2789929)Instructions burned: 24 (million)
% 0.79/0.57 % (2789935)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1133517205:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.79/0.57 % (2789925)Instruction limit reached!
% 0.79/0.57 % (2789925)------------------------------
% 0.79/0.57 % (2789925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.57 % (2789925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.57 % (2789925)CaDiCaL version: 2.1.3
% 0.79/0.57 % (2789925)Termination reason: Instruction limit
% 0.79/0.57 % (2789925)Termination phase: Function definition elimination
% 0.79/0.57 % (2789925)Time elapsed: 0.042 s
% 0.79/0.57 % (2789925)Peak memory usage: 11 MB
% 0.79/0.57 % (2789925)Instructions burned: 96 (million)
% 0.79/0.57 % (2789935)Instruction limit reached!
% 0.79/0.57 % (2789935)------------------------------
% 0.79/0.57 % (2789935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.61 % (2789935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.61 % (2789935)CaDiCaL version: 2.1.3
% 1.36/0.61 % (2789935)Termination reason: Instruction limit
% 1.36/0.61 % (2789935)Termination phase: shuffling
% 1.36/0.61 % (2789935)Time elapsed: 0.003 s
% 1.36/0.61 % (2789935)Peak memory usage: 10 MB
% 1.36/0.61 % (2789935)Instructions burned: 2 (million)
% 1.36/0.61 % (2789941)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3341169243:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.36/0.61 % (2789941)Instruction limit reached!
% 1.36/0.61 % (2789941)------------------------------
% 1.36/0.61 % (2789941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.61 % (2789941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.61 % (2789941)CaDiCaL version: 2.1.3
% 1.36/0.61 % (2789941)Termination reason: Instruction limit
% 1.36/0.61 % (2789941)Termination phase: shuffling
% 1.36/0.61 % (2789941)Time elapsed: 0.005 s
% 1.36/0.61 % (2789941)Peak memory usage: 10 MB
% 1.36/0.61 % (2789941)Instructions burned: 5 (million)
% 1.36/0.61 % (2789942)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.36/0.61 % (2789944)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4035988268:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.36/0.61 % (2789942)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2100342859:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.36/0.61 % (2789944)Instruction limit reached!
% 1.36/0.61 % (2789944)------------------------------
% 1.36/0.61 % (2789944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.61 % (2789944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.61 % (2789944)CaDiCaL version: 2.1.3
% 1.36/0.61 % (2789944)Termination reason: Instruction limit
% 1.36/0.61 % (2789944)Termination phase: shuffling
% 1.36/0.61 % (2789944)Time elapsed: 0.006 s
% 1.36/0.61 % (2789944)Peak memory usage: 10 MB
% 1.36/0.61 % (2789944)Instructions burned: 14 (million)
% 1.36/0.61 % (2789942)Instruction limit reached!
% 1.36/0.61 % (2789942)------------------------------
% 1.36/0.61 % (2789942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.61 % (2789942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.61 % (2789942)CaDiCaL version: 2.1.3
% 1.36/0.61 % (2789942)Termination reason: Instruction limit
% 1.36/0.61 % (2789942)Termination phase: shuffling
% 1.36/0.61 % (2789942)Time elapsed: 0.006 s
% 1.36/0.61 % (2789942)Peak memory usage: 10 MB
% 1.36/0.61 % (2789942)Instructions burned: 7 (million)
% 1.36/0.61 % (2789945)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
% 1.36/0.61 % (2789945)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.36/0.61 % (2789930)Instruction limit reached!
% 1.36/0.61 % (2789930)------------------------------
% 1.36/0.61 % (2789930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.61 % (2789930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.61 % (2789930)CaDiCaL version: 2.1.3
% 1.36/0.61 % (2789930)Termination reason: Instruction limit
% 1.36/0.61 % (2789930)Termination phase: Function definition elimination
% 1.36/0.61 % (2789930)Time elapsed: 0.061 s
% 1.36/0.61 % (2789930)Peak memory usage: 11 MB
% 1.36/0.61 % (2789930)Instructions burned: 76 (million)
% 1.36/0.61 % (2789945)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1743659046:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.36/0.61 % (2789947)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=3589059576:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.36/0.61 % (2789951)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.83/0.65 % (2789951)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=3959655646:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.83/0.65 % (2789951)Instruction limit reached!
% 1.83/0.65 % (2789951)------------------------------
% 1.83/0.65 % (2789951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.65 % (2789951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.65 % (2789951)CaDiCaL version: 2.1.3
% 1.83/0.65 % (2789951)Termination reason: Instruction limit
% 1.83/0.65 % (2789951)Termination phase: shuffling
% 1.83/0.65 % (2789951)Time elapsed: 0.001 s
% 1.83/0.65 % (2789951)Peak memory usage: 10 MB
% 1.83/0.65 % (2789951)Instructions burned: 3 (million)
% 1.83/0.65 % (2789952)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=804851449:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.83/0.65 % (2789950)lrs+10_1_si=on:cs=on:random_seed=642950175:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.83/0.65 % (2789945)Instruction limit reached!
% 1.83/0.65 % (2789945)------------------------------
% 1.83/0.65 % (2789945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.65 % (2789945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.65 % (2789945)CaDiCaL version: 2.1.3
% 1.83/0.65 % (2789945)Termination reason: Instruction limit
% 1.83/0.65 % (2789945)Termination phase: Property scanning
% 1.83/0.65 % (2789945)Time elapsed: 0.024 s
% 1.83/0.65 % (2789945)Peak memory usage: 10 MB
% 1.83/0.65 % (2789945)Instructions burned: 28 (million)
% 1.83/0.65 % (2789950)Instruction limit reached!
% 1.83/0.65 % (2789950)------------------------------
% 1.83/0.65 % (2789950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.65 % (2789950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.65 % (2789950)CaDiCaL version: 2.1.3
% 1.83/0.65 % (2789950)Termination reason: Instruction limit
% 1.83/0.65 % (2789950)Termination phase: shuffling
% 1.83/0.65 % (2789950)Time elapsed: 0.008 s
% 1.83/0.65 % (2789950)Peak memory usage: 10 MB
% 1.83/0.65 % (2789950)Instructions burned: 9 (million)
% 1.83/0.65 % (2789952)Instruction limit reached!
% 1.83/0.65 % (2789952)------------------------------
% 1.83/0.65 % (2789952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.65 % (2789952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.65 % (2789952)CaDiCaL version: 2.1.3
% 1.83/0.65 % (2789952)Termination reason: Instruction limit
% 1.83/0.65 % (2789952)Termination phase: SInE selection
% 1.83/0.65 % (2789952)Time elapsed: 0.019 s
% 1.83/0.65 % (2789952)Peak memory usage: 11 MB
% 1.83/0.65 % (2789952)Instructions burned: 39 (million)
% 1.83/0.65 % (2789931)Instruction limit reached!
% 1.83/0.65 % (2789931)------------------------------
% 1.83/0.65 % (2789931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.65 % (2789931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.65 % (2789931)CaDiCaL version: 2.1.3
% 1.83/0.65 % (2789931)Termination reason: Instruction limit
% 1.83/0.65 % (2789931)Termination phase: Function definition elimination
% 1.83/0.65 % (2789931)Time elapsed: 0.107 s
% 1.83/0.65 % (2789931)Peak memory usage: 11 MB
% 1.83/0.65 % (2789931)Instructions burned: 162 (million)
% 1.83/0.65 % (2789959)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4239500080:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.83/0.65 % (2789956)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3618265698:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.83/0.65 % (2789959)Instruction limit reached!
% 1.83/0.65 % (2789959)------------------------------
% 1.83/0.65 % (2789959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.65 % (2789959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.65 % (2789959)CaDiCaL version: 2.1.3
% 1.83/0.65 % (2789959)Termination reason: Instruction limit
% 1.83/0.65 % (2789959)Termination phase: Property scanning
% 1.83/0.65 % (2789959)Time elapsed: 0.011 s
% 1.83/0.65 % (2789959)Peak memory usage: 10 MB
% 1.83/0.65 % (2789959)Instructions burned: 25 (million)
% 1.83/0.65 % (2789960)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=825322331:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.20/0.73 % (2789961)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4280284173:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.20/0.73 % (2789947)Instruction limit reached!
% 2.20/0.73 % (2789947)------------------------------
% 2.20/0.73 % (2789947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789947)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789947)Termination reason: Instruction limit
% 2.20/0.73 % (2789947)Termination phase: Function definition elimination
% 2.20/0.73 % (2789947)Time elapsed: 0.065 s
% 2.20/0.73 % (2789947)Peak memory usage: 11 MB
% 2.20/0.73 % (2789947)Instructions burned: 86 (million)
% 2.20/0.73 % (2789965)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=105185401: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)
% 2.20/0.73 % (2789965)Instruction limit reached!
% 2.20/0.73 % (2789965)------------------------------
% 2.20/0.73 % (2789965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789965)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789965)Termination reason: Instruction limit
% 2.20/0.73 % (2789965)Termination phase: shuffling
% 2.20/0.73 % (2789965)Time elapsed: 0.001 s
% 2.20/0.73 % (2789965)Peak memory usage: 10 MB
% 2.20/0.73 % (2789965)Instructions burned: 3 (million)
% 2.20/0.73 % (2789960)Instruction limit reached!
% 2.20/0.73 % (2789960)------------------------------
% 2.20/0.73 % (2789960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789960)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789960)Termination reason: Instruction limit
% 2.20/0.73 % (2789960)Termination phase: shuffling
% 2.20/0.73 % (2789960)Time elapsed: 0.013 s
% 2.20/0.73 % (2789960)Peak memory usage: 10 MB
% 2.20/0.73 % (2789960)Instructions burned: 15 (million)
% 2.20/0.73 % (2789963)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2898207293:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.20/0.73 % (2789963)Instruction limit reached!
% 2.20/0.73 % (2789963)------------------------------
% 2.20/0.73 % (2789963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789963)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789963)Termination reason: Instruction limit
% 2.20/0.73 % (2789963)Termination phase: shuffling
% 2.20/0.73 % (2789963)Time elapsed: 0.012 s
% 2.20/0.73 % (2789963)Peak memory usage: 10 MB
% 2.20/0.73 % (2789963)Instructions burned: 14 (million)
% 2.20/0.73 % (2789956)Refutation not found, incomplete strategy
% 2.20/0.73 % (2789956)------------------------------
% 2.20/0.73 % (2789956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789956)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789956)Termination reason: Refutation not found, incomplete strategy
% 2.20/0.73 % (2789956)Time elapsed: 0.043 s
% 2.20/0.73 % (2789956)Peak memory usage: 13 MB
% 2.20/0.73 % (2789956)Instructions burned: 51 (million)
% 2.20/0.73 % (2789956)------------------------------
% 2.20/0.73 % (2789956)------------------------------
% 2.20/0.73 % (2789971)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3942995680:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.20/0.73 % (2789971)Instruction limit reached!
% 2.20/0.73 % (2789971)------------------------------
% 2.20/0.73 % (2789971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789971)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789971)Termination reason: Instruction limit
% 2.20/0.73 % (2789971)Termination phase: Property scanning
% 2.20/0.73 % (2789971)Time elapsed: 0.011 s
% 2.20/0.73 % (2789971)Peak memory usage: 10 MB
% 2.20/0.73 % (2789971)Instructions burned: 25 (million)
% 2.20/0.73 % (2789972)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=572532961:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.20/0.73 % (2789973)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.20/0.73 % (2789973)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.20/0.73 % (2789970)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2646499908:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.20/0.73 % (2789973)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=3203370712:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.20/0.73 % (2789973)Instruction limit reached!
% 2.20/0.73 % (2789973)------------------------------
% 2.20/0.73 % (2789973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789973)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789973)Termination reason: Instruction limit
% 2.20/0.73 % (2789973)Termination phase: shuffling
% 2.20/0.73 % (2789973)Time elapsed: 0.006 s
% 2.20/0.73 % (2789973)Peak memory usage: 10 MB
% 2.20/0.73 % (2789973)Instructions burned: 14 (million)
% 2.20/0.73 % (2789974)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.20/0.73 % (2789974)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=3864759466:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.20/0.73 % (2789977)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=637904954:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.20/0.73 % (2789970)Instruction limit reached!
% 2.20/0.73 % (2789970)------------------------------
% 2.20/0.73 % (2789970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789970)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789970)Termination reason: Instruction limit
% 2.20/0.73 % (2789970)Termination phase: Property scanning
% 2.20/0.73 % (2789970)Time elapsed: 0.022 s
% 2.20/0.73 % (2789970)Peak memory usage: 10 MB
% 2.20/0.73 % (2789970)Instructions burned: 27 (million)
% 2.20/0.73 % (2789974)Instruction limit reached!
% 2.20/0.73 % (2789974)------------------------------
% 2.20/0.73 % (2789974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789974)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789974)Termination reason: Instruction limit
% 2.20/0.73 % (2789974)Termination phase: shuffling
% 2.20/0.73 % (2789974)Time elapsed: 0.007 s
% 2.20/0.73 % (2789974)Peak memory usage: 10 MB
% 2.20/0.73 % (2789974)Instructions burned: 8 (million)
% 2.20/0.73 % (2789980)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3555407016:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.20/0.73 % (2789980)Instruction limit reached!
% 2.20/0.73 % (2789980)------------------------------
% 2.20/0.73 % (2789980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789980)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789980)Termination reason: Instruction limit
% 2.20/0.73 % (2789980)Termination phase: shuffling
% 2.20/0.73 % (2789980)Time elapsed: 0.004 s
% 2.20/0.73 % (2789980)Peak memory usage: 10 MB
% 2.20/0.73 % (2789980)Instructions burned: 9 (million)
% 2.20/0.73 % (2789977)Instruction limit reached!
% 2.20/0.73 % (2789977)------------------------------
% 2.20/0.73 % (2789977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789977)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789977)Termination reason: Instruction limit
% 2.20/0.73 % (2789977)Termination phase: Property scanning
% 2.20/0.73 % (2789977)Time elapsed: 0.017 s
% 2.20/0.73 % (2789977)Peak memory usage: 10 MB
% 2.20/0.73 % (2789977)Instructions burned: 32 (million)
% 2.20/0.73 % (2789972)Instruction limit reached!
% 2.20/0.73 % (2789972)------------------------------
% 2.20/0.73 % (2789972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789972)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789972)Termination reason: Instruction limit
% 2.20/0.73 % (2789972)Termination phase: Property scanning
% 2.20/0.73 % (2789972)Time elapsed: 0.051 s
% 2.20/0.73 % (2789972)Peak memory usage: 11 MB
% 2.20/0.73 % (2789972)Instructions burned: 61 (million)
% 2.20/0.73 % (2789986)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1003973754:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.20/0.73 % (2789983)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=595889250:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.20/0.73 % (2789984)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2112394539:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.20/0.73 % (2789987)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2833076954:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.20/0.73 % (2789989)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=328631770:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.20/0.73 % (2789984)Instruction limit reached!
% 2.20/0.73 % (2789984)------------------------------
% 2.20/0.73 % (2789984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789984)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789984)Termination reason: Instruction limit
% 2.20/0.73 % (2789984)Termination phase: shuffling
% 2.20/0.73 % (2789984)Time elapsed: 0.016 s
% 2.20/0.73 % (2789984)Peak memory usage: 10 MB
% 2.20/0.73 % (2789984)Instructions burned: 20 (million)
% 2.20/0.73 % (2789983)Instruction limit reached!
% 2.20/0.73 % (2789983)------------------------------
% 2.20/0.73 % (2789983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789983)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789983)Termination reason: Instruction limit
% 2.20/0.73 % (2789983)Termination phase: Property scanning
% 2.20/0.73 % (2789983)Time elapsed: 0.023 s
% 2.20/0.73 % (2789983)Peak memory usage: 10 MB
% 2.20/0.73 % (2789983)Instructions burned: 28 (million)
% 2.20/0.73 % (2789961) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2789919-2789961"...
% 2.20/0.73 % (2789961)...printing done.
% 2.20/0.73 % (2789995)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.20/0.73 % (2789961)Refutation found. Thanks to Tanya!
% 2.20/0.73 % SZS status Theorem for theBenchmark
% 2.20/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.20/0.73 % (2789961)------------------------------
% 2.20/0.73 % (2789961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.73 % (2789961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.73 % (2789961)CaDiCaL version: 2.1.3
% 2.20/0.73 % (2789961)Termination reason: Refutation
% 2.20/0.73 % (2789961)Time elapsed: 0.142 s
% 2.20/0.73 % (2789961)Peak memory usage: 14 MB
% 2.20/0.73 % (2789961)Instructions burned: 169 (million)
% 2.20/0.73 % (2789919)Success in time 0.344 s
% 2.20/0.73 % Vampire exiting
%------------------------------------------------------------------------------