%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM677^4 : 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:31 AM UTC 2026
% Result : Theorem 0.65s 0.45s
% Output : Refutation 0.65s
% 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 : 899 ( 120 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 1162 ( 7 ~; 32 |; 0 &; 963 @)
% ( 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 : 170 ( 166 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_134,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_137,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_140,type,
vIMP: $o > $o > $o ).
thf(func_def_141,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_144,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_145,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_146,type,
vNOT: $o > $o ).
thf(func_def_147,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_148,type,
vAND: $o > $o > $o ).
thf(func_def_149,type,
vOR: $o > $o > $o ).
thf(func_def_150,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK1: $i > $i ).
thf(func_def_152,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK3: ( $i > $i ) > $i > ( $i > $i ) > $i ).
thf(func_def_154,type,
sK4: $i > $i > $i > $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 > $i > $i > $i ).
thf(func_def_158,type,
sK8: $i > $i > $o ).
thf(func_def_159,type,
sK9: $i > $i > $o ).
thf(func_def_160,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_161,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_162,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_167,type,
sK17: $i > $i > $o ).
thf(func_def_168,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_169,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK20: ( $i > $o ) > $i ).
thf(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,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
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(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/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(f245,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 @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19h) ).
thf(f246,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 @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f245]) ).
thf(f275,plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f276,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f275]) ).
thf(f316,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f356,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f359,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 @ X5 @ X1 ) @ ( n_pl @ X7 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f246]) ).
thf(f360,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 @ Y2 @ Y0 ) @ ( n_pl @ Y3 @ Y1 ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f359]) ).
thf(f479,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(f480,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 @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f479]) ).
thf(f534,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f644,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 @ Y2 @ Y0 ) @ ( n_pl @ Y3 @ Y1 ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f360]) ).
thf(f680,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 @ Y2 @ Y0 ) @ ( n_pl @ Y3 @ Y1 ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f644]) ).
thf(f684,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f697,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f356]) ).
thf(f752,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f756,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f276]) ).
thf(f766,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f316]) ).
thf(f767,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f534]) ).
thf(f772,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 @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f480]) ).
thf(f780,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,[],[f756,f766]) ).
thf(f781,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f767,f684]) ).
thf(f782,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f752,f697]) ).
thf(f791,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 @ Y2 @ Y0 )
@ ( n_pl @ Y3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f680,f780,f780,f780,f780,f782,f781,f781]) ).
thf(f859,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 @ Y0 @ Y2 )
@ ( n_pl @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f772,f780,f780,f780,f781,f781]) ).
thf(f1213,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 @ Y2 @ Y0 ) @ ( n_pl @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f791]) ).
thf(f1214,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( Y0 = Y1 )
=> ( ( l_some @ nat @ ( diffprop @ Y2 @ Y3 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y2 @ Y0 ) @ ( n_pl @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
@ sK13 ) ),
inference(sigma_proxy_clausification,[],[f1213]) ).
thf(f1215,plain,
( $false
= ( ( in @ sK13 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( sK13 = Y0 )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ sK13 ) @ ( n_pl @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1214]) ).
thf(f1216,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( sK13 = Y0 )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ sK13 ) @ ( n_pl @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1215]) ).
thf(f1217,plain,
( ( in @ sK13 @ nat )
= $true ),
inference(imp_proxy_clausification,[],[f1215]) ).
thf(f1218,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( sK13 = Y0 )
=> ( ( l_some @ nat @ ( diffprop @ Y1 @ Y2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y1 @ sK13 ) @ ( n_pl @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
@ sK14 ) ),
inference(sigma_proxy_clausification,[],[f1216]) ).
thf(f1219,plain,
( ( ( in @ sK14 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ sK13 ) @ ( n_pl @ Y1 @ sK14 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1218]) ).
thf(f1220,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ sK13 ) @ ( n_pl @ Y1 @ sK14 ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1219]) ).
thf(f1222,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ Y0 @ Y1 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ Y0 @ sK13 ) @ ( n_pl @ Y1 @ sK14 ) ) ) ) ) ) ) )
@ sK15 ) ),
inference(sigma_proxy_clausification,[],[f1220]) ).
thf(f1223,plain,
( ( ( in @ sK15 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ sK15 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ Y0 @ sK14 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1222]) ).
thf(f1224,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ sK15 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ Y0 @ sK14 ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1223]) ).
thf(f1225,plain,
( $true
= ( in @ sK15 @ nat ) ),
inference(imp_proxy_clausification,[],[f1223]) ).
thf(f1226,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ sK15 @ Y0 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ Y0 @ sK14 ) ) ) ) ) )
@ sK16 )
= $false ),
inference(sigma_proxy_clausification,[],[f1224]) ).
thf(f1227,plain,
( ( ( in @ sK16 @ nat )
=> ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ sK16 @ sK14 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1226]) ).
thf(f1228,plain,
( ( ( sK13 = sK14 )
=> ( ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ sK16 @ sK14 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1227]) ).
thf(f1229,plain,
( $true
= ( in @ sK16 @ nat ) ),
inference(imp_proxy_clausification,[],[f1227]) ).
thf(f1230,plain,
( ( ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ sK16 @ sK14 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1228]) ).
thf(f1231,plain,
( $true
= ( sK13 = sK14 ) ),
inference(imp_proxy_clausification,[],[f1228]) ).
thf(f1232,plain,
sK14 = sK13,
inference(equality_proxy_clausification,[],[f1231]) ).
thf(f1233,plain,
( ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ sK16 @ sK14 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1230]) ).
thf(f1234,plain,
( $true
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) ),
inference(imp_proxy_clausification,[],[f1230]) ).
thf(f1393,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,[],[f859]) ).
thf(f1394,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 @ Y0 @ Y2 ) @ ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1393]) ).
thf(f1395,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 @ X1 @ Y1 ) @ ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1394]) ).
thf(f1396,plain,
! [X1: $i] :
( ( $true
= ( !! @ $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 ) ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1395]) ).
thf(f1397,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [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 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1396]) ).
thf(f1398,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( 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 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1397]) ).
thf(f1399,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 @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1398]) ).
thf(f1400,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $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 @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1399]) ).
thf(f1401,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( in @ X3 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X2 @ X3 ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1400]) ).
thf(f1402,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X2 @ X3 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1401]) ).
thf(f1403,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X3 ) @ ( n_pl @ X2 @ X3 ) ) ) )
| ( ( l_some @ nat @ ( diffprop @ X1 @ X2 ) )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X3 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1402]) ).
thf(f1492,plain,
( $false
= ( l_some @ nat @ ( diffprop @ ( n_pl @ sK15 @ sK13 ) @ ( n_pl @ sK16 @ sK13 ) ) ) ),
inference(forward_demodulation,[],[f1233,f1232]) ).
thf(f1917,plain,
( ( ( in @ sK15 @ nat )
= $false )
| ( $false
= ( in @ sK16 @ nat ) )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) )
| ( ( in @ sK13 @ nat )
= $false )
| ( $true = $false ) ),
inference(superposition,[],[f1403,f1492]) ).
thf(f1920,plain,
( ( $false
= ( in @ sK16 @ nat ) )
| ( ( in @ sK13 @ nat )
= $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) )
| ( ( in @ sK15 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1917]) ).
thf(f1939,plain,
( ( ( in @ sK13 @ nat )
= $false )
| ( $true = $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) )
| ( ( in @ sK15 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1920,f1229]) ).
thf(f1940,plain,
( ( ( in @ sK13 @ nat )
= $false )
| ( ( in @ sK15 @ nat )
= $false )
| ( $false
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) ) ),
inference(trivial_inequality_removal,[],[f1939]) ).
thf(f1943,plain,
( ( $false
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) )
| ( $true = $false )
| ( ( in @ sK15 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1940,f1217]) ).
thf(f1944,plain,
( ( $false
= ( l_some @ nat @ ( diffprop @ sK15 @ sK16 ) ) )
| ( ( in @ sK15 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1943]) ).
thf(f1947,plain,
( ( $true = $false )
| ( ( in @ sK15 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1944,f1234]) ).
thf(f1948,plain,
( ( in @ sK15 @ nat )
= $false ),
inference(trivial_inequality_removal,[],[f1947]) ).
thf(f1951,plain,
$true = $false,
inference(superposition,[],[f1948,f1225]) ).
thf(f1953,plain,
$false,
inference(trivial_inequality_removal,[],[f1951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM677^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:35:06 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.65/0.42 % (2039915)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.65/0.42 % (2039925)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2813261417:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.65/0.42 % (2039926)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.65/0.42 % (2039926)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.65/0.42 % (2039920)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1561317826:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.65/0.42 % (2039923)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=3221997672:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.65/0.42 % (2039922)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2115800342:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.65/0.42 % (2039924)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=81096263:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.65/0.42 % (2039926)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=2107095999:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.65/0.42 % (2039922)Instruction limit reached!
% 0.65/0.42 % (2039922)------------------------------
% 0.65/0.42 % (2039922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (2039922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (2039922)CaDiCaL version: 2.1.3
% 0.65/0.42 % (2039922)Termination reason: Instruction limit
% 0.65/0.42 % (2039922)Termination phase: shuffling
% 0.65/0.42 % (2039922)Time elapsed: 0.002 s
% 0.65/0.42 % (2039922)Peak memory usage: 10 MB
% 0.65/0.42 % (2039922)Instructions burned: 4 (million)
% 0.65/0.42 % (2039921)lrs+10_16_si=on:nwc=1.5:random_seed=3128060563:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.65/0.42 % (2039925)Instruction limit reached!
% 0.65/0.42 % (2039925)------------------------------
% 0.65/0.42 % (2039925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (2039925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (2039925)CaDiCaL version: 2.1.3
% 0.65/0.42 % (2039925)Termination reason: Instruction limit
% 0.65/0.42 % (2039925)Termination phase: Function definition elimination
% 0.65/0.42 % (2039925)Time elapsed: 0.018 s
% 0.65/0.42 % (2039925)Peak memory usage: 11 MB
% 0.65/0.42 % (2039925)Instructions burned: 76 (million)
% 0.65/0.42 % (2039924)Instruction limit reached!
% 0.65/0.42 % (2039924)------------------------------
% 0.65/0.42 % (2039924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (2039924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (2039924)CaDiCaL version: 2.1.3
% 0.65/0.42 % (2039924)Termination reason: Instruction limit
% 0.65/0.42 % (2039924)Termination phase: Property scanning
% 0.65/0.42 % (2039924)Time elapsed: 0.011 s
% 0.65/0.42 % (2039924)Peak memory usage: 10 MB
% 0.65/0.42 % (2039924)Instructions burned: 25 (million)
% 0.65/0.42 % (2039921)Instruction limit reached!
% 0.65/0.42 % (2039921)------------------------------
% 0.65/0.42 % (2039921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (2039921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (2039921)CaDiCaL version: 2.1.3
% 0.65/0.42 % (2039921)Termination reason: Instruction limit
% 0.65/0.42 % (2039921)Termination phase: shuffling
% 0.65/0.42 % (2039921)Time elapsed: 0.015 s
% 0.65/0.42 % (2039921)Peak memory usage: 10 MB
% 0.65/0.42 % (2039921)Instructions burned: 19 (million)
% 0.65/0.42 % (2039933)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2624799948:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.42 % (2039935)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3296167820:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.65/0.44 % (2039935)Instruction limit reached!
% 0.65/0.44 % (2039935)------------------------------
% 0.65/0.44 % (2039935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (2039935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (2039935)CaDiCaL version: 2.1.3
% 0.65/0.44 % (2039935)Termination reason: Instruction limit
% 0.65/0.44 % (2039935)Termination phase: shuffling
% 0.65/0.44 % (2039935)Time elapsed: 0.002 s
% 0.65/0.44 % (2039935)Peak memory usage: 10 MB
% 0.65/0.44 % (2039935)Instructions burned: 9 (million)
% 0.65/0.44 % (2039936)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (2039933)Instruction limit reached!
% 0.65/0.44 % (2039933)------------------------------
% 0.65/0.44 % (2039933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (2039933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (2039933)CaDiCaL version: 2.1.3
% 0.65/0.44 % (2039933)Termination reason: Instruction limit
% 0.65/0.44 % (2039933)Termination phase: shuffling
% 0.65/0.44 % (2039933)Time elapsed: 0.006 s
% 0.65/0.44 % (2039933)Peak memory usage: 10 MB
% 0.65/0.44 % (2039933)Instructions burned: 6 (million)
% 0.65/0.44 % (2039936)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2749274365:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.65/0.44 % (2039940)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.65/0.44 % (2039940)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (2039936)Instruction limit reached!
% 0.65/0.44 % (2039936)------------------------------
% 0.65/0.44 % (2039936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (2039936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (2039936)CaDiCaL version: 2.1.3
% 0.65/0.44 % (2039936)Termination reason: Instruction limit
% 0.65/0.44 % (2039936)Termination phase: shuffling
% 0.65/0.44 % (2039936)Time elapsed: 0.004 s
% 0.65/0.44 % (2039936)Peak memory usage: 10 MB
% 0.65/0.44 % (2039936)Instructions burned: 9 (million)
% 0.65/0.44 % (2039940)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=184073200:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.65/0.44 % (2039920)Instruction limit reached!
% 0.65/0.44 % (2039920)------------------------------
% 0.65/0.44 % (2039920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (2039920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (2039920)CaDiCaL version: 2.1.3
% 0.65/0.44 % (2039920)Termination reason: Instruction limit
% 0.65/0.44 % (2039920)Termination phase: Function definition elimination
% 0.65/0.44 % (2039920)Time elapsed: 0.039 s
% 0.65/0.44 % (2039920)Peak memory usage: 11 MB
% 0.65/0.44 % (2039920)Instructions burned: 89 (million)
% 0.65/0.44 % (2039940)Instruction limit reached!
% 0.65/0.44 % (2039940)------------------------------
% 0.65/0.44 % (2039940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (2039940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (2039940)CaDiCaL version: 2.1.3
% 0.65/0.44 % (2039940)Termination reason: Instruction limit
% 0.65/0.44 % (2039940)Termination phase: Property scanning
% 0.65/0.44 % (2039940)Time elapsed: 0.007 s
% 0.65/0.44 % (2039940)Peak memory usage: 10 MB
% 0.65/0.44 % (2039940)Instructions burned: 29 (million)
% 0.65/0.44 % (2039937)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=812648464:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.65/0.44 % (2039937)Instruction limit reached!
% 0.65/0.44 % (2039937)------------------------------
% 0.65/0.44 % (2039937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (2039937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (2039937)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039937)Termination reason: Instruction limit
% 0.65/0.45 % (2039937)Termination phase: shuffling
% 0.65/0.45 % (2039937)Time elapsed: 0.006 s
% 0.65/0.45 % (2039937)Peak memory usage: 10 MB
% 0.65/0.45 % (2039937)Instructions burned: 14 (million)
% 0.65/0.45 % (2039946)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2326297467:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.65/0.45 % (2039945)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.65/0.45 % (2039944)lrs+10_1_si=on:cs=on:random_seed=1476556388:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.65/0.45 % (2039945)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=2212348385:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.45 % (2039944)Instruction limit reached!
% 0.65/0.45 % (2039944)------------------------------
% 0.65/0.45 % (2039944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039941)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=3568233751:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.65/0.45 % (2039944)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039944)Termination reason: Instruction limit
% 0.65/0.45 % (2039944)Termination phase: shuffling
% 0.65/0.45 % (2039944)Time elapsed: 0.004 s
% 0.65/0.45 % (2039944)Peak memory usage: 10 MB
% 0.65/0.45 % (2039944)Instructions burned: 9 (million)
% 0.65/0.45 % (2039945)Instruction limit reached!
% 0.65/0.45 % (2039945)------------------------------
% 0.65/0.45 % (2039945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039945)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039945)Termination reason: Instruction limit
% 0.65/0.45 % (2039945)Termination phase: shuffling
% 0.65/0.45 % (2039945)Time elapsed: 0.002 s
% 0.65/0.45 % (2039945)Peak memory usage: 10 MB
% 0.65/0.45 % (2039945)Instructions burned: 3 (million)
% 0.65/0.45 % (2039946)Instruction limit reached!
% 0.65/0.45 % (2039946)------------------------------
% 0.65/0.45 % (2039946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039946)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039946)Termination reason: Instruction limit
% 0.65/0.45 % (2039946)Termination phase: SInE selection
% 0.65/0.45 % (2039946)Time elapsed: 0.009 s
% 0.65/0.45 % (2039946)Peak memory usage: 11 MB
% 0.65/0.45 % (2039946)Instructions burned: 40 (million)
% 0.65/0.45 % (2039926)Instruction limit reached!
% 0.65/0.45 % (2039926)------------------------------
% 0.65/0.45 % (2039926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039926)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039926)Termination reason: Instruction limit
% 0.65/0.45 % (2039926)Termination phase: Function definition elimination
% 0.65/0.45 % (2039926)Time elapsed: 0.065 s
% 0.65/0.45 % (2039926)Peak memory usage: 11 MB
% 0.65/0.45 % (2039926)Instructions burned: 159 (million)
% 0.65/0.45 % (2039948)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1451194241:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.65/0.45 % (2039955)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=394532878:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.65/0.45 % (2039953)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2556173693:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.65/0.45 % (2039954)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1698215753:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.45 % (2039956)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4132018104:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.45 % (2039954)Instruction limit reached!
% 0.65/0.45 % (2039954)------------------------------
% 0.65/0.45 % (2039954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039954)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039954)Termination reason: Instruction limit
% 0.65/0.45 % (2039954)Termination phase: shuffling
% 0.65/0.45 % (2039954)Time elapsed: 0.007 s
% 0.65/0.45 % (2039954)Peak memory usage: 10 MB
% 0.65/0.45 % (2039954)Instructions burned: 16 (million)
% 0.65/0.45 % (2039953)Instruction limit reached!
% 0.65/0.45 % (2039953)------------------------------
% 0.65/0.45 % (2039953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039953)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039953)Termination reason: Instruction limit
% 0.65/0.45 % (2039953)Termination phase: Property scanning
% 0.65/0.45 % (2039953)Time elapsed: 0.012 s
% 0.65/0.45 % (2039953)Peak memory usage: 10 MB
% 0.65/0.45 % (2039953)Instructions burned: 26 (million)
% 0.65/0.45 % (2039956)Instruction limit reached!
% 0.65/0.45 % (2039956)------------------------------
% 0.65/0.45 % (2039956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039956)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039956)Termination reason: Instruction limit
% 0.65/0.45 % (2039956)Termination phase: shuffling
% 0.65/0.45 % (2039956)Time elapsed: 0.007 s
% 0.65/0.45 % (2039956)Peak memory usage: 10 MB
% 0.65/0.45 % (2039956)Instructions burned: 15 (million)
% 0.65/0.45 % (2039948)Refutation not found, incomplete strategy
% 0.65/0.45 % (2039948)------------------------------
% 0.65/0.45 % (2039948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039948)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039948)Termination reason: Refutation not found, incomplete strategy
% 0.65/0.45 % (2039948)Time elapsed: 0.026 s
% 0.65/0.45 % (2039948)Peak memory usage: 13 MB
% 0.65/0.45 % (2039948)Instructions burned: 57 (million)
% 0.65/0.45 % (2039948)------------------------------
% 0.65/0.45 % (2039948)------------------------------
% 0.65/0.45 % (2039941)Instruction limit reached!
% 0.65/0.45 % (2039941)------------------------------
% 0.65/0.45 % (2039941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039941)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039941)Termination reason: Instruction limit
% 0.65/0.45 % (2039941)Termination phase: Function definition elimination
% 0.65/0.45 % (2039941)Time elapsed: 0.037 s
% 0.65/0.45 % (2039941)Peak memory usage: 11 MB
% 0.65/0.45 % (2039941)Instructions burned: 88 (million)
% 0.65/0.45 % (2039962)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2347278767: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)
% 0.65/0.45 % (2039962)Instruction limit reached!
% 0.65/0.45 % (2039962)------------------------------
% 0.65/0.45 % (2039962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039962)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039962)Termination reason: Instruction limit
% 0.65/0.45 % (2039962)Termination phase: shuffling
% 0.65/0.45 % (2039962)Time elapsed: 0.003 s
% 0.65/0.45 % (2039962)Peak memory usage: 10 MB
% 0.65/0.45 % (2039962)Instructions burned: 5 (million)
% 0.65/0.45 % (2039963)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1542084971:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.65/0.45 % (2039964)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3838082487:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.65/0.45 % (2039966)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
% 0.65/0.45 % (2039966)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.65/0.45 % (2039955) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2039915-2039955"...
% 0.65/0.45 % (2039966)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=3859268995:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.45 % (2039965)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1313603123:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.65/0.45 % (2039955)...printing done.
% 0.65/0.45 % (2039955)Refutation found. Thanks to Tanya!
% 0.65/0.45 % SZS status Theorem for theBenchmark
% 0.65/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.65/0.45 % (2039955)------------------------------
% 0.65/0.45 % (2039955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (2039955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (2039955)CaDiCaL version: 2.1.3
% 0.65/0.45 % (2039955)Termination reason: Refutation
% 0.65/0.45 % (2039955)Time elapsed: 0.043 s
% 0.65/0.45 % (2039955)Peak memory usage: 14 MB
% 0.65/0.45 % (2039955)Instructions burned: 185 (million)
% 0.65/0.45 % (2039915)Success in time 0.177 s
% 0.65/0.45 % Vampire exiting
%------------------------------------------------------------------------------