%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM665^4 : 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 : 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 08:18:27 AM UTC 2026
% Result : Theorem 6.94s 1.57s
% Output : Refutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 21
% Syntax : Number of formulae : 214 ( 102 unt; 0 typ; 3 def)
% Number of atoms : 2665 ( 668 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 2899 ( 60 ~; 241 |; 0 &;2199 @)
% ( 3 <=>; 334 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 196 ( 192 usr; 11 con; 0-7 aty)
% ( 62 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 891 ( 28 sgn 115 !; 0 ?; 891 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
is_of: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
eps: ( $i > $o ) > $i ).
thf(func_def_4,type,
in: $i > $i > $o ).
thf(func_def_5,type,
d_Subq: $i > $i > $o ).
thf(func_def_7,type,
union: $i > $i ).
thf(func_def_8,type,
power: $i > $i ).
thf(func_def_9,type,
repl: $i > ( $i > $i ) > $i ).
thf(func_def_10,type,
d_Union_closed: $i > $o ).
thf(func_def_11,type,
d_Power_closed: $i > $o ).
thf(func_def_12,type,
d_Repl_closed: $i > $o ).
thf(func_def_13,type,
d_ZF_closed: $i > $o ).
thf(func_def_14,type,
univof: $i > $i ).
thf(func_def_15,type,
if: $o > $i > $i > $i ).
thf(func_def_16,type,
nIn: $i > $i > $o ).
thf(func_def_17,type,
d_UPair: $i > $i > $i ).
thf(func_def_18,type,
d_Sing: $i > $i ).
thf(func_def_19,type,
binunion: $i > $i > $i ).
thf(func_def_20,type,
famunion: $i > ( $i > $i ) > $i ).
thf(func_def_21,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
d_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_23,type,
setminus: $i > $i > $i ).
thf(func_def_24,type,
d_In_rec_G: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_25,type,
d_In_rec: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_26,type,
ordsucc: $i > $i ).
thf(func_def_27,type,
nat_p: $i > $o ).
thf(func_def_29,type,
d_Inj1: $i > $i ).
thf(func_def_30,type,
d_Inj0: $i > $i ).
thf(func_def_31,type,
d_Unj: $i > $i ).
thf(func_def_32,type,
pair: $i > $i > $i ).
thf(func_def_33,type,
proj0: $i > $i ).
thf(func_def_34,type,
proj1: $i > $i ).
thf(func_def_35,type,
d_Sigma: $i > ( $i > $i ) > $i ).
thf(func_def_36,type,
setprod: $i > $i > $i ).
thf(func_def_37,type,
ap: $i > $i > $i ).
thf(func_def_38,type,
pair_p: $i > $o ).
thf(func_def_39,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_40,type,
imp: $o > $o > $o ).
thf(func_def_41,type,
d_not: $o > $o ).
thf(func_def_42,type,
wel: $o > $o ).
thf(func_def_43,type,
obvious: $o ).
thf(func_def_44,type,
l_ec: $o > $o > $o ).
thf(func_def_45,type,
d_and: $o > $o > $o ).
thf(func_def_46,type,
l_or: $o > $o > $o ).
thf(func_def_47,type,
orec: $o > $o > $o ).
thf(func_def_48,type,
l_iff: $o > $o > $o ).
thf(func_def_49,type,
all: $i > ( $i > $o ) > $o ).
thf(func_def_50,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(func_def_51,type,
l_some: $i > ( $i > $o ) > $o ).
thf(func_def_52,type,
or3: $o > $o > $o > $o ).
thf(func_def_53,type,
and3: $o > $o > $o > $o ).
thf(func_def_54,type,
ec3: $o > $o > $o > $o ).
thf(func_def_55,type,
orec3: $o > $o > $o > $o ).
thf(func_def_56,type,
e_is: $i > $i > $i > $o ).
thf(func_def_57,type,
amone: $i > ( $i > $o ) > $o ).
thf(func_def_58,type,
one: $i > ( $i > $o ) > $o ).
thf(func_def_59,type,
ind: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
injective: $i > $i > $i > $o ).
thf(func_def_61,type,
image: $i > $i > $i > $i > $o ).
thf(func_def_62,type,
tofs: $i > $i > $i > $i > $i ).
thf(func_def_63,type,
soft: $i > $i > $i > $i > $i ).
thf(func_def_64,type,
inverse: $i > $i > $i > $i ).
thf(func_def_65,type,
surjective: $i > $i > $i > $o ).
thf(func_def_66,type,
bijective: $i > $i > $i > $o ).
thf(func_def_67,type,
invf: $i > $i > $i > $i ).
thf(func_def_68,type,
inj_h: $i > $i > $i > $i > $i > $i ).
thf(func_def_69,type,
e_in: $i > ( $i > $o ) > $i > $i ).
thf(func_def_70,type,
out: $i > ( $i > $o ) > $i > $i ).
thf(func_def_71,type,
d_pair: $i > $i > $i > $i > $i ).
thf(func_def_72,type,
first: $i > $i > $i > $i ).
thf(func_def_73,type,
second: $i > $i > $i > $i ).
thf(func_def_74,type,
prop1: $o > $i > $i > $i > $i > $o ).
thf(func_def_75,type,
ite: $o > $i > $i > $i > $i ).
thf(func_def_76,type,
wissel_wa: $i > $i > $i > $i > $i ).
thf(func_def_77,type,
wissel_wb: $i > $i > $i > $i > $i ).
thf(func_def_78,type,
wissel: $i > $i > $i > $i ).
thf(func_def_79,type,
changef: $i > $i > $i > $i > $i > $i ).
thf(func_def_80,type,
r_ec: $o > $o > $o ).
thf(func_def_81,type,
esti: $i > $i > $i > $o ).
thf(func_def_82,type,
empty: $i > $i > $o ).
thf(func_def_83,type,
nonempty: $i > $i > $o ).
thf(func_def_84,type,
incl: $i > $i > $i > $o ).
thf(func_def_85,type,
st_disj: $i > $i > $i > $o ).
thf(func_def_86,type,
nissetprop: $i > $i > $i > $i > $o ).
thf(func_def_87,type,
unmore: $i > $i > $i > $i ).
thf(func_def_88,type,
ecelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
ecp: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_90,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_91,type,
ect: $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
ectset: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_93,type,
ectelt: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_94,type,
ecect: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_95,type,
fixfu: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_96,type,
d_10_prop1: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i > $o ).
thf(func_def_97,type,
prop2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $o ).
thf(func_def_98,type,
indeq: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_99,type,
fixfu2: $i > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_100,type,
d_11_i: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
thf(func_def_101,type,
indeq2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i ).
thf(func_def_103,type,
n_is: $i > $i > $o ).
thf(func_def_104,type,
nis: $i > $i > $o ).
thf(func_def_105,type,
n_in: $i > $i > $o ).
thf(func_def_106,type,
n_some: ( $i > $o ) > $o ).
thf(func_def_107,type,
n_all: ( $i > $o ) > $o ).
thf(func_def_108,type,
n_one: ( $i > $o ) > $o ).
thf(func_def_110,type,
cond1: $i > $o ).
thf(func_def_111,type,
cond2: $i > $o ).
thf(func_def_112,type,
i1_s: ( $i > $o ) > $i ).
thf(func_def_113,type,
d_22_prop1: $i > $o ).
thf(func_def_114,type,
d_23_prop1: $i > $o ).
thf(func_def_115,type,
d_24_prop1: $i > $o ).
thf(func_def_116,type,
d_24_prop2: $i > $i > $o ).
thf(func_def_117,type,
prop3: $i > $i > $i > $o ).
thf(func_def_118,type,
prop4: $i > $o ).
thf(func_def_119,type,
d_24_g: $i > $i ).
thf(func_def_120,type,
plus: $i > $i ).
thf(func_def_121,type,
n_pl: $i > $i > $i ).
thf(func_def_122,type,
d_25_prop1: $i > $i > $i > $o ).
thf(func_def_123,type,
d_26_prop1: $i > $i > $o ).
thf(func_def_124,type,
d_27_prop1: $i > $i > $o ).
thf(func_def_125,type,
d_28_prop1: $i > $i > $i > $o ).
thf(func_def_126,type,
diffprop: $i > $i > $i > $o ).
thf(func_def_127,type,
d_29_ii: $i > $i > $o ).
thf(func_def_128,type,
iii: $i > $i > $o ).
thf(func_def_129,type,
d_29_prop1: $i > $i > $o ).
thf(func_def_130,type,
moreis: $i > $i > $o ).
thf(func_def_131,type,
lessis: $i > $i > $o ).
thf(func_def_132,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_134,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_137,type,
vIMP: $o > $o > $o ).
thf(func_def_138,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_140,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_141,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
vNOT: $o > $o ).
thf(func_def_143,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_144,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_145,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_146,type,
db6:
!>[X0: $tType] : X0 ).
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,
sP0: ( $i > $o ) > $o ).
thf(func_def_151,type,
sP1: ( $i > $i ) > $i > $i > $o ).
thf(func_def_152,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK3: $i > $i > $i > $i ).
thf(func_def_154,type,
sK4: $i > $i ).
thf(func_def_155,type,
sK5: $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_156,type,
sK6: $i > ( $i > $i ) > ( $i > $i ) > $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 > $i > $o ).
thf(func_def_162,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK15: $i > $i > $i > $i ).
thf(func_def_166,type,
sK16: $i > $i > $o ).
thf(func_def_167,type,
sK17: $i > $i > $o ).
thf(func_def_168,type,
sK18: $i > $i > $o ).
thf(func_def_169,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_172,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_177,type,
sK27: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_178,type,
sK28: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_179,type,
sK29: ( $i > $i > $i ) > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_180,type,
sK30: ( $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_181,type,
sK31: ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_182,type,
sK32: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_183,type,
sK33: $i > $i ).
thf(func_def_184,type,
sK34: $i > $i ).
thf(func_def_185,type,
sK35: $i > $i ).
thf(func_def_186,type,
sK36: $i > $i ).
thf(func_def_187,type,
sK37: $i > $i ).
thf(func_def_188,type,
sK38: $i > $i ).
thf(func_def_189,type,
sK39: $i > $i ).
thf(func_def_190,type,
sK40: $i > $i ).
thf(func_def_191,type,
sK41: $i > $i > $i ).
thf(func_def_192,type,
sK42: $i > $i ).
thf(func_def_193,type,
sK43: $i > $i ).
thf(func_def_194,type,
sK44: $i > $i ).
thf(f1,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(f74,axiom,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(f75,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(f81,axiom,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
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(f203,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )
= diffprop ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_diffprop) ).
thf(f205,axiom,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) )
= d_29_ii ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(f206,axiom,
( ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) )
= iii ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii) ).
thf(f216,axiom,
( moreis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_moreis) ).
thf(f217,axiom,
( ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )
= lessis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lessis) ).
thf(f223,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_not @ ( iii @ X0 @ X1 ) )
=> ( moreis @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10f) ).
thf(f225,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( iii @ X0 @ X1 )
=> ( d_not @ ( moreis @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10h) ).
thf(f228,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] :
( ( iii @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz15) ).
thf(f229,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] :
( ( lessis @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(f231,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] :
( ( moreis @ X0 @ X1 )
=> ( ( d_29_ii @ X1 @ X2 )
=> ( d_29_ii @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16c) ).
thf(f232,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] :
( ( moreis @ X0 @ X1 )
=> ( ( d_29_ii @ X1 @ X2 )
=> ( d_29_ii @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f231]) ).
thf(f237,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( d_29_ii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f216]) ).
thf(f257,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f267,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] :
( ( lessis @ X1 @ X3 )
=> ( ( iii @ X3 @ X5 )
=> ( iii @ X1 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f229]) ).
thf(f268,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] :
( ( lessis @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f267]) ).
thf(f269,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f217]) ).
thf(f278,plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(rectify,[],[f75]) ).
thf(f279,plain,
( d_not
= ( ^ [Y0: $o] : ( imp @ Y0 @ $false ) ) ),
inference(fool_elimination,[],[f278]) ).
thf(f295,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f315,plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(rectify,[],[f74]) ).
thf(f316,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f325,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f205]) ).
thf(f481,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( ( iii @ X1 @ X3 )
=> ( d_not @ ( moreis @ X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f225]) ).
thf(f482,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( iii @ Y0 @ Y1 )
=> ( d_not @ ( moreis @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f481]) ).
thf(f483,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f498,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] :
( ( moreis @ X1 @ X3 )
=> ( ( d_29_ii @ X3 @ X5 )
=> ( d_29_ii @ X1 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f232]) ).
thf(f499,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] :
( ( moreis @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y1 @ Y2 )
=> ( d_29_ii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f498]) ).
thf(f515,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f568,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f577,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] :
( ( iii @ X1 @ X3 )
=> ( ( iii @ X3 @ X5 )
=> ( iii @ X1 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f228]) ).
thf(f578,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] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f577]) ).
thf(f594,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) )
= all_of ),
inference(rectify,[],[f2]) ).
thf(f595,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f594]) ).
thf(f598,plain,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X3: $i] :
( ( d_not @ ( iii @ X1 @ X3 ) )
=> ( moreis @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f223]) ).
thf(f599,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( d_not @ ( iii @ Y0 @ Y1 ) )
=> ( moreis @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f598]) ).
thf(f602,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] :
( ( moreis @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y1 @ Y2 )
=> ( d_29_ii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(flattening,[],[f499]) ).
thf(f669,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f295]) ).
thf(f677,plain,
( e_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 ) ) ),
inference(cnf_transformation,[],[f483]) ).
thf(f683,plain,
( imp
= ( ^ [Y0: $o,Y1: $o] :
( Y0
=> Y1 ) ) ),
inference(cnf_transformation,[],[f316]) ).
thf(f690,plain,
( all_of
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( is_of @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f595]) ).
thf(f692,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( n_is @ Y0 @ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f515]) ).
thf(f704,plain,
( n_is
= ( e_is @ nat ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f714,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] :
( ( moreis @ Y0 @ Y1 )
=> ( ( d_29_ii @ Y1 @ Y2 )
=> ( d_29_ii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f602]) ).
thf(f715,plain,
( is_of
= ( ^ [Y0: $i,Y1: $i > $o] : ( Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f257]) ).
thf(f727,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( d_not @ ( iii @ Y0 @ Y1 ) )
=> ( moreis @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f599]) ).
thf(f729,plain,
( $true
= ( all_of
@ ^ [Y0: $i] : ( in @ Y0 @ nat )
@ ^ [Y0: $i] :
( all_of
@ ^ [Y1: $i] : ( in @ Y1 @ nat )
@ ^ [Y1: $i] :
( ( iii @ Y0 @ Y1 )
=> ( d_not @ ( moreis @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f482]) ).
thf(f747,plain,
( n_some
= ( l_some @ nat ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f756,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] :
( ( lessis @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f268]) ).
thf(f759,plain,
( d_not
= ( ^ [Y0: $o] : ( imp @ Y0 @ $false ) ) ),
inference(cnf_transformation,[],[f279]) ).
thf(f765,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( iii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f269]) ).
thf(f768,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] : ( l_or @ ( d_29_ii @ Y0 @ Y1 ) @ ( n_is @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f783,plain,
( l_or
= ( ^ [Y0: $o] : ( imp @ ( d_not @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f568]) ).
thf(f799,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] : ( n_some @ ( diffprop @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f325]) ).
thf(f803,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] :
( ( iii @ Y0 @ Y1 )
=> ( ( iii @ Y1 @ Y2 )
=> ( iii @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f578]) ).
thf(f815,plain,
( n_is
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ nat ) ),
inference(definition_unfolding,[],[f704,f677]) ).
thf(f816,plain,
( diffprop
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( Y4 = Y5 )
@ nat
@ Y0
@ ( n_pl @ Y1 @ Y2 ) ) ) ),
inference(definition_unfolding,[],[f692,f815]) ).
thf(f817,plain,
( iii
= ( ^ [Y0: $i,Y1: $i] :
( l_some @ nat
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] :
( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y2
@ ( n_pl @ Y3 @ Y4 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f669,f747,f816]) ).
thf(f818,plain,
( d_not
= ( ^ [Y0: $o] :
( ^ [Y1: $o,Y2: $o] :
( Y1
=> Y2 )
@ Y0
@ $false ) ) ),
inference(definition_unfolding,[],[f759,f683]) ).
thf(f819,plain,
( l_or
= ( ^ [Y0: $o] :
( ^ [Y1: $o,Y2: $o] :
( Y1
=> Y2 )
@ ( ^ [Y1: $o] :
( ^ [Y2: $o,Y3: $o] :
( Y2
=> Y3 )
@ Y1
@ $false )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f783,f683,f818]) ).
thf(f821,plain,
( d_29_ii
= ( ^ [Y0: $i,Y1: $i] :
( l_some @ nat
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] :
( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y2
@ ( n_pl @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f799,f747,f816]) ).
thf(f823,plain,
( moreis
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ ( ^ [Y3: $o] :
( ^ [Y4: $o,Y5: $o] :
( Y4
=> Y5 )
@ Y3
@ $false )
@ Y2 ) )
@ ( ^ [Y2: $i,Y3: $i] :
( l_some @ nat
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] :
( ^ [Y7: $i,Y8: $i,Y9: $i] : ( Y8 = Y9 )
@ nat
@ Y4
@ ( n_pl @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] : ( Y3 = Y4 )
@ nat
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f768,f819,f821,f815]) ).
thf(f824,plain,
( lessis
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ ( ^ [Y3: $o] :
( ^ [Y4: $o,Y5: $o] :
( Y4
=> Y5 )
@ Y3
@ $false )
@ Y2 ) )
@ ( ^ [Y2: $i,Y3: $i] :
( l_some @ nat
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] :
( ^ [Y7: $i,Y8: $i,Y9: $i] : ( Y8 = Y9 )
@ nat
@ Y4
@ ( n_pl @ Y5 @ Y6 ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i,Y4: $i] : ( Y3 = Y4 )
@ nat
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f765,f819,f817,f815]) ).
thf(f836,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,[],[f690,f715]) ).
thf(f871,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] :
( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ ( ^ [Y6: $o] :
( ^ [Y7: $o,Y8: $o] :
( Y7
=> Y8 )
@ Y6
@ $false )
@ Y5 ) )
@ ( ^ [Y5: $i,Y6: $i] :
( l_some @ nat
@ ( ^ [Y7: $i,Y8: $i,Y9: $i] :
( ^ [Y10: $i,Y11: $i,Y12: $i] : ( Y11 = Y12 )
@ nat
@ Y7
@ ( n_pl @ Y8 @ Y9 ) )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 )
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y3
@ Y4 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y3
@ Y4 ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y3
@ Y4 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f714,f836,f836,f836,f823,f821,f821]) ).
thf(f878,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: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ Y2
@ $false )
@ ( ^ [Y2: $i,Y3: $i] :
( l_some @ nat
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] :
( ^ [Y7: $i,Y8: $i,Y9: $i] : ( Y8 = Y9 )
@ nat
@ Y4
@ ( n_pl @ Y5 @ Y6 ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 ) )
=> ( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $o] :
( ^ [Y5: $o,Y6: $o] :
( Y5
=> Y6 )
@ ( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ Y5
@ $false )
@ Y4 ) )
@ ( ^ [Y4: $i,Y5: $i] :
( l_some @ nat
@ ( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ^ [Y9: $i,Y10: $i,Y11: $i] : ( Y10 = Y11 )
@ nat
@ Y6
@ ( n_pl @ Y7 @ Y8 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( Y5 = Y6 )
@ nat
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f727,f836,f836,f818,f817,f823]) ).
thf(f879,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] :
( l_some @ nat
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] :
( ^ [Y7: $i,Y8: $i,Y9: $i] : ( Y8 = Y9 )
@ nat
@ Y4
@ ( n_pl @ Y5 @ Y6 ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
=> ( ^ [Y2: $o] :
( ^ [Y3: $o,Y4: $o] :
( Y3
=> Y4 )
@ Y2
@ $false )
@ ( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $o] :
( ^ [Y5: $o,Y6: $o] :
( Y5
=> Y6 )
@ ( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ Y5
@ $false )
@ Y4 ) )
@ ( ^ [Y4: $i,Y5: $i] :
( l_some @ nat
@ ( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ^ [Y9: $i,Y10: $i,Y11: $i] : ( Y10 = Y11 )
@ nat
@ Y6
@ ( n_pl @ Y7 @ Y8 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( Y5 = Y6 )
@ nat
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f729,f836,f836,f817,f818,f823]) ).
thf(f892,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] :
( ^ [Y5: $o] :
( ^ [Y6: $o,Y7: $o] :
( Y6
=> Y7 )
@ ( ^ [Y6: $o] :
( ^ [Y7: $o,Y8: $o] :
( Y7
=> Y8 )
@ Y6
@ $false )
@ Y5 ) )
@ ( ^ [Y5: $i,Y6: $i] :
( l_some @ nat
@ ( ^ [Y7: $i,Y8: $i,Y9: $i] :
( ^ [Y10: $i,Y11: $i,Y12: $i] : ( Y11 = Y12 )
@ nat
@ Y7
@ ( n_pl @ Y8 @ Y9 ) )
@ Y6
@ Y5 ) )
@ Y3
@ Y4 )
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] : ( Y6 = Y7 )
@ nat
@ Y3
@ Y4 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f756,f836,f836,f836,f824,f817,f817]) ).
thf(f920,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
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y0
@ Y1 )
=> ( ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i,Y4: $i] :
( l_some @ nat
@ ( ^ [Y5: $i,Y6: $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i,Y10: $i] : ( Y9 = Y10 )
@ nat
@ Y5
@ ( n_pl @ Y6 @ Y7 ) )
@ Y4
@ Y3 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f803,f836,f836,f836,f817,f817,f817]) ).
thf(f950,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f878]) ).
thf(f951,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f950]) ).
thf(f952,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f951]) ).
thf(f953,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f952]) ).
thf(f954,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) ) ) )
@ X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f953]) ).
thf(f955,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ nat )
=> ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f954]) ).
thf(f956,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f955]) ).
thf(f957,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f956]) ).
thf(f958,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false ) )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false ) )
| ( $true
= ( X1 = X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f957]) ).
thf(f960,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( X1 = X2 ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false ) ) ),
inference(imp_proxy_clausification,[],[f958]) ).
thf(f961,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f960]) ).
thf(f963,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 = X2 )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f961]) ).
thf(f1016,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> $false ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f879]) ).
thf(f1017,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> $false ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1016]) ).
thf(f1018,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> $false ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1017]) ).
thf(f1019,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> $false ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1018]) ).
thf(f1020,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X1
= ( n_pl @ Y0 @ Y1 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> $false ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1019]) ).
thf(f1021,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> $false ) ) ) ) ),
inference(beta-eta_normalization,[],[f1020]) ).
thf(f1022,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> $false ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1021]) ).
thf(f1023,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> $false ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1022]) ).
thf(f1024,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $false
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $true = $false ) ),
inference(imp_proxy_clausification,[],[f1023]) ).
thf(f1025,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $false
= ( X1 = X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1024]) ).
thf(f1026,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true = $false )
| ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) )
=> $false ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1024]) ).
thf(f1027,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $true = $false ) ),
inference(imp_proxy_clausification,[],[f1026]) ).
thf(f1028,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $true = $false )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) ) ),
inference(duplicate_literal_removal,[],[f1027]) ).
thf(f1029,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1028]) ).
thf(f1030,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $true = $false )
| ( X1 != X2 )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f1025]) ).
thf(f1031,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( X1 != X2 ) ),
inference(trivial_inequality_removal,[],[f1030]) ).
thf(f1316,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f892]) ).
thf(f1317,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1316]) ).
thf(f1318,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1317]) ).
thf(f1319,plain,
! [X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1318]) ).
thf(f1320,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> $false )
=> ( X1 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1319]) ).
thf(f1321,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1320]) ).
thf(f1322,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1321]) ).
thf(f1323,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) )
@ X3 ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1322]) ).
thf(f1324,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X3 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1323]) ).
thf(f1325,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1324]) ).
thf(f1326,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X3 @ nat ) ) ),
inference(imp_proxy_clausification,[],[f1325]) ).
thf(f1327,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> $false )
=> ( X1 = X2 ) ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1326]) ).
thf(f1328,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $false
= ( in @ X3 @ nat ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( X1 = X2 ) ) ),
inference(imp_proxy_clausification,[],[f1327]) ).
thf(f1332,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1328]) ).
thf(f1440,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f920]) ).
thf(f1441,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y0 @ Y3 ) ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y1 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y2
= ( n_pl @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1440]) ).
thf(f1442,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1441]) ).
thf(f1443,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1442]) ).
thf(f1444,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ X1 @ Y2 ) ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ Y0 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( Y1
= ( n_pl @ X1 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1443]) ).
thf(f1445,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X2 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1444]) ).
thf(f1446,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1445]) ).
thf(f1447,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( X2
= ( n_pl @ X1 @ Y1 ) ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X2 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( Y0
= ( n_pl @ X1 @ Y1 ) ) ) ) ) )
@ X3 ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(pi_proxy_clausification,[],[f1446]) ).
thf(f1448,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $true
= ( ( in @ X3 @ nat )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(beta-eta_normalization,[],[f1447]) ).
thf(f1449,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( in @ X3 @ nat ) )
| ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) ) )
| ( ( in @ X2 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1448]) ).
thf(f1450,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $true
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false ) ),
inference(imp_proxy_clausification,[],[f1449]) ).
thf(f1451,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X1 @ Y0 ) ) ) )
| ( ( in @ X1 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X3
= ( n_pl @ X2 @ Y0 ) ) ) )
| ( $false
= ( in @ X3 @ nat ) )
| ( ( in @ X2 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X2
= ( n_pl @ X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1450]) ).
thf(f1547,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y1 @ Y3 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y2 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f871]) ).
thf(f1548,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y1 @ Y3 ) ) )
=> $false )
=> ( Y0 = Y1 ) )
=> ( ( l_some @ nat
@ ^ [Y3: $i] :
( Y1
= ( n_pl @ Y2 @ Y3 ) ) )
=> ( l_some @ nat
@ ^ [Y3: $i] :
( Y0
= ( n_pl @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK23 ) ),
inference(sigma_proxy_clausification,[],[f1547]) ).
thf(f1549,plain,
( ( ( in @ sK23 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( sK23
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( sK23 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( sK23
= ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1548]) ).
thf(f1550,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( sK23
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( sK23 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( sK23
= ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1549]) ).
thf(f1551,plain,
( $true
= ( in @ sK23 @ nat ) ),
inference(imp_proxy_clausification,[],[f1549]) ).
thf(f1552,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y2: $i] :
( sK23
= ( n_pl @ Y0 @ Y2 ) ) )
=> $false )
=> ( sK23 = Y0 ) )
=> ( ( l_some @ nat
@ ^ [Y2: $i] :
( Y0
= ( n_pl @ Y1 @ Y2 ) ) )
=> ( l_some @ nat
@ ^ [Y2: $i] :
( sK23
= ( n_pl @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK24 ) ),
inference(sigma_proxy_clausification,[],[f1550]) ).
thf(f1553,plain,
( $false
= ( ( in @ sK24 @ nat )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK23
= ( n_pl @ sK24 @ Y1 ) ) )
=> $false )
=> ( sK23 = sK24 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK24
= ( n_pl @ Y0 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( sK23
= ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1552]) ).
thf(f1554,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK23
= ( n_pl @ sK24 @ Y1 ) ) )
=> $false )
=> ( sK23 = sK24 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK24
= ( n_pl @ Y0 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( sK23
= ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1553]) ).
thf(f1555,plain,
( $true
= ( in @ sK24 @ nat ) ),
inference(imp_proxy_clausification,[],[f1553]) ).
thf(f1556,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK23
= ( n_pl @ sK24 @ Y1 ) ) )
=> $false )
=> ( sK23 = sK24 ) )
=> ( ( l_some @ nat
@ ^ [Y1: $i] :
( sK24
= ( n_pl @ Y0 @ Y1 ) ) )
=> ( l_some @ nat
@ ^ [Y1: $i] :
( sK23
= ( n_pl @ Y0 @ Y1 ) ) ) ) ) )
@ sK25 ) ),
inference(sigma_proxy_clausification,[],[f1554]) ).
thf(f1557,plain,
( $false
= ( ( in @ sK25 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
=> $false )
=> ( sK23 = sK24 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK24
= ( n_pl @ sK25 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1556]) ).
thf(f1558,plain,
( $false
= ( ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
=> $false )
=> ( sK23 = sK24 ) )
=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK24
= ( n_pl @ sK25 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1557]) ).
thf(f1559,plain,
( $true
= ( in @ sK25 @ nat ) ),
inference(imp_proxy_clausification,[],[f1557]) ).
thf(f1560,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK24
= ( n_pl @ sK25 @ Y0 ) ) )
=> ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1558]) ).
thf(f1561,plain,
( $true
= ( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
=> $false )
=> ( sK23 = sK24 ) ) ),
inference(imp_proxy_clausification,[],[f1558]) ).
thf(f1562,plain,
( ( $false
= ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
=> $false ) )
| ( $true
= ( sK23 = sK24 ) ) ),
inference(imp_proxy_clausification,[],[f1561]) ).
thf(f1564,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
= $true )
| ( $true
= ( sK23 = sK24 ) ) ),
inference(imp_proxy_clausification,[],[f1562]) ).
thf(f1565,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
= $true )
| ( sK24 = sK23 ) ),
inference(equality_proxy_clausification,[],[f1564]) ).
thf(f1567,plain,
( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1560]) ).
thf(f1568,plain,
( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK24
= ( n_pl @ sK25 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1560]) ).
thf(f1688,definition,
( spl26_1
<=> ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
thf(f1690,plain,
( ( ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK24 @ Y0 ) ) )
= $true )
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f1688]) ).
thf(f1692,definition,
( spl26_2
<=> ( sK24 = sK23 ) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
thf(f1694,plain,
( ( sK24 = sK23 )
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f1692]) ).
thf(f1695,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f1565,f1692,f1688]) ).
thf(f1832,plain,
( ( sK24 != sK25 )
| ( $false
= ( in @ sK24 @ nat ) )
| ( $true = $false )
| ( $false
= ( in @ sK25 @ nat ) ) ),
inference(constrained_superposition,[],[f1031,f1568]) ).
thf(f1841,plain,
( ( $false
= ( in @ sK24 @ nat ) )
| ( $false
= ( in @ sK25 @ nat ) )
| ( sK24 != sK25 ) ),
inference(trivial_inequality_removal,[],[f1832]) ).
thf(f1848,plain,
( ( sK24 != sK25 )
| ( $true = $false )
| ( $false
= ( in @ sK25 @ nat ) ) ),
inference(forward_demodulation,[],[f1841,f1555]) ).
thf(f1849,plain,
( ( $false
= ( in @ sK25 @ nat ) )
| ( sK24 != sK25 ) ),
inference(trivial_inequality_removal,[],[f1848]) ).
thf(f1856,plain,
( ( sK24 != sK25 )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1849,f1559]) ).
thf(f1857,plain,
sK24 != sK25,
inference(trivial_inequality_removal,[],[f1856]) ).
thf(f1872,plain,
( ( $true = $false )
| ( $false
= ( in @ sK24 @ nat ) )
| ( $false
= ( in @ sK25 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK24 @ Y0 ) ) ) ) ),
inference(constrained_superposition,[],[f1029,f1568]) ).
thf(f1880,plain,
( ( $false
= ( in @ sK25 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK24 @ Y0 ) ) ) )
| ( $false
= ( in @ sK24 @ nat ) ) ),
inference(trivial_inequality_removal,[],[f1872]) ).
thf(f1888,plain,
( ( $false
= ( in @ sK24 @ nat ) )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK24 @ Y0 ) ) ) ) ),
inference(forward_demodulation,[],[f1880,f1559]) ).
thf(f1889,plain,
( ( $false
= ( in @ sK24 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK24 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f1888]) ).
thf(f1896,plain,
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK24 @ Y0 ) ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1889,f1555]) ).
thf(f1897,plain,
( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK24 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f1896]) ).
thf(f1954,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( in @ sK25 @ nat ) )
| ( $false
= ( in @ sK23 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f1567,f1451]) ).
thf(f1961,plain,
! [X0: $i] :
( ( $false
= ( in @ sK25 @ nat ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( $false
= ( in @ sK23 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f1954]) ).
thf(f1971,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( $false
= ( in @ sK23 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1961,f1559]) ).
thf(f1972,plain,
! [X0: $i] :
( ( $false
= ( in @ sK23 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK25 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f1971]) ).
thf(f1983,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( $true = $false )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(forward_demodulation,[],[f1972,f1551]) ).
thf(f1984,plain,
! [X0: $i] :
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( X0
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f1983]) ).
thf(f1995,plain,
( ( $false
= ( in @ sK24 @ nat ) )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK24
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ~ spl26_1 ),
inference(constrained_superposition,[],[f1984,f1690]) ).
thf(f2008,plain,
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK24
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( $false
= ( in @ sK24 @ nat ) )
| ~ spl26_1 ),
inference(trivial_inequality_removal,[],[f1995]) ).
thf(f2017,plain,
( ( $false
= ( in @ sK24 @ nat ) )
| ( $true = $false )
| ~ spl26_1 ),
inference(forward_demodulation,[],[f2008,f1568]) ).
thf(f2018,plain,
( ( $false
= ( in @ sK24 @ nat ) )
| ~ spl26_1 ),
inference(trivial_inequality_removal,[],[f2017]) ).
thf(f2021,plain,
( ( $true = $false )
| ~ spl26_1 ),
inference(constrained_superposition,[],[f1555,f2018]) ).
thf(f2027,plain,
( $false
| ~ spl26_1 ),
inference(trivial_inequality_removal,[],[f2021]) ).
thf(f2028,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f2027]) ).
thf(f2187,definition,
( spl26_15
<=> ( sK23 = sK25 ) ),
introduced(definition,[new_symbols(definition,[spl26_15])],[avatar_definition]) ).
thf(f2188,plain,
( ( sK23 = sK25 )
| ~ spl26_15 ),
inference(avatar_component_clause,[],[f2187]) ).
thf(f2189,plain,
( ( sK23 != sK25 )
| spl26_15 ),
inference(avatar_component_clause,[],[f2187]) ).
thf(f2311,plain,
( ( sK24 != sK23 )
| ~ spl26_15 ),
inference(constrained_superposition,[],[f1857,f2188]) ).
thf(f2318,plain,
( $false
| ~ spl26_2
| ~ spl26_15 ),
inference(forward_subsumption_resolution,[],[f2311,f1694]) ).
thf(f2319,plain,
( ~ spl26_2
| ~ spl26_15 ),
inference(avatar_contradiction_clause,[],[f2318]) ).
thf(f2622,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( in @ sK25 @ nat ) )
| ( $false
= ( in @ sK24 @ nat ) )
| ( sK24 != X0 ) ),
inference(constrained_superposition,[],[f1897,f1332]) ).
thf(f2636,plain,
! [X0: $i] :
( ( $false
= ( in @ sK25 @ nat ) )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( in @ sK24 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( sK24 != X0 ) ),
inference(trivial_inequality_removal,[],[f2622]) ).
thf(f2668,plain,
! [X0: $i] :
( ( $false
= ( in @ sK24 @ nat ) )
| ( sK24 != X0 )
| ( ( in @ X0 @ nat )
= $false )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) ) ),
inference(forward_demodulation,[],[f2636,f1559]) ).
thf(f2669,plain,
! [X0: $i] :
( ( sK24 != X0 )
| ( $false
= ( in @ sK24 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false ) ),
inference(trivial_inequality_removal,[],[f2668]) ).
thf(f2714,plain,
( ! [X0: $i] :
( ( sK23 != X0 )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( $false
= ( in @ sK24 @ nat ) )
| ( ( in @ X0 @ nat )
= $false ) )
| ~ spl26_2 ),
inference(forward_demodulation,[],[f2669,f1694]) ).
thf(f2733,plain,
( ! [X0: $i] :
( ( sK23 != X0 )
| ( $true = $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) )
| ( ( in @ X0 @ nat )
= $false ) )
| ~ spl26_2 ),
inference(forward_demodulation,[],[f2714,f1555]) ).
thf(f2734,plain,
( ! [X0: $i] :
( ( sK23 != X0 )
| ( ( in @ X0 @ nat )
= $false )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ X0 @ Y0 ) ) ) ) )
| ~ spl26_2 ),
inference(trivial_inequality_removal,[],[f2733]) ).
thf(f2960,plain,
( ( $false
= ( in @ sK23 @ nat ) )
| ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK23 @ Y0 ) ) ) )
| ~ spl26_2 ),
inference(equality_resolution,[],[f2734]) ).
thf(f2961,plain,
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK23 @ Y0 ) ) ) )
| ( $true = $false )
| ~ spl26_2 ),
inference(forward_demodulation,[],[f2960,f1551]) ).
thf(f2962,plain,
( ( $false
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK25
= ( n_pl @ sK23 @ Y0 ) ) ) )
| ~ spl26_2 ),
inference(trivial_inequality_removal,[],[f2961]) ).
thf(f2973,plain,
( ( $false
= ( in @ sK23 @ nat ) )
| ( $true = $false )
| ( sK23 = sK25 )
| ( $false
= ( in @ sK25 @ nat ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ~ spl26_2 ),
inference(constrained_superposition,[],[f963,f2962]) ).
thf(f2987,plain,
( ( $false
= ( in @ sK25 @ nat ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( sK23 = sK25 )
| ( $false
= ( in @ sK23 @ nat ) )
| ~ spl26_2 ),
inference(trivial_inequality_removal,[],[f2973]) ).
thf(f3003,plain,
( ( $false
= ( in @ sK23 @ nat ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( $false
= ( in @ sK25 @ nat ) )
| ~ spl26_2
| spl26_15 ),
inference(forward_subsumption_resolution,[],[f2987,f2189]) ).
thf(f3017,plain,
( ( $false
= ( in @ sK25 @ nat ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ( $true = $false )
| ~ spl26_2
| spl26_15 ),
inference(forward_demodulation,[],[f3003,f1551]) ).
thf(f3018,plain,
( ( $false
= ( in @ sK25 @ nat ) )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ~ spl26_2
| spl26_15 ),
inference(trivial_inequality_removal,[],[f3017]) ).
thf(f3025,plain,
( ( $true = $false )
| ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ~ spl26_2
| spl26_15 ),
inference(forward_demodulation,[],[f3018,f1559]) ).
thf(f3026,plain,
( ( $true
= ( l_some @ nat
@ ^ [Y0: $i] :
( sK23
= ( n_pl @ sK25 @ Y0 ) ) ) )
| ~ spl26_2
| spl26_15 ),
inference(trivial_inequality_removal,[],[f3025]) ).
thf(f3030,plain,
( ( $true = $false )
| ~ spl26_2
| spl26_15 ),
inference(forward_demodulation,[],[f3026,f1567]) ).
thf(f3031,plain,
( $false
| ~ spl26_2
| spl26_15 ),
inference(trivial_inequality_removal,[],[f3030]) ).
thf(f3032,plain,
( ~ spl26_2
| spl26_15 ),
inference(avatar_contradiction_clause,[],[f3031]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f1695]) ).
cnf(s15,plain,
~ spl26_1,
inference(sat_conversion,[],[f2028]) ).
cnf(s25,plain,
( ~ spl26_2
| ~ spl26_15 ),
inference(sat_conversion,[],[f2319]) ).
cnf(s29,plain,
( ~ spl26_2
| spl26_15 ),
inference(sat_conversion,[],[f3032]) ).
cnf(s30,plain,
spl26_2,
inference(rat,[],[s1,s15]) ).
cnf(s31,plain,
spl26_15,
inference(rat,[],[s29,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s25,s31,s30]) ).
thf(f3033,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM665^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n010.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 12:34:33 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.25/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.51 % (2787983)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.67/0.51 % (2787993)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2394306066:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.67/0.51 % (2787992)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3800523559:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.67/0.51 % (2787990)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4286540134:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.67/0.51 % (2787989)lrs+10_16_si=on:nwc=1.5:random_seed=2811051269:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.67/0.51 % (2787991)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=3444786590:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.67/0.51 % (2787994)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.67/0.51 % (2787994)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.67/0.51 % (2787990)Instruction limit reached!
% 0.67/0.51 % (2787990)------------------------------
% 0.67/0.51 % (2787990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2787990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2787990)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2787990)Termination reason: Instruction limit
% 0.67/0.51 % (2787990)Termination phase: shuffling
% 0.67/0.51 % (2787990)Time elapsed: 0.004 s
% 0.67/0.51 % (2787990)Peak memory usage: 10 MB
% 0.67/0.51 % (2787990)Instructions burned: 3 (million)
% 0.67/0.51 % (2787994)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=2517129023:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.67/0.51 % (2787988)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3600548208:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.67/0.51 % (2787989)Instruction limit reached!
% 0.67/0.51 % (2787989)------------------------------
% 0.67/0.51 % (2787989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2787989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2787989)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2787989)Termination reason: Instruction limit
% 0.67/0.51 % (2787989)Termination phase: shuffling
% 0.67/0.51 % (2787989)Time elapsed: 0.016 s
% 0.67/0.51 % (2787989)Peak memory usage: 10 MB
% 0.67/0.51 % (2787989)Instructions burned: 18 (million)
% 0.67/0.51 % (2787993)Instruction limit reached!
% 0.67/0.51 % (2787993)------------------------------
% 0.67/0.51 % (2787993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2787993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2787993)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2787993)Termination reason: Instruction limit
% 0.67/0.51 % (2787993)Termination phase: Function definition elimination
% 0.67/0.51 % (2787993)Time elapsed: 0.032 s
% 0.67/0.51 % (2787993)Peak memory usage: 11 MB
% 0.67/0.51 % (2787993)Instructions burned: 78 (million)
% 0.67/0.51 % (2787992)Instruction limit reached!
% 0.67/0.51 % (2787992)------------------------------
% 0.67/0.51 % (2787992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (2787992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (2787992)CaDiCaL version: 2.1.3
% 0.67/0.51 % (2787992)Termination reason: Instruction limit
% 0.67/0.51 % (2787992)Termination phase: Property scanning
% 0.67/0.51 % (2787992)Time elapsed: 0.021 s
% 0.67/0.51 % (2787992)Peak memory usage: 10 MB
% 0.67/0.51 % (2787992)Instructions burned: 24 (million)
% 0.67/0.51 % (2788005)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2908373401:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.67/0.51 % (2788000)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2709978128:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.41/0.55 % (2788000)Instruction limit reached!
% 1.41/0.55 % (2788000)------------------------------
% 1.41/0.55 % (2788000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.55 % (2788000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.55 % (2788005)Instruction limit reached!
% 1.41/0.55 % (2788005)------------------------------
% 1.41/0.55 % (2788005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.55 % (2788000)CaDiCaL version: 2.1.3
% 1.41/0.55 % (2788000)Termination reason: Instruction limit
% 1.41/0.55 % (2788000)Termination phase: shuffling
% 1.41/0.55 % (2788000)Time elapsed: 0.003 s
% 1.41/0.55 % (2788005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.55 % (2788000)Peak memory usage: 10 MB
% 1.41/0.55 % (2788000)Instructions burned: 2 (million)
% 1.41/0.55 % (2788005)CaDiCaL version: 2.1.3
% 1.41/0.55 % (2788005)Termination reason: Instruction limit
% 1.41/0.55 % (2788005)Termination phase: shuffling
% 1.41/0.55 % (2788005)Time elapsed: 0.007 s
% 1.41/0.55 % (2788005)Peak memory usage: 10 MB
% 1.41/0.55 % (2788005)Instructions burned: 14 (million)
% 1.41/0.55 % (2788004)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.41/0.55 % (2788003)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2952134543:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.41/0.55 % (2788004)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=806735586:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.41/0.55 % (2788003)Instruction limit reached!
% 1.41/0.55 % (2788003)------------------------------
% 1.41/0.55 % (2788003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.55 % (2788003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.55 % (2788003)CaDiCaL version: 2.1.3
% 1.41/0.55 % (2788003)Termination reason: Instruction limit
% 1.41/0.55 % (2788003)Termination phase: shuffling
% 1.41/0.55 % (2788003)Time elapsed: 0.005 s
% 1.41/0.55 % (2788003)Peak memory usage: 10 MB
% 1.41/0.55 % (2788003)Instructions burned: 6 (million)
% 1.41/0.55 % (2788004)Instruction limit reached!
% 1.41/0.55 % (2788004)------------------------------
% 1.41/0.55 % (2788004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.55 % (2788004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.55 % (2788004)CaDiCaL version: 2.1.3
% 1.41/0.55 % (2788004)Termination reason: Instruction limit
% 1.41/0.55 % (2788004)Termination phase: shuffling
% 1.41/0.55 % (2788004)Time elapsed: 0.006 s
% 1.41/0.55 % (2788004)Peak memory usage: 10 MB
% 1.41/0.55 % (2788004)Instructions burned: 7 (million)
% 1.41/0.55 % (2788009)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
% 1.41/0.55 % (2788009)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.41/0.55 % (2788009)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1442769591:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.41/0.55 % (2787988)Instruction limit reached!
% 1.41/0.55 % (2787988)------------------------------
% 1.41/0.55 % (2787988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.55 % (2787988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.55 % (2787988)CaDiCaL version: 2.1.3
% 1.41/0.55 % (2787988)Termination reason: Instruction limit
% 1.41/0.55 % (2787988)Termination phase: Function definition elimination
% 1.41/0.55 % (2787988)Time elapsed: 0.067 s
% 1.41/0.55 % (2787988)Peak memory usage: 11 MB
% 1.41/0.55 % (2787988)Instructions burned: 88 (million)
% 1.41/0.55 % (2788010)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=1356244801:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.41/0.55 % (2788009)Instruction limit reached!
% 1.41/0.55 % (2788009)------------------------------
% 1.41/0.55 % (2788009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.60 % (2788009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.60 % (2788009)CaDiCaL version: 2.1.3
% 1.41/0.60 % (2788009)Termination reason: Instruction limit
% 1.41/0.60 % (2788009)Termination phase: Property scanning
% 1.41/0.60 % (2788009)Time elapsed: 0.014 s
% 1.41/0.60 % (2788009)Peak memory usage: 10 MB
% 1.41/0.60 % (2788009)Instructions burned: 29 (million)
% 1.41/0.60 % (2788012)lrs+10_1_si=on:cs=on:random_seed=2524184703:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.41/0.60 % (2788013)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.41/0.60 % (2788013)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=1898770871:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.41/0.60 % (2788012)Instruction limit reached!
% 1.41/0.60 % (2788012)------------------------------
% 1.41/0.60 % (2788012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.60 % (2788012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.60 % (2788012)CaDiCaL version: 2.1.3
% 1.41/0.60 % (2788012)Termination reason: Instruction limit
% 1.41/0.60 % (2788012)Termination phase: shuffling
% 1.41/0.60 % (2788012)Time elapsed: 0.008 s
% 1.41/0.60 % (2788012)Peak memory usage: 10 MB
% 1.41/0.60 % (2788012)Instructions burned: 8 (million)
% 1.41/0.60 % (2788013)Instruction limit reached!
% 1.41/0.60 % (2788013)------------------------------
% 1.41/0.60 % (2788013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.60 % (2788013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.60 % (2788013)CaDiCaL version: 2.1.3
% 1.41/0.60 % (2788013)Termination reason: Instruction limit
% 1.41/0.60 % (2788013)Termination phase: shuffling
% 1.41/0.60 % (2788013)Time elapsed: 0.002 s
% 1.41/0.60 % (2788013)Peak memory usage: 10 MB
% 1.41/0.60 % (2788013)Instructions burned: 2 (million)
% 1.41/0.60 % (2788017)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2907063906:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.41/0.60 % (2788015)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2663238799:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.41/0.60 % (2787994)Instruction limit reached!
% 1.41/0.60 % (2787994)------------------------------
% 1.41/0.60 % (2787994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.60 % (2787994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.60 % (2787994)CaDiCaL version: 2.1.3
% 1.41/0.60 % (2787994)Termination reason: Instruction limit
% 1.41/0.60 % (2787994)Termination phase: Function definition elimination
% 1.41/0.60 % (2787994)Time elapsed: 0.107 s
% 1.41/0.60 % (2787994)Peak memory usage: 11 MB
% 1.41/0.60 % (2787994)Instructions burned: 158 (million)
% 1.41/0.60 % (2788017)Refutation not found, incomplete strategy
% 1.41/0.60 % (2788017)------------------------------
% 1.41/0.60 % (2788017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.60 % (2788017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.60 % (2788017)CaDiCaL version: 2.1.3
% 1.41/0.60 % (2788017)Termination reason: Refutation not found, incomplete strategy
% 1.41/0.60 % (2788017)Time elapsed: 0.023 s
% 1.41/0.60 % (2788017)Peak memory usage: 13 MB
% 1.41/0.60 % (2788017)Instructions burned: 48 (million)
% 1.41/0.60 % (2788017)------------------------------
% 1.41/0.60 % (2788017)------------------------------
% 1.41/0.60 % (2788021)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2482277849:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.60 % (2788020)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1305465967:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.41/0.60 % (2788021)Instruction limit reached!
% 1.41/0.60 % (2788021)------------------------------
% 1.41/0.60 % (2788021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.60 % (2788021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.69 % (2788021)CaDiCaL version: 2.1.3
% 2.27/0.69 % (2788021)Termination reason: Instruction limit
% 2.27/0.69 % (2788021)Termination phase: shuffling
% 2.27/0.69 % (2788021)Time elapsed: 0.013 s
% 2.27/0.69 % (2788021)Peak memory usage: 10 MB
% 2.27/0.69 % (2788021)Instructions burned: 14 (million)
% 2.27/0.69 % (2788025)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2405279927:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.27/0.69 % (2788015)Instruction limit reached!
% 2.27/0.69 % (2788015)------------------------------
% 2.27/0.69 % (2788015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.69 % (2788015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.69 % (2788015)CaDiCaL version: 2.1.3
% 2.27/0.69 % (2788015)Termination reason: Instruction limit
% 2.27/0.69 % (2788015)Termination phase: SInE selection
% 2.27/0.69 % (2788015)Time elapsed: 0.032 s
% 2.27/0.69 % (2788015)Peak memory usage: 11 MB
% 2.27/0.69 % (2788015)Instructions burned: 38 (million)
% 2.27/0.69 % (2788010)Instruction limit reached!
% 2.27/0.69 % (2788010)------------------------------
% 2.27/0.69 % (2788010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.69 % (2788010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.69 % (2788010)CaDiCaL version: 2.1.3
% 2.27/0.69 % (2788010)Termination reason: Instruction limit
% 2.27/0.69 % (2788010)Termination phase: Function definition elimination
% 2.27/0.69 % (2788010)Time elapsed: 0.065 s
% 2.27/0.69 % (2788010)Peak memory usage: 11 MB
% 2.27/0.69 % (2788010)Instructions burned: 87 (million)
% 2.27/0.69 % (2788024)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1921090372:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.27/0.69 % (2788025)Instruction limit reached!
% 2.27/0.69 % (2788025)------------------------------
% 2.27/0.69 % (2788025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.69 % (2788025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.69 % (2788025)CaDiCaL version: 2.1.3
% 2.27/0.69 % (2788025)Termination reason: Instruction limit
% 2.27/0.69 % (2788025)Termination phase: shuffling
% 2.27/0.69 % (2788025)Time elapsed: 0.006 s
% 2.27/0.69 % (2788025)Peak memory usage: 10 MB
% 2.27/0.69 % (2788025)Instructions burned: 14 (million)
% 2.27/0.69 % (2788020)Instruction limit reached!
% 2.27/0.69 % (2788020)------------------------------
% 2.27/0.69 % (2788020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.69 % (2788020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.69 % (2788020)CaDiCaL version: 2.1.3
% 2.27/0.69 % (2788020)Termination reason: Instruction limit
% 2.27/0.69 % (2788020)Termination phase: Property scanning
% 2.27/0.69 % (2788020)Time elapsed: 0.023 s
% 2.27/0.69 % (2788020)Peak memory usage: 10 MB
% 2.27/0.69 % (2788020)Instructions burned: 26 (million)
% 2.27/0.69 % (2788033)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2287715850:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.27/0.69 % (2788029)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3516163243:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.27/0.69 % (2788030)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2421460666:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.27/0.69 % (2788032)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1743511835:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.27/0.69 % (2788029)Instruction limit reached!
% 2.27/0.69 % (2788029)------------------------------
% 2.27/0.69 % (2788029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.69 % (2788029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.69 % (2788029)CaDiCaL version: 2.1.3
% 2.27/0.69 % (2788029)Termination reason: Instruction limit
% 2.27/0.69 % (2788029)Termination phase: shuffling
% 2.27/0.69 % (2788029)Time elapsed: 0.003 s
% 2.27/0.69 % (2788029)Peak memory usage: 10 MB
% 2.27/0.69 % (2788029)Instructions burned: 3 (million)
% 2.27/0.69 % (2788034)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
% 2.95/0.84 % (2788034)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.95/0.84 % (2788034)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=1607885257:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.95/0.84 % (2788033)Instruction limit reached!
% 2.95/0.84 % (2788033)------------------------------
% 2.95/0.84 % (2788033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.84 % (2788033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.84 % (2788033)CaDiCaL version: 2.1.3
% 2.95/0.84 % (2788033)Termination reason: Instruction limit
% 2.95/0.84 % (2788033)Termination phase: Property scanning
% 2.95/0.84 % (2788033)Time elapsed: 0.026 s
% 2.95/0.84 % (2788033)Peak memory usage: 11 MB
% 2.95/0.84 % (2788033)Instructions burned: 60 (million)
% 2.95/0.84 % (2788034)Instruction limit reached!
% 2.95/0.84 % (2788034)------------------------------
% 2.95/0.84 % (2788034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.84 % (2788034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.84 % (2788032)Instruction limit reached!
% 2.95/0.84 % (2788032)------------------------------
% 2.95/0.84 % (2788032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.84 % (2788034)CaDiCaL version: 2.1.3
% 2.95/0.84 % (2788032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.84 % (2788034)Termination reason: Instruction limit
% 2.95/0.84 % (2788034)Termination phase: shuffling
% 2.95/0.84 % (2788034)Time elapsed: 0.012 s
% 2.95/0.84 % (2788034)Peak memory usage: 10 MB
% 2.95/0.84 % (2788032)CaDiCaL version: 2.1.3
% 2.95/0.84 % (2788032)Termination reason: Instruction limit
% 2.95/0.84 % (2788032)Termination phase: Property scanning
% 2.95/0.84 % (2788034)Instructions burned: 14 (million)
% 2.95/0.84 % (2788032)Time elapsed: 0.020 s
% 2.95/0.84 % (2788032)Peak memory usage: 10 MB
% 2.95/0.84 % (2788032)Instructions burned: 23 (million)
% 2.95/0.84 % (2788030)Instruction limit reached!
% 2.95/0.84 % (2788030)------------------------------
% 2.95/0.84 % (2788030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.84 % (2788030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.84 % (2788030)CaDiCaL version: 2.1.3
% 2.95/0.84 % (2788030)Termination reason: Instruction limit
% 2.95/0.84 % (2788030)Termination phase: Property scanning
% 2.95/0.84 % (2788030)Time elapsed: 0.022 s
% 2.95/0.84 % (2788030)Peak memory usage: 10 MB
% 2.95/0.84 % (2788030)Instructions burned: 27 (million)
% 2.95/0.84 % (2788041)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=333561536:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.95/0.84 % (2788039)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.95/0.84 % (2788039)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=2272056383:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.95/0.84 % (2788041)Instruction limit reached!
% 2.95/0.84 % (2788041)------------------------------
% 2.95/0.84 % (2788041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.84 % (2788041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.84 % (2788041)CaDiCaL version: 2.1.3
% 2.95/0.84 % (2788041)Termination reason: Instruction limit
% 2.95/0.84 % (2788041)Termination phase: Property scanning
% 2.95/0.84 % (2788041)Time elapsed: 0.014 s
% 2.95/0.84 % (2788041)Peak memory usage: 10 MB
% 2.95/0.84 % (2788041)Instructions burned: 32 (million)
% 2.95/0.84 % (2788039)Instruction limit reached!
% 2.95/0.84 % (2788039)------------------------------
% 2.95/0.84 % (2788039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.84 % (2788039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.84 % (2788039)CaDiCaL version: 2.1.3
% 2.95/0.84 % (2788039)Termination reason: Instruction limit
% 2.95/0.84 % (2788039)Termination phase: shuffling
% 2.95/0.84 % (2788039)Time elapsed: 0.009 s
% 3.57/0.95 % (2788039)Peak memory usage: 10 MB
% 3.57/0.95 % (2788039)Instructions burned: 8 (million)
% 3.57/0.95 % (2788043)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2848941240:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 3.57/0.95 % (2788042)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3130992288:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 3.57/0.95 % (2788044)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3135683121:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 3.57/0.95 % (2788042)Instruction limit reached!
% 3.57/0.95 % (2788042)------------------------------
% 3.57/0.95 % (2788042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.95 % (2788042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.95 % (2788042)CaDiCaL version: 2.1.3
% 3.57/0.95 % (2788042)Termination reason: Instruction limit
% 3.57/0.95 % (2788042)Termination phase: shuffling
% 3.57/0.95 % (2788042)Time elapsed: 0.007 s
% 3.57/0.95 % (2788042)Peak memory usage: 10 MB
% 3.57/0.95 % (2788042)Instructions burned: 7 (million)
% 3.57/0.95 % (2788047)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3962673880:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 3.57/0.95 % (2788044)Instruction limit reached!
% 3.57/0.95 % (2788044)------------------------------
% 3.57/0.95 % (2788044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.95 % (2788044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.95 % (2788044)CaDiCaL version: 2.1.3
% 3.57/0.95 % (2788044)Termination reason: Instruction limit
% 3.57/0.95 % (2788044)Termination phase: shuffling
% 3.57/0.95 % (2788044)Time elapsed: 0.018 s
% 3.57/0.95 % (2788044)Peak memory usage: 10 MB
% 3.57/0.95 % (2788044)Instructions burned: 21 (million)
% 3.57/0.95 % (2788043)Instruction limit reached!
% 3.57/0.95 % (2788043)------------------------------
% 3.57/0.95 % (2788043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.95 % (2788043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.95 % (2788043)CaDiCaL version: 2.1.3
% 3.57/0.95 % (2788043)Termination reason: Instruction limit
% 3.57/0.95 % (2788043)Termination phase: Property scanning
% 3.57/0.95 % (2788043)Time elapsed: 0.021 s
% 3.57/0.95 % (2788043)Peak memory usage: 10 MB
% 3.57/0.95 % (2788043)Instructions burned: 24 (million)
% 3.57/0.95 % (2788048)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3940863154:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 3.57/0.95 % (2788052)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3422071:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 3.57/0.95 % (2788055)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.57/0.95 % (2788054)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1879812276:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 3.57/0.95 % (2788055)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3002123170:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.57/0.95 % (2788055)Instruction limit reached!
% 3.57/0.95 % (2788055)------------------------------
% 3.57/0.95 % (2788055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.95 % (2788055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.95 % (2788055)CaDiCaL version: 2.1.3
% 3.57/0.95 % (2788055)Termination reason: Instruction limit
% 3.57/0.95 % (2788055)Termination phase: shuffling
% 3.57/0.95 % (2788055)Time elapsed: 0.006 s
% 3.57/0.95 % (2788055)Peak memory usage: 10 MB
% 3.57/0.95 % (2788055)Instructions burned: 7 (million)
% 3.57/0.95 % (2788054)Instruction limit reached!
% 3.57/0.95 % (2788054)------------------------------
% 3.57/0.95 % (2788054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.95 % (2788054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.95 % (2788054)CaDiCaL version: 2.1.3
% 3.57/0.95 % (2788054)Termination reason: Instruction limit
% 3.57/0.95 % (2788054)Termination phase: Property scanning
% 3.57/1.08 % (2788054)Time elapsed: 0.037 s
% 3.57/1.08 % (2788054)Peak memory usage: 11 MB
% 3.57/1.08 % (2788054)Instructions burned: 42 (million)
% 3.57/1.08 % (2788060)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2474547746:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 3.57/1.08 % (2788061)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3550018052:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.57/1.08 % (2788048)Instruction limit reached!
% 3.57/1.08 % (2788048)------------------------------
% 3.57/1.08 % (2788048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/1.08 % (2788048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.08 % (2788048)CaDiCaL version: 2.1.3
% 3.57/1.08 % (2788048)Termination reason: Instruction limit
% 3.57/1.08 % (2788048)Termination phase: Function definition elimination
% 3.57/1.08 % (2788048)Time elapsed: 0.103 s
% 3.57/1.08 % (2788048)Peak memory usage: 11 MB
% 3.57/1.08 % (2788048)Instructions burned: 143 (million)
% 3.57/1.08 % (2788064)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.57/1.08 % (2788064)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=985545239:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2995 on theBenchmark for (2995ds/6Mi)
% 3.57/1.08 % (2788064)Instruction limit reached!
% 3.57/1.08 % (2788064)------------------------------
% 3.57/1.08 % (2788064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/1.08 % (2788064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.08 % (2788064)CaDiCaL version: 2.1.3
% 3.57/1.08 % (2788064)Termination reason: Instruction limit
% 3.57/1.08 % (2788064)Termination phase: shuffling
% 3.57/1.08 % (2788064)Time elapsed: 0.006 s
% 3.57/1.08 % (2788064)Peak memory usage: 10 MB
% 3.57/1.08 % (2788064)Instructions burned: 7 (million)
% 3.57/1.08 % (2788061)Refutation not found, incomplete strategy
% 3.57/1.08 % (2788061)------------------------------
% 3.57/1.08 % (2788061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/1.08 % (2788061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.08 % (2788061)CaDiCaL version: 2.1.3
% 3.57/1.08 % (2788061)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.08 % (2788061)Time elapsed: 0.064 s
% 3.57/1.08 % (2788061)Peak memory usage: 13 MB
% 3.57/1.08 % (2788061)Instructions burned: 77 (million)
% 3.57/1.08 % (2788061)------------------------------
% 3.57/1.08 % (2788061)------------------------------
% 3.57/1.08 % (2788052)Instruction limit reached!
% 3.57/1.08 % (2788052)------------------------------
% 3.57/1.08 % (2788052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/1.08 % (2788052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.08 % (2788052)CaDiCaL version: 2.1.3
% 3.57/1.08 % (2788052)Termination reason: Instruction limit
% 3.57/1.08 % (2788052)Termination phase: Saturation
% 3.57/1.08 % (2788052)Time elapsed: 0.156 s
% 3.57/1.08 % (2788052)Peak memory usage: 14 MB
% 3.57/1.08 % (2788052)Instructions burned: 194 (million)
% 3.57/1.08 % (2788024)Instruction limit reached!
% 3.57/1.08 % (2788024)------------------------------
% 3.57/1.08 % (2788024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/1.08 % (2788024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.08 % (2788024)CaDiCaL version: 2.1.3
% 3.57/1.08 % (2788024)Termination reason: Instruction limit
% 3.57/1.08 % (2788024)Termination phase: Saturation
% 3.57/1.08 % (2788024)Time elapsed: 0.286 s
% 3.57/1.08 % (2788024)Peak memory usage: 14 MB
% 3.57/1.08 % (2788024)Instructions burned: 327 (million)
% 3.57/1.08 % (2788066)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1173811519:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2995 on theBenchmark for (2995ds/22Mi)
% 3.57/1.08 % (2788067)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2518430998:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 3.57/1.08 % (2788068)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1020986060:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 5.20/1.17 % (2788069)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2738766003:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 5.20/1.17 % (2788066)Instruction limit reached!
% 5.20/1.17 % (2788066)------------------------------
% 5.20/1.17 % (2788066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.20/1.17 % (2788066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.17 % (2788066)CaDiCaL version: 2.1.3
% 5.20/1.17 % (2788066)Termination reason: Instruction limit
% 5.20/1.17 % (2788066)Termination phase: Property scanning
% 5.20/1.17 % (2788066)Time elapsed: 0.021 s
% 5.20/1.17 % (2788066)Peak memory usage: 10 MB
% 5.20/1.17 % (2788066)Instructions burned: 22 (million)
% 5.20/1.17 % (2788067)Instruction limit reached!
% 5.20/1.17 % (2788067)------------------------------
% 5.20/1.17 % (2788067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.20/1.17 % (2788067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.17 % (2788067)CaDiCaL version: 2.1.3
% 5.20/1.17 % (2788067)Termination reason: Instruction limit
% 5.20/1.17 % (2788067)Termination phase: shuffling
% 5.20/1.17 % (2788067)Time elapsed: 0.017 s
% 5.20/1.17 % (2788067)Peak memory usage: 10 MB
% 5.20/1.17 % (2788067)Instructions burned: 19 (million)
% 5.20/1.17 % (2788060)Instruction limit reached!
% 5.20/1.17 % (2788060)------------------------------
% 5.20/1.17 % (2788060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.20/1.17 % (2788060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.17 % (2788060)CaDiCaL version: 2.1.3
% 5.20/1.17 % (2788060)Termination reason: Instruction limit
% 5.20/1.17 % (2788060)Termination phase: Saturation
% 5.20/1.17 % (2788060)Time elapsed: 0.162 s
% 5.20/1.17 % (2788060)Peak memory usage: 13 MB
% 5.20/1.17 % (2788060)Instructions burned: 181 (million)
% 5.20/1.17 % (2788074)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=821315319:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2994 on theBenchmark for (2994ds/45Mi)
% 5.20/1.17 % (2788075)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1211711083:i=480:rtra=on_2994 on theBenchmark for (2994ds/480Mi)
% 5.20/1.17 % (2788076)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=520861264:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2994 on theBenchmark for (2994ds/21Mi)
% 5.20/1.17 % (2788074)Instruction limit reached!
% 5.20/1.17 % (2788074)------------------------------
% 5.20/1.17 % (2788074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.20/1.17 % (2788074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.17 % (2788074)CaDiCaL version: 2.1.3
% 5.20/1.17 % (2788074)Termination reason: Instruction limit
% 5.20/1.17 % (2788074)Termination phase: SInE selection
% 5.20/1.17 % (2788074)Time elapsed: 0.039 s
% 5.20/1.17 % (2788074)Peak memory usage: 10 MB
% 5.20/1.17 % (2788074)Instructions burned: 45 (million)
% 5.20/1.17 % (2788076)Instruction limit reached!
% 5.20/1.17 % (2788076)------------------------------
% 5.20/1.17 % (2788076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.20/1.17 % (2788076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.17 % (2788076)CaDiCaL version: 2.1.3
% 5.20/1.17 % (2788076)Termination reason: Instruction limit
% 5.20/1.17 % (2788076)Termination phase: Property scanning
% 5.20/1.17 % (2788076)Time elapsed: 0.019 s
% 5.20/1.17 % (2788076)Peak memory usage: 10 MB
% 5.20/1.17 % (2788076)Instructions burned: 21 (million)
% 5.20/1.17 % (2788080)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 5.20/1.17 % (2788080)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3123597745:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/200Mi)
% 5.20/1.17 % (2788075)Refutation not found, incomplete strategy
% 5.20/1.17 % (2788075)------------------------------
% 5.20/1.17 % (2788075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.30/1.30 % (2788081)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=778016477:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2993 on theBenchmark for (2993ds/13Mi)
% 6.30/1.30 % (2788075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.30 % (2788075)CaDiCaL version: 2.1.3
% 6.30/1.30 % (2788075)Termination reason: Refutation not found, incomplete strategy
% 6.30/1.30 % (2788075)Time elapsed: 0.074 s
% 6.30/1.30 % (2788075)Peak memory usage: 13 MB
% 6.30/1.30 % (2788075)Instructions burned: 84 (million)
% 6.30/1.30 % (2787991)Instruction limit reached!
% 6.30/1.30 % (2787991)------------------------------
% 6.30/1.30 % (2787991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.30/1.30 % (2787991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.30 % (2787991)CaDiCaL version: 2.1.3
% 6.30/1.30 % (2787991)Termination reason: Instruction limit
% 6.30/1.30 % (2787991)Termination phase: Saturation
% 6.30/1.30 % (2787991)Time elapsed: 0.585 s
% 6.30/1.30 % (2787991)Peak memory usage: 16 MB
% 6.30/1.30 % (2787991)Instructions burned: 635 (million)
% 6.30/1.30 % (2788075)------------------------------
% 6.30/1.30 % (2788075)------------------------------
% 6.30/1.30 % (2788081)Instruction limit reached!
% 6.30/1.30 % (2788081)------------------------------
% 6.30/1.30 % (2788081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.30/1.30 % (2788081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.30 % (2788081)CaDiCaL version: 2.1.3
% 6.30/1.30 % (2788081)Termination reason: Instruction limit
% 6.30/1.30 % (2788081)Termination phase: shuffling
% 6.30/1.30 % (2788081)Time elapsed: 0.011 s
% 6.30/1.30 % (2788081)Peak memory usage: 10 MB
% 6.30/1.30 % (2788081)Instructions burned: 13 (million)
% 6.30/1.30 % (2788086)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2499229136:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/31Mi)
% 6.30/1.30 % (2788084)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=285895342:i=66:s2at=3:nm=2:rtra=on:rawr=on_2993 on theBenchmark for (2993ds/66Mi)
% 6.30/1.30 % (2788086)Instruction limit reached!
% 6.30/1.30 % (2788086)------------------------------
% 6.30/1.30 % (2788086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.30/1.30 % (2788086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.30 % (2788086)CaDiCaL version: 2.1.3
% 6.30/1.30 % (2788086)Termination reason: Instruction limit
% 6.30/1.30 % (2788086)Termination phase: Property scanning
% 6.30/1.30 % (2788086)Time elapsed: 0.026 s
% 6.30/1.30 % (2788086)Peak memory usage: 10 MB
% 6.30/1.30 % (2788086)Instructions burned: 31 (million)
% 6.30/1.30 % (2788068)Instruction limit reached!
% 6.30/1.30 % (2788068)------------------------------
% 6.30/1.30 % (2788068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.30/1.30 % (2788068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.30 % (2788068)CaDiCaL version: 2.1.3
% 6.30/1.30 % (2788068)Termination reason: Instruction limit
% 6.30/1.30 % (2788068)Termination phase: Property scanning
% 6.30/1.30 % (2788068)Time elapsed: 0.197 s
% 6.30/1.30 % (2788068)Peak memory usage: 11 MB
% 6.30/1.30 % (2788068)Instructions burned: 317 (million)
% 6.30/1.30 % (2788085)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1998101677:i=51:fsr=off:rtra=on_2993 on theBenchmark for (2993ds/51Mi)
% 6.30/1.30 % (2788089)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=960055730:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2992 on theBenchmark for (2992ds/137Mi)
% 6.30/1.30 % (2788090)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1247777271:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.30/1.30 % (2788047)Instruction limit reached!
% 6.30/1.30 % (2788047)------------------------------
% 6.30/1.30 % (2788047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.30/1.30 % (2788047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.30 % (2788047)CaDiCaL version: 2.1.3
% 6.30/1.30 % (2788047)Termination reason: Instruction limit
% 6.94/1.56 % (2788047)Termination phase: Property scanning
% 6.94/1.56 % (2788047)Time elapsed: 0.459 s
% 6.94/1.56 % (2788047)Peak memory usage: 11 MB
% 6.94/1.56 % (2788047)Instructions burned: 1241 (million)
% 6.94/1.56 % (2788084)Instruction limit reached!
% 6.94/1.56 % (2788084)------------------------------
% 6.94/1.56 % (2788084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.56 % (2788084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.56 % (2788084)CaDiCaL version: 2.1.3
% 6.94/1.56 % (2788084)Termination reason: Instruction limit
% 6.94/1.56 % (2788084)Termination phase: Function definition elimination
% 6.94/1.56 % (2788084)Time elapsed: 0.054 s
% 6.94/1.56 % (2788084)Peak memory usage: 11 MB
% 6.94/1.56 % (2788084)Instructions burned: 67 (million)
% 6.94/1.56 % (2788095)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.94/1.56 % (2788095)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1417846950:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2992 on theBenchmark for (2992ds/180Mi)
% 6.94/1.57 % (2788090)Instruction limit reached!
% 6.94/1.57 % (2788090)------------------------------
% 6.94/1.57 % (2788090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788090)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788090)Termination reason: Instruction limit
% 6.94/1.57 % (2788090)Termination phase: Property scanning
% 6.94/1.57 % (2788090)Time elapsed: 0.030 s
% 6.94/1.57 % (2788090)Peak memory usage: 10 MB
% 6.94/1.57 % (2788090)Instructions burned: 36 (million)
% 6.94/1.57 % (2788080)Instruction limit reached!
% 6.94/1.57 % (2788080)------------------------------
% 6.94/1.57 % (2788080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788080)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788080)Termination reason: Instruction limit
% 6.94/1.57 % (2788080)Termination phase: Function definition elimination
% 6.94/1.57 % (2788080)Time elapsed: 0.152 s
% 6.94/1.57 % (2788080)Peak memory usage: 11 MB
% 6.94/1.57 % (2788080)Instructions burned: 202 (million)
% 6.94/1.57 % (2788085)Instruction limit reached!
% 6.94/1.57 % (2788085)------------------------------
% 6.94/1.57 % (2788085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788085)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788085)Termination reason: Instruction limit
% 6.94/1.57 % (2788085)Termination phase: Function definition elimination
% 6.94/1.57 % (2788085)Time elapsed: 0.066 s
% 6.94/1.57 % (2788085)Peak memory usage: 11 MB
% 6.94/1.57 % (2788085)Instructions burned: 52 (million)
% 6.94/1.57 % (2788094)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1236491018:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2992 on theBenchmark for (2992ds/67Mi)
% 6.94/1.57 % (2788097)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2942425023:st=2:i=246:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/246Mi)
% 6.94/1.57 % (2788098)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=466876423:cond=on:i=96:bd=all:rtra=on_2992 on theBenchmark for (2992ds/96Mi)
% 6.94/1.57 % (2788100)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=588293832:i=427:sd=1:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/427Mi)
% 6.94/1.57 % (2788095)Instruction limit reached!
% 6.94/1.57 % (2788095)------------------------------
% 6.94/1.57 % (2788095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788095)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788095)Termination reason: Instruction limit
% 6.94/1.57 % (2788095)Termination phase: Function definition elimination
% 6.94/1.57 % (2788095)Time elapsed: 0.062 s
% 6.94/1.57 % (2788095)Peak memory usage: 11 MB
% 6.94/1.57 % (2788095)Instructions burned: 183 (million)
% 6.94/1.57 % (2788094)Instruction limit reached!
% 6.94/1.57 % (2788094)------------------------------
% 6.94/1.57 % (2788094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788094)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788094)Termination reason: Instruction limit
% 6.94/1.57 % (2788094)Termination phase: Function definition elimination
% 6.94/1.57 % (2788094)Time elapsed: 0.056 s
% 6.94/1.57 % (2788094)Peak memory usage: 11 MB
% 6.94/1.57 % (2788094)Instructions burned: 67 (million)
% 6.94/1.57 % (2788104)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1823351303:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/874Mi)
% 6.94/1.57 % (2788100)Refutation not found, incomplete strategy
% 6.94/1.57 % (2788100)------------------------------
% 6.94/1.57 % (2788100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788100)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788100)Termination reason: Refutation not found, incomplete strategy
% 6.94/1.57 % (2788100)Time elapsed: 0.039 s
% 6.94/1.57 % (2788100)Peak memory usage: 13 MB
% 6.94/1.57 % (2788100)Instructions burned: 44 (million)
% 6.94/1.57 % (2788100)------------------------------
% 6.94/1.57 % (2788100)------------------------------
% 6.94/1.57 % (2788089)Instruction limit reached!
% 6.94/1.57 % (2788089)------------------------------
% 6.94/1.57 % (2788089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788089)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788089)Termination reason: Instruction limit
% 6.94/1.57 % (2788089)Termination phase: Saturation
% 6.94/1.57 % (2788089)Time elapsed: 0.133 s
% 6.94/1.57 % (2788089)Peak memory usage: 13 MB
% 6.94/1.57 % (2788089)Instructions burned: 138 (million)
% 6.94/1.57 % (2788097)Refutation not found, incomplete strategy
% 6.94/1.57 % (2788097)------------------------------
% 6.94/1.57 % (2788097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788097)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788097)Termination reason: Refutation not found, incomplete strategy
% 6.94/1.57 % (2788097)Time elapsed: 0.071 s
% 6.94/1.57 % (2788097)Peak memory usage: 13 MB
% 6.94/1.57 % (2788097)Instructions burned: 82 (million)
% 6.94/1.57 % (2788097)------------------------------
% 6.94/1.57 % (2788097)------------------------------
% 6.94/1.57 % (2788105)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1980472457:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/515Mi)
% 6.94/1.57 % (2788098)Instruction limit reached!
% 6.94/1.57 % (2788098)------------------------------
% 6.94/1.57 % (2788098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788098)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788098)Termination reason: Instruction limit
% 6.94/1.57 % (2788098)Termination phase: Function definition elimination
% 6.94/1.57 % (2788098)Time elapsed: 0.071 s
% 6.94/1.57 % (2788098)Peak memory usage: 11 MB
% 6.94/1.57 % (2788098)Instructions burned: 97 (million)
% 6.94/1.57 % (2788107)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=130542449:st=1.5:i=130:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/130Mi)
% 6.94/1.57 % (2788108)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3714238457:i=44:ep=R:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/44Mi)
% 6.94/1.57 % (2788110)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2712364120:s2a=on:i=571:nm=16:rtra=on_2991 on theBenchmark for (2991ds/571Mi)
% 6.94/1.57 % (2788111)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1376012849:i=450:rtra=on:ixr=off:ntd=on_2991 on theBenchmark for (2991ds/450Mi)
% 6.94/1.57 % (2788108)Instruction limit reached!
% 6.94/1.57 % (2788108)------------------------------
% 6.94/1.57 % (2788108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788108)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788108)Termination reason: Instruction limit
% 6.94/1.57 % (2788108)Termination phase: Property scanning
% 6.94/1.57 % (2788108)Time elapsed: 0.036 s
% 6.94/1.57 % (2788108)Peak memory usage: 11 MB
% 6.94/1.57 % (2788108)Instructions burned: 45 (million)
% 6.94/1.57 % (2788116)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=344257777:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/95Mi)
% 6.94/1.57 % (2788107)Instruction limit reached!
% 6.94/1.57 % (2788107)------------------------------
% 6.94/1.57 % (2788107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788107)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788107)Termination reason: Instruction limit
% 6.94/1.57 % (2788107)Termination phase: Saturation
% 6.94/1.57 % (2788107)Time elapsed: 0.115 s
% 6.94/1.57 % (2788107)Peak memory usage: 13 MB
% 6.94/1.57 % (2788107)Instructions burned: 130 (million)
% 6.94/1.57 % (2788116)Instruction limit reached!
% 6.94/1.57 % (2788116)------------------------------
% 6.94/1.57 % (2788116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788116)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788116)Termination reason: Instruction limit
% 6.94/1.57 % (2788116)Termination phase: Function definition elimination
% 6.94/1.57 % (2788116)Time elapsed: 0.070 s
% 6.94/1.57 % (2788116)Peak memory usage: 11 MB
% 6.94/1.57 % (2788116)Instructions burned: 96 (million)
% 6.94/1.57 % (2788118)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3607252188:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2989 on theBenchmark for (2989ds/65Mi)
% 6.94/1.57 % (2788120)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=3402609038:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2989 on theBenchmark for (2989ds/105Mi)
% 6.94/1.57 % (2788118)Instruction limit reached!
% 6.94/1.57 % (2788118)------------------------------
% 6.94/1.57 % (2788118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788118)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788118)Termination reason: Instruction limit
% 6.94/1.57 % (2788118)Termination phase: Function definition elimination
% 6.94/1.57 % (2788118)Time elapsed: 0.055 s
% 6.94/1.57 % (2788118)Peak memory usage: 11 MB
% 6.94/1.57 % (2788118)Instructions burned: 66 (million)
% 6.94/1.57 % (2788122)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3555296407:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2988 on theBenchmark for (2988ds/5755Mi)
% 6.94/1.57 % (2788120)Instruction limit reached!
% 6.94/1.57 % (2788120)------------------------------
% 6.94/1.57 % (2788120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788120)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788120)Termination reason: Instruction limit
% 6.94/1.57 % (2788120)Termination phase: Function definition elimination
% 6.94/1.57 % (2788120)Time elapsed: 0.077 s
% 6.94/1.57 % (2788120)Peak memory usage: 11 MB
% 6.94/1.57 % (2788120)Instructions burned: 106 (million)
% 6.94/1.57 % (2788124)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3204938839:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2988 on theBenchmark for (2988ds/375Mi)
% 6.94/1.57 % (2788105) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2787983-2788105"...
% 6.94/1.57 % (2788111)Instruction limit reached!
% 6.94/1.57 % (2788111)------------------------------
% 6.94/1.57 % (2788111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788111)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788111)Termination reason: Instruction limit
% 6.94/1.57 % (2788111)Termination phase: Property scanning
% 6.94/1.57 % (2788111)Time elapsed: 0.296 s
% 6.94/1.57 % (2788111)Peak memory usage: 11 MB
% 6.94/1.57 % (2788111)Instructions burned: 450 (million)
% 6.94/1.57 % (2788105)...printing done.
% 6.94/1.57 % (2788105)Refutation found. Thanks to Tanya!
% 6.94/1.57 % SZS status Theorem for theBenchmark
% 6.94/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 6.94/1.57 % (2788105)------------------------------
% 6.94/1.57 % (2788105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.57 % (2788105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.57 % (2788105)CaDiCaL version: 2.1.3
% 6.94/1.57 % (2788105)Termination reason: Refutation
% 6.94/1.57 % (2788105)Time elapsed: 0.350 s
% 6.94/1.57 % (2788105)Peak memory usage: 15 MB
% 6.94/1.57 % (2788105)Instructions burned: 425 (million)
% 6.94/1.57 % (2787983)Success in time 1.254 s
% 6.94/1.57 % Vampire exiting
%------------------------------------------------------------------------------