%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP078^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:08:14 AM UTC 2026
% Result : Theorem 0.30s 0.41s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 77 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 298 ( 24 ~; 19 |; 0 &; 249 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 174 ( 171 usr; 12 con; 0-4 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_list_a: $tType ).
thf(type_def_6,type,
multiset_nat: $tType ).
thf(type_def_7,type,
multiset_int: $tType ).
thf(type_def_8,type,
multiset_a: $tType ).
thf(type_def_9,type,
set_real: $tType ).
thf(type_def_10,type,
list_nat: $tType ).
thf(type_def_11,type,
set_nat: $tType ).
thf(type_def_12,type,
set_int: $tType ).
thf(type_def_13,type,
list_a: $tType ).
thf(type_def_14,type,
set_a: $tType ).
thf(type_def_15,type,
real: $tType ).
thf(type_def_16,type,
nat: $tType ).
thf(type_def_17,type,
int: $tType ).
thf(type_def_18,type,
a: $tType ).
thf(type_def_19,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
inverse_inverse_real: real > real ).
thf(func_def_1,type,
bij_betw_nat_int: ( nat > int ) > set_nat > set_int > $o ).
thf(func_def_2,type,
bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
thf(func_def_3,type,
bij_betw_nat_real: ( nat > real ) > set_nat > set_real > $o ).
thf(func_def_4,type,
bij_betw_nat_a: ( nat > a ) > set_nat > set_a > $o ).
thf(func_def_5,type,
comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
thf(func_def_6,type,
comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
thf(func_def_7,type,
comp_l728830689st_nat: ( list_nat > list_a ) > ( list_nat > list_nat ) > list_nat > list_a ).
thf(func_def_8,type,
comp_l1234327363st_nat: ( list_a > list_a ) > ( list_nat > list_a ) > list_nat > list_a ).
thf(func_def_9,type,
comp_m1386984005et_nat: ( multiset_nat > multiset_nat ) > ( multiset_nat > multiset_nat ) > multiset_nat > multiset_nat ).
thf(func_def_10,type,
comp_m1844659105et_nat: ( multiset_nat > multiset_a ) > ( multiset_nat > multiset_nat ) > multiset_nat > multiset_a ).
thf(func_def_11,type,
comp_m346803701et_nat: ( multiset_nat > nat ) > ( multiset_nat > multiset_nat ) > multiset_nat > nat ).
thf(func_def_12,type,
comp_m1962190563et_nat: ( multiset_a > multiset_nat ) > ( multiset_nat > multiset_a ) > multiset_nat > multiset_nat ).
thf(func_def_13,type,
comp_m540523139et_nat: ( multiset_a > multiset_a ) > ( multiset_nat > multiset_a ) > multiset_nat > multiset_a ).
thf(func_def_14,type,
comp_m1512105363et_nat: ( multiset_a > nat ) > ( multiset_nat > multiset_a ) > multiset_nat > nat ).
thf(func_def_15,type,
comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
thf(func_def_16,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(func_def_17,type,
comp_nat_a_nat: ( nat > a ) > ( nat > nat ) > nat > a ).
thf(func_def_18,type,
comp_a_nat_nat: ( a > nat ) > ( nat > a ) > nat > nat ).
thf(func_def_19,type,
comp_a_a_nat: ( a > a ) > ( nat > a ) > nat > a ).
thf(func_def_20,type,
inj_on_int_int: ( int > int ) > set_int > $o ).
thf(func_def_21,type,
inj_on_int_nat: ( int > nat ) > set_int > $o ).
thf(func_def_22,type,
inj_on_nat_int: ( nat > int ) > set_nat > $o ).
thf(func_def_23,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_24,type,
inj_on_nat_real: ( nat > real ) > set_nat > $o ).
thf(func_def_25,type,
inj_on_nat_a: ( nat > a ) > set_nat > $o ).
thf(func_def_26,type,
uminus_uminus_int: int > int ).
thf(func_def_27,type,
uminus_uminus_real: real > real ).
thf(func_def_28,type,
zero_zero_int: int ).
thf(func_def_29,type,
zero_z2005226153et_nat: multiset_nat ).
thf(func_def_30,type,
zero_zero_multiset_a: multiset_a ).
thf(func_def_31,type,
zero_zero_nat: nat ).
thf(func_def_32,type,
zero_zero_real: real ).
thf(func_def_33,type,
if_int: $o > int > int > int ).
thf(func_def_34,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_35,type,
if_real: $o > real > real > real ).
thf(func_def_36,type,
nat2: int > nat ).
thf(func_def_37,type,
ring_1_of_int_int: int > int ).
thf(func_def_38,type,
ring_1_of_int_real: int > real ).
thf(func_def_39,type,
gen_length_a: nat > list_a > nat ).
thf(func_def_40,type,
map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
thf(func_def_41,type,
map_nat_a: ( nat > a ) > list_nat > list_a ).
thf(func_def_42,type,
map_a_nat: ( a > nat ) > list_a > list_nat ).
thf(func_def_43,type,
map_a_a: ( a > a ) > list_a > list_a ).
thf(func_def_44,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(func_def_45,type,
map_tailrec_nat_a: ( nat > a ) > list_nat > list_a ).
thf(func_def_46,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_47,type,
nth_a: list_a > nat > a ).
thf(func_def_48,type,
upt: nat > nat > list_nat ).
thf(func_def_49,type,
image_mset_nat_int: ( nat > int ) > multiset_nat > multiset_int ).
thf(func_def_50,type,
image_mset_nat_nat: ( nat > nat ) > multiset_nat > multiset_nat ).
thf(func_def_51,type,
image_mset_nat_a: ( nat > a ) > multiset_nat > multiset_a ).
thf(func_def_52,type,
image_mset_a_nat: ( a > nat ) > multiset_a > multiset_nat ).
thf(func_def_53,type,
image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
thf(func_def_54,type,
mset_nat: list_nat > multiset_nat ).
thf(func_def_55,type,
mset_a: list_a > multiset_a ).
thf(func_def_56,type,
mset_set_int: set_int > multiset_int ).
thf(func_def_57,type,
mset_set_nat: set_nat > multiset_nat ).
thf(func_def_58,type,
mset_set_a: set_a > multiset_a ).
thf(func_def_59,type,
size_multiset_nat: ( nat > nat ) > multiset_nat > nat ).
thf(func_def_60,type,
size_multiset_a: ( a > nat ) > multiset_a > nat ).
thf(func_def_61,type,
semiri2019852685at_int: nat > int ).
thf(func_def_62,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_63,type,
semiri2110766477t_real: nat > real ).
thf(func_def_64,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_65,type,
size_size_list_a: list_a > nat ).
thf(func_def_66,type,
size_s1679505588et_nat: multiset_nat > nat ).
thf(func_def_67,type,
size_size_multiset_a: multiset_a > nat ).
thf(func_def_68,type,
ord_less_int: int > int > $o ).
thf(func_def_69,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_70,type,
ord_less_real: real > real > $o ).
thf(func_def_71,type,
ord_less_set_int: set_int > set_int > $o ).
thf(func_def_72,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(func_def_73,type,
ord_less_set_real: set_real > set_real > $o ).
thf(func_def_74,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_75,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_76,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_77,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(func_def_78,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_79,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(func_def_80,type,
image_int_nat: ( int > nat ) > set_int > set_nat ).
thf(func_def_81,type,
image_nat_int: ( nat > int ) > set_nat > set_int ).
thf(func_def_82,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_83,type,
image_nat_real: ( nat > real ) > set_nat > set_real ).
thf(func_def_84,type,
image_nat_a: ( nat > a ) > set_nat > set_a ).
thf(func_def_85,type,
set_or1199280219an_int: int > int > set_int ).
thf(func_def_86,type,
set_or562006527an_nat: nat > nat > set_nat ).
thf(func_def_87,type,
set_or2075149659n_real: real > real > set_real ).
thf(func_def_88,type,
set_ord_lessThan_int: int > set_int ).
thf(func_def_89,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(func_def_90,type,
set_or1211449801n_real: real > set_real ).
thf(func_def_91,type,
member_int: int > set_int > $o ).
thf(func_def_92,type,
member_list_a: list_a > set_list_a > $o ).
thf(func_def_93,type,
member_nat: nat > set_nat > $o ).
thf(func_def_94,type,
member_real: real > set_real > $o ).
thf(func_def_95,type,
f: nat > nat ).
thf(func_def_96,type,
xs: list_a ).
thf(func_def_97,type,
ys: list_a ).
thf(func_def_101,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_102,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_103,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_104,type,
vAND: $o > $o > $o ).
thf(func_def_105,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_106,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_107,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_108,type,
vIMP: $o > $o > $o ).
thf(func_def_109,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_110,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_111,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_112,type,
sK0: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_113,type,
sK1: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_114,type,
sK2: set_nat > ( nat > nat ) > nat > nat ).
thf(func_def_115,type,
sK3: nat > ( nat > a > $o ) > a ).
thf(func_def_116,type,
sK4: list_a > ( nat > a > $o ) > nat > nat ).
thf(func_def_117,type,
sK5: ( nat > a > $o ) > nat > list_a ).
thf(func_def_118,type,
sK6: ( nat > a > $o ) > nat > nat ).
thf(func_def_119,type,
sK7: multiset_a > list_a ).
thf(func_def_120,type,
sK8: set_nat > set_nat > nat > nat ).
thf(func_def_121,type,
sK9: ( nat > $o ) > nat ).
thf(func_def_122,type,
sK10: int > nat ).
thf(func_def_123,type,
sK11: int > nat ).
thf(func_def_124,type,
sK12: int > nat ).
thf(func_def_125,type,
sK13: int > nat ).
thf(func_def_126,type,
sK14: ( nat > nat ) > set_nat > ( nat > $o ) > nat ).
thf(func_def_127,type,
sK15: set_nat > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_128,type,
sK16: real > nat ).
thf(func_def_129,type,
sK17: int > nat ).
thf(func_def_130,type,
sK18: int > nat ).
thf(func_def_131,type,
sK19: nat > ( nat > $o ) > nat ).
thf(func_def_132,type,
sK20: nat > ( nat > $o ) > nat ).
thf(func_def_133,type,
sK21: ( real > $o ) > nat ).
thf(func_def_134,type,
sK22: ( real > $o ) > real ).
thf(func_def_135,type,
sK23: ( real > $o ) > real ).
thf(func_def_136,type,
sK24: real > nat ).
thf(func_def_137,type,
sK25: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_138,type,
sK26: ( int > int > $o ) > int ).
thf(func_def_139,type,
sK27: ( int > int > $o ) > int ).
thf(func_def_140,type,
sK28: int > nat ).
thf(func_def_141,type,
sK29: ( nat > $o ) > nat ).
thf(func_def_142,type,
sK30: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_143,type,
sK31: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_144,type,
sK32: list_a > list_a > nat ).
thf(func_def_145,type,
sK33: real > real > real ).
thf(func_def_146,type,
sK34: set_nat > ( nat > nat ) > ( nat > $o ) > nat ).
thf(func_def_147,type,
sK35: set_nat > ( nat > nat ) > nat ).
thf(func_def_148,type,
sK36: set_nat > ( nat > nat ) > nat ).
thf(func_def_149,type,
sK37: real > real ).
thf(func_def_150,type,
sK38: set_nat > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_151,type,
sK39: ( nat > int ) > set_nat > ( nat > int ) > nat ).
thf(func_def_152,type,
sK40: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_153,type,
sK41: set_nat > ( nat > int ) > int > nat ).
thf(func_def_154,type,
sK42: real > nat ).
thf(func_def_155,type,
sK43: nat > list_a ).
thf(func_def_156,type,
sK44: ( nat > $o ) > nat > nat ).
thf(func_def_157,type,
sK45: ( nat > $o ) > nat > nat ).
thf(func_def_158,type,
sK46: real > real ).
thf(func_def_159,type,
sK47: set_nat > ( nat > int ) > ( int > $o ) > nat ).
thf(func_def_160,type,
sK48: set_nat > ( nat > int ) > ( nat > int ) > nat ).
thf(func_def_161,type,
sK49: int > nat ).
thf(func_def_162,type,
sK50: int > nat ).
thf(func_def_163,type,
sK51: ( nat > $o ) > nat ).
thf(func_def_164,type,
sK52: multiset_nat > list_nat ).
thf(func_def_165,type,
sK53: ( list_a > $o ) > list_a ).
thf(func_def_166,type,
sK54: ( nat > int ) > set_nat > ( int > $o ) > int ).
thf(func_def_167,type,
sK55: ( nat > int ) > ( nat > int ) > set_nat > nat ).
thf(func_def_168,type,
sK56: int > ( nat > $o ) > nat ).
thf(func_def_169,type,
vNOT: $o > $o ).
thf(f1,axiom,
inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C1_C) ).
thf(f4,axiom,
( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C2_C) ).
thf(f72,axiom,
! [X1: set_nat,X0: nat > nat] :
( ( inj_on_nat_nat @ X0 @ X1 )
=> ( ( image_mset_nat_nat @ X0 @ ( mset_set_nat @ X1 ) )
= ( mset_set_nat @ ( image_nat_nat @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_image__mset__mset__set) ).
thf(f357,conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f358,negated_conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f381,plain,
inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ),
inference(rectify,[],[f1]) ).
thf(f382,plain,
( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= $true ),
inference(fool_elimination,[],[f381]) ).
thf(f585,plain,
! [X0: set_nat,X1: nat > nat] :
( ( inj_on_nat_nat @ X1 @ X0 )
=> ( ( image_mset_nat_nat @ X1 @ ( mset_set_nat @ X0 ) )
= ( mset_set_nat @ ( image_nat_nat @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f72]) ).
thf(f586,plain,
! [X0: set_nat,X1: nat > nat] :
( ( ( inj_on_nat_nat @ X1 @ X0 )
= $true )
=> ( ( image_mset_nat_nat @ X1 @ ( mset_set_nat @ X0 ) )
= ( mset_set_nat @ ( image_nat_nat @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f585]) ).
thf(f783,plain,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(flattening,[],[f358]) ).
thf(f868,plain,
! [X0: set_nat,X1: nat > nat] :
( ( ( inj_on_nat_nat @ X1 @ X0 )
!= $true )
| ( ( image_mset_nat_nat @ X1 @ ( mset_set_nat @ X0 ) )
= ( mset_set_nat @ ( image_nat_nat @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f586]) ).
thf(f1303,plain,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(cnf_transformation,[],[f783]) ).
thf(f1625,plain,
( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= $true ),
inference(cnf_transformation,[],[f382]) ).
thf(f1667,plain,
! [X0: set_nat,X1: nat > nat] :
( ( ( image_mset_nat_nat @ X1 @ ( mset_set_nat @ X0 ) )
= ( mset_set_nat @ ( image_nat_nat @ X1 @ X0 ) ) )
| ( ( inj_on_nat_nat @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f868]) ).
thf(f1688,plain,
( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f2045,definition,
( spl57_9
<=> ( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
thf(f2047,plain,
( ( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= $true )
| ~ spl57_9 ),
inference(avatar_component_clause,[],[f2045]) ).
thf(f2048,plain,
spl57_9,
inference(avatar_split_clause,[],[f1625,f2045]) ).
thf(f2065,definition,
( spl57_13
<=> ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl57_13])],[avatar_definition]) ).
thf(f2067,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
| spl57_13 ),
inference(avatar_component_clause,[],[f2065]) ).
thf(f2068,plain,
~ spl57_13,
inference(avatar_split_clause,[],[f1303,f2065]) ).
thf(f2155,definition,
( spl57_31
<=> ( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ),
introduced(definition,[new_symbols(definition,[spl57_31])],[avatar_definition]) ).
thf(f2157,plain,
( ( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) )
| ~ spl57_31 ),
inference(avatar_component_clause,[],[f2155]) ).
thf(f2158,plain,
spl57_31,
inference(avatar_split_clause,[],[f1688,f2155]) ).
thf(f2336,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) )
| ( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
!= $true )
| spl57_13 ),
inference(superposition,[],[f2067,f1667]) ).
thf(f2340,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) )
| ~ spl57_9
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f2336,f2047]) ).
thf(f2341,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
| ~ spl57_9
| spl57_13
| ~ spl57_31 ),
inference(forward_demodulation,[],[f2340,f2157]) ).
thf(f2342,plain,
( $false
| ~ spl57_9
| spl57_13
| ~ spl57_31 ),
inference(trivial_inequality_removal,[],[f2341]) ).
thf(f2343,plain,
( ~ spl57_9
| spl57_13
| ~ spl57_31 ),
inference(avatar_contradiction_clause,[],[f2342]) ).
cnf(s9,plain,
spl57_9,
inference(sat_conversion,[],[f2048]) ).
cnf(s14,plain,
~ spl57_13,
inference(sat_conversion,[],[f2068]) ).
cnf(s50,plain,
spl57_31,
inference(sat_conversion,[],[f2158]) ).
cnf(s69,plain,
( ~ spl57_9
| spl57_13
| ~ spl57_31 ),
inference(sat_conversion,[],[f2343]) ).
cnf(s71,plain,
~ spl57_9,
inference(rat,[],[s69,s50,s14]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s9,s71]) ).
thf(f2344,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP078^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n007.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:46:11 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.21/0.31 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
% 0.30/0.41 % (3833462)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.41 % (3833470)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=729619560: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)
% 0.30/0.41 % (3833467)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3818010205:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.41 % (3833469)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1927427545:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.41 % (3833468)lrs+10_16_si=on:nwc=1.5:random_seed=2533217139:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.41 % (3833471)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=263293450:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.41 % (3833473)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.41 % (3833473)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
% 0.30/0.41 % (3833469)Instruction limit reached!
% 0.30/0.41 % (3833469)------------------------------
% 0.30/0.41 % (3833469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (3833469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (3833469)CaDiCaL version: 2.1.3
% 0.30/0.41 % (3833469)Termination reason: Instruction limit
% 0.30/0.41 % (3833469)Termination phase: shuffling
% 0.30/0.41 % (3833469)Time elapsed: 0.002 s
% 0.30/0.41 % (3833469)Peak memory usage: 10 MB
% 0.30/0.41 % (3833469)Instructions burned: 4 (million)
% 0.30/0.41 % (3833472)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=813655671:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.41 % (3833473)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=958017960:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.41 % (3833468)Instruction limit reached!
% 0.30/0.41 % (3833468)------------------------------
% 0.30/0.41 % (3833468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (3833468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (3833468)CaDiCaL version: 2.1.3
% 0.30/0.41 % (3833468)Termination reason: Instruction limit
% 0.30/0.41 % (3833468)Termination phase: Property scanning
% 0.30/0.41 % (3833468)Time elapsed: 0.009 s
% 0.30/0.41 % (3833468)Peak memory usage: 10 MB
% 0.30/0.41 % (3833468)Instructions burned: 18 (million)
% 0.30/0.41 % (3833471)Instruction limit reached!
% 0.30/0.41 % (3833471)------------------------------
% 0.30/0.41 % (3833471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (3833471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (3833471)CaDiCaL version: 2.1.3
% 0.30/0.41 % (3833471)Termination reason: Instruction limit
% 0.30/0.41 % (3833471)Termination phase: Property scanning
% 0.30/0.41 % (3833471)Time elapsed: 0.012 s
% 0.30/0.41 % (3833471)Peak memory usage: 10 MB
% 0.30/0.41 % (3833471)Instructions burned: 25 (million)
% 0.30/0.41 % (3833481)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2740646507:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.41 % (3833483)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.41 % (3833482)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2327876400:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.30/0.41 % (3833481)Instruction limit reached!
% 0.30/0.41 % (3833481)------------------------------
% 0.30/0.41 % (3833481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (3833481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (3833481)CaDiCaL version: 2.1.3
% 0.30/0.41 % (3833481)Termination reason: Instruction limit
% 0.30/0.41 % (3833481)Termination phase: shuffling
% 0.30/0.41 % (3833481)Time elapsed: 0.002 s
% 0.30/0.41 % (3833481)Peak memory usage: 10 MB
% 0.30/0.41 % (3833481)Instructions burned: 3 (million)
% 0.30/0.41 % (3833470) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3833462-3833470"...
% 0.30/0.41 % (3833482)Instruction limit reached!
% 0.30/0.41 % (3833482)------------------------------
% 0.30/0.41 % (3833482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (3833482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (3833482)CaDiCaL version: 2.1.3
% 0.30/0.41 % (3833482)Termination reason: Instruction limit
% 0.30/0.41 % (3833482)Termination phase: shuffling
% 0.30/0.41 % (3833482)Time elapsed: 0.003 s
% 0.30/0.41 % (3833482)Peak memory usage: 10 MB
% 0.30/0.41 % (3833482)Instructions burned: 5 (million)
% 0.30/0.41 % (3833483)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=140499282:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/0.41 % (3833470)...printing done.
% 0.30/0.41 % (3833470)Refutation found. Thanks to Tanya!
% 0.30/0.41 % SZS status Theorem for theBenchmark
% 0.30/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.41 % (3833470)------------------------------
% 0.30/0.41 % (3833470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (3833470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (3833470)CaDiCaL version: 2.1.3
% 0.30/0.41 % (3833470)Termination reason: Refutation
% 0.30/0.41 % (3833470)Time elapsed: 0.040 s
% 0.30/0.41 % (3833470)Peak memory usage: 15 MB
% 0.30/0.41 % (3833470)Instructions burned: 142 (million)
% 0.30/0.41 % (3833462)Success in time 0.091 s
% 0.30/0.41 % Vampire exiting
%------------------------------------------------------------------------------