%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP053^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:08:08 AM UTC 2026
% Result : Theorem 0.19s 0.39s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 21 unt; 0 typ; 5 def)
% Number of atoms : 73 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 281 ( 29 ~; 24 |; 0 &; 222 @)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 163 ( 161 usr; 16 con; 0-4 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
produc1864880952at_nat: $tType ).
thf(type_def_6,type,
produc787001653at_nat: $tType ).
thf(type_def_7,type,
produc2082277813at_nat: $tType ).
thf(type_def_8,type,
produc1190591575at_nat: $tType ).
thf(type_def_9,type,
produc1271302400at_nat: $tType ).
thf(type_def_10,type,
produc1695820582at_nat: $tType ).
thf(type_def_11,type,
list_P559422087at_nat: $tType ).
thf(type_def_12,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_13,type,
product_prod_nat_nat: $tType ).
thf(type_def_14,type,
capacity: $tType ).
thf(type_def_15,type,
nat: $tType ).
thf(type_def_16,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
thf(func_def_1,type,
dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).
thf(func_def_2,type,
isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_3,type,
isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_4,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_5,type,
min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(func_def_6,type,
one_one_nat: nat ).
thf(func_def_7,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_8,type,
nil_Pr1308055047at_nat: list_P559422087at_nat ).
thf(func_def_9,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(func_def_10,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(func_def_11,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_12,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_13,type,
produc1682925677at_nat: ( nat > nat > nat ) > produc1695820582at_nat > produc2082277813at_nat ).
thf(func_def_14,type,
produc696256106at_nat: ( nat > product_prod_nat_nat > product_prod_nat_nat ) > produc1190591575at_nat > produc1864880952at_nat ).
thf(func_def_15,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_16,type,
produc1933845336at_nat: nat > product_prod_nat_nat > produc1695820582at_nat ).
thf(func_def_17,type,
produc869658639at_nat: nat > produc1695820582at_nat > produc1190591575at_nat ).
thf(func_def_18,type,
produc947540346at_nat: product_prod_nat_nat > nat > produc1271302400at_nat ).
thf(func_def_19,type,
produc365964781at_nat: produc1695820582at_nat > ( nat > nat > nat ) > produc787001653at_nat ).
thf(func_def_20,type,
produc1728816653at_nat: produc2082277813at_nat > produc787001653at_nat ).
thf(func_def_21,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_22,type,
produc857968056at_nat: produc1695820582at_nat > produc1271302400at_nat ).
thf(func_def_23,type,
produc2019146714at_nat: produc1271302400at_nat > produc1695820582at_nat ).
thf(func_def_24,type,
produc411855757at_nat: produc787001653at_nat > produc2082277813at_nat ).
thf(func_def_25,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_26,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_27,type,
c: product_prod_nat_nat > capacity ).
thf(func_def_28,type,
p: list_P559422087at_nat ).
thf(func_def_29,type,
p1: list_P559422087at_nat ).
thf(func_def_30,type,
p2: list_P559422087at_nat ).
thf(func_def_31,type,
p3: list_P559422087at_nat ).
thf(func_def_32,type,
s: nat ).
thf(func_def_33,type,
t: nat ).
thf(func_def_34,type,
u: nat ).
thf(func_def_35,type,
v: nat ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vIMP: $o > $o > $o ).
thf(func_def_51,type,
vNOT: $o > $o ).
thf(func_def_52,type,
sP0: nat > nat > nat > $o ).
thf(func_def_53,type,
sP1: nat > nat > nat > $o ).
thf(func_def_54,type,
sK2: produc1695820582at_nat > nat ).
thf(func_def_55,type,
sK3: produc1695820582at_nat > nat ).
thf(func_def_56,type,
sK4: produc1695820582at_nat > nat ).
thf(func_def_57,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_58,type,
sK6: produc2082277813at_nat > nat > nat > nat ).
thf(func_def_59,type,
sK7: produc2082277813at_nat > produc1695820582at_nat ).
thf(func_def_60,type,
sK8: nat > nat > nat ).
thf(func_def_61,type,
sK9: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_62,type,
sK10: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_63,type,
sK11: produc2082277813at_nat > nat ).
thf(func_def_64,type,
sK12: produc2082277813at_nat > nat ).
thf(func_def_65,type,
sK13: produc2082277813at_nat > nat ).
thf(func_def_66,type,
sK14: produc2082277813at_nat > nat > nat > nat ).
thf(func_def_67,type,
sK15: ( nat > $o ) > nat > nat > nat ).
thf(func_def_68,type,
sK16: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(func_def_69,type,
sK17: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_70,type,
sK18: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_71,type,
sK19: nat > nat > nat ).
thf(func_def_72,type,
sK20: nat > nat > nat ).
thf(func_def_73,type,
sK21: nat > nat > nat > list_P559422087at_nat ).
thf(func_def_74,type,
sK22: nat > list_P559422087at_nat > nat ).
thf(func_def_75,type,
sK23: ( produc2082277813at_nat > $o ) > nat ).
thf(func_def_76,type,
sK24: ( produc2082277813at_nat > $o ) > nat > nat > nat ).
thf(func_def_77,type,
sK25: ( produc2082277813at_nat > $o ) > nat ).
thf(func_def_78,type,
sK26: ( produc2082277813at_nat > $o ) > nat ).
thf(func_def_79,type,
sK27: list_P559422087at_nat > nat > nat ).
thf(func_def_80,type,
sK28: product_prod_nat_nat > nat ).
thf(func_def_81,type,
sK29: product_prod_nat_nat > nat ).
thf(func_def_82,type,
sK30: nat > ( nat > $o ) > nat ).
thf(func_def_83,type,
sK31: ( nat > $o ) > nat ).
thf(func_def_84,type,
sK32: ( produc1695820582at_nat > $o ) > nat ).
thf(func_def_85,type,
sK33: ( produc1695820582at_nat > $o ) > nat ).
thf(func_def_86,type,
sK34: ( produc1695820582at_nat > $o ) > nat ).
thf(func_def_87,type,
sK35: ( produc1695820582at_nat > $o ) > product_prod_nat_nat ).
thf(func_def_88,type,
sK36: ( produc1695820582at_nat > $o ) > nat ).
thf(func_def_89,type,
sK37: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_90,type,
sK38: ( nat > nat > $o ) > nat ).
thf(func_def_91,type,
sK39: ( nat > nat > $o ) > nat ).
thf(func_def_92,type,
sK40: ( nat > nat > $o ) > nat ).
thf(func_def_93,type,
sK41: ( nat > nat > $o ) > nat ).
thf(func_def_94,type,
sK42: ( nat > nat > $o ) > nat ).
thf(func_def_95,type,
sK43: ( nat > $o ) > nat ).
thf(func_def_96,type,
sK44: nat > ( nat > $o ) > nat ).
thf(func_def_97,type,
sK45: ( nat > $o ) > nat ).
thf(func_def_98,type,
sK46: ( product_prod_nat_nat > capacity ) > nat > nat > list_P559422087at_nat ).
thf(func_def_99,type,
sK47: ( produc1695820582at_nat > $o ) > product_prod_nat_nat ).
thf(func_def_100,type,
sK48: ( produc1695820582at_nat > $o ) > nat ).
thf(func_def_101,type,
sK49: ( nat > nat ) > nat ).
thf(func_def_102,type,
sK50: ( nat > nat ) > nat ).
thf(func_def_103,type,
sK51: ( nat > nat > $o ) > nat ).
thf(func_def_104,type,
sK52: ( nat > nat > $o ) > nat ).
thf(func_def_105,type,
sK53: ( nat > nat > $o ) > nat ).
thf(func_def_106,type,
sK54: ( nat > nat > $o ) > nat ).
thf(func_def_107,type,
sK55: ( nat > nat ) > nat ).
thf(func_def_108,type,
sK56: ( nat > nat ) > nat ).
thf(func_def_109,type,
sK57: nat > nat > nat ).
thf(func_def_110,type,
sK58: list_P559422087at_nat > nat > nat ).
thf(func_def_111,type,
sK59: product_prod_nat_nat > nat ).
thf(func_def_112,type,
sK60: product_prod_nat_nat > nat ).
thf(func_def_113,type,
sK61: nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(func_def_114,type,
sK62: ( produc2082277813at_nat > $o ) > nat ).
thf(func_def_115,type,
sK63: ( produc2082277813at_nat > $o ) > nat > nat > nat ).
thf(func_def_116,type,
sK64: ( produc2082277813at_nat > $o ) > product_prod_nat_nat ).
thf(func_def_117,type,
sK65: produc1695820582at_nat > nat ).
thf(func_def_118,type,
sK66: produc1695820582at_nat > product_prod_nat_nat ).
thf(func_def_119,type,
sK67: produc1695820582at_nat > nat ).
thf(func_def_120,type,
sK68: produc1695820582at_nat > product_prod_nat_nat ).
thf(func_def_121,type,
sK69: nat > nat > nat ).
thf(func_def_122,type,
sK70: ( nat > nat ) > nat ).
thf(func_def_123,type,
sK71: ( nat > nat ) > nat ).
thf(func_def_124,type,
sK72: produc2082277813at_nat > nat ).
thf(func_def_125,type,
sK73: produc2082277813at_nat > nat ).
thf(func_def_126,type,
sK74: produc2082277813at_nat > nat ).
thf(func_def_127,type,
sK75: produc2082277813at_nat > nat > nat > nat ).
thf(func_def_128,type,
sK76: produc2082277813at_nat > nat > nat > nat ).
thf(func_def_129,type,
sK77: produc2082277813at_nat > produc1695820582at_nat ).
thf(func_def_130,type,
sK78: nat > nat > nat > nat ).
thf(func_def_131,type,
sK79: produc2082277813at_nat > nat > nat > nat ).
thf(func_def_132,type,
sK80: produc2082277813at_nat > product_prod_nat_nat ).
thf(func_def_133,type,
sK81: produc2082277813at_nat > nat ).
thf(func_def_134,type,
sK82: ( nat > nat ) > nat ).
thf(func_def_135,type,
sK83: ( nat > nat ) > nat ).
thf(func_def_136,type,
sK84: ( produc2082277813at_nat > $o ) > nat > nat > nat ).
thf(func_def_137,type,
sK85: ( produc2082277813at_nat > $o ) > produc1695820582at_nat ).
thf(func_def_138,type,
sK86: nat > nat > list_P559422087at_nat ).
thf(func_def_139,type,
sK87: ( nat > nat ) > nat ).
thf(func_def_140,type,
sK88: ( nat > nat ) > nat ).
thf(func_def_141,type,
sK89: ( nat > nat ) > nat ).
thf(func_def_142,type,
sK90: ( nat > nat ) > nat ).
thf(func_def_143,type,
sK91: nat > nat > ( product_prod_nat_nat > capacity ) > nat > nat ).
thf(func_def_144,type,
sK92: nat > nat > list_P559422087at_nat ).
thf(func_def_145,type,
sK93: nat > nat > list_P559422087at_nat ).
thf(func_def_146,type,
sK94: nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_147,type,
sK95: ( product_prod_nat_nat > capacity ) > nat > nat > ( nat > $o ) > nat ).
thf(func_def_148,type,
sK96: produc1864880952at_nat > product_prod_nat_nat ).
thf(func_def_149,type,
sK97: produc1864880952at_nat > nat ).
thf(func_def_150,type,
sK98: produc1864880952at_nat > nat ).
thf(func_def_151,type,
sK99: produc1864880952at_nat > nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_152,type,
sK100: nat > nat > ( product_prod_nat_nat > capacity ) > nat ).
thf(func_def_153,type,
sK101: ( produc2082277813at_nat > $o ) > produc1695820582at_nat ).
thf(func_def_154,type,
sK102: ( produc2082277813at_nat > $o ) > nat > nat > nat ).
thf(func_def_155,type,
sK103: nat > list_P559422087at_nat > nat ).
thf(func_def_157,type,
inv_plus_plus_nat_105: nat > nat > nat ).
thf(func_def_158,type,
inv_plus_plus_nat_106: nat > nat > nat ).
thf(f1,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_MIN_H) ).
thf(f3,axiom,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062min__dist_As_At_A_061_Alength_Ap1_A_L_A_I1_A_L_Alength_Ap2_J_A_092_060Longrightarrow_062_Amin__dist_Au_At_A_061_A1_A_L_Alength_Ap2_092_060close_062) ).
thf(f4,axiom,
( ( min_dist_capacity @ c @ v @ t )
= ( size_s1990949619at_nat @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062min__dist_Av_At_A_061_Alength_Ap2_092_060close_062) ).
thf(f29,axiom,
! [X0: nat,X2: nat,X1: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ X0 @ X1 ) @ X2 )
= ( plus_plus_nat @ X0 @ ( plus_plus_nat @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(f255,conjecture,
( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f256,negated_conjecture,
( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(negated_conjecture,[status(cth)],[f255]) ).
thf(f672,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus_nat @ X0 @ ( plus_plus_nat @ X2 @ X1 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ X0 @ X2 ) @ X1 ) ),
inference(rectify,[],[f29]) ).
thf(f707,plain,
( ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) )
!= ( min_dist_capacity @ c @ u @ t ) ),
inference(flattening,[],[f256]) ).
thf(f730,plain,
( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
| ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f1211,plain,
( ( size_s1990949619at_nat @ p2 )
= ( min_dist_capacity @ c @ v @ t ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f1225,plain,
( ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) )
!= ( min_dist_capacity @ c @ u @ t ) ),
inference(cnf_transformation,[],[f707]) ).
thf(f1231,plain,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f1243,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( plus_plus_nat @ X0 @ ( plus_plus_nat @ X2 @ X1 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ X0 @ X2 ) @ X1 ) ),
inference(cnf_transformation,[],[f672]) ).
thf(f1272,plain,
( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
| ( ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) )
= ( min_dist_capacity @ c @ u @ t ) ) ),
inference(cnf_transformation,[],[f730]) ).
thf(f1645,definition,
( spl104_4
<=> ( ( size_s1990949619at_nat @ p2 )
= ( min_dist_capacity @ c @ v @ t ) ) ),
introduced(definition,[new_symbols(definition,[spl104_4])],[avatar_definition]) ).
thf(f1647,plain,
( ( ( size_s1990949619at_nat @ p2 )
= ( min_dist_capacity @ c @ v @ t ) )
| ~ spl104_4 ),
inference(avatar_component_clause,[],[f1645]) ).
thf(f1648,plain,
spl104_4,
inference(avatar_split_clause,[],[f1211,f1645]) ).
thf(f1660,definition,
( spl104_7
<=> ( ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) )
= ( min_dist_capacity @ c @ u @ t ) ) ),
introduced(definition,[new_symbols(definition,[spl104_7])],[avatar_definition]) ).
thf(f1664,definition,
( spl104_8
<=> ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl104_8])],[avatar_definition]) ).
thf(f1666,plain,
( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
| spl104_8 ),
inference(avatar_component_clause,[],[f1664]) ).
thf(f1667,plain,
( spl104_7
| ~ spl104_8 ),
inference(avatar_split_clause,[],[f1272,f1664,f1660]) ).
thf(f1679,definition,
( spl104_11
<=> ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl104_11])],[avatar_definition]) ).
thf(f1681,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) )
| ~ spl104_11 ),
inference(avatar_component_clause,[],[f1679]) ).
thf(f1682,plain,
spl104_11,
inference(avatar_split_clause,[],[f1231,f1679]) ).
thf(f1740,plain,
~ spl104_7,
inference(avatar_split_clause,[],[f1225,f1660]) ).
thf(f1791,plain,
( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( min_dist_capacity @ c @ v @ t ) ) ) )
| ~ spl104_4
| spl104_8 ),
inference(forward_demodulation,[],[f1666,f1647]) ).
thf(f1793,definition,
( spl104_33
<=> ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( min_dist_capacity @ c @ v @ t ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl104_33])],[avatar_definition]) ).
thf(f1795,plain,
( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( min_dist_capacity @ c @ v @ t ) ) ) )
| spl104_33 ),
inference(avatar_component_clause,[],[f1793]) ).
thf(f1796,plain,
( ~ spl104_33
| ~ spl104_4
| spl104_8 ),
inference(avatar_split_clause,[],[f1791,f1664,f1645,f1793]) ).
thf(f1889,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
| ~ spl104_11 ),
inference(forward_demodulation,[],[f1681,f1243]) ).
thf(f1890,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( min_dist_capacity @ c @ v @ t ) ) ) )
| ~ spl104_4
| ~ spl104_11 ),
inference(forward_demodulation,[],[f1889,f1647]) ).
thf(f1891,plain,
( $false
| ~ spl104_4
| ~ spl104_11
| spl104_33 ),
inference(forward_subsumption_resolution,[],[f1890,f1795]) ).
thf(f1892,plain,
( ~ spl104_4
| ~ spl104_11
| spl104_33 ),
inference(avatar_contradiction_clause,[],[f1891]) ).
cnf(s4,plain,
spl104_4,
inference(sat_conversion,[],[f1648]) ).
cnf(s7,plain,
( spl104_7
| ~ spl104_8 ),
inference(sat_conversion,[],[f1667]) ).
cnf(s10,plain,
spl104_11,
inference(sat_conversion,[],[f1682]) ).
cnf(s23,plain,
~ spl104_7,
inference(sat_conversion,[],[f1740]) ).
cnf(s35,plain,
( ~ spl104_4
| spl104_8
| ~ spl104_33 ),
inference(sat_conversion,[],[f1796]) ).
cnf(s42,plain,
( ~ spl104_4
| ~ spl104_11
| spl104_33 ),
inference(sat_conversion,[],[f1892]) ).
cnf(s43,plain,
~ spl104_8,
inference(rat,[],[s7,s23]) ).
cnf(s47,plain,
spl104_33,
inference(rat,[],[s42,s10,s4]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s35,s43,s47,s4]) ).
thf(f1893,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP053^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:43:45 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.39 % (266406)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.39 % (266415)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3993735964:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.39 % (266417)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.39 % (266417)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
% 0.19/0.39 % (266415)Instruction limit reached!
% 0.19/0.39 % (266415)------------------------------
% 0.19/0.39 % (266415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266415)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266415)Termination reason: Instruction limit
% 0.19/0.39 % (266415)Termination phase: Preprocessing 1
% 0.19/0.39 % (266415)Time elapsed: 0.006 s
% 0.19/0.39 % (266415)Peak memory usage: 10 MB
% 0.19/0.39 % (266415)Instructions burned: 29 (million)
% 0.19/0.39 % (266412)lrs+10_16_si=on:nwc=1.5:random_seed=3574512185:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.39 % (266413)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2866744329:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.39 % (266416)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3708027503:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.39 % (266417)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=3001652984:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.39 % (266414)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=2706702860: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)
% 0.19/0.39 % (266413)Instruction limit reached!
% 0.19/0.39 % (266413)------------------------------
% 0.19/0.39 % (266413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266413)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266413)Termination reason: Instruction limit
% 0.19/0.39 % (266413)Termination phase: shuffling
% 0.19/0.39 % (266413)Time elapsed: 0.002 s
% 0.19/0.39 % (266413)Peak memory usage: 10 MB
% 0.19/0.39 % (266413)Instructions burned: 4 (million)
% 0.19/0.39 % (266412)Instruction limit reached!
% 0.19/0.39 % (266412)------------------------------
% 0.19/0.39 % (266412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266412)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266412)Termination reason: Instruction limit
% 0.19/0.39 % (266412)Termination phase: Property scanning
% 0.19/0.39 % (266412)Time elapsed: 0.009 s
% 0.19/0.39 % (266412)Peak memory usage: 10 MB
% 0.19/0.39 % (266412)Instructions burned: 20 (million)
% 0.19/0.39 % (266411)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=640921415:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.39 % (266425)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=612854290:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.39 % (266425)Instruction limit reached!
% 0.19/0.39 % (266425)------------------------------
% 0.19/0.39 % (266425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266425)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266425)Termination reason: Instruction limit
% 0.19/0.39 % (266425)Termination phase: shuffling
% 0.19/0.39 % (266425)Time elapsed: 0.002 s
% 0.19/0.39 % (266425)Peak memory usage: 10 MB
% 0.19/0.39 % (266425)Instructions burned: 8 (million)
% 0.19/0.39 % (266426)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.39 % (266429)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=981429699:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/0.39 % (266426)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1859165177:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.39 % (266429)Instruction limit reached!
% 0.19/0.39 % (266429)------------------------------
% 0.19/0.39 % (266429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266429)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266429)Termination reason: Instruction limit
% 0.19/0.39 % (266429)Termination phase: shuffling
% 0.19/0.39 % (266429)Time elapsed: 0.003 s
% 0.19/0.39 % (266429)Peak memory usage: 10 MB
% 0.19/0.39 % (266429)Instructions burned: 13 (million)
% 0.19/0.39 % (266426)Instruction limit reached!
% 0.19/0.39 % (266426)------------------------------
% 0.19/0.39 % (266426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266426)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266426)Termination reason: Instruction limit
% 0.19/0.39 % (266426)Termination phase: shuffling
% 0.19/0.39 % (266426)Time elapsed: 0.004 s
% 0.19/0.39 % (266426)Peak memory usage: 10 MB
% 0.19/0.39 % (266426)Instructions burned: 9 (million)
% 0.19/0.39 % (266432)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
% 0.19/0.39 % (266432)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.39 % (266432)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3679111132:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.19/0.39 % (266432)Instruction limit reached!
% 0.19/0.39 % (266432)------------------------------
% 0.19/0.39 % (266432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266432)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266432)Termination reason: Instruction limit
% 0.19/0.39 % (266432)Termination phase: shuffling
% 0.19/0.39 % (266432)Time elapsed: 0.007 s
% 0.19/0.39 % (266432)Peak memory usage: 10 MB
% 0.19/0.39 % (266432)Instructions burned: 28 (million)
% 0.19/0.39 % (266421)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1719753900:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.39 % (266433)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=593192625:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.19/0.39 % (266437)lrs+10_1_si=on:cs=on:random_seed=4262625507:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.19/0.39 % (266437)Instruction limit reached!
% 0.19/0.39 % (266437)------------------------------
% 0.19/0.39 % (266437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266437)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266437)Termination reason: Instruction limit
% 0.19/0.39 % (266437)Termination phase: shuffling
% 0.19/0.39 % (266437)Time elapsed: 0.002 s
% 0.19/0.39 % (266437)Peak memory usage: 10 MB
% 0.19/0.39 % (266437)Instructions burned: 9 (million)
% 0.19/0.39 % (266414) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-266406-266414"...
% 0.19/0.39 % (266421)Instruction limit reached!
% 0.19/0.39 % (266421)------------------------------
% 0.19/0.39 % (266421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.39 % (266421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.39 % (266421)CaDiCaL version: 2.1.3
% 0.19/0.39 % (266421)Termination reason: Instruction limit
% 0.19/0.39 % (266421)Termination phase: shuffling
% 0.19/0.39 % (266421)Time elapsed: 0.009 s
% 0.19/0.39 % (266421)Peak memory usage: 10 MB
% 0.19/0.39 % (266421)Instructions burned: 2 (million)
% 0.19/0.39 % (266414)...printing done.
% 0.19/0.39 % (266414)Refutation found. Thanks to Tanya!
% 0.19/0.39 % SZS status Theorem for theBenchmark
% 0.19/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.40 % (266414)------------------------------
% 0.19/0.40 % (266414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.40 % (266414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.40 % (266414)CaDiCaL version: 2.1.3
% 0.19/0.40 % (266414)Termination reason: Refutation
% 0.19/0.40 % (266414)Time elapsed: 0.063 s
% 0.19/0.40 % (266414)Peak memory usage: 14 MB
% 0.19/0.40 % (266414)Instructions burned: 121 (million)
% 0.19/0.40 % (266406)Success in time 0.112 s
% 0.19/0.40 % Vampire exiting
%------------------------------------------------------------------------------