%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP049^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:10:30 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 184 ( 11 ~; 4 |; 8 &; 152 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 267 ( 263 usr; 5 con; 0-5 aty)
% ( 0 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 32 ^; 0 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_6,type,
produc842455143at_nat: $tType ).
thf(type_def_7,type,
set_Pr1287749686at_nat: $tType ).
thf(type_def_8,type,
set_Pr1746169692at_nat: $tType ).
thf(type_def_9,type,
produc1271302400at_nat: $tType ).
thf(type_def_10,type,
produc1695820582at_nat: $tType ).
thf(type_def_11,type,
set_se1612935105at_nat: $tType ).
thf(type_def_12,type,
list_P559422087at_nat: $tType ).
thf(type_def_13,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_14,type,
product_prod_nat_nat: $tType ).
thf(type_def_15,type,
set_set_nat: $tType ).
thf(type_def_16,type,
list_nat: $tType ).
thf(type_def_17,type,
set_nat: $tType ).
thf(type_def_18,type,
nat: $tType ).
thf(type_def_19,type,
a: $tType ).
thf(type_def_20,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
thf(func_def_1,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(func_def_2,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_3,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_4,type,
finite277291581at_nat: set_Pr1746169692at_nat > $o ).
thf(func_def_5,type,
finite2000257047at_nat: set_Pr1287749686at_nat > $o ).
thf(func_def_6,type,
finite48957584at_nat: set_Pr1490359111at_nat > $o ).
thf(func_def_7,type,
finite2012248349et_nat: set_set_nat > $o ).
thf(func_def_8,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(func_def_9,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(func_def_10,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(func_def_11,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(func_def_12,type,
adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_13,type,
connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
thf(func_def_14,type,
incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_15,type,
incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_16,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_17,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_18,type,
isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_19,type,
outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_20,type,
outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_21,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_22,type,
set_nat2: list_nat > set_nat ).
thf(func_def_23,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(func_def_24,type,
ord_le1578155910_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_25,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_26,type,
ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(func_def_27,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_28,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_29,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_30,type,
ord_le148299708at_nat: set_Pr1746169692at_nat > set_Pr1746169692at_nat > $o ).
thf(func_def_31,type,
ord_le1837363350at_nat: set_Pr1287749686at_nat > set_Pr1287749686at_nat > $o ).
thf(func_def_32,type,
ord_le465611495at_nat: set_Pr1490359111at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_33,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_34,type,
produc1933845336at_nat: nat > product_prod_nat_nat > produc1695820582at_nat ).
thf(func_def_35,type,
produc947540346at_nat: product_prod_nat_nat > nat > produc1271302400at_nat ).
thf(func_def_36,type,
produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).
thf(func_def_37,type,
produc45129834at_nat: set_nat > ( nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_38,type,
produc894163943at_nat: set_nat > ( nat > set_Pr1986765409at_nat ) > set_Pr1746169692at_nat ).
thf(func_def_39,type,
produc2055342601at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > set_nat ) > set_Pr1287749686at_nat ).
thf(func_def_40,type,
produc2056081288at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > set_Pr1986765409at_nat ) > set_Pr1490359111at_nat ).
thf(func_def_41,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_42,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(func_def_43,type,
domain37934156at_nat: set_Pr1490359111at_nat > set_Pr1986765409at_nat ).
thf(func_def_44,type,
image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).
thf(func_def_45,type,
image_981520924at_nat: set_Pr1746169692at_nat > set_nat > set_Pr1986765409at_nat ).
thf(func_def_46,type,
image_2142699582at_nat: set_Pr1287749686at_nat > set_Pr1986765409at_nat > set_nat ).
thf(func_def_47,type,
image_1655366419at_nat: set_Pr1490359111at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_48,type,
range_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(func_def_49,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_50,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_51,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(func_def_52,type,
collec1606769740at_nat: ( set_Pr1986765409at_nat > $o ) > set_se1612935105at_nat ).
thf(func_def_53,type,
transi1645084429cl_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_54,type,
transi1484096900at_nat: set_Pr1490359111at_nat > set_Pr1490359111at_nat ).
thf(func_def_55,type,
member_nat: nat > set_nat > $o ).
thf(func_def_56,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_57,type,
member1293241661at_nat: produc1695820582at_nat > set_Pr1746169692at_nat > $o ).
thf(func_def_58,type,
member868723479at_nat: produc1271302400at_nat > set_Pr1287749686at_nat > $o ).
thf(func_def_59,type,
member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_60,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_61,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(func_def_62,type,
c: product_prod_nat_nat > a ).
thf(func_def_63,type,
s: nat ).
thf(func_def_64,type,
t: nat ).
thf(func_def_68,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_69,type,
vAND: $o > $o > $o ).
thf(func_def_70,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_71,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_72,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_73,type,
vOR: $o > $o > $o ).
thf(func_def_74,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_75,type,
vIMP: $o > $o > $o ).
thf(func_def_76,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_77,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_78,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_79,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_80,type,
vNOT: $o > $o ).
thf(func_def_81,type,
sP0: nat > nat > nat > $o ).
thf(func_def_82,type,
sP1: nat > nat > nat > $o ).
thf(func_def_83,type,
sP2: nat > nat > nat > $o ).
thf(func_def_84,type,
sK3: nat > nat > list_P559422087at_nat ).
thf(func_def_85,type,
sK4: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_86,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_87,type,
sK6: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_88,type,
sK7: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_89,type,
sK8: ( product_prod_nat_nat > nat > $o ) > set_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_90,type,
sK9: ( product_prod_nat_nat > nat > $o ) > set_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_91,type,
sK10: ( nat > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_nat > product_prod_nat_nat ).
thf(func_def_92,type,
sK11: ( nat > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_nat > nat ).
thf(func_def_93,type,
sK12: ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_94,type,
sK13: ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_95,type,
sK14: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(func_def_96,type,
sK15: set_nat > set_set_nat > set_nat ).
thf(func_def_97,type,
sK16: nat > set_nat > nat ).
thf(func_def_98,type,
sK17: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(func_def_99,type,
sK18: set_nat > set_set_nat > set_nat ).
thf(func_def_100,type,
sK19: nat > set_nat > nat ).
thf(func_def_101,type,
sK20: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_102,type,
sK21: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_103,type,
sK22: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_104,type,
sK23: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_105,type,
sK24: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_106,type,
sK25: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_107,type,
sK26: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_108,type,
sK27: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_109,type,
sK28: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_110,type,
sK29: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_111,type,
sK30: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_112,type,
sK31: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_113,type,
sK32: set_Pr1986765409at_nat > list_P559422087at_nat ).
thf(func_def_114,type,
sK33: set_nat > list_nat ).
thf(func_def_115,type,
sK34: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(func_def_116,type,
sK35: ( product_prod_nat_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_117,type,
sK36: ( product_prod_nat_nat > set_nat ) > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_118,type,
sK37: ( nat > set_Pr1986765409at_nat ) > set_nat > nat ).
thf(func_def_119,type,
sK38: ( nat > set_nat ) > set_nat > nat ).
thf(func_def_120,type,
sK39: set_Pr1986765409at_nat > set_Pr1490359111at_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_121,type,
sK40: set_nat > set_Pr1746169692at_nat > product_prod_nat_nat > nat ).
thf(func_def_122,type,
sK41: set_Pr1986765409at_nat > set_Pr1287749686at_nat > nat > product_prod_nat_nat ).
thf(func_def_123,type,
sK42: set_nat > set_Pr1986765409at_nat > nat > nat ).
thf(func_def_124,type,
sK43: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_125,type,
sK44: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_126,type,
sK45: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_127,type,
sK46: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_128,type,
sK47: set_Pr1490359111at_nat > nat > nat > nat > nat > nat ).
thf(func_def_129,type,
sK48: set_Pr1490359111at_nat > nat > nat > nat > nat > nat ).
thf(func_def_130,type,
sK49: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_131,type,
sK50: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_132,type,
sK51: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_133,type,
sK52: ( nat > nat > $o ) > set_Pr1490359111at_nat > nat > nat > nat ).
thf(func_def_134,type,
sK53: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_135,type,
sK54: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_136,type,
sK55: product_prod_nat_nat > nat ).
thf(func_def_137,type,
sK56: product_prod_nat_nat > nat ).
thf(func_def_138,type,
sK57: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_139,type,
sK58: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_140,type,
sK59: product_prod_nat_nat > nat ).
thf(func_def_141,type,
sK60: product_prod_nat_nat > nat ).
thf(func_def_142,type,
sK61: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_143,type,
sK62: ( product_prod_nat_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > produc842455143at_nat > product_prod_nat_nat ).
thf(func_def_144,type,
sK63: ( product_prod_nat_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > produc842455143at_nat > product_prod_nat_nat ).
thf(func_def_145,type,
sK64: ( product_prod_nat_nat > set_nat ) > set_Pr1986765409at_nat > produc1271302400at_nat > product_prod_nat_nat ).
thf(func_def_146,type,
sK65: ( product_prod_nat_nat > set_nat ) > set_Pr1986765409at_nat > produc1271302400at_nat > nat ).
thf(func_def_147,type,
sK66: ( nat > set_Pr1986765409at_nat ) > set_nat > produc1695820582at_nat > nat ).
thf(func_def_148,type,
sK67: ( nat > set_Pr1986765409at_nat ) > set_nat > produc1695820582at_nat > product_prod_nat_nat ).
thf(func_def_149,type,
sK68: ( nat > set_nat ) > set_nat > product_prod_nat_nat > nat ).
thf(func_def_150,type,
sK69: ( nat > set_nat ) > set_nat > product_prod_nat_nat > nat ).
thf(func_def_151,type,
sK70: set_Pr1986765409at_nat > nat > nat > nat ).
thf(func_def_152,type,
sK71: set_Pr1986765409at_nat > nat > nat > nat ).
thf(func_def_153,type,
sK72: ( nat > $o ) > set_Pr1986765409at_nat > nat > nat ).
thf(func_def_154,type,
sK73: ( nat > $o ) > set_Pr1986765409at_nat > nat > nat ).
thf(func_def_155,type,
sK74: ( nat > nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_156,type,
sK75: ( nat > nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_157,type,
sK76: ( nat > nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_158,type,
sK77: ( nat > nat > $o ) > nat ).
thf(func_def_159,type,
sK78: set_Pr1986765409at_nat > nat > nat > nat ).
thf(func_def_160,type,
sK79: ( nat > $o ) > set_Pr1986765409at_nat > nat > nat ).
thf(func_def_161,type,
sK80: ( nat > $o ) > set_Pr1986765409at_nat > nat > nat ).
thf(func_def_162,type,
sK81: ( product_prod_nat_nat > set_Pr1986765409at_nat ) > ( product_prod_nat_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_163,type,
sK82: ( product_prod_nat_nat > set_nat ) > ( product_prod_nat_nat > set_nat ) > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_164,type,
sK83: ( nat > set_Pr1986765409at_nat ) > ( nat > set_Pr1986765409at_nat ) > set_nat > nat ).
thf(func_def_165,type,
sK84: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_166,type,
sK85: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_167,type,
sK86: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_168,type,
sK87: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_169,type,
sK88: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_170,type,
sK89: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_171,type,
sK90: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_172,type,
sK91: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_173,type,
sK92: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_174,type,
sK93: ( set_nat > set_nat ) > set_nat ).
thf(func_def_175,type,
sK94: ( set_nat > set_nat ) > set_nat ).
thf(func_def_176,type,
sK95: ( nat > set_nat ) > nat ).
thf(func_def_177,type,
sK96: ( nat > set_nat ) > nat ).
thf(func_def_178,type,
sK97: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_179,type,
sK98: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_180,type,
sK99: ( set_nat > nat ) > set_nat ).
thf(func_def_181,type,
sK100: ( set_nat > nat ) > set_nat ).
thf(func_def_182,type,
sK101: ( nat > nat ) > nat ).
thf(func_def_183,type,
sK102: ( nat > nat ) > nat ).
thf(func_def_184,type,
sK103: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_185,type,
sK104: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_186,type,
sK105: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_187,type,
sK106: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_188,type,
sK107: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_189,type,
sK108: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_190,type,
sK109: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_191,type,
sK110: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_192,type,
sK111: ( set_nat > set_nat ) > set_nat ).
thf(func_def_193,type,
sK112: ( set_nat > set_nat ) > set_nat ).
thf(func_def_194,type,
sK113: ( set_nat > nat ) > set_nat ).
thf(func_def_195,type,
sK114: ( set_nat > nat ) > set_nat ).
thf(func_def_196,type,
sK115: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_197,type,
sK116: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_198,type,
sK117: ( nat > set_nat ) > nat ).
thf(func_def_199,type,
sK118: ( nat > set_nat ) > nat ).
thf(func_def_200,type,
sK119: ( nat > nat ) > nat ).
thf(func_def_201,type,
sK120: ( nat > nat ) > nat ).
thf(func_def_202,type,
sK121: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_203,type,
sK122: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_204,type,
sK123: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_205,type,
sK124: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_206,type,
sK125: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_207,type,
sK126: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_208,type,
sK127: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_209,type,
sK128: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_210,type,
sK129: ( set_nat > set_nat ) > set_nat ).
thf(func_def_211,type,
sK130: ( set_nat > set_nat ) > set_nat ).
thf(func_def_212,type,
sK131: ( set_nat > nat ) > set_nat ).
thf(func_def_213,type,
sK132: ( set_nat > nat ) > set_nat ).
thf(func_def_214,type,
sK133: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_215,type,
sK134: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_216,type,
sK135: ( nat > set_nat ) > nat ).
thf(func_def_217,type,
sK136: ( nat > set_nat ) > nat ).
thf(func_def_218,type,
sK137: ( nat > nat ) > nat ).
thf(func_def_219,type,
sK138: ( nat > nat ) > nat ).
thf(func_def_220,type,
sK139: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_221,type,
sK140: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_222,type,
sK141: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_223,type,
sK142: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_224,type,
sK143: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_225,type,
sK144: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_226,type,
sK145: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_227,type,
sK146: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_228,type,
sK147: ( set_nat > set_nat ) > set_nat ).
thf(func_def_229,type,
sK148: ( set_nat > set_nat ) > set_nat ).
thf(func_def_230,type,
sK149: ( set_nat > nat ) > set_nat ).
thf(func_def_231,type,
sK150: ( set_nat > nat ) > set_nat ).
thf(func_def_232,type,
sK151: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_233,type,
sK152: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_234,type,
sK153: ( nat > set_nat ) > nat ).
thf(func_def_235,type,
sK154: ( nat > set_nat ) > nat ).
thf(func_def_236,type,
sK155: ( nat > nat ) > nat ).
thf(func_def_237,type,
sK156: ( nat > nat ) > nat ).
thf(func_def_238,type,
sK157: ( nat > nat > $o ) > nat ).
thf(func_def_239,type,
sK158: ( nat > nat > $o ) > nat ).
thf(func_def_240,type,
sK159: ( nat > nat > $o ) > nat ).
thf(func_def_241,type,
sK160: ( nat > nat > $o ) > nat ).
thf(func_def_242,type,
sK161: nat > nat > list_P559422087at_nat ).
thf(func_def_243,type,
sK162: nat > nat > list_P559422087at_nat ).
thf(func_def_244,type,
sK163: nat > list_P559422087at_nat > nat ).
thf(func_def_245,type,
sK164: nat > list_P559422087at_nat > nat ).
thf(func_def_246,type,
sK165: nat > nat > list_P559422087at_nat ).
thf(func_def_247,type,
sK166: nat > nat > set_Pr1986765409at_nat > nat ).
thf(func_def_248,type,
sK167: nat > nat > nat ).
thf(func_def_249,type,
sK168: nat > nat > set_Pr1986765409at_nat > nat ).
thf(func_def_250,type,
sK169: nat > nat > set_Pr1986765409at_nat > nat ).
thf(func_def_251,type,
sK170: nat > nat > set_Pr1986765409at_nat > nat ).
thf(func_def_252,type,
sK171: set_Pr1986765409at_nat > nat > set_nat > nat ).
thf(func_def_253,type,
sK172: set_nat > list_nat > nat ).
thf(func_def_254,type,
sK173: set_Pr1986765409at_nat > list_P559422087at_nat > product_prod_nat_nat ).
thf(func_def_255,type,
sK174: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_256,type,
sK175: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_257,type,
sK176: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_258,type,
sK177: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_259,type,
sK178: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_260,type,
sK179: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_261,type,
sK180: ( nat > nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_262,type,
sK181: ( product_prod_nat_nat > nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_263,type,
sK182: ( nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_264,type,
sK183: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(f2,axiom,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062) ).
thf(f4,axiom,
finite772653738at_nat @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__E) ).
thf(f50,axiom,
( edmond475474835dges_a
= ( ^ [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( collec7649004at_nat
@ ^ [X3: product_prod_nat_nat] :
? [X4: list_P559422087at_nat] :
( ( isShortestPath_a @ X0 @ X1 @ X4 @ X2 )
& ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_ek__analysis__defs_OspEdges__def) ).
thf(f355,conjecture,
finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f356,negated_conjecture,
~ ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f359,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) ),
inference(rectify,[],[f2]) ).
thf(f360,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
= $true )
=> ( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true ) ),
inference(fool_elimination,[],[f359]) ).
thf(f361,plain,
finite772653738at_nat @ ( e_a @ c ),
inference(rectify,[],[f4]) ).
thf(f362,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(fool_elimination,[],[f361]) ).
thf(f451,plain,
( edmond475474835dges_a
= ( ^ [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( collec7649004at_nat
@ ^ [X3: product_prod_nat_nat] :
? [X4: list_P559422087at_nat] :
( ( isShortestPath_a @ X0 @ X1 @ X4 @ X2 )
& ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X4 ) ) ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f452,plain,
( edmond475474835dges_a
= ( ^ [Y0: product_prod_nat_nat > a,Y1: nat,Y2: nat] :
( collec7649004at_nat
@ ^ [Y3: product_prod_nat_nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y4: list_P559422087at_nat] :
( ( member701585322at_nat @ Y3 @ ( set_Pr2131844118at_nat @ Y4 ) )
& ( isShortestPath_a @ Y0 @ Y1 @ Y4 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f451]) ).
thf(f1010,plain,
~ ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ),
inference(rectify,[],[f356]) ).
thf(f1011,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
!= $true ),
inference(fool_elimination,[],[f1010]) ).
thf(f1054,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
!= $true ),
inference(flattening,[],[f1011]) ).
thf(f1055,plain,
( ( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true )
| ( ( finite772653738at_nat @ ( e_a @ c ) )
!= $true ) ),
inference(ennf_transformation,[],[f360]) ).
thf(f1574,plain,
( ( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true )
| ( ( finite772653738at_nat @ ( e_a @ c ) )
!= $true ) ),
inference(cnf_transformation,[],[f1055]) ).
thf(f1576,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(cnf_transformation,[],[f362]) ).
thf(f1636,plain,
( edmond475474835dges_a
= ( ^ [Y0: product_prod_nat_nat > a,Y1: nat,Y2: nat] :
( collec7649004at_nat
@ ^ [Y3: product_prod_nat_nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y4: list_P559422087at_nat] :
( ( member701585322at_nat @ Y3 @ ( set_Pr2131844118at_nat @ Y4 ) )
& ( isShortestPath_a @ Y0 @ Y1 @ Y4 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f452]) ).
thf(f2053,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
!= $true ),
inference(cnf_transformation,[],[f1054]) ).
thf(f2060,plain,
( ( $true
= ( finite772653738at_nat
@ ( ^ [Y0: product_prod_nat_nat > a,Y1: nat,Y2: nat] :
( collec7649004at_nat
@ ^ [Y3: product_prod_nat_nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y4: list_P559422087at_nat] :
( ( member701585322at_nat @ Y3 @ ( set_Pr2131844118at_nat @ Y4 ) )
& ( isShortestPath_a @ Y0 @ Y1 @ Y4 @ Y2 ) ) ) )
@ c
@ s
@ t ) ) )
| ( ( finite772653738at_nat @ ( e_a @ c ) )
!= $true ) ),
inference(definition_unfolding,[],[f1574,f1636]) ).
thf(f2144,plain,
( $true
!= ( finite772653738at_nat
@ ( ^ [Y0: product_prod_nat_nat > a,Y1: nat,Y2: nat] :
( collec7649004at_nat
@ ^ [Y3: product_prod_nat_nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y4: list_P559422087at_nat] :
( ( member701585322at_nat @ Y3 @ ( set_Pr2131844118at_nat @ Y4 ) )
& ( isShortestPath_a @ Y0 @ Y1 @ Y4 @ Y2 ) ) ) )
@ c
@ s
@ t ) ) ),
inference(definition_unfolding,[],[f2053,f1636]) ).
thf(f2192,plain,
( $true
!= ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Y0: product_prod_nat_nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ Y1 ) )
& ( isShortestPath_a @ c @ s @ Y1 @ t ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2144]) ).
thf(f2549,plain,
( ( $true
= ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Y0: product_prod_nat_nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ Y1 ) )
& ( isShortestPath_a @ c @ s @ Y1 @ t ) ) ) ) ) )
| ( ( finite772653738at_nat @ ( e_a @ c ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f2060]) ).
thf(f2553,plain,
$false,
inference(global_subsumption,[],[f2549,f1576,f2192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP049^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:43:47 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.32 % (3313981)Will run a generic schedule for satisfiability detection.
% 0.20/0.32 % (3314005)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=770260543:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.32 % (3314004)% WARNING: option uhcvi not known.
% 0.20/0.32 % (3314003)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3628627541_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.32 % (3314006)dis+10_1_sil=32000:sp=arity:random_seed=4254881626:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.32 % (3314004)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3819596306:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.32 % (3314007)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=358413703:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.32 % (3314009)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2077110515:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.32 % (3314010)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1146677124:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.32 % (3314004)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.32 % (3314007)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.32 % (3314005) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3313981-3314005"...
% 0.20/0.32 % (3314005)...printing done.
% 0.20/0.32 % (3314005)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.33 % (3314005)------------------------------
% 0.20/0.33 % (3314005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3314005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3314005)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3314005)Termination reason: Refutation
% 0.20/0.33 % (3314005)Time elapsed: 0.043 s
% 0.20/0.33 % (3314005)Peak memory usage: 14 MB
% 0.20/0.33 % (3314005)Instructions burned: 186 (million)
% 0.20/0.33 % (3313981)Success in time 0.096 s
% 0.20/0.33 % Vampire exiting
%------------------------------------------------------------------------------