%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP050^1 : 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 : 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 08:10:30 AM UTC 2026
% Result : Theorem 17.03s 2.85s
% Output : Refutation 17.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 91 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 510 ( 42 ~; 30 |; 1 &; 396 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 543 ( 539 usr; 14 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 110 ( 20 ^; 90 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_se1612935105at_nat: $tType ).
thf(type_def_6,type,
list_P559422087at_nat: $tType ).
thf(type_def_7,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_8,type,
product_prod_nat_nat: $tType ).
thf(type_def_9,type,
set_set_nat: $tType ).
thf(type_def_10,type,
list_nat: $tType ).
thf(type_def_11,type,
set_nat: $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
a: $tType ).
thf(type_def_14,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,
edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(func_def_3,type,
finite_card_nat: set_nat > nat ).
thf(func_def_4,type,
finite447719721at_nat: set_Pr1986765409at_nat > nat ).
thf(func_def_5,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_6,type,
finite772653738at_nat: set_Pr1986765409at_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,
incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_14,type,
incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_15,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_16,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_17,type,
outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_18,type,
outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_19,type,
pathVertices: nat > list_P559422087at_nat > list_nat ).
thf(func_def_20,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_21,type,
inf_inf_nat: nat > nat > nat ).
thf(func_def_22,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_23,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_24,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_25,type,
cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_26,type,
nil_Pr1308055047at_nat: list_P559422087at_nat ).
thf(func_def_27,type,
set_nat2: list_nat > set_nat ).
thf(func_def_28,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(func_def_29,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(func_def_30,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_31,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_32,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_33,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_34,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_35,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_36,type,
member_nat: nat > set_nat > $o ).
thf(func_def_37,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_38,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_39,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(func_def_40,type,
c: product_prod_nat_nat > a ).
thf(func_def_41,type,
edges: set_Pr1986765409at_nat ).
thf(func_def_42,type,
p: list_P559422087at_nat ).
thf(func_def_43,type,
s: nat ).
thf(func_def_44,type,
t: nat ).
thf(func_def_48,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vNOT: $o > $o ).
thf(func_def_58,type,
sP0: nat > nat > nat > $o ).
thf(func_def_59,type,
sP1: nat > nat > nat > $o ).
thf(func_def_60,type,
sP2: nat > nat > nat > $o ).
thf(func_def_61,type,
sK3: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_62,type,
sK4: set_nat > set_nat > nat ).
thf(func_def_63,type,
sK5: ( nat > nat > $o ) > nat ).
thf(func_def_64,type,
sK6: ( nat > nat > $o ) > nat ).
thf(func_def_65,type,
sK7: ( nat > nat > $o ) > nat ).
thf(func_def_66,type,
sK8: ( nat > nat > $o ) > nat ).
thf(func_def_67,type,
sK9: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_68,type,
sK10: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_69,type,
sK11: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_70,type,
sK12: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_71,type,
sK13: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_72,type,
sK14: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_73,type,
sK15: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_74,type,
sK16: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_75,type,
sK17: ( set_nat > set_nat ) > set_nat ).
thf(func_def_76,type,
sK18: ( set_nat > set_nat ) > set_nat ).
thf(func_def_77,type,
sK19: ( set_nat > nat ) > set_nat ).
thf(func_def_78,type,
sK20: ( set_nat > nat ) > set_nat ).
thf(func_def_79,type,
sK21: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_80,type,
sK22: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_81,type,
sK23: ( nat > set_nat ) > nat ).
thf(func_def_82,type,
sK24: ( nat > set_nat ) > nat ).
thf(func_def_83,type,
sK25: ( nat > nat ) > nat ).
thf(func_def_84,type,
sK26: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK27: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_86,type,
sK28: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_87,type,
sK29: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_88,type,
sK30: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_89,type,
sK31: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_90,type,
sK32: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_91,type,
sK33: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_92,type,
sK34: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_93,type,
sK35: ( set_nat > set_nat ) > set_nat ).
thf(func_def_94,type,
sK36: ( set_nat > set_nat ) > set_nat ).
thf(func_def_95,type,
sK37: ( set_nat > nat ) > set_nat ).
thf(func_def_96,type,
sK38: ( set_nat > nat ) > set_nat ).
thf(func_def_97,type,
sK39: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_98,type,
sK40: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_99,type,
sK41: ( nat > set_nat ) > nat ).
thf(func_def_100,type,
sK42: ( nat > set_nat ) > nat ).
thf(func_def_101,type,
sK43: ( nat > nat ) > nat ).
thf(func_def_102,type,
sK44: ( nat > nat ) > nat ).
thf(func_def_103,type,
sK45: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_104,type,
sK46: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_105,type,
sK47: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_106,type,
sK48: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_107,type,
sK49: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_108,type,
sK50: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_109,type,
sK51: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_110,type,
sK52: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_111,type,
sK53: ( set_nat > set_nat ) > set_nat ).
thf(func_def_112,type,
sK54: ( set_nat > set_nat ) > set_nat ).
thf(func_def_113,type,
sK55: ( set_nat > nat ) > set_nat ).
thf(func_def_114,type,
sK56: ( set_nat > nat ) > set_nat ).
thf(func_def_115,type,
sK57: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_116,type,
sK58: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_117,type,
sK59: ( nat > set_nat ) > nat ).
thf(func_def_118,type,
sK60: ( nat > set_nat ) > nat ).
thf(func_def_119,type,
sK61: ( nat > nat ) > nat ).
thf(func_def_120,type,
sK62: ( nat > nat ) > nat ).
thf(func_def_121,type,
sK63: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_122,type,
sK64: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_123,type,
sK65: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_124,type,
sK66: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_125,type,
sK67: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_126,type,
sK68: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_127,type,
sK69: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_128,type,
sK70: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_129,type,
sK71: ( set_nat > set_nat ) > set_nat ).
thf(func_def_130,type,
sK72: ( set_nat > set_nat ) > set_nat ).
thf(func_def_131,type,
sK73: ( nat > set_nat ) > nat ).
thf(func_def_132,type,
sK74: ( nat > set_nat ) > nat ).
thf(func_def_133,type,
sK75: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_134,type,
sK76: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_135,type,
sK77: ( set_nat > nat ) > set_nat ).
thf(func_def_136,type,
sK78: ( set_nat > nat ) > set_nat ).
thf(func_def_137,type,
sK79: ( nat > nat ) > nat ).
thf(func_def_138,type,
sK80: ( nat > nat ) > nat ).
thf(func_def_139,type,
sK81: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_140,type,
sK82: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_141,type,
sK83: nat > list_P559422087at_nat > nat ).
thf(func_def_142,type,
sK84: nat > list_P559422087at_nat > nat ).
thf(func_def_143,type,
sK85: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_144,type,
sK86: ( nat > $o ) > ( nat > $o ) > set_nat > nat ).
thf(func_def_145,type,
sK87: nat > list_P559422087at_nat > nat ).
thf(func_def_146,type,
sK88: nat > list_P559422087at_nat > nat ).
thf(func_def_147,type,
sK89: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(func_def_148,type,
sK90: set_nat > set_set_nat > set_nat ).
thf(func_def_149,type,
sK91: nat > set_nat > nat ).
thf(func_def_150,type,
sK92: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(func_def_151,type,
sK93: set_nat > set_set_nat > set_nat ).
thf(func_def_152,type,
sK94: nat > set_nat > nat ).
thf(func_def_153,type,
sK95: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_154,type,
sK96: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_155,type,
sK97: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_156,type,
sK98: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_157,type,
sK99: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_158,type,
sK100: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_159,type,
sK101: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_160,type,
sK102: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_161,type,
sK103: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_162,type,
sK104: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_163,type,
sK105: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_164,type,
sK106: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_165,type,
sK107: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_166,type,
sK108: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_167,type,
sK109: ( nat > nat > nat ) > nat ).
thf(func_def_168,type,
sK110: ( nat > nat > nat ) > nat ).
thf(func_def_169,type,
sK111: ( nat > nat > nat ) > nat ).
thf(func_def_170,type,
sK112: ( nat > nat > nat ) > nat ).
thf(func_def_171,type,
sK113: ( nat > nat > nat ) > nat ).
thf(func_def_172,type,
sK114: ( nat > nat > nat ) > nat ).
thf(func_def_173,type,
sK115: ( nat > nat > nat ) > nat ).
thf(func_def_174,type,
sK116: set_Pr1986765409at_nat > list_P559422087at_nat ).
thf(func_def_175,type,
sK117: set_nat > list_nat ).
thf(func_def_176,type,
sK118: nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_177,type,
sK119: nat > set_nat > set_nat ).
thf(func_def_178,type,
sK120: nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_179,type,
sK121: nat > set_nat > set_nat ).
thf(func_def_180,type,
sK122: set_Pr1986765409at_nat > nat > set_Pr1986765409at_nat ).
thf(func_def_181,type,
sK123: set_nat > nat > set_nat ).
thf(func_def_182,type,
sK124: list_nat > nat > nat ).
thf(func_def_183,type,
sK125: list_nat > nat > list_nat ).
thf(func_def_184,type,
sK126: list_nat > nat > list_nat ).
thf(func_def_185,type,
sK127: list_P559422087at_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_186,type,
sK128: list_P559422087at_nat > product_prod_nat_nat > list_P559422087at_nat ).
thf(func_def_187,type,
sK129: list_P559422087at_nat > product_prod_nat_nat > list_P559422087at_nat ).
thf(func_def_188,type,
sK130: ( nat > $o ) > nat ).
thf(func_def_189,type,
sK131: nat > ( nat > $o ) > nat ).
thf(func_def_190,type,
sK132: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_191,type,
sK133: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_192,type,
sK134: nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_193,type,
sK135: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_194,type,
sK136: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_195,type,
sK137: nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_196,type,
sK138: nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_197,type,
sK139: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_198,type,
sK140: $o > nat > list_P559422087at_nat > nat > nat ).
thf(func_def_199,type,
sK141: $o > nat > list_P559422087at_nat > nat > nat ).
thf(func_def_200,type,
sK142: $o > nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_201,type,
sK143: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_202,type,
sK144: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_203,type,
sK145: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_204,type,
sK146: ( nat > list_P559422087at_nat > nat > $o ) > list_P559422087at_nat ).
thf(func_def_205,type,
sK147: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_206,type,
sK148: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_207,type,
sK149: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_208,type,
sK150: product_prod_nat_nat ).
thf(func_def_209,type,
sK151: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(func_def_210,type,
sK152: set_nat > nat > nat ).
thf(func_def_211,type,
sK153: set_nat > nat ).
thf(func_def_212,type,
sK154: set_nat > nat ).
thf(func_def_213,type,
sK155: nat > set_nat > nat ).
thf(func_def_214,type,
sK156: set_nat > nat ).
thf(func_def_215,type,
sK157: nat > set_nat > nat ).
thf(func_def_216,type,
sK158: set_nat > set_nat > nat ).
thf(func_def_217,type,
sK159: set_nat > nat > nat ).
thf(func_def_218,type,
sK160: set_nat > nat > nat ).
thf(func_def_219,type,
sK161: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_220,type,
sK162: nat > set_nat > nat ).
thf(func_def_221,type,
sK163: set_nat > nat ).
thf(func_def_222,type,
sK164: set_nat > nat ).
thf(func_def_223,type,
sK165: set_nat > nat ).
thf(func_def_224,type,
sK166: set_nat > list_nat > nat ).
thf(func_def_225,type,
sK167: set_nat > list_nat > nat ).
thf(func_def_226,type,
sK168: set_Pr1986765409at_nat > list_P559422087at_nat > product_prod_nat_nat ).
thf(func_def_227,type,
sK169: set_Pr1986765409at_nat > list_P559422087at_nat > product_prod_nat_nat ).
thf(func_def_228,type,
sK170: nat > set_nat > nat ).
thf(func_def_229,type,
sK171: set_nat > nat ).
thf(func_def_230,type,
sK172: set_nat > set_nat > nat ).
thf(func_def_231,type,
sK173: set_nat > nat > nat ).
thf(func_def_232,type,
sK174: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_233,type,
sK175: set_nat > nat ).
thf(func_def_234,type,
sK176: set_nat > set_nat > nat ).
thf(func_def_235,type,
sK177: set_nat > nat > nat ).
thf(func_def_236,type,
sK178: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_237,type,
sK179: set_nat > nat ).
thf(func_def_238,type,
sK180: set_nat > set_nat > nat ).
thf(func_def_239,type,
sK181: set_nat > nat > nat ).
thf(func_def_240,type,
sK182: set_nat > nat > nat ).
thf(func_def_241,type,
sK183: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_242,type,
sK184: set_nat > set_nat > set_nat > nat ).
thf(func_def_243,type,
sK185: set_nat > set_nat > set_nat > nat ).
thf(func_def_244,type,
sK186: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_245,type,
sK187: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_246,type,
sK188: set_nat > set_nat > nat ).
thf(func_def_247,type,
sK189: set_nat > set_nat > nat ).
thf(func_def_248,type,
sK190: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_249,type,
sK191: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_250,type,
sK192: set_nat > set_nat > nat ).
thf(func_def_251,type,
sK193: set_nat > set_nat > nat ).
thf(func_def_252,type,
sK194: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_253,type,
sK195: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_254,type,
sK196: set_nat > set_nat > nat ).
thf(func_def_255,type,
sK197: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_256,type,
sK198: set_nat > set_nat > nat ).
thf(func_def_257,type,
sK199: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_258,type,
sK200: set_nat > set_nat > nat ).
thf(func_def_259,type,
sK201: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_260,type,
sK202: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_261,type,
sK203: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_262,type,
sK204: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_263,type,
sK205: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_264,type,
sK206: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_265,type,
sK207: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_266,type,
sK208: ( set_nat > set_nat > set_nat ) > nat ).
thf(func_def_267,type,
sK209: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_268,type,
sK210: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_269,type,
sK211: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_270,type,
sK212: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_271,type,
sK213: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_272,type,
sK214: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_273,type,
sK215: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_274,type,
sK216: set_nat > set_nat > nat ).
thf(func_def_275,type,
sK217: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_276,type,
sK218: set_nat > set_nat > nat ).
thf(func_def_277,type,
sK219: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_278,type,
sK220: set_nat > set_nat > nat ).
thf(func_def_279,type,
sK221: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_280,type,
sK222: set_nat > set_nat > nat ).
thf(func_def_281,type,
sK223: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_282,type,
sK224: set_nat > set_nat > set_nat > nat ).
thf(func_def_283,type,
sK225: set_nat > set_nat > set_nat > nat ).
thf(func_def_284,type,
sK226: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_285,type,
sK227: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_286,type,
sK228: set_nat > set_nat > nat ).
thf(func_def_287,type,
sK229: set_nat > set_nat > nat ).
thf(func_def_288,type,
sK230: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_289,type,
sK231: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_290,type,
sK232: set_nat > set_nat > nat ).
thf(func_def_291,type,
sK233: set_nat > set_nat > nat ).
thf(func_def_292,type,
sK234: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_293,type,
sK235: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_294,type,
sK236: set_nat > set_nat > nat ).
thf(func_def_295,type,
sK237: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_296,type,
sK238: set_nat > set_nat > nat ).
thf(func_def_297,type,
sK239: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_298,type,
sK240: set_nat > nat > nat ).
thf(func_def_299,type,
sK241: set_nat > nat > nat ).
thf(func_def_300,type,
sK242: set_nat > nat > nat ).
thf(func_def_301,type,
sK243: set_nat > set_nat > set_set_nat > nat ).
thf(func_def_302,type,
sK244: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_se1612935105at_nat > product_prod_nat_nat ).
thf(func_def_303,type,
sK245: set_nat > nat > nat ).
thf(func_def_304,type,
sK246: set_nat > nat > nat ).
thf(func_def_305,type,
sK247: set_nat > nat > nat ).
thf(func_def_306,type,
sK248: set_nat > set_nat > set_set_nat > nat ).
thf(func_def_307,type,
sK249: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_se1612935105at_nat > product_prod_nat_nat ).
thf(func_def_308,type,
sK250: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_309,type,
sK251: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_310,type,
sK252: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_311,type,
sK253: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_312,type,
sK254: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_313,type,
sK255: ( product_prod_nat_nat > a ) > nat ).
thf(func_def_314,type,
sK256: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_315,type,
sK257: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_316,type,
sK258: ( product_prod_nat_nat > a ) > nat ).
thf(func_def_317,type,
sK259: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_318,type,
sK260: ( product_prod_nat_nat > a ) > nat ).
thf(func_def_319,type,
sK261: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_320,type,
sK262: nat > nat ).
thf(func_def_321,type,
sK263: nat > nat ).
thf(func_def_322,type,
sK264: nat > nat ).
thf(func_def_323,type,
sK265: nat > nat ).
thf(func_def_324,type,
sK266: nat > nat ).
thf(func_def_325,type,
sK267: nat > nat ).
thf(func_def_326,type,
sK268: nat ).
thf(func_def_327,type,
sK269: nat ).
thf(func_def_328,type,
sK270: set_nat > set_nat > nat ).
thf(func_def_329,type,
sK271: set_nat > nat > nat ).
thf(func_def_330,type,
sK272: set_nat > nat > nat ).
thf(func_def_331,type,
sK273: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_332,type,
sK274: set_nat > set_nat > nat ).
thf(func_def_333,type,
sK275: set_nat > nat > nat ).
thf(func_def_334,type,
sK276: set_nat > nat > nat ).
thf(func_def_335,type,
sK277: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_336,type,
sK278: set_nat > set_nat > set_nat > nat ).
thf(func_def_337,type,
sK279: set_nat > set_nat > set_nat > nat ).
thf(func_def_338,type,
sK280: set_nat > set_nat > nat ).
thf(func_def_339,type,
sK281: set_nat > set_nat > nat ).
thf(func_def_340,type,
sK282: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_341,type,
sK283: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_342,type,
sK284: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_343,type,
sK285: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_344,type,
sK286: set_nat > set_nat > set_nat > nat ).
thf(func_def_345,type,
sK287: set_nat > set_nat > set_nat > nat ).
thf(func_def_346,type,
sK288: set_nat > set_nat > nat ).
thf(func_def_347,type,
sK289: set_nat > set_nat > nat ).
thf(func_def_348,type,
sK290: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_349,type,
sK291: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_350,type,
sK292: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_351,type,
sK293: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_352,type,
sK294: list_nat > nat ).
thf(func_def_353,type,
sK295: set_nat > set_nat > nat ).
thf(func_def_354,type,
sK296: set_nat > nat > nat ).
thf(func_def_355,type,
sK297: set_nat > set_nat > nat ).
thf(func_def_356,type,
sK298: set_nat > nat > nat ).
thf(func_def_357,type,
sK299: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_358,type,
sK300: ( product_prod_nat_nat > a ) > list_P559422087at_nat > ( product_prod_nat_nat > a ) > product_prod_nat_nat ).
thf(func_def_359,type,
sK301: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_360,type,
sK302: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_361,type,
sK303: nat > ( product_prod_nat_nat > a ) > nat ).
thf(func_def_362,type,
sK304: ( product_prod_nat_nat > a ) > nat ).
thf(func_def_363,type,
sK305: set_nat > set_nat > nat ).
thf(func_def_364,type,
sK306: set_nat > set_nat > nat ).
thf(func_def_365,type,
sK307: set_nat > set_nat > nat ).
thf(func_def_366,type,
sK308: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_367,type,
sK309: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_368,type,
sK310: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_369,type,
sK311: set_nat > set_nat > nat ).
thf(func_def_370,type,
sK312: set_nat > set_nat > nat ).
thf(func_def_371,type,
sK313: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_372,type,
sK314: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_373,type,
sK315: set_nat > set_nat > nat ).
thf(func_def_374,type,
sK316: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_375,type,
sK317: set_nat > set_nat > nat ).
thf(func_def_376,type,
sK318: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_377,type,
sK319: set_nat > set_nat > nat ).
thf(func_def_378,type,
sK320: set_nat > set_nat > nat ).
thf(func_def_379,type,
sK321: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_380,type,
sK322: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_381,type,
sK323: set_nat > set_nat > set_nat > nat ).
thf(func_def_382,type,
sK324: set_nat > set_nat > set_nat > nat ).
thf(func_def_383,type,
sK325: set_nat > set_nat > nat ).
thf(func_def_384,type,
sK326: set_nat > set_nat > nat ).
thf(func_def_385,type,
sK327: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_386,type,
sK328: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_387,type,
sK329: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_388,type,
sK330: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_389,type,
sK331: nat ).
thf(func_def_390,type,
sK332: ( product_prod_nat_nat > a ) > list_P559422087at_nat > product_prod_nat_nat ).
thf(func_def_391,type,
sK333: set_nat > set_nat > nat ).
thf(func_def_392,type,
sK334: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_393,type,
sK335: set_nat > set_nat > nat ).
thf(func_def_394,type,
sK336: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_395,type,
sK337: set_nat > set_nat > nat ).
thf(func_def_396,type,
sK338: set_nat > set_nat > nat ).
thf(func_def_397,type,
sK339: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_398,type,
sK340: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_399,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_400,type,
sK341: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_401,type,
sK342: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_402,type,
sK343: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_403,type,
sK344: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_404,type,
sK345: set_nat > set_nat > nat ).
thf(func_def_405,type,
sK346: set_nat > set_nat > nat ).
thf(func_def_406,type,
sK347: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_407,type,
sK348: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_408,type,
sK349: ( nat > set_nat ) > set_nat > nat > nat ).
thf(func_def_409,type,
sK350: ( nat > set_nat ) > nat ).
thf(func_def_410,type,
sK351: ( nat > set_nat ) > set_nat > nat > nat ).
thf(func_def_411,type,
sK352: set_nat > set_nat > nat ).
thf(func_def_412,type,
sK353: ( set_nat > set_nat ) > set_nat > set_nat > nat ).
thf(func_def_413,type,
sK354: ( set_nat > set_nat ) > nat ).
thf(func_def_414,type,
sK355: set_nat > set_nat > nat ).
thf(func_def_415,type,
sK356: ( set_nat > set_nat ) > set_nat > set_nat > nat ).
thf(func_def_416,type,
sK357: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_417,type,
sK358: ( set_Pr1986765409at_nat > set_nat ) > set_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_418,type,
sK359: ( set_Pr1986765409at_nat > set_nat ) > nat ).
thf(func_def_419,type,
sK360: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_420,type,
sK361: ( set_Pr1986765409at_nat > set_nat ) > set_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_421,type,
sK362: ( nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > nat > product_prod_nat_nat ).
thf(func_def_422,type,
sK363: ( nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_423,type,
sK364: ( nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > nat > product_prod_nat_nat ).
thf(func_def_424,type,
sK365: set_nat > set_nat > nat ).
thf(func_def_425,type,
sK366: ( set_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > set_nat > product_prod_nat_nat ).
thf(func_def_426,type,
sK367: ( set_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_427,type,
sK368: set_nat > set_nat > nat ).
thf(func_def_428,type,
sK369: ( set_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > set_nat > product_prod_nat_nat ).
thf(func_def_429,type,
sK370: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_430,type,
sK371: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_431,type,
sK372: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_432,type,
sK373: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_433,type,
sK374: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_434,type,
sK375: set_nat > nat > ( nat > set_nat ) > nat ).
thf(func_def_435,type,
sK376: ( nat > set_nat ) > nat ).
thf(func_def_436,type,
sK377: set_nat > nat > ( nat > set_nat ) > nat ).
thf(func_def_437,type,
sK378: set_Pr1986765409at_nat > nat > ( nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_438,type,
sK379: ( nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_439,type,
sK380: set_Pr1986765409at_nat > nat > ( nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_440,type,
sK381: set_nat > set_nat > nat ).
thf(func_def_441,type,
sK382: set_nat > set_nat > nat ).
thf(func_def_442,type,
sK383: set_nat > set_nat > ( set_nat > set_nat ) > nat ).
thf(func_def_443,type,
sK384: set_nat > set_nat > nat ).
thf(func_def_444,type,
sK385: ( set_nat > set_nat ) > nat ).
thf(func_def_445,type,
sK386: set_nat > set_nat > ( set_nat > set_nat ) > nat ).
thf(func_def_446,type,
sK387: set_nat > set_nat > nat ).
thf(func_def_447,type,
sK388: set_Pr1986765409at_nat > set_nat > ( set_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_448,type,
sK389: set_nat > set_nat > nat ).
thf(func_def_449,type,
sK390: ( set_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_450,type,
sK391: set_Pr1986765409at_nat > set_nat > ( set_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_451,type,
sK392: set_nat > set_nat > nat ).
thf(func_def_452,type,
sK393: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_453,type,
sK394: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_454,type,
sK395: set_nat > set_Pr1986765409at_nat > ( set_Pr1986765409at_nat > set_nat ) > nat ).
thf(func_def_455,type,
sK396: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_456,type,
sK397: ( set_Pr1986765409at_nat > set_nat ) > nat ).
thf(func_def_457,type,
sK398: set_nat > set_Pr1986765409at_nat > ( set_Pr1986765409at_nat > set_nat ) > nat ).
thf(func_def_458,type,
sK399: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_459,type,
sK400: set_Pr1986765409at_nat > set_Pr1986765409at_nat > ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_460,type,
sK401: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_461,type,
sK402: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_462,type,
sK403: set_Pr1986765409at_nat > set_Pr1986765409at_nat > ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_463,type,
sK404: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_464,type,
sK405: ( nat > set_nat ) > nat ).
thf(func_def_465,type,
sK406: ( nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_466,type,
sK407: set_nat > set_nat > nat ).
thf(func_def_467,type,
sK408: set_nat > set_nat > nat ).
thf(func_def_468,type,
sK409: set_nat > set_nat > nat ).
thf(func_def_469,type,
sK410: ( set_nat > set_nat ) > nat ).
thf(func_def_470,type,
sK411: set_nat > set_nat > nat ).
thf(func_def_471,type,
sK412: set_nat > set_nat > nat ).
thf(func_def_472,type,
sK413: ( set_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_473,type,
sK414: set_nat > set_nat > nat ).
thf(func_def_474,type,
sK415: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_475,type,
sK416: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_476,type,
sK417: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_477,type,
sK418: ( set_Pr1986765409at_nat > set_nat ) > nat ).
thf(func_def_478,type,
sK419: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_479,type,
sK420: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_480,type,
sK421: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_481,type,
sK422: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_482,type,
sK423: ( nat > set_nat ) > nat ).
thf(func_def_483,type,
sK424: ( nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_484,type,
sK425: set_nat > set_nat > nat ).
thf(func_def_485,type,
sK426: set_nat > set_nat > nat ).
thf(func_def_486,type,
sK427: set_nat > set_nat > nat ).
thf(func_def_487,type,
sK428: ( set_nat > set_nat ) > nat ).
thf(func_def_488,type,
sK429: set_nat > set_nat > nat ).
thf(func_def_489,type,
sK430: set_nat > set_nat > nat ).
thf(func_def_490,type,
sK431: ( set_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_491,type,
sK432: set_nat > set_nat > nat ).
thf(func_def_492,type,
sK433: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_493,type,
sK434: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_494,type,
sK435: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_495,type,
sK436: ( set_Pr1986765409at_nat > set_nat ) > nat ).
thf(func_def_496,type,
sK437: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_497,type,
sK438: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_498,type,
sK439: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > product_prod_nat_nat ).
thf(func_def_499,type,
sK440: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_500,type,
sK441: set_nat > set_nat > nat ).
thf(func_def_501,type,
sK442: set_nat > set_nat > nat ).
thf(func_def_502,type,
sK443: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_503,type,
sK444: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_504,type,
sK445: set_nat > set_nat > nat ).
thf(func_def_505,type,
sK446: set_nat > set_nat > nat ).
thf(func_def_506,type,
sK447: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_507,type,
sK448: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_508,type,
sK449: set_nat > set_nat > nat ).
thf(func_def_509,type,
sK450: set_nat > set_nat > nat ).
thf(func_def_510,type,
sK451: set_nat > set_nat > nat ).
thf(func_def_511,type,
sK452: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_512,type,
sK453: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_513,type,
sK454: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_514,type,
sK455: set_nat > set_nat > nat ).
thf(func_def_515,type,
sK456: set_nat > set_nat > nat ).
thf(func_def_516,type,
sK457: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_517,type,
sK458: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_518,type,
sK459: set_nat > set_nat > nat ).
thf(func_def_519,type,
sK460: set_nat > set_nat > nat ).
thf(func_def_520,type,
sK461: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_521,type,
sK462: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_522,type,
sK463: set_nat > set_nat > nat ).
thf(func_def_523,type,
sK464: set_nat > set_nat > nat ).
thf(func_def_524,type,
sK465: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_525,type,
sK466: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_526,type,
sK467: set_nat > set_nat > nat ).
thf(func_def_527,type,
sK468: set_nat > set_nat > nat ).
thf(func_def_528,type,
sK469: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_529,type,
sK470: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_530,type,
sK471: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_531,type,
sK472: ( product_prod_nat_nat > a ) > nat > nat ).
thf(func_def_532,type,
sK473: set_nat > set_nat > nat ).
thf(func_def_533,type,
sK474: set_nat > set_nat > nat ).
thf(func_def_534,type,
sK475: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_535,type,
sK476: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_536,type,
sK477: nat ).
thf(func_def_537,type,
sK478: nat ).
thf(func_def_539,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_540,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_541,type,
db5:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
isShortestPath_a @ c @ s @ p @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_SP) ).
thf(f2,axiom,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_SP__EDGES) ).
thf(f19,axiom,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: product_prod_nat_nat] :
( ( isPath_a @ c @ X0 @ X1 @ X2 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
=> ( member701585322at_nat @ X3 @ ( e_a @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_isPath__edgeset) ).
thf(f20,axiom,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( isShortestPath_a @ c @ X0 @ X1 @ X2 )
=> ( isPath_a @ c @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_shortestPath__is__path) ).
thf(f125,axiom,
( ord_le841296385at_nat
= ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ X0 )
=> ( member701585322at_nat @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subset__iff) ).
thf(f150,axiom,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X0 @ X1 )
=> ( ( member701585322at_nat @ X0 @ X2 )
=> ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_IntI) ).
thf(f161,axiom,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
=> ~ ( ( member701585322at_nat @ X0 @ X1 )
=> ~ ( member701585322at_nat @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_IntE) ).
thf(f354,conjecture,
ord_le841296385at_nat @ edges @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f355,negated_conjecture,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(negated_conjecture,[status(cth)],[f354]) ).
thf(f356,plain,
isShortestPath_a @ c @ s @ p @ t,
inference(rectify,[],[f1]) ).
thf(f357,plain,
( ( isShortestPath_a @ c @ s @ p @ t )
= $true ),
inference(fool_elimination,[],[f356]) ).
thf(f358,plain,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
inference(rectify,[],[f2]) ).
thf(f359,plain,
( ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) )
= $true ),
inference(fool_elimination,[],[f358]) ).
thf(f392,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: product_prod_nat_nat] :
( ( isPath_a @ c @ X0 @ X1 @ X2 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
=> ( member701585322at_nat @ X3 @ ( e_a @ c ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f393,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: product_prod_nat_nat] :
( ( ( isPath_a @ c @ X0 @ X1 @ X2 )
= $true )
=> ( ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
= $true )
=> ( ( member701585322at_nat @ X3 @ ( e_a @ c ) )
= $true ) ) ),
inference(fool_elimination,[],[f392]) ).
thf(f394,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( isShortestPath_a @ c @ X0 @ X1 @ X2 )
=> ( isPath_a @ c @ X0 @ X1 @ X2 ) ),
inference(rectify,[],[f20]) ).
thf(f395,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( ( isShortestPath_a @ c @ X0 @ X1 @ X2 )
= $true )
=> ( ( isPath_a @ c @ X0 @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f394]) ).
thf(f594,plain,
( ord_le841296385at_nat
= ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ X0 )
=> ( member701585322at_nat @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f125]) ).
thf(f595,plain,
( ord_le841296385at_nat
= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f594]) ).
thf(f644,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X0 @ X1 )
=> ( ( member701585322at_nat @ X0 @ X2 )
=> ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f150]) ).
thf(f645,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ X1 )
= $true )
=> ( ( ( member701585322at_nat @ X0 @ X2 )
= $true )
=> ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[],[f644]) ).
thf(f666,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
=> ~ ( ( member701585322at_nat @ X0 @ X1 )
=> ~ ( member701585322at_nat @ X0 @ X2 ) ) ),
inference(rectify,[],[f161]) ).
thf(f667,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
= $true )
=> ~ ( ( ( member701585322at_nat @ X0 @ X1 )
= $true )
=> ( ( member701585322at_nat @ X0 @ X2 )
!= $true ) ) ),
inference(fool_elimination,[],[f666]) ).
thf(f1017,plain,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(rectify,[],[f355]) ).
thf(f1018,plain,
( ( ord_le841296385at_nat @ edges @ ( e_a @ c ) )
!= $true ),
inference(fool_elimination,[],[f1017]) ).
thf(f1024,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
= $true )
=> ~ ( ( ( member701585322at_nat @ X0 @ X1 )
= $true )
=> ( ( member701585322at_nat @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f667]) ).
thf(f1041,plain,
( ( ord_le841296385at_nat @ edges @ ( e_a @ c ) )
!= $true ),
inference(flattening,[],[f1018]) ).
thf(f1048,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: product_prod_nat_nat] :
( ( ( member701585322at_nat @ X3 @ ( e_a @ c ) )
= $true )
| ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
!= $true )
| ( ( isPath_a @ c @ X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f393]) ).
thf(f1049,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: product_prod_nat_nat] :
( ( ( member701585322at_nat @ X3 @ ( e_a @ c ) )
= $true )
| ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
!= $true )
| ( ( isPath_a @ c @ X0 @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f1048]) ).
thf(f1050,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( ( isPath_a @ c @ X0 @ X1 @ X2 )
= $true )
| ( ( isShortestPath_a @ c @ X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f395]) ).
thf(f1216,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
= $true )
| ( ( member701585322at_nat @ X0 @ X2 )
!= $true )
| ( ( member701585322at_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f645]) ).
thf(f1217,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
= $true )
| ( ( member701585322at_nat @ X0 @ X2 )
!= $true )
| ( ( member701585322at_nat @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f1216]) ).
thf(f1223,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( ( member701585322at_nat @ X0 @ X2 )
= $true )
& ( ( member701585322at_nat @ X0 @ X1 )
= $true ) )
| ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
!= $true ) ),
inference(ennf_transformation,[],[f1024]) ).
thf(f1499,plain,
( ( isShortestPath_a @ c @ s @ p @ t )
= $true ),
inference(cnf_transformation,[],[f357]) ).
thf(f1500,plain,
( ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) )
= $true ),
inference(cnf_transformation,[],[f359]) ).
thf(f1519,plain,
! [X2: nat,X3: product_prod_nat_nat,X0: nat,X1: list_P559422087at_nat] :
( ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
!= $true )
| ( ( member701585322at_nat @ X3 @ ( e_a @ c ) )
= $true )
| ( ( isPath_a @ c @ X0 @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f1049]) ).
thf(f1520,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( ( isShortestPath_a @ c @ X0 @ X1 @ X2 )
!= $true )
| ( ( isPath_a @ c @ X0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f1050]) ).
thf(f1679,plain,
( ord_le841296385at_nat
= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f595]) ).
thf(f1706,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ X2 )
!= $true )
| ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
= $true )
| ( ( member701585322at_nat @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f1217]) ).
thf(f1718,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ X0 @ ( inf_in586391887at_nat @ X1 @ X2 ) )
!= $true )
| ( ( member701585322at_nat @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f1223]) ).
thf(f1984,plain,
( ( ord_le841296385at_nat @ edges @ ( e_a @ c ) )
!= $true ),
inference(cnf_transformation,[],[f1041]) ).
thf(f1990,plain,
( $true
= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) )
@ edges
@ ( set_Pr2131844118at_nat @ p ) ) ),
inference(definition_unfolding,[],[f1500,f1679]) ).
thf(f2381,plain,
( $true
!= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) )
@ edges
@ ( e_a @ c ) ) ),
inference(definition_unfolding,[],[f1984,f1679]) ).
thf(f2442,plain,
( $true
!= ( !! @ product_prod_nat_nat
@ ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) ) ) ),
inference(beta-eta_normalization,[],[f2381]) ).
thf(f2443,plain,
( $false
= ( ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) )
@ sK150 ) ),
inference(sigma_proxy_clausification,[],[f2442]) ).
thf(f2444,plain,
( $false
= ( ( member701585322at_nat @ sK150 @ edges )
=> ( member701585322at_nat @ sK150 @ ( e_a @ c ) ) ) ),
inference(beta-eta_normalization,[],[f2443]) ).
thf(f2445,plain,
( $false
= ( member701585322at_nat @ sK150 @ ( e_a @ c ) ) ),
inference(imp_proxy_clausification,[],[f2444]) ).
thf(f2446,plain,
( $true
= ( member701585322at_nat @ sK150 @ edges ) ),
inference(imp_proxy_clausification,[],[f2444]) ).
thf(f5375,plain,
( $true
= ( !! @ product_prod_nat_nat
@ ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(beta-eta_normalization,[],[f1990]) ).
thf(f5376,plain,
! [X1: product_prod_nat_nat] :
( $true
= ( ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ p ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f5375]) ).
thf(f5377,plain,
! [X1: product_prod_nat_nat] :
( $true
= ( ( member701585322at_nat @ X1 @ edges )
=> ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(beta-eta_normalization,[],[f5376]) ).
thf(f5378,plain,
! [X1: product_prod_nat_nat] :
( ( $true
= ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ p ) ) )
| ( $false
= ( member701585322at_nat @ X1 @ edges ) ) ),
inference(imp_proxy_clausification,[],[f5377]) ).
thf(f6922,plain,
! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true
= ( member701585322at_nat @ sK150 @ ( inf_in586391887at_nat @ X0 @ edges ) ) )
| ( $true
!= ( member701585322at_nat @ sK150 @ X0 ) ) ),
inference(constrained_superposition,[],[f1706,f2446]) ).
thf(f6941,plain,
! [X0: set_Pr1986765409at_nat] :
( ( $true
!= ( member701585322at_nat @ sK150 @ X0 ) )
| ( $true
= ( member701585322at_nat @ sK150 @ ( inf_in586391887at_nat @ X0 @ edges ) ) ) ),
inference(trivial_inequality_removal,[],[f6922]) ).
thf(f6944,plain,
( ( $true != $true )
| ( $true
= ( member701585322at_nat @ sK150 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ edges ) ) )
| ( $false
= ( member701585322at_nat @ sK150 @ edges ) ) ),
inference(constrained_superposition,[],[f6941,f5378]) ).
thf(f6960,plain,
( ( $true
= ( member701585322at_nat @ sK150 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ edges ) ) )
| ( $false
= ( member701585322at_nat @ sK150 @ edges ) ) ),
inference(trivial_inequality_removal,[],[f6944]) ).
thf(f6962,plain,
( ( $true = $false )
| ( $true
= ( member701585322at_nat @ sK150 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ edges ) ) ) ),
inference(forward_demodulation,[],[f6960,f2446]) ).
thf(f6963,plain,
( $true
= ( member701585322at_nat @ sK150 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ edges ) ) ),
inference(trivial_inequality_removal,[],[f6962]) ).
thf(f7033,plain,
( ( $true != $true )
| ( $true
= ( member701585322at_nat @ sK150 @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(constrained_superposition,[],[f1718,f6963]) ).
thf(f7039,plain,
( $true
= ( member701585322at_nat @ sK150 @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(trivial_inequality_removal,[],[f7033]) ).
thf(f9787,plain,
( ( $true != $true )
| ( $true
= ( isPath_a @ c @ s @ p @ t ) ) ),
inference(constrained_superposition,[],[f1520,f1499]) ).
thf(f9793,plain,
( $true
= ( isPath_a @ c @ s @ p @ t ) ),
inference(trivial_inequality_removal,[],[f9787]) ).
thf(f10281,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true
= ( member701585322at_nat @ sK150 @ ( e_a @ c ) ) )
| ( $true
!= ( isPath_a @ c @ X0 @ p @ X1 ) ) ),
inference(constrained_superposition,[],[f1519,f7039]) ).
thf(f10297,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( member701585322at_nat @ sK150 @ ( e_a @ c ) ) )
| ( $true
!= ( isPath_a @ c @ X0 @ p @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f10281]) ).
thf(f10298,plain,
! [X0: nat,X1: nat] :
( ( $true = $false )
| ( $true
!= ( isPath_a @ c @ X0 @ p @ X1 ) ) ),
inference(forward_demodulation,[],[f10297,f2445]) ).
thf(f10299,plain,
! [X0: nat,X1: nat] :
( $true
!= ( isPath_a @ c @ X0 @ p @ X1 ) ),
inference(trivial_inequality_removal,[],[f10298]) ).
thf(f21437,plain,
$false,
inference(forward_subsumption_resolution,[],[f9793,f10299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP050^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:41:25 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 6.45/1.18 % (3820900)Will run a generic schedule for satisfiability detection.
% 6.45/1.18 % (3820913)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=129557395:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.45/1.18 % (3820908)% WARNING: option uhcvi not known.
% 6.45/1.18 % (3820912)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=435027071:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.45/1.18 % (3820906)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2615692196_2999 on theBenchmark for (2999ds/0Mi)
% 6.45/1.18 % (3820910)dis+10_1_sil=32000:sp=arity:random_seed=3883593538:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.45/1.18 % (3820908)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=395968972:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.45/1.18 % (3820909)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2609008599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.45/1.18 % (3820911)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2465692493:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.45/1.18 % (3820908)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.18 % (3820911)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.18 % (3820913)Instruction limit reached!
% 6.45/1.18 % (3820913)------------------------------
% 6.45/1.18 % (3820913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.18 % (3820913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.18 % (3820913)CaDiCaL version: 2.1.3
% 6.45/1.18 % (3820913)Termination reason: Instruction limit
% 6.45/1.18 % (3820913)Termination phase: Saturation
% 6.45/1.18 % (3820913)Time elapsed: 0.036 s
% 6.45/1.18 % (3820913)Peak memory usage: 13 MB
% 6.45/1.18 % (3820913)Instructions burned: 164 (million)
% 6.45/1.18 % (3820935)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3794671592:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.45/1.18 % (3820910)Instruction limit reached!
% 6.45/1.18 % (3820910)------------------------------
% 6.45/1.18 % (3820910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.18 % (3820910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.18 % (3820910)CaDiCaL version: 2.1.3
% 6.45/1.18 % (3820910)Termination reason: Instruction limit
% 6.45/1.18 % (3820910)Termination phase: Property scanning
% 6.45/1.18 % (3820910)Time elapsed: 0.042 s
% 6.45/1.18 % (3820910)Peak memory usage: 11 MB
% 6.45/1.18 % (3820910)Instructions burned: 103 (million)
% 6.45/1.18 % (3820911)Instruction limit reached!
% 6.45/1.18 % (3820911)------------------------------
% 6.45/1.18 % (3820911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.18 % (3820911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.18 % (3820911)CaDiCaL version: 2.1.3
% 6.45/1.18 % (3820911)Termination reason: Instruction limit
% 6.45/1.18 % (3820911)Termination phase: Property scanning
% 6.45/1.18 % (3820911)Time elapsed: 0.047 s
% 6.45/1.18 % (3820911)Peak memory usage: 11 MB
% 6.45/1.18 % (3820911)Instructions burned: 117 (million)
% 6.45/1.18 % (3820912)Instruction limit reached!
% 6.45/1.18 % (3820912)------------------------------
% 6.45/1.18 % (3820912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.18 % (3820912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.18 % (3820912)CaDiCaL version: 2.1.3
% 6.45/1.18 % (3820912)Termination reason: Instruction limit
% 6.45/1.18 % (3820912)Termination phase: Property scanning
% 6.45/1.18 % (3820912)Time elapsed: 0.055 s
% 6.45/1.18 % (3820912)Peak memory usage: 11 MB
% 6.45/1.18 % (3820912)Instructions burned: 136 (million)
% 6.45/1.18 % Exception at run slice level
% 6.45/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.18 % (3820908)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.45/1.18 % (3820941)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=677105313:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.45/1.18 % (3820943)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=615570200:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 16.59/2.75 % Exception at run slice level
% 16.59/2.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.59/2.75 % (3820946)ott-21_1_sil=16000:fs=off:random_seed=1202639438:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 16.59/2.75 % (3820948)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2870414700:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 16.59/2.75 % (3820943)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.59/2.75 % (3820957)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2502560122:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.59/2.75 % (3820941)Instruction limit reached!
% 16.59/2.75 % (3820941)------------------------------
% 16.59/2.75 % (3820941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.59/2.75 % (3820941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.59/2.75 % (3820941)CaDiCaL version: 2.1.3
% 16.59/2.75 % (3820941)Termination reason: Instruction limit
% 16.59/2.75 % (3820941)Termination phase: Property scanning
% 16.59/2.75 % (3820941)Time elapsed: 0.054 s
% 16.59/2.75 % (3820941)Peak memory usage: 11 MB
% 16.59/2.75 % (3820941)Instructions burned: 134 (million)
% 16.59/2.75 % (3820943)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.59/2.75 % (3820981)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2006876560:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.59/2.75 % (3820946)Instruction limit reached!
% 16.59/2.75 % (3820946)------------------------------
% 16.59/2.75 % (3820946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.59/2.75 % (3820946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.59/2.75 % (3820946)CaDiCaL version: 2.1.3
% 16.59/2.75 % (3820946)Termination reason: Instruction limit
% 16.59/2.75 % (3820946)Termination phase: Saturation
% 16.59/2.75 % (3820946)Time elapsed: 0.075 s
% 16.59/2.75 % (3820946)Peak memory usage: 13 MB
% 16.59/2.75 % (3820946)Instructions burned: 181 (million)
% 16.59/2.75 % Exception at run slice level
% 16.59/2.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.59/2.75 % (3820998)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3893606227:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 16.59/2.75 % (3820999)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2599898751:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 16.59/2.75 % (3820999)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.59/2.75 % (3820948)Instruction limit reached!
% 16.59/2.75 % (3820948)------------------------------
% 16.59/2.75 % (3820948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.59/2.75 % (3820948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.59/2.75 % (3820948)CaDiCaL version: 2.1.3
% 16.59/2.75 % (3820948)Termination reason: Instruction limit
% 16.59/2.75 % (3820948)Termination phase: Saturation
% 16.59/2.75 % (3820948)Time elapsed: 0.127 s
% 16.59/2.75 % (3820948)Peak memory usage: 15 MB
% 16.59/2.75 % (3820948)Instructions burned: 480 (million)
% 16.59/2.75 % (3821011)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3993503771:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 16.59/2.75 % (3821011)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.59/2.75 % Exception at run slice level
% 16.59/2.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.59/2.75 % (3821022)fmb+10_1_sil=64000:random_seed=1084852236:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 16.59/2.75 % (3821022)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 16.59/2.75 % Exception at run slice level
% 16.59/2.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.59/2.75 % (3821040)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3288974372:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 16.59/2.75 % (3820943)Instruction limit reached!
% 16.59/2.75 % (3820943)------------------------------
% 16.59/2.75 % (3820943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3820943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3820943)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3820943)Termination reason: Instruction limit
% 17.03/2.85 % (3820943)Termination phase: Saturation
% 17.03/2.85 % (3820943)Time elapsed: 0.312 s
% 17.03/2.85 % (3820943)Peak memory usage: 17 MB
% 17.03/2.85 % (3820943)Instructions burned: 685 (million)
% 17.03/2.85 % (3821052)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1067915167:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 17.03/2.85 % Exception at run slice level
% 17.03/2.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.03/2.85 % (3821059)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3554682448:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 17.03/2.85 % (3821011)Instruction limit reached!
% 17.03/2.85 % (3821011)------------------------------
% 17.03/2.85 % (3821011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3821011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3821011)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3821011)Termination reason: Instruction limit
% 17.03/2.85 % (3821011)Termination phase: Saturation
% 17.03/2.85 % (3821011)Time elapsed: 0.218 s
% 17.03/2.85 % (3821011)Peak memory usage: 20 MB
% 17.03/2.85 % (3821011)Instructions burned: 882 (million)
% 17.03/2.85 % (3821059)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.03/2.85 % (3821068)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3030388113:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 17.03/2.85 % Exception at run slice level
% 17.03/2.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.03/2.85 % (3821068)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.03/2.85 % (3821068)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.03/2.85 % (3821073)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=982383987:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 17.03/2.85 % (3820999)Instruction limit reached!
% 17.03/2.85 % (3820999)------------------------------
% 17.03/2.85 % (3820999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3820999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3820999)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3820999)Termination reason: Instruction limit
% 17.03/2.85 % (3820999)Termination phase: Saturation
% 17.03/2.85 % (3820999)Time elapsed: 0.346 s
% 17.03/2.85 % (3820999)Peak memory usage: 19 MB
% 17.03/2.85 % (3820999)Instructions burned: 694 (million)
% 17.03/2.85 % Exception at run slice level
% 17.03/2.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.03/2.85 % (3821078)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3188266345:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 17.03/2.85 % (3821084)ott-2_1_sil=16000:newcnf=on:random_seed=1096719738:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 17.03/2.85 % (3821084)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.03/2.85 % Exception at run slice level
% 17.03/2.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.03/2.85 % (3821104)ott+10_1_sil=32000:tgt=ground:random_seed=3545871008:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 17.03/2.85 % (3820981)Instruction limit reached!
% 17.03/2.85 % (3820981)------------------------------
% 17.03/2.85 % (3820981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3820981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3820981)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3820981)Termination reason: Instruction limit
% 17.03/2.85 % (3820981)Termination phase: Saturation
% 17.03/2.85 % (3820981)Time elapsed: 0.685 s
% 17.03/2.85 % (3820981)Peak memory usage: 19 MB
% 17.03/2.85 % (3820981)Instructions burned: 1179 (million)
% 17.03/2.85 % (3821137)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1182067860:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 17.03/2.85 % Exception at run slice level
% 17.03/2.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.03/2.85 % (3821149)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1437992701:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 17.03/2.85 % (3821068)Instruction limit reached!
% 17.03/2.85 % (3821068)------------------------------
% 17.03/2.85 % (3821068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3821068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3821068)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3821068)Termination reason: Instruction limit
% 17.03/2.85 % (3821068)Termination phase: Saturation
% 17.03/2.85 % (3821068)Time elapsed: 0.489 s
% 17.03/2.85 % (3821068)Peak memory usage: 18 MB
% 17.03/2.85 % (3821068)Instructions burned: 1475 (million)
% 17.03/2.85 % (3821167)dis+21_1_sil=32000:sas=cadical:random_seed=3580103314:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 17.03/2.85 % (3821149)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.03/2.85 % (3821084)Instruction limit reached!
% 17.03/2.85 % (3821084)------------------------------
% 17.03/2.85 % (3821084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3821084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3821084)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3821084)Termination reason: Instruction limit
% 17.03/2.85 % (3821084)Termination phase: Saturation
% 17.03/2.85 % (3821084)Time elapsed: 0.490 s
% 17.03/2.85 % (3821084)Peak memory usage: 17 MB
% 17.03/2.85 % (3821084)Instructions burned: 869 (million)
% 17.03/2.85 % (3821212)ott+11_1_sil=16000:gs=on:random_seed=2040714502:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2989 on theBenchmark for (2989ds/2251Mi)
% 17.03/2.85 % (3821212)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.03/2.85 % (3821167)Instruction limit reached!
% 17.03/2.85 % (3821167)------------------------------
% 17.03/2.85 % (3821167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3821167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3821167)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3821167)Termination reason: Instruction limit
% 17.03/2.85 % (3821167)Termination phase: Saturation
% 17.03/2.85 % (3821167)Time elapsed: 0.886 s
% 17.03/2.85 % (3821167)Peak memory usage: 29 MB
% 17.03/2.85 % (3821167)Instructions burned: 3777 (million)
% 17.03/2.85 % (3821297)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3473774214:fmbsr=1.6:i=67534_2981 on theBenchmark for (2981ds/67534Mi)
% 17.03/2.85 % Exception at run slice level
% 17.03/2.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.03/2.85 % (3821299)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=2468473973:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2980 on theBenchmark for (2980ds/4591Mi)
% 17.03/2.85 % (3821212)Instruction limit reached!
% 17.03/2.85 % (3821212)------------------------------
% 17.03/2.85 % (3821212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3821212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3821212)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3821212)Termination reason: Instruction limit
% 17.03/2.85 % (3821212)Termination phase: Saturation
% 17.03/2.85 % (3821212)Time elapsed: 1.010 s
% 17.03/2.85 % (3821212)Peak memory usage: 22 MB
% 17.03/2.85 % (3821212)Instructions burned: 2252 (million)
% 17.03/2.85 % (3821301)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3886280967:i=29340_2978 on theBenchmark for (2978ds/29340Mi)
% 17.03/2.85 % (3821149)Instruction limit reached!
% 17.03/2.85 % (3821149)------------------------------
% 17.03/2.85 % (3821149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.85 % (3821149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.85 % (3821149)CaDiCaL version: 2.1.3
% 17.03/2.85 % (3821149)Termination reason: Instruction limit
% 17.03/2.85 % (3821149)Termination phase: Saturation
% 17.03/2.85 % (3821149)Time elapsed: 1.526 s
% 17.03/2.85 % (3821149)Peak memory usage: 23 MB
% 17.03/2.85 % (3821149)Instructions burned: 3513 (million)
% 17.03/2.85 % (3821303)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=631208900:i=5211_2975 on theBenchmark for (2975ds/5211Mi)
% 17.03/2.85 % (3821059) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3820900-3821059"...
% 17.03/2.85 % (3821059)...printing done.
% 17.03/2.85 % (3821059)Refutation found. Thanks to Tanya!
% 17.03/2.85 % SZS status Theorem for theBenchmark
% 17.03/2.85 % SZS output start Proof for theBenchmark
% See solution above
% 17.03/2.86 % (3821059)------------------------------
% 17.03/2.86 % (3821059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.03/2.86 % (3821059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.03/2.86 % (3821059)CaDiCaL version: 2.1.3
% 17.03/2.86 % (3821059)Termination reason: Refutation
% 17.03/2.86 % (3821059)Time elapsed: 2.143 s
% 17.03/2.86 % (3821059)Peak memory usage: 27 MB
% 17.03/2.86 % (3821059)Instructions burned: 4658 (million)
% 17.03/2.86 % (3820900)Success in time 2.619 s
% 17.03/2.86 % Vampire exiting
%------------------------------------------------------------------------------