%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT171^2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:21:49 AM UTC 2026
% Result : Theorem 0.88s 0.59s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 246 ( 28 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 419 ( 18 ~; 11 |; 0 &; 385 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 277 ( 274 usr; 16 con; 0-6 aty)
% Number of variables : 13 ( 0 sgn 0 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
arrow_475358991le_alt: $tType ).
thf(type_def_6,type,
arrow_1429601828e_indi: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
product_unit: $tType ).
thf(type_def_9,type,
produc1501160679le_alt: $tType ).
thf(type_def_10,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
all: ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_1,type,
arrow_797024463le_IIA: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_2,type,
arrow_823908191le_Lin: ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_3,type,
arrow_734252939e_Prof: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_4,type,
arrow_789600939_above: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(func_def_5,type,
arrow_2098199487_below: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(func_def_6,type,
arrow_1212662430ctator: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ).
thf(func_def_7,type,
arrow_2054445623_mkbot: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(func_def_8,type,
arrow_55669061_mktop: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(func_def_9,type,
arrow_1706409458nimity: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_10,type,
finite120663670_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > nat ).
thf(func_def_11,type,
finite28306938_alt_o: ( ( produc1501160679le_alt > $o ) > $o ) > nat ).
thf(func_def_12,type,
finite_card_o: ( $o > $o ) > nat ).
thf(func_def_13,type,
finite97476818e_indi: ( arrow_1429601828e_indi > $o ) > nat ).
thf(func_def_14,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(func_def_15,type,
finite1949902593t_unit: ( product_unit > $o ) > nat ).
thf(func_def_16,type,
finite537683861le_alt: ( produc1501160679le_alt > $o ) > nat ).
thf(func_def_17,type,
finite1956767223_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_18,type,
finite2112685307_alt_o: ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_19,type,
finite_finite_o: ( $o > $o ) > $o ).
thf(func_def_20,type,
finite664979089e_indi: ( arrow_1429601828e_indi > $o ) > $o ).
thf(func_def_21,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(func_def_22,type,
finite449174868le_alt: ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_23,type,
in_rel1252994498le_alt: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o ).
thf(func_def_24,type,
inj_on1284293749_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_25,type,
inj_on743426285_alt_o: ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_26,type,
inj_on1877294875e_indi: ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_27,type,
inj_on867909093le_alt: ( $o > produc1501160679le_alt ) > ( $o > $o ) > $o ).
thf(func_def_28,type,
inj_on1190919077_alt_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > $o ) > $o ).
thf(func_def_29,type,
inj_on978774663di_nat: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > $o ).
thf(func_def_30,type,
inj_on_nat_nat: ( nat > nat ) > ( nat > $o ) > $o ).
thf(func_def_31,type,
inj_on1911943593_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_32,type,
pi_Arr195212324lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_33,type,
pi_Arr338314351e_indi: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ).
thf(func_def_34,type,
pi_Arr830584606t_unit: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit ) > $o ).
thf(func_def_35,type,
pi_Arr1304755663_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_36,type,
pi_Arr952516694lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_37,type,
pi_Arr1232280765e_indi: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ).
thf(func_def_38,type,
pi_Arr1963174508t_unit: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit ) > $o ).
thf(func_def_39,type,
pi_Pro763888199_alt_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_40,type,
pi_Pro422690258lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_41,type,
pi_Pro468373057e_indi: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ).
thf(func_def_42,type,
pi_Pro1306850800t_unit: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > product_unit > $o ) > ( ( produc1501160679le_alt > $o ) > product_unit ) > $o ).
thf(func_def_43,type,
pi_o_A1186128886_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_44,type,
pi_o_A1182933120_alt_o: ( $o > $o ) > ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_45,type,
pi_o_P553196292_alt_o: ( $o > $o ) > ( $o > ( produc1501160679le_alt > $o ) > $o ) > ( $o > produc1501160679le_alt > $o ) > $o ).
thf(func_def_46,type,
pi_o_nat: ( $o > $o ) > ( $o > nat > $o ) > ( $o > nat ) > $o ).
thf(func_def_47,type,
pi_o_P657324555le_alt: ( $o > $o ) > ( $o > produc1501160679le_alt > $o ) > ( $o > produc1501160679le_alt ) > $o ).
thf(func_def_48,type,
pi_Arr1564509167_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_49,type,
pi_Arr1060328391_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_50,type,
pi_Arr1929480907_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_51,type,
pi_Arr251692973di_nat: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > nat > $o ) > ( arrow_1429601828e_indi > nat ) > $o ).
thf(func_def_52,type,
pi_Arr329216900le_alt: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt ) > $o ).
thf(func_def_53,type,
pi_nat_o: ( nat > $o ) > ( nat > $o > $o ) > ( nat > $o ) > $o ).
thf(func_def_54,type,
pi_nat1219304995e_indi: ( nat > $o ) > ( nat > arrow_1429601828e_indi > $o ) > ( nat > arrow_1429601828e_indi ) > $o ).
thf(func_def_55,type,
pi_nat_nat: ( nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > $o ).
thf(func_def_56,type,
pi_nat_Product_unit: ( nat > $o ) > ( nat > product_unit > $o ) > ( nat > product_unit ) > $o ).
thf(func_def_57,type,
pi_Pro1782982558_alt_o: ( product_unit > $o ) > ( product_unit > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_58,type,
pi_Pro1662176984_alt_o: ( product_unit > $o ) > ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_59,type,
pi_Pro1312660828_alt_o: ( product_unit > $o ) > ( product_unit > ( produc1501160679le_alt > $o ) > $o ) > ( product_unit > produc1501160679le_alt > $o ) > $o ).
thf(func_def_60,type,
pi_Product_unit_nat: ( product_unit > $o ) > ( product_unit > nat > $o ) > ( product_unit > nat ) > $o ).
thf(func_def_61,type,
pi_Pro701847987le_alt: ( product_unit > $o ) > ( product_unit > produc1501160679le_alt > $o ) > ( product_unit > produc1501160679le_alt ) > $o ).
thf(func_def_62,type,
pi_Pro1701359055_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_63,type,
pi_Pro1767455108e_indi: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > arrow_1429601828e_indi > $o ) > ( produc1501160679le_alt > arrow_1429601828e_indi ) > $o ).
thf(func_def_64,type,
pi_Pro1475896499t_unit: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > product_unit > $o ) > ( produc1501160679le_alt > product_unit ) > $o ).
thf(func_def_65,type,
one_one_nat: nat ).
thf(func_def_66,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_67,type,
zero_zero_nat: nat ).
thf(func_def_68,type,
hilber598459244di_nat: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > nat ) > nat > arrow_1429601828e_indi ).
thf(func_def_69,type,
hilber195283148at_nat: ( nat > $o ) > ( nat > nat ) > nat > nat ).
thf(func_def_70,type,
if_Pro1561232536_alt_o: $o > ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).
thf(func_def_71,type,
suc: nat > nat ).
thf(func_def_72,type,
ord_le1859604819lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_73,type,
ord_le157835011lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_74,type,
ord_le910298367lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_75,type,
ord_less_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_76,type,
ord_le777687553indi_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > $o ) > $o ).
thf(func_def_77,type,
ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_78,type,
ord_le232288914unit_o: ( product_unit > $o ) > ( product_unit > $o ) > $o ).
thf(func_def_79,type,
ord_le988258430_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_80,type,
ord_less_o: $o > $o > $o ).
thf(func_def_81,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_82,type,
ord_le134800455lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_83,type,
ord_le1992928527lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_84,type,
ord_le1063113995lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_85,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_86,type,
ord_le2080035663_alt_o: ( arrow_475358991le_alt > arrow_475358991le_alt > $o ) > ( arrow_475358991le_alt > arrow_475358991le_alt > $o ) > $o ).
thf(func_def_87,type,
ord_le1799070453indi_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > $o ) > $o ).
thf(func_def_88,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_89,type,
ord_le1511552390unit_o: ( product_unit > $o ) > ( product_unit > $o ) > $o ).
thf(func_def_90,type,
ord_le97612146_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_91,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_92,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_93,type,
top_to1969627639lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_94,type,
top_to2122763103lt_o_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_95,type,
top_to1842727771lt_o_o: ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_96,type,
top_top_o_o: $o > $o ).
thf(func_def_97,type,
top_to988227749indi_o: arrow_1429601828e_indi > $o ).
thf(func_def_98,type,
top_top_nat_o: nat > $o ).
thf(func_def_99,type,
top_to1984820022unit_o: product_unit > $o ).
thf(func_def_100,type,
top_to1841428258_alt_o: produc1501160679le_alt > $o ).
thf(func_def_101,type,
top_top_o: $o ).
thf(func_def_102,type,
produc1347929815le_alt: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt ).
thf(func_def_103,type,
ord_at4362885an_nat: nat > nat > nat > $o ).
thf(func_def_104,type,
collec2009291517_alt_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(func_def_105,type,
collec682858041_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(func_def_106,type,
collec94295101_alt_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_107,type,
collec22405327e_indi: ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi > $o ).
thf(func_def_108,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(func_def_109,type,
collect_Product_unit: ( product_unit > $o ) > product_unit > $o ).
thf(func_def_110,type,
collec869865362le_alt: ( produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).
thf(func_def_111,type,
image_484224243di_nat: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > nat > $o ).
thf(func_def_112,type,
member1823529808lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_113,type,
member1452482393e_indi: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o ).
thf(func_def_114,type,
member1924666376t_unit: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(func_def_115,type,
member616898751_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_116,type,
member939334982lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_117,type,
member44294883e_indi: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o ).
thf(func_def_118,type,
member843528338t_unit: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(func_def_119,type,
member530241719_alt_o: ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_120,type,
member1961363906lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( ( produc1501160679le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_121,type,
member304866663e_indi: ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o ).
thf(func_def_122,type,
member221730070t_unit: ( ( produc1501160679le_alt > $o ) > product_unit ) > ( ( ( produc1501160679le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(func_def_123,type,
member1957863580_alt_o: ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_124,type,
member1394214384_alt_o: ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_125,type,
member1862122484_alt_o: ( $o > produc1501160679le_alt > $o ) > ( ( $o > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_126,type,
member_o_nat: ( $o > nat ) > ( ( $o > nat ) > $o ) > $o ).
thf(func_def_127,type,
member492167345le_alt: ( $o > produc1501160679le_alt ) > ( ( $o > produc1501160679le_alt ) > $o ) > $o ).
thf(func_def_128,type,
member811956313_alt_o: ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_129,type,
member1234151027_alt_o: ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_130,type,
member526088951_alt_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_131,type,
member1315464153di_nat: ( arrow_1429601828e_indi > nat ) > ( ( arrow_1429601828e_indi > nat ) > $o ) > $o ).
thf(func_def_132,type,
member351225838le_alt: ( arrow_1429601828e_indi > produc1501160679le_alt ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt ) > $o ) > $o ).
thf(func_def_133,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_134,type,
member1391860553e_indi: ( nat > arrow_1429601828e_indi ) > ( ( nat > arrow_1429601828e_indi ) > $o ) > $o ).
thf(func_def_135,type,
member_nat_nat: ( nat > nat ) > ( ( nat > nat ) > $o ) > $o ).
thf(func_def_136,type,
member616671224t_unit: ( nat > product_unit ) > ( ( nat > product_unit ) > $o ) > $o ).
thf(func_def_137,type,
member1536989448_alt_o: ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_138,type,
member283501700_alt_o: ( product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_139,type,
member1661784200_alt_o: ( product_unit > produc1501160679le_alt > $o ) > ( ( product_unit > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_140,type,
member1827227242it_nat: ( product_unit > nat ) > ( ( product_unit > nat ) > $o ) > $o ).
thf(func_def_141,type,
member495332125le_alt: ( product_unit > produc1501160679le_alt ) > ( ( product_unit > produc1501160679le_alt ) > $o ) > $o ).
thf(func_def_142,type,
member377231867_alt_o: ( produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(func_def_143,type,
member1640632174e_indi: ( produc1501160679le_alt > arrow_1429601828e_indi ) > ( ( produc1501160679le_alt > arrow_1429601828e_indi ) > $o ) > $o ).
thf(func_def_144,type,
member593902749t_unit: ( produc1501160679le_alt > product_unit ) > ( ( produc1501160679le_alt > product_unit ) > $o ) > $o ).
thf(func_def_145,type,
member_o: $o > ( $o > $o ) > $o ).
thf(func_def_146,type,
member2052026769e_indi: arrow_1429601828e_indi > ( arrow_1429601828e_indi > $o ) > $o ).
thf(func_def_147,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(func_def_148,type,
member_Product_unit: product_unit > ( product_unit > $o ) > $o ).
thf(func_def_149,type,
member214075476le_alt: produc1501160679le_alt > ( produc1501160679le_alt > $o ) > $o ).
thf(func_def_150,type,
f: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).
thf(func_def_151,type,
lab: produc1501160679le_alt > $o ).
thf(func_def_152,type,
lba: produc1501160679le_alt > $o ).
thf(func_def_153,type,
p: arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_154,type,
a: arrow_475358991le_alt ).
thf(func_def_155,type,
b: arrow_475358991le_alt ).
thf(func_def_156,type,
c: arrow_475358991le_alt ).
thf(func_def_157,type,
d: arrow_475358991le_alt ).
thf(func_def_158,type,
e: arrow_475358991le_alt ).
thf(func_def_159,type,
h: arrow_1429601828e_indi > nat ).
thf(func_def_160,type,
n: nat ).
thf(func_def_162,type,
vAND: $o > $o > $o ).
thf(func_def_165,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_166,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_167,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_168,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_169,type,
sP0: arrow_1429601828e_indi > $o ).
thf(func_def_170,type,
sP1: arrow_1429601828e_indi > $o ).
thf(func_def_171,type,
sP2: arrow_475358991le_alt > arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o ).
thf(func_def_172,type,
sP3: arrow_475358991le_alt > arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o ).
thf(func_def_173,type,
sP4: arrow_475358991le_alt > arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o ).
thf(func_def_174,type,
sP5: arrow_475358991le_alt > arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o ).
thf(func_def_175,type,
sK6: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_176,type,
sK7: ( nat > $o ) > nat > nat ).
thf(func_def_177,type,
sK8: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_178,type,
sK9: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_179,type,
sK10: ( nat > $o ) > nat > nat ).
thf(func_def_180,type,
sK11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_181,type,
sK12: nat > nat ).
thf(func_def_182,type,
sK13: nat > nat > nat ).
thf(func_def_183,type,
sK14: nat > nat > nat ).
thf(func_def_184,type,
sK15: nat > nat > nat ).
thf(func_def_185,type,
sK16: ( product_unit > $o ) > ( product_unit > $o ) > product_unit ).
thf(func_def_186,type,
sK17: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(func_def_187,type,
sK18: ( nat > nat ) > nat ).
thf(func_def_188,type,
sK19: ( nat > nat ) > nat ).
thf(func_def_189,type,
sK20: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > arrow_1429601828e_indi ).
thf(func_def_190,type,
sK21: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_191,type,
sK22: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_192,type,
sK23: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_193,type,
sK24: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_194,type,
sK25: arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_195,type,
sK26: ( produc1501160679le_alt > $o > $o ) > ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt ).
thf(func_def_196,type,
sK27: produc1501160679le_alt > $o ).
thf(func_def_197,type,
sK28: nat ).
thf(func_def_198,type,
sK29: nat > nat ).
thf(func_def_199,type,
sK30: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt ).
thf(func_def_200,type,
sK31: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).
thf(func_def_201,type,
sK32: nat > nat > nat ).
thf(func_def_202,type,
sK33: ( nat > arrow_1429601828e_indi ) > ( arrow_1429601828e_indi > nat ) > nat ).
thf(func_def_203,type,
sK34: ( arrow_1429601828e_indi > nat ) > arrow_1429601828e_indi ).
thf(func_def_204,type,
sK35: ( arrow_1429601828e_indi > nat ) > arrow_1429601828e_indi ).
thf(func_def_205,type,
sK36: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_206,type,
sK37: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_207,type,
sK38: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_208,type,
sK39: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_209,type,
sK40: produc1501160679le_alt > $o ).
thf(func_def_210,type,
sK41: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > produc1501160679le_alt > $o ).
thf(func_def_211,type,
sK42: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_212,type,
sK43: nat > nat > nat ).
thf(func_def_213,type,
sK44: ( produc1501160679le_alt > $o > $o ) > ( produc1501160679le_alt > $o > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt ).
thf(func_def_214,type,
sK45: ( nat > nat ) > nat ).
thf(func_def_215,type,
sK46: ( nat > nat ) > nat ).
thf(func_def_216,type,
sK47: ( nat > $o ) > nat ).
thf(func_def_217,type,
sK48: nat > ( nat > $o ) > nat ).
thf(func_def_218,type,
sK49: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_219,type,
sK50: ( produc1501160679le_alt > $o ) > ( $o > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt ).
thf(func_def_220,type,
sK51: nat > nat ).
thf(func_def_221,type,
sK52: ( nat > $o ) > nat > nat ).
thf(func_def_222,type,
sK53: arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_223,type,
sK54: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_224,type,
sK55: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_225,type,
sK56: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_226,type,
sK57: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_227,type,
sK58: nat > nat ).
thf(func_def_228,type,
sK59: produc1501160679le_alt > $o ).
thf(func_def_229,type,
sK60: ( nat > $o ) > nat ).
thf(func_def_230,type,
sK61: arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_231,type,
sK62: arrow_1429601828e_indi > nat ).
thf(func_def_232,type,
sK63: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_233,type,
sK64: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt ).
thf(func_def_234,type,
sK65: nat > nat > nat ).
thf(func_def_235,type,
sK66: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_236,type,
sK67: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_237,type,
sK68: ( nat > $o ) > nat ).
thf(func_def_238,type,
sK69: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_239,type,
sK70: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_240,type,
sK71: ( nat > $o ) > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_241,type,
sK72: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_242,type,
sK73: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_243,type,
sK74: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ).
thf(func_def_244,type,
sK75: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_245,type,
sK76: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_246,type,
sK77: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_247,type,
sK78: arrow_475358991le_alt > arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > arrow_1429601828e_indi ).
thf(func_def_248,type,
sK79: ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_249,type,
sK80: ( nat > nat ) > nat ).
thf(func_def_250,type,
sK81: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_251,type,
sK82: ( nat > nat ) > nat ).
thf(func_def_252,type,
sK83: ( nat > nat ) > nat ).
thf(func_def_253,type,
sK84: ( nat > nat ) > ( nat > $o ) > nat ).
thf(func_def_254,type,
sK85: ( nat > nat ) > ( nat > $o ) > nat ).
thf(func_def_255,type,
sK86: ( ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ).
thf(func_def_256,type,
sK87: nat > ( nat > $o ) > nat ).
thf(func_def_257,type,
sK88: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_258,type,
sK89: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_259,type,
sK90: nat > nat > nat ).
thf(func_def_260,type,
sK91: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_261,type,
sK92: nat > nat ).
thf(func_def_262,type,
sK93: ( nat > $o ) > ( nat > nat ) > nat ).
thf(func_def_263,type,
sK94: ( nat > $o ) > ( nat > nat ) > nat ).
thf(func_def_264,type,
sK95: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_265,type,
sK96: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi ).
thf(func_def_266,type,
sK97: nat > ( nat > $o ) > nat ).
thf(func_def_267,type,
sK98: ( nat > $o ) > nat ).
thf(func_def_268,type,
sK99: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o > $o ) > produc1501160679le_alt ).
thf(func_def_269,type,
sK100: nat ).
thf(func_def_270,type,
sK101: ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_271,type,
sK102: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(func_def_272,type,
vNOT: $o > $o ).
thf(f14,axiom,
( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_789600939_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ X0 ) @ e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(f15,axiom,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_789600939_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ X0 ) @ e ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
thf(f704,conjecture,
member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f705,negated_conjecture,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) ),
inference(negated_conjecture,[status(cth)],[f704]) ).
thf(f942,plain,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) ),
inference(rectify,[],[f705]) ).
thf(f943,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(fool_elimination,[],[f942]) ).
thf(f1152,plain,
( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_789600939_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ X0 ) @ e ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f1153,plain,
( $true
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(fool_elimination,[],[f1152]) ).
thf(f1881,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_789600939_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ X0 ) @ e ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f1882,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(fool_elimination,[],[f1881]) ).
thf(f2047,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(flattening,[],[f943]) ).
thf(f4204,plain,
( $true
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(cnf_transformation,[],[f1153]) ).
thf(f4285,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(cnf_transformation,[],[f1882]) ).
thf(f4441,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(cnf_transformation,[],[f2047]) ).
thf(f4750,plain,
( ( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false )
| ( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f4285]) ).
thf(f5010,definition,
( spl103_28
<=> ( $true
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl103_28])],[avatar_definition]) ).
thf(f5012,plain,
( ( $true
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) )
| ~ spl103_28 ),
inference(avatar_component_clause,[],[f5010]) ).
thf(f5019,definition,
( spl103_30
<=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl103_30])],[avatar_definition]) ).
thf(f5023,definition,
( spl103_31
<=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl103_31])],[avatar_definition]) ).
thf(f5025,plain,
( ( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_789600939_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false )
| ~ spl103_31 ),
inference(avatar_component_clause,[],[f5023]) ).
thf(f5026,plain,
( spl103_30
| spl103_31 ),
inference(avatar_split_clause,[],[f4750,f5023,f5019]) ).
thf(f5037,plain,
spl103_28,
inference(avatar_split_clause,[],[f4204,f5010]) ).
thf(f5388,plain,
~ spl103_30,
inference(avatar_split_clause,[],[f4441,f5019]) ).
thf(f5702,plain,
( ( $true = $false )
| ~ spl103_28
| ~ spl103_31 ),
inference(superposition,[],[f5025,f5012]) ).
thf(f5710,plain,
( $false
| ~ spl103_28
| ~ spl103_31 ),
inference(trivial_inequality_removal,[],[f5702]) ).
thf(f5711,plain,
( ~ spl103_28
| ~ spl103_31 ),
inference(avatar_contradiction_clause,[],[f5710]) ).
cnf(s22,plain,
( spl103_30
| spl103_31 ),
inference(sat_conversion,[],[f5026]) ).
cnf(s25,plain,
spl103_28,
inference(sat_conversion,[],[f5037]) ).
cnf(s115,plain,
~ spl103_30,
inference(sat_conversion,[],[f5388]) ).
cnf(s154,plain,
( ~ spl103_28
| ~ spl103_31 ),
inference(sat_conversion,[],[f5711]) ).
cnf(s169,plain,
~ spl103_31,
inference(rat,[],[s154,s25]) ).
cnf(s171,plain,
$false,
inference(rat,[],[s22,s169,s115]) ).
thf(f5717,plain,
$false,
inference(avatar_sat_refutation,[],[s171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n015.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:37:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.88/0.58 % (3526317)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.88/0.58 % (3526326)lrs+10_16_si=on:nwc=1.5:random_seed=3834102261:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.88/0.58 % (3526326)Instruction limit reached!
% 0.88/0.58 % (3526326)------------------------------
% 0.88/0.58 % (3526326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.58 % (3526326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.58 % (3526326)CaDiCaL version: 2.1.3
% 0.88/0.58 % (3526326)Termination reason: Instruction limit
% 0.88/0.58 % (3526326)Termination phase: shuffling
% 0.88/0.58 % (3526326)Time elapsed: 0.005 s
% 0.88/0.58 % (3526326)Peak memory usage: 11 MB
% 0.88/0.58 % (3526326)Instructions burned: 20 (million)
% 0.88/0.58 % (3526330)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3860287579:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.88/0.58 % (3526325)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1666529355:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.88/0.58 % (3526327)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2153662060:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.88/0.58 % (3526329)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=964061697:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.88/0.58 % (3526328)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1491229953:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.88/0.58 % (3526327)Instruction limit reached!
% 0.88/0.58 % (3526327)------------------------------
% 0.88/0.58 % (3526327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.58 % (3526327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.58 % (3526327)CaDiCaL version: 2.1.3
% 0.88/0.58 % (3526327)Termination reason: Instruction limit
% 0.88/0.58 % (3526327)Termination phase: shuffling
% 0.88/0.58 % (3526327)Time elapsed: 0.004 s
% 0.88/0.58 % (3526327)Peak memory usage: 10 MB
% 0.88/0.58 % (3526327)Instructions burned: 4 (million)
% 0.88/0.58 % (3526331)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.88/0.58 % (3526331)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.88/0.58 % (3526340)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2459201221:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.88/0.58 % (3526340)Instruction limit reached!
% 0.88/0.58 % (3526340)------------------------------
% 0.88/0.58 % (3526340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.58 % (3526340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.58 % (3526340)CaDiCaL version: 2.1.3
% 0.88/0.58 % (3526340)Termination reason: Instruction limit
% 0.88/0.58 % (3526340)Termination phase: shuffling
% 0.88/0.58 % (3526340)Time elapsed: 0.002 s
% 0.88/0.58 % (3526340)Peak memory usage: 10 MB
% 0.88/0.58 % (3526340)Instructions burned: 3 (million)
% 0.88/0.58 % (3526329)Instruction limit reached!
% 0.88/0.58 % (3526329)------------------------------
% 0.88/0.58 % (3526329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.58 % (3526329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.58 % (3526329)CaDiCaL version: 2.1.3
% 0.88/0.58 % (3526329)Termination reason: Instruction limit
% 0.88/0.58 % (3526329)Termination phase: shuffling
% 0.88/0.58 % (3526329)Time elapsed: 0.020 s
% 0.88/0.58 % (3526329)Peak memory usage: 11 MB
% 0.88/0.58 % (3526329)Instructions burned: 24 (million)
% 0.88/0.58 % (3526331)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=476874051:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.88/0.58 % (3526349)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.88/0.59 % (3526346)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2377523333:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.88/0.59 % (3526349)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1262513350:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.88/0.59 % (3526330)Instruction limit reached!
% 0.88/0.59 % (3526330)------------------------------
% 0.88/0.59 % (3526330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526330)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526330)Termination reason: Instruction limit
% 0.88/0.59 % (3526330)Termination phase: Property scanning
% 0.88/0.59 % (3526330)Time elapsed: 0.046 s
% 0.88/0.59 % (3526330)Peak memory usage: 11 MB
% 0.88/0.59 % (3526330)Instructions burned: 75 (million)
% 0.88/0.59 % (3526346)Instruction limit reached!
% 0.88/0.59 % (3526346)------------------------------
% 0.88/0.59 % (3526346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526346)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526346)Termination reason: Instruction limit
% 0.88/0.59 % (3526346)Termination phase: shuffling
% 0.88/0.59 % (3526346)Time elapsed: 0.005 s
% 0.88/0.59 % (3526346)Peak memory usage: 11 MB
% 0.88/0.59 % (3526346)Instructions burned: 5 (million)
% 0.88/0.59 % (3526349)Instruction limit reached!
% 0.88/0.59 % (3526349)------------------------------
% 0.88/0.59 % (3526349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526349)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526349)Termination reason: Instruction limit
% 0.88/0.59 % (3526349)Termination phase: shuffling
% 0.88/0.59 % (3526349)Time elapsed: 0.005 s
% 0.88/0.59 % (3526349)Peak memory usage: 10 MB
% 0.88/0.59 % (3526349)Instructions burned: 7 (million)
% 0.88/0.59 % (3526351)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2444310511:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.88/0.59 % (3526351)Instruction limit reached!
% 0.88/0.59 % (3526351)------------------------------
% 0.88/0.59 % (3526351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526351)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526351)Termination reason: Instruction limit
% 0.88/0.59 % (3526351)Termination phase: shuffling
% 0.88/0.59 % (3526351)Time elapsed: 0.011 s
% 0.88/0.59 % (3526351)Peak memory usage: 10 MB
% 0.88/0.59 % (3526351)Instructions burned: 13 (million)
% 0.88/0.59 % (3526325)Instruction limit reached!
% 0.88/0.59 % (3526325)------------------------------
% 0.88/0.59 % (3526325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526325)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526325)Termination reason: Instruction limit
% 0.88/0.59 % (3526325)Termination phase: SInE selection
% 0.88/0.59 % (3526325)Time elapsed: 0.070 s
% 0.88/0.59 % (3526325)Peak memory usage: 12 MB
% 0.88/0.59 % (3526325)Instructions burned: 88 (million)
% 0.88/0.59 % (3526362)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.88/0.59 % (3526362)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.88/0.59 % (3526362)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3608676546:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 0.88/0.59 % (3526364)lrs+10_1_si=on:cs=on:random_seed=2841842704:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.88/0.59 % (3526363)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2640934300:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.88/0.59 % (3526364)Instruction limit reached!
% 0.88/0.59 % (3526364)------------------------------
% 0.88/0.59 % (3526364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526364)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526364)Termination reason: Instruction limit
% 0.88/0.59 % (3526364)Termination phase: shuffling
% 0.88/0.59 % (3526364)Time elapsed: 0.007 s
% 0.88/0.59 % (3526364)Peak memory usage: 10 MB
% 0.88/0.59 % (3526364)Instructions burned: 8 (million)
% 0.88/0.59 % (3526369)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.88/0.59 % (3526369)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2444039850:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.88/0.59 % (3526371)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2178850976:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.88/0.59 % (3526369)Instruction limit reached!
% 0.88/0.59 % (3526369)------------------------------
% 0.88/0.59 % (3526369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526369)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526369)Termination reason: Instruction limit
% 0.88/0.59 % (3526369)Termination phase: shuffling
% 0.88/0.59 % (3526369)Time elapsed: 0.003 s
% 0.88/0.59 % (3526369)Peak memory usage: 10 MB
% 0.88/0.59 % (3526369)Instructions burned: 2 (million)
% 0.88/0.59 % (3526362)Instruction limit reached!
% 0.88/0.59 % (3526362)------------------------------
% 0.88/0.59 % (3526362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526362)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526362)Termination reason: Instruction limit
% 0.88/0.59 % (3526362)Termination phase: shuffling
% 0.88/0.59 % (3526362)Time elapsed: 0.025 s
% 0.88/0.59 % (3526362)Peak memory usage: 11 MB
% 0.88/0.59 % (3526362)Instructions burned: 29 (million)
% 0.88/0.59 % (3526380)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1673400438:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.88/0.59 % (3526371)Instruction limit reached!
% 0.88/0.59 % (3526371)------------------------------
% 0.88/0.59 % (3526371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526371)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526371)Termination reason: Instruction limit
% 0.88/0.59 % (3526371)Termination phase: shuffling
% 0.88/0.59 % (3526371)Time elapsed: 0.030 s
% 0.88/0.59 % (3526371)Peak memory usage: 11 MB
% 0.88/0.59 % (3526371)Instructions burned: 38 (million)
% 0.88/0.59 % (3526386)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2407224311:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.88/0.59 % (3526389)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2169577938:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.88/0.59 % (3526363)Instruction limit reached!
% 0.88/0.59 % (3526363)------------------------------
% 0.88/0.59 % (3526363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526363)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526363)Termination reason: Instruction limit
% 0.88/0.59 % (3526363)Termination phase: Property scanning
% 0.88/0.59 % (3526363)Time elapsed: 0.070 s
% 0.88/0.59 % (3526363)Peak memory usage: 12 MB
% 0.88/0.59 % (3526363)Instructions burned: 87 (million)
% 0.88/0.59 % (3526389)Instruction limit reached!
% 0.88/0.59 % (3526389)------------------------------
% 0.88/0.59 % (3526389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526389)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526389)Termination reason: Instruction limit
% 0.88/0.59 % (3526389)Termination phase: shuffling
% 0.88/0.59 % (3526389)Time elapsed: 0.013 s
% 0.88/0.59 % (3526389)Peak memory usage: 10 MB
% 0.88/0.59 % (3526389)Instructions burned: 15 (million)
% 0.88/0.59 % (3526386)Instruction limit reached!
% 0.88/0.59 % (3526386)------------------------------
% 0.88/0.59 % (3526386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526386)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526386)Termination reason: Instruction limit
% 0.88/0.59 % (3526386)Termination phase: shuffling
% 0.88/0.59 % (3526386)Time elapsed: 0.021 s
% 0.88/0.59 % (3526386)Peak memory usage: 11 MB
% 0.88/0.59 % (3526386)Instructions burned: 25 (million)
% 0.88/0.59 % (3526394)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=110876675:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.88/0.59 % (3526328) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3526317-3526328"...
% 0.88/0.59 % (3526328)...printing done.
% 0.88/0.59 % (3526328)Refutation found. Thanks to Tanya!
% 0.88/0.59 % SZS status Theorem for theBenchmark
% 0.88/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.88/0.59 % (3526328)------------------------------
% 0.88/0.59 % (3526328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.59 % (3526328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.59 % (3526328)CaDiCaL version: 2.1.3
% 0.88/0.59 % (3526328)Termination reason: Refutation
% 0.88/0.59 % (3526328)Time elapsed: 0.159 s
% 0.88/0.59 % (3526328)Peak memory usage: 16 MB
% 0.88/0.59 % (3526328)Instructions burned: 322 (million)
% 0.88/0.59 % (3526317)Success in time 0.239 s
% 0.88/0.59 % Vampire exiting
%------------------------------------------------------------------------------