%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT171^1 : TPTP v9.3.1. Released v5.3.0.
% 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 08:21:49 AM UTC 2026
% Result : Theorem 0.80s 0.41s
% Output : Refutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 213 ( 25 equ; 0 cnn)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 372 ( 10 ~; 4 |; 0 &; 355 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 122 ( 119 usr; 10 con; 0-6 aty)
% Number of variables : 12 ( 0 sgn 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
arrow_1346734812le_alt: $tType ).
thf(type_def_6,type,
arrow_1092341143e_indi: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
produc1832616231le_alt: $tType ).
thf(type_def_9,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
all: ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_1,type,
arrow_1724561858le_IIA: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_2,type,
arrow_1751445586le_Lin: ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_3,type,
arrow_1605628760e_Prof: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(func_def_4,type,
arrow_452340254_above: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(func_def_5,type,
arrow_1098709355ctator: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ).
thf(func_def_6,type,
arrow_1717184938_mkbot: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(func_def_7,type,
arrow_1865892024_mktop: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(func_def_8,type,
arrow_1889221221nimity: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_9,type,
finite1907699781e_indi: ( arrow_1092341143e_indi > $o ) > nat ).
thf(func_def_10,type,
inj_on945046484di_nat: ( arrow_1092341143e_indi > nat ) > ( arrow_1092341143e_indi > $o ) > $o ).
thf(func_def_11,type,
pi_Arr1422400881lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_12,type,
pi_Arr1941314005e_indi: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
thf(func_def_13,type,
pi_Arr1021537730_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_14,type,
pi_Arr1767527177lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_15,type,
pi_Arr170420797e_indi: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
thf(func_def_16,type,
pi_Pro410810898lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > $o > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_17,type,
pi_Pro1340600692e_indi: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
thf(func_def_18,type,
pi_o_A1302557673_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_19,type,
pi_o_A71242893_alt_o: ( $o > $o ) > ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(func_def_20,type,
pi_o_P1538584260_alt_o: ( $o > $o ) > ( $o > ( produc1832616231le_alt > $o ) > $o ) > ( $o > produc1832616231le_alt > $o ) > $o ).
thf(func_def_21,type,
pi_o_P988780107le_alt: ( $o > $o ) > ( $o > produc1832616231le_alt > $o ) > ( $o > produc1832616231le_alt ) > $o ).
thf(func_def_22,type,
pi_Arr1140519125_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_23,type,
pi_Arr651234977_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(func_def_24,type,
pi_Arr418143960_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(func_def_25,type,
pi_Arr1055270199le_alt: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt ) > $o ).
thf(func_def_26,type,
pi_Pro539263375_alt_o: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o > $o ) > ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_27,type,
pi_Pro1535452471e_indi: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > arrow_1092341143e_indi > $o ) > ( produc1832616231le_alt > arrow_1092341143e_indi ) > $o ).
thf(func_def_28,type,
hilber564731065di_nat: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > nat ) > nat > arrow_1092341143e_indi ).
thf(func_def_29,type,
if_Pro399136856_alt_o: $o > ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(func_def_30,type,
ord_le939309728lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_31,type,
ord_le972845494lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_32,type,
ord_le898419007lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_33,type,
ord_le316791758indi_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > $o ) > $o ).
thf(func_def_34,type,
ord_le1973646398_alt_o: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_35,type,
ord_less_o: $o > $o > $o ).
thf(func_def_36,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_37,type,
top_to1049332548lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_38,type,
top_to790289938lt_o_o: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(func_def_39,type,
top_to1830848411lt_o_o: ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_40,type,
top_top_o_o: $o > $o ).
thf(func_def_41,type,
top_to527331954indi_o: arrow_1092341143e_indi > $o ).
thf(func_def_42,type,
top_to679332578_alt_o: produc1832616231le_alt > $o ).
thf(func_def_43,type,
top_top_o: $o ).
thf(func_def_44,type,
produc990411159le_alt: arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt ).
thf(func_def_45,type,
collec2125720304_alt_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(func_def_46,type,
collec1718651462_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(func_def_47,type,
collec1079683069_alt_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_48,type,
collec1832628290e_indi: ( arrow_1092341143e_indi > $o ) > arrow_1092341143e_indi > $o ).
thf(func_def_49,type,
collec1201320914le_alt: ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(func_def_50,type,
member903234717lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_51,type,
member986213183e_indi: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
thf(func_def_52,type,
member733327538_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_53,type,
member1754345465lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_54,type,
member1208133347e_indi: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
thf(func_def_55,type,
member1949484546lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( ( produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_56,type,
member1255309082e_indi: ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
thf(func_def_57,type,
member1710515983_alt_o: ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_58,type,
member537117565_alt_o: ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_59,type,
member1099673524_alt_o: ( $o > produc1832616231le_alt > $o ) > ( ( $o > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_60,type,
member1368218865le_alt: ( $o > produc1832616231le_alt ) > ( ( $o > produc1832616231le_alt ) > $o ) > $o ).
thf(func_def_61,type,
member24189887_alt_o: ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_62,type,
member1079651021_alt_o: ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_63,type,
member1561882372_alt_o: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_64,type,
member1621875105le_alt: ( arrow_1092341143e_indi > produc1832616231le_alt ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt ) > $o ) > $o ).
thf(func_def_65,type,
member1362619835_alt_o: ( produc1832616231le_alt > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
thf(func_def_66,type,
member1486844321e_indi: ( produc1832616231le_alt > arrow_1092341143e_indi ) > ( ( produc1832616231le_alt > arrow_1092341143e_indi ) > $o ) > $o ).
thf(func_def_67,type,
member_o: $o > ( $o > $o ) > $o ).
thf(func_def_68,type,
member1714766084e_indi: arrow_1092341143e_indi > ( arrow_1092341143e_indi > $o ) > $o ).
thf(func_def_69,type,
member545531028le_alt: produc1832616231le_alt > ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_70,type,
f: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(func_def_71,type,
lab: produc1832616231le_alt > $o ).
thf(func_def_72,type,
lba: produc1832616231le_alt > $o ).
thf(func_def_73,type,
p: arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(func_def_74,type,
a: arrow_1346734812le_alt ).
thf(func_def_75,type,
b: arrow_1346734812le_alt ).
thf(func_def_76,type,
c: arrow_1346734812le_alt ).
thf(func_def_77,type,
d: arrow_1346734812le_alt ).
thf(func_def_78,type,
e: arrow_1346734812le_alt ).
thf(func_def_79,type,
h: arrow_1092341143e_indi > nat ).
thf(func_def_80,type,
n: nat ).
thf(func_def_84,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_85,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_86,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_87,type,
sP0: arrow_1092341143e_indi > $o ).
thf(func_def_88,type,
sP1: arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > ( produc1832616231le_alt > $o ) > $o ).
thf(func_def_89,type,
sP2: arrow_1092341143e_indi > $o ).
thf(func_def_90,type,
sP3: arrow_1092341143e_indi > $o ).
thf(func_def_91,type,
sK4: arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_92,type,
sK5: arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_93,type,
sK6: arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_94,type,
sK7: arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_95,type,
sK8: arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_96,type,
sK9: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_97,type,
sK10: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_98,type,
sK11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(func_def_99,type,
sK12: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(func_def_100,type,
sK13: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_101,type,
sK14: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_102,type,
sK15: arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_103,type,
sK16: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(func_def_104,type,
sK17: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_105,type,
sK18: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_106,type,
sK19: arrow_1346734812le_alt > arrow_1346734812le_alt > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ).
thf(func_def_107,type,
sK20: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_108,type,
sK21: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt ).
thf(func_def_109,type,
sK22: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > nat ) > arrow_1092341143e_indi ).
thf(func_def_110,type,
sK23: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > nat ) > arrow_1092341143e_indi ).
thf(func_def_111,type,
sK24: ( arrow_1092341143e_indi > nat ) > ( nat > arrow_1092341143e_indi ) > nat ).
thf(func_def_112,type,
sK25: ( arrow_1092341143e_indi > nat ) > arrow_1092341143e_indi ).
thf(func_def_113,type,
sK26: ( arrow_1092341143e_indi > nat ) > arrow_1092341143e_indi ).
thf(func_def_114,type,
sK27: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(func_def_115,type,
sK28: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > arrow_1346734812le_alt ).
thf(func_def_116,type,
sK29: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > arrow_1346734812le_alt ).
thf(func_def_117,type,
sK30: arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(func_def_118,type,
sK31: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(func_def_119,type,
vNOT: $o > $o ).
thf(f14,axiom,
( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_452340254_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ X0 ) @ e ) ) ) ) ),
file('/export/starexec/sandbox/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,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_452340254_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ X0 ) @ e ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
thf(f202,conjecture,
member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f203,negated_conjecture,
~ ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) ),
inference(negated_conjecture,[status(cth)],[f202]) ).
thf(f228,plain,
( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_452340254_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ X0 ) @ e ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f229,plain,
( $true
= ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(fool_elimination,[],[f228]) ).
thf(f230,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_452340254_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ X0 ) @ e ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f231,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
= ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(fool_elimination,[],[f230]) ).
thf(f595,plain,
~ ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) ),
inference(rectify,[],[f203]) ).
thf(f596,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(fool_elimination,[],[f595]) ).
thf(f644,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(flattening,[],[f596]) ).
thf(f953,plain,
( $true
= ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(cnf_transformation,[],[f229]) ).
thf(f954,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
= ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f1207,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(cnf_transformation,[],[f644]) ).
thf(f1323,plain,
( ( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
= $true )
| ( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f954]) ).
thf(f1468,definition,
( spl32_21
<=> ( $true
= ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl32_21])],[avatar_definition]) ).
thf(f1470,plain,
( ( $true
= ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) )
| ~ spl32_21 ),
inference(avatar_component_clause,[],[f1468]) ).
thf(f1476,plain,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_452340254_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false ),
inference(forward_subsumption_resolution,[],[f1323,f1207]) ).
thf(f1477,plain,
spl32_21,
inference(avatar_split_clause,[],[f953,f1468]) ).
thf(f1532,plain,
( ( $true = $false )
| ~ spl32_21 ),
inference(forward_demodulation,[],[f1470,f1476]) ).
thf(f1533,plain,
( $false
| ~ spl32_21 ),
inference(trivial_inequality_removal,[],[f1532]) ).
thf(f1534,plain,
~ spl32_21,
inference(avatar_contradiction_clause,[],[f1533]) ).
cnf(s24,plain,
spl32_21,
inference(sat_conversion,[],[f1477]) ).
cnf(s27,plain,
~ spl32_21,
inference(sat_conversion,[],[f1534]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s24,s27]) ).
thf(f1535,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:32:09 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.80/0.41 % (3357674)Will run a generic schedule for satisfiability detection.
% 0.80/0.41 % (3357682)dis+10_1_sil=32000:sp=arity:random_seed=1676026450:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.80/0.41 % (3357680)% WARNING: option uhcvi not known.
% 0.80/0.41 % (3357680)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2281685623:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.80/0.41 % (3357679)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3563206282_2999 on theBenchmark for (2999ds/0Mi)
% 0.80/0.41 % (3357683)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1430240714:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.80/0.41 % (3357685)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4234233262:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.80/0.41 % (3357681)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3887302158:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.80/0.41 % (3357680)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.80/0.41 % (3357684)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2350108970:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.80/0.41 % (3357683)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.80/0.41 % (3357680)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.80/0.41 % Exception at run slice level
% 0.80/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.80/0.41 % (3357682)Instruction limit reached!
% 0.80/0.41 % (3357682)------------------------------
% 0.80/0.41 % (3357682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (3357682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (3357682)CaDiCaL version: 2.1.3
% 0.80/0.41 % (3357682)Termination reason: Instruction limit
% 0.80/0.41 % (3357682)Termination phase: Saturation
% 0.80/0.41 % (3357682)Time elapsed: 0.046 s
% 0.80/0.41 % (3357682)Peak memory usage: 13 MB
% 0.80/0.41 % (3357682)Instructions burned: 104 (million)
% 0.80/0.41 % (3357693)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1186104298:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.80/0.41 % Exception at run slice level
% 0.80/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.80/0.41 % (3357683)Instruction limit reached!
% 0.80/0.41 % (3357683)------------------------------
% 0.80/0.41 % (3357683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (3357683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (3357683)CaDiCaL version: 2.1.3
% 0.80/0.41 % (3357683)Termination reason: Instruction limit
% 0.80/0.41 % (3357683)Termination phase: Saturation
% 0.80/0.41 % (3357683)Time elapsed: 0.095 s
% 0.80/0.41 % (3357683)Peak memory usage: 12 MB
% 0.80/0.41 % (3357683)Instructions burned: 116 (million)
% 0.80/0.41 % (3357697)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=989926997:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.80/0.41 % (3357694)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1359476146:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.80/0.41 % (3357697)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.80/0.41 % (3357698)ott-21_1_sil=16000:fs=off:random_seed=332242033:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.80/0.41 % (3357684) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3357674-3357684"...
% 0.80/0.41 % (3357684)...printing done.
% 0.80/0.41 % (3357684)Refutation found. Thanks to Tanya!
% 0.80/0.41 % SZS status Theorem for theBenchmark
% 0.80/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.80/0.41 % (3357684)------------------------------
% 0.80/0.41 % (3357684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (3357684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (3357684)CaDiCaL version: 2.1.3
% 0.80/0.41 % (3357684)Termination reason: Refutation
% 0.80/0.41 % (3357684)Time elapsed: 0.105 s
% 0.80/0.41 % (3357684)Peak memory usage: 14 MB
% 0.80/0.41 % (3357684)Instructions burned: 128 (million)
% 0.80/0.41 % (3357674)Success in time 0.171 s
% 0.80/0.41 % Vampire exiting
%------------------------------------------------------------------------------