%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP140^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:31 AM UTC 2026
% Result : Theorem 0.32s 0.46s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 78 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 404 ( 30 ~; 21 |; 15 &; 320 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 37 ( 36 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 238 ( 235 usr; 16 con; 0-4 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1475944804lle_fm: $tType ).
thf(type_def_6,type,
produc1250255278lle_fm: $tType ).
thf(type_def_7,type,
set_Pr2012908090lle_tv: $tType ).
thf(type_def_8,type,
set_Pr698334450lle_tv: $tType ).
thf(type_def_9,type,
produc1720769084lle_tv: $tType ).
thf(type_def_10,type,
set_Pr2061825550lle_tv: $tType ).
thf(type_def_11,type,
set_Pr1943077434tv_nat: $tType ).
thf(type_def_12,type,
set_Pr292927124lle_tv: $tType ).
thf(type_def_13,type,
produc1852595672lle_tv: $tType ).
thf(type_def_14,type,
set_Pr1723822845lle_tv: $tType ).
thf(type_def_15,type,
set_Pr2120184979lle_fm: $tType ).
thf(type_def_16,type,
produc1443694919lle_tv: $tType ).
thf(type_def_17,type,
produc696645085lle_fm: $tType ).
thf(type_def_18,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_19,type,
set_Pr2014382200lle_tv: $tType ).
thf(type_def_20,type,
set_Pr1019238018lle_fm: $tType ).
thf(type_def_21,type,
set_Pr840833727at_nat: $tType ).
thf(type_def_22,type,
set_Pr560526279lle_tv: $tType ).
thf(type_def_23,type,
produc1647334210lle_tv: $tType ).
thf(type_def_24,type,
produc450659916lle_fm: $tType ).
thf(type_def_25,type,
set_Pr1357842111at_nat: $tType ).
thf(type_def_26,type,
produc596913417at_nat: $tType ).
thf(type_def_27,type,
produc931990033lle_tv: $tType ).
thf(type_def_28,type,
set_Pr1725653840tv_nat: $tType ).
thf(type_def_29,type,
set_Pr13445366lle_tv: $tType ).
thf(type_def_30,type,
produc1281043295at_nat: $tType ).
thf(type_def_31,type,
produc194167194tv_nat: $tType ).
thf(type_def_32,type,
produc270694976lle_tv: $tType ).
thf(type_def_33,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_34,type,
set_Pa1764573435lle_tv: $tType ).
thf(type_def_35,type,
product_prod_nat_nat: $tType ).
thf(type_def_36,type,
paraco1605129243lle_tv: $tType ).
thf(type_def_37,type,
paraco1604210848lle_fm: $tType ).
thf(type_def_38,type,
list_char: $tType ).
thf(type_def_39,type,
set_nat: $tType ).
thf(type_def_40,type,
nat: $tType ).
thf(type_def_41,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_1,type,
inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
thf(func_def_2,type,
inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
thf(func_def_3,type,
inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
thf(func_def_4,type,
inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
thf(func_def_5,type,
inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
thf(func_def_6,type,
inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_7,type,
inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
thf(func_def_8,type,
the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
thf(func_def_9,type,
the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_10,type,
if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_11,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_12,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_13,type,
ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o ).
thf(func_def_14,type,
ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o ).
thf(func_def_15,type,
order_769474267at_nat: ( nat > nat ) > $o ).
thf(func_def_16,type,
top_top_nat_o: nat > $o ).
thf(func_def_17,type,
top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
thf(func_def_18,type,
top_to632227436_nat_o: product_prod_nat_nat > $o ).
thf(func_def_19,type,
top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
thf(func_def_20,type,
top_to900819589_nat_o: produc194167194tv_nat > $o ).
thf(func_def_21,type,
top_top_o: $o ).
thf(func_def_22,type,
top_top_set_nat: set_nat ).
thf(func_def_23,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(func_def_24,type,
top_to138697918lle_tv: set_Pr2061825550lle_tv ).
thf(func_def_25,type,
top_to775056195lle_fm: set_Pr2120184979lle_fm ).
thf(func_def_26,type,
top_to1541413903at_nat: set_Pr1357842111at_nat ).
thf(func_def_27,type,
top_to449985143lle_tv: set_Pr560526279lle_tv ).
thf(func_def_28,type,
top_to1555900337at_nat: set_Pr1986765409at_nat ).
thf(func_def_29,type,
top_to1411004326lle_tv: set_Pr13445366lle_tv ).
thf(func_def_30,type,
top_to975729152tv_nat: set_Pr1725653840tv_nat ).
thf(func_def_31,type,
top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
thf(func_def_32,type,
paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
thf(func_def_33,type,
paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_34,type,
paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
thf(func_def_35,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(func_def_36,type,
paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_37,type,
paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_38,type,
paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_39,type,
paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_40,type,
paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
thf(func_def_41,type,
paraco367965286_Truth: paraco1604210848lle_fm ).
thf(func_def_42,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(func_def_43,type,
paraco793048302_Indet: nat > paraco1605129243lle_tv ).
thf(func_def_44,type,
paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_45,type,
paraco327635598_valid: paraco1604210848lle_fm > $o ).
thf(func_def_46,type,
paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
thf(func_def_47,type,
produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).
thf(func_def_48,type,
produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(func_def_49,type,
produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).
thf(func_def_50,type,
produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
thf(func_def_51,type,
produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
thf(func_def_52,type,
produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).
thf(func_def_53,type,
produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).
thf(func_def_54,type,
produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).
thf(func_def_55,type,
produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).
thf(func_def_56,type,
produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv ).
thf(func_def_57,type,
produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).
thf(func_def_58,type,
produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(func_def_59,type,
produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
thf(func_def_60,type,
produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(func_def_61,type,
produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
thf(func_def_62,type,
produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
thf(func_def_63,type,
produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
thf(func_def_64,type,
produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
thf(func_def_65,type,
produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
thf(func_def_66,type,
produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
thf(func_def_67,type,
produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(func_def_68,type,
produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_69,type,
produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
thf(func_def_70,type,
produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
thf(func_def_71,type,
produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(func_def_72,type,
produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
thf(func_def_73,type,
produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
thf(func_def_74,type,
produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
thf(func_def_75,type,
produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
thf(func_def_76,type,
produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
thf(func_def_77,type,
produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
thf(func_def_78,type,
produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(func_def_79,type,
produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(func_def_80,type,
produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_81,type,
produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
thf(func_def_82,type,
produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
thf(func_def_83,type,
produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
thf(func_def_84,type,
produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_85,type,
produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
thf(func_def_86,type,
produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
thf(func_def_87,type,
produc500618325at_nat: produc596913417at_nat > nat > nat ).
thf(func_def_88,type,
produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
thf(func_def_89,type,
produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
thf(func_def_90,type,
produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
thf(func_def_91,type,
produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
thf(func_def_92,type,
inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_93,type,
inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
thf(func_def_94,type,
inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
thf(func_def_95,type,
inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
thf(func_def_96,type,
total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_97,type,
total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
thf(func_def_98,type,
total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_99,type,
total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).
thf(func_def_100,type,
total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).
thf(func_def_101,type,
total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).
thf(func_def_102,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_103,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_104,type,
collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).
thf(func_def_105,type,
collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
thf(func_def_106,type,
collec791369802at_nat: ( produc1281043295at_nat > $o ) > set_Pr1357842111at_nat ).
thf(func_def_107,type,
collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
thf(func_def_108,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_109,type,
collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
thf(func_def_110,type,
collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
thf(func_def_111,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_112,type,
image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
thf(func_def_113,type,
image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
thf(func_def_114,type,
image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_115,type,
image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
thf(func_def_116,type,
image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
thf(func_def_117,type,
image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
thf(func_def_118,type,
image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
thf(func_def_119,type,
image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).
thf(func_def_120,type,
image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).
thf(func_def_121,type,
image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_122,type,
image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
thf(func_def_123,type,
image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
thf(func_def_124,type,
image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
thf(func_def_125,type,
image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
thf(func_def_126,type,
image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
thf(func_def_127,type,
image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
thf(func_def_128,type,
image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
thf(func_def_129,type,
image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
thf(func_def_130,type,
image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
thf(func_def_131,type,
image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
thf(func_def_132,type,
image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
thf(func_def_133,type,
image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
thf(func_def_134,type,
accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
thf(func_def_135,type,
lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).
thf(func_def_136,type,
lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).
thf(func_def_137,type,
lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
thf(func_def_138,type,
lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).
thf(func_def_139,type,
lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).
thf(func_def_140,type,
lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).
thf(func_def_141,type,
wf_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_142,type,
wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o ).
thf(func_def_143,type,
same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).
thf(func_def_144,type,
same_f1138187694lle_tv: ( ( nat > nat ) > $o ) > ( ( nat > nat ) > set_Pr2014382200lle_tv ) > set_Pr698334450lle_tv ).
thf(func_def_145,type,
member_nat: nat > set_nat > $o ).
thf(func_def_146,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_147,type,
member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).
thf(func_def_148,type,
member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
thf(func_def_149,type,
member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o ).
thf(func_def_150,type,
member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
thf(func_def_151,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_152,type,
member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
thf(func_def_153,type,
member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
thf(func_def_154,type,
member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).
thf(func_def_155,type,
member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
thf(func_def_156,type,
member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
thf(func_def_157,type,
member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
thf(func_def_158,type,
member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).
thf(func_def_159,type,
member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).
thf(func_def_160,type,
f: nat > nat ).
thf(func_def_161,type,
i: list_char > paraco1605129243lle_tv ).
thf(func_def_162,type,
p1: paraco1604210848lle_fm ).
thf(func_def_163,type,
p2: paraco1604210848lle_fm ).
thf(func_def_167,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_168,type,
vAND: $o > $o > $o ).
thf(func_def_169,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_170,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_171,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_172,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_173,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_174,type,
vIMP: $o > $o > $o ).
thf(func_def_175,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_176,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_177,type,
vNOT: $o > $o ).
thf(func_def_178,type,
vOR: $o > $o > $o ).
thf(func_def_179,type,
sP0: ( paraco1604210848lle_fm > $o ) > $o ).
thf(func_def_180,type,
sP1: ( paraco1604210848lle_fm > $o ) > $o ).
thf(func_def_181,type,
sP2: ( paraco1604210848lle_fm > $o ) > $o ).
thf(func_def_182,type,
sP3: ( paraco1604210848lle_fm > $o ) > $o ).
thf(func_def_183,type,
sK4: ( produc696645085lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_184,type,
sK5: ( produc696645085lle_fm > $o ) > list_char > paraco1605129243lle_tv ).
thf(func_def_185,type,
sK6: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_186,type,
sK7: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_187,type,
sK8: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_188,type,
sK9: paraco1604210848lle_fm > list_char ).
thf(func_def_189,type,
sK10: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_190,type,
sK11: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_191,type,
sK12: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_192,type,
sK13: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_193,type,
sK14: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_194,type,
sK15: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_195,type,
sK16: paraco1604210848lle_fm > list_char ).
thf(func_def_196,type,
sK17: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_197,type,
sK18: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_198,type,
sK19: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_199,type,
sK20: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_200,type,
sK21: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_201,type,
sK22: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_202,type,
sK23: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_203,type,
sK24: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_204,type,
sK25: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_205,type,
sK26: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_206,type,
sK27: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_207,type,
sK28: ( paraco1604210848lle_fm > $o ) > list_char ).
thf(func_def_208,type,
sK29: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_209,type,
sK30: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_210,type,
sK31: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_211,type,
sK32: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_212,type,
sK33: produc696645085lle_fm > list_char ).
thf(func_def_213,type,
sK34: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_214,type,
sK35: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_215,type,
sK36: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_216,type,
sK37: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_217,type,
sK38: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_218,type,
sK39: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_219,type,
sK40: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_220,type,
sK41: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_221,type,
sK42: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_222,type,
sK43: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_223,type,
sK44: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_224,type,
sK45: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_225,type,
sK46: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_226,type,
sK47: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_227,type,
sK48: ( produc696645085lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_228,type,
sK49: ( produc696645085lle_fm > $o ) > list_char > paraco1605129243lle_tv ).
thf(func_def_229,type,
sK50: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_230,type,
sK51: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_231,type,
sK52: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_232,type,
sK53: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_233,type,
sK54: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_234,type,
sK55: ( paraco1604210848lle_fm > $o ) > list_char ).
thf(func_def_235,type,
sK56: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_236,type,
sK57: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(f1,axiom,
( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ i @ p1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_a_H_H) ).
thf(f2,axiom,
( ( paraco1325918602e_eval @ i @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_a) ).
thf(f3,axiom,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ p2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_a_H) ).
thf(f6,axiom,
! [X1: paraco1604210848lle_fm,X2: paraco1604210848lle_fm,X0: list_char > paraco1605129243lle_tv] :
( ( ( ( paraco1325918602e_eval @ X0 @ X1 )
!= ( paraco1325918602e_eval @ X0 @ X2 ) )
=> ( ( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X0 @ X1 ) )
=> ( ( paraco1325918602e_eval @ X0 @ ( paraco69239110le_Con @ X1 @ X2 ) )
= ( paraco1325918602e_eval @ X0 @ X2 ) ) )
& ( ( ( paraco1325918602e_eval @ X0 @ X1 )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X0 @ X2 ) )
=> ( ( paraco1325918602e_eval @ X0 @ ( paraco69239110le_Con @ X1 @ X2 ) )
= ( paraco1325918602e_eval @ X0 @ X1 ) ) )
& ( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ X0 @ X2 ) )
=> ( ( paraco1344940915le_Det @ $false )
= ( paraco1325918602e_eval @ X0 @ ( paraco69239110le_Con @ X1 @ X2 ) ) ) ) ) ) ) )
& ( ( ( paraco1325918602e_eval @ X0 @ X1 )
= ( paraco1325918602e_eval @ X0 @ X2 ) )
=> ( ( paraco1325918602e_eval @ X0 @ ( paraco69239110le_Con @ X1 @ X2 ) )
= ( paraco1325918602e_eval @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_eval_Osimps_I4_J) ).
thf(f358,conjecture,
( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
= ( paraco1325918602e_eval @ i @ p1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f359,negated_conjecture,
( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
!= ( paraco1325918602e_eval @ i @ p1 ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f396,plain,
! [X0: paraco1604210848lle_fm,X1: paraco1604210848lle_fm,X2: list_char > paraco1605129243lle_tv] :
( ( ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X0 )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ X1 ) )
=> ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) )
& ( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ X2 @ X1 ) )
=> ( ( paraco1344940915le_Det @ $false )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) ) ) ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f397,plain,
! [X0: paraco1604210848lle_fm,X2: list_char > paraco1605129243lle_tv,X1: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1344940915le_Det @ $false )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) ) ) )
& ( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ X0 ) )
=> ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f396]) ).
thf(f517,plain,
( ( paraco1325918602e_eval @ i @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
inference(rectify,[],[f2]) ).
thf(f518,plain,
( ( paraco1325918602e_eval @ i @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
inference(fool_elimination,[],[f517]) ).
thf(f682,plain,
( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ i @ p1 ) ),
inference(rectify,[],[f1]) ).
thf(f683,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(fool_elimination,[],[f682]) ).
thf(f838,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) ) ),
inference(flattening,[],[f359]) ).
thf(f848,plain,
! [X1: paraco1604210848lle_fm,X0: paraco1604210848lle_fm,X2: list_char > paraco1605129243lle_tv] :
( ( ( ( ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) )
| ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ X2 @ X0 ) ) )
& ( ( ( ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1344940915le_Det @ $false )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) ) )
| ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ X0 ) ) ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ X0 ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1325918602e_eval @ X2 @ X0 ) )
| ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X0 @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f397]) ).
thf(f880,plain,
! [X0: paraco1604210848lle_fm,X1: paraco1604210848lle_fm,X2: list_char > paraco1605129243lle_tv] :
( ( ( ( ( ( paraco1325918602e_eval @ X2 @ X0 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X1 @ X0 ) ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ X2 @ X0 ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X1 @ X0 ) ) ) )
& ( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ X0 ) )
| ( ( paraco1344940915le_Det @ $false )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X1 @ X0 ) ) ) ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1344940915le_Det @ $true ) ) ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ X0 ) ) )
& ( ( ( paraco1325918602e_eval @ X2 @ X1 )
!= ( paraco1325918602e_eval @ X2 @ X0 ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f848]) ).
thf(f914,plain,
( ( paraco1325918602e_eval @ i @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
inference(cnf_transformation,[],[f518]) ).
thf(f923,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ p2 ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f931,plain,
! [X2: list_char > paraco1605129243lle_tv,X0: paraco1604210848lle_fm,X1: paraco1604210848lle_fm] :
( ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ ( paraco69239110le_Con @ X1 @ X0 ) ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1325918602e_eval @ X2 @ X0 ) )
| ( ( paraco1325918602e_eval @ X2 @ X1 )
= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f880]) ).
thf(f952,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) ) ),
inference(cnf_transformation,[],[f838]) ).
thf(f975,plain,
( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(cnf_transformation,[],[f683]) ).
thf(f980,plain,
( ( ( paraco1325918602e_eval @ i @ p1 )
= ( paraco1325918602e_eval @ i @ p2 ) )
| ( ( paraco1325918602e_eval @ i @ p1 )
!= ( paraco1325918602e_eval @ i @ p1 ) )
| ( ( paraco1325918602e_eval @ i @ p2 )
!= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1325918602e_eval @ i @ p1 )
= ( paraco1344940915le_Det @ $true ) ) ),
inference(superposition,[],[f952,f931]) ).
thf(f983,plain,
( ( ( paraco1325918602e_eval @ i @ p1 )
= ( paraco1325918602e_eval @ i @ p2 ) )
| ( ( paraco1325918602e_eval @ i @ p1 )
= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1325918602e_eval @ i @ p2 )
!= ( paraco1344940915le_Det @ $true ) ) ),
inference(trivial_inequality_removal,[],[f980]) ).
thf(f984,plain,
( ( ( paraco1325918602e_eval @ i @ p1 )
= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1325918602e_eval @ i @ p2 )
!= ( paraco1344940915le_Det @ $true ) ) ),
inference(forward_subsumption_resolution,[],[f983,f923]) ).
thf(f985,plain,
( ( paraco1325918602e_eval @ i @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(forward_subsumption_resolution,[],[f984,f975]) ).
thf(f986,plain,
$false,
inference(forward_subsumption_resolution,[],[f985,f914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP140^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:59:15 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.21/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/0.45 % (3137182)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.45 % (3137194)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4235955780:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.32/0.45 % (3137196)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.32/0.45 % (3137196)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
% 0.32/0.45 % (3137194)Instruction limit reached!
% 0.32/0.45 % (3137194)------------------------------
% 0.32/0.45 % (3137194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137194)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137194)Termination reason: Instruction limit
% 0.32/0.45 % (3137194)Termination phase: Property scanning
% 0.32/0.45 % (3137194)Time elapsed: 0.006 s
% 0.32/0.45 % (3137194)Peak memory usage: 11 MB
% 0.32/0.45 % (3137194)Instructions burned: 25 (million)
% 0.32/0.45 % (3137190)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2130973473:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.45 % (3137191)lrs+10_16_si=on:nwc=1.5:random_seed=1166834884:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.45 % (3137192)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3897403818:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.45 % (3137193)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=552806292: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)
% 0.32/0.45 % (3137195)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2771948912:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.32/0.45 % (3137196)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=1761459869:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.32/0.45 % (3137192)Instruction limit reached!
% 0.32/0.45 % (3137192)------------------------------
% 0.32/0.45 % (3137192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137192)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137192)Termination reason: Instruction limit
% 0.32/0.45 % (3137192)Termination phase: shuffling
% 0.32/0.45 % (3137192)Time elapsed: 0.002 s
% 0.32/0.45 % (3137192)Peak memory usage: 10 MB
% 0.32/0.45 % (3137192)Instructions burned: 3 (million)
% 0.32/0.45 % (3137191)Instruction limit reached!
% 0.32/0.45 % (3137191)------------------------------
% 0.32/0.45 % (3137191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137191)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137191)Termination reason: Instruction limit
% 0.32/0.45 % (3137191)Termination phase: shuffling
% 0.32/0.45 % (3137191)Time elapsed: 0.008 s
% 0.32/0.45 % (3137191)Peak memory usage: 10 MB
% 0.32/0.45 % (3137191)Instructions burned: 18 (million)
% 0.32/0.45 % (3137201)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4198223875:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.45 % (3137201)Instruction limit reached!
% 0.32/0.45 % (3137201)------------------------------
% 0.32/0.45 % (3137201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137201)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137201)Termination reason: Instruction limit
% 0.32/0.45 % (3137201)Termination phase: shuffling
% 0.32/0.45 % (3137201)Time elapsed: 0.002 s
% 0.32/0.45 % (3137201)Peak memory usage: 10 MB
% 0.32/0.45 % (3137201)Instructions burned: 3 (million)
% 0.32/0.45 % (3137205)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=333670733:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.32/0.45 % (3137206)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.32/0.45 % (3137205)Instruction limit reached!
% 0.32/0.45 % (3137205)------------------------------
% 0.32/0.45 % (3137205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137205)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137205)Termination reason: Instruction limit
% 0.32/0.45 % (3137205)Termination phase: shuffling
% 0.32/0.45 % (3137205)Time elapsed: 0.003 s
% 0.32/0.45 % (3137205)Peak memory usage: 10 MB
% 0.32/0.45 % (3137205)Instructions burned: 6 (million)
% 0.32/0.45 % (3137206)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2276988990:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.32/0.45 % (3137209)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2667416765:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.32/0.45 % (3137206)Instruction limit reached!
% 0.32/0.45 % (3137206)------------------------------
% 0.32/0.45 % (3137206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137206)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137206)Termination reason: Instruction limit
% 0.32/0.45 % (3137206)Termination phase: shuffling
% 0.32/0.45 % (3137206)Time elapsed: 0.004 s
% 0.32/0.45 % (3137206)Peak memory usage: 10 MB
% 0.32/0.45 % (3137206)Instructions burned: 8 (million)
% 0.32/0.45 % (3137209)Instruction limit reached!
% 0.32/0.45 % (3137209)------------------------------
% 0.32/0.45 % (3137209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3137209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3137209)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3137209)Termination reason: Instruction limit
% 0.32/0.45 % (3137209)Termination phase: shuffling
% 0.32/0.45 % (3137209)Time elapsed: 0.004 s
% 0.32/0.45 % (3137209)Peak memory usage: 10 MB
% 0.32/0.46 % (3137209)Instructions burned: 16 (million)
% 0.32/0.46 % (3137195)Instruction limit reached!
% 0.32/0.46 % (3137195)------------------------------
% 0.32/0.46 % (3137195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137195)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137195)Termination reason: Instruction limit
% 0.32/0.46 % (3137195)Termination phase: Property scanning
% 0.32/0.46 % (3137195)Time elapsed: 0.036 s
% 0.32/0.46 % (3137195)Peak memory usage: 12 MB
% 0.32/0.46 % (3137195)Instructions burned: 77 (million)
% 0.32/0.46 % (3137210)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
% 0.32/0.46 % (3137210)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.32/0.46 % (3137190)Instruction limit reached!
% 0.32/0.46 % (3137190)------------------------------
% 0.32/0.46 % (3137190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137190)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137190)Termination reason: Instruction limit
% 0.32/0.46 % (3137190)Termination phase: Property scanning
% 0.32/0.46 % (3137190)Time elapsed: 0.041 s
% 0.32/0.46 % (3137190)Peak memory usage: 12 MB
% 0.32/0.46 % (3137190)Instructions burned: 89 (million)
% 0.32/0.46 % (3137210)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2570158186:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.32/0.46 % (3137214)lrs+10_1_si=on:cs=on:random_seed=32609930:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.32/0.46 % (3137214)Instruction limit reached!
% 0.32/0.46 % (3137214)------------------------------
% 0.32/0.46 % (3137214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137214)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137214)Termination reason: Instruction limit
% 0.32/0.46 % (3137214)Termination phase: shuffling
% 0.32/0.46 % (3137214)Time elapsed: 0.002 s
% 0.32/0.46 % (3137214)Peak memory usage: 10 MB
% 0.32/0.46 % (3137214)Instructions burned: 9 (million)
% 0.32/0.46 % (3137213)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=2392103694:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.32/0.46 % (3137215)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.32/0.46 % (3137215)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=389337621:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.46 % (3137210)Instruction limit reached!
% 0.32/0.46 % (3137210)------------------------------
% 0.32/0.46 % (3137210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137210)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137210)Termination reason: Instruction limit
% 0.32/0.46 % (3137210)Termination phase: shuffling
% 0.32/0.46 % (3137210)Time elapsed: 0.013 s
% 0.32/0.46 % (3137210)Peak memory usage: 11 MB
% 0.32/0.46 % (3137210)Instructions burned: 29 (million)
% 0.32/0.46 % (3137219)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4100921519:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.32/0.46 % (3137215)Instruction limit reached!
% 0.32/0.46 % (3137215)------------------------------
% 0.32/0.46 % (3137215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137216)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2547733560:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.32/0.46 % (3137215)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137215)Termination reason: Instruction limit
% 0.32/0.46 % (3137215)Termination phase: shuffling
% 0.32/0.46 % (3137215)Time elapsed: 0.004 s
% 0.32/0.46 % (3137215)Peak memory usage: 10 MB
% 0.32/0.46 % (3137215)Instructions burned: 7 (million)
% 0.32/0.46 % (3137196)Instruction limit reached!
% 0.32/0.46 % (3137196)------------------------------
% 0.32/0.46 % (3137196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137196)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137196)Termination reason: Instruction limit
% 0.32/0.46 % (3137196)Termination phase: Saturation
% 0.32/0.46 % (3137196)Time elapsed: 0.070 s
% 0.32/0.46 % (3137196)Peak memory usage: 14 MB
% 0.32/0.46 % (3137196)Instructions burned: 159 (million)
% 0.32/0.46 % (3137219) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3137182-3137219"...
% 0.32/0.46 % (3137219)...printing done.
% 0.32/0.46 % (3137222)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3228048794:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.32/0.46 % (3137216)Instruction limit reached!
% 0.32/0.46 % (3137216)------------------------------
% 0.32/0.46 % (3137216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137216)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137216)Termination reason: Instruction limit
% 0.32/0.46 % (3137216)Termination phase: Preprocessing 3
% 0.32/0.46 % (3137216)Time elapsed: 0.018 s
% 0.32/0.46 % (3137216)Peak memory usage: 11 MB
% 0.32/0.46 % (3137216)Instructions burned: 39 (million)
% 0.32/0.46 % (3137219)Refutation found. Thanks to Tanya!
% 0.32/0.46 % SZS status Theorem for theBenchmark
% 0.32/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/0.46 % (3137219)------------------------------
% 0.32/0.46 % (3137219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (3137219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (3137219)CaDiCaL version: 2.1.3
% 0.32/0.46 % (3137219)Termination reason: Refutation
% 0.32/0.46 % (3137219)Time elapsed: 0.015 s
% 0.32/0.46 % (3137219)Peak memory usage: 13 MB
% 0.32/0.46 % (3137219)Instructions burned: 60 (million)
% 0.32/0.46 % (3137182)Success in time 0.139 s
% 0.32/0.46 % Vampire exiting
%------------------------------------------------------------------------------