%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP027^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:08:01 AM UTC 2026
% Result : Theorem 0.82s 0.54s
% Output : Refutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 227 ( 95 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 887 ( 34 ~; 27 |; 38 &; 760 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 55 ( 54 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 238 ( 235 usr; 5 con; 0-6 aty)
% Number of variables : 71 ( 18 ^; 52 !; 1 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
carrie1954260683t_unit: $tType ).
thf(type_def_6,type,
carrie1948989069_d_a_e: $tType ).
thf(type_def_7,type,
carrie1105631105xt_a_b: $tType ).
thf(type_def_8,type,
set_a_a_c_d_c_d: $tType ).
thf(type_def_9,type,
set_c_d_c_d_c_d: $tType ).
thf(type_def_10,type,
set_a_a_a_a_a_d: $tType ).
thf(type_def_11,type,
set_a_a_a_a_a: $tType ).
thf(type_def_12,type,
set_a_c_d_c_d: $tType ).
thf(type_def_13,type,
set_c_d_a_a_a: $tType ).
thf(type_def_14,type,
set_c_d_c_d_a: $tType ).
thf(type_def_15,type,
set_c_d_a_a_a2: $tType ).
thf(type_def_16,type,
set_a_a_a_c_d: $tType ).
thf(type_def_17,type,
set_a_a_a_a_a2: $tType ).
thf(type_def_18,type,
set_a_a_c_d_d: $tType ).
thf(type_def_19,type,
set_a_a_c_d_a: $tType ).
thf(type_def_20,type,
set_a_a_a_a_d: $tType ).
thf(type_def_21,type,
set_a_a_a_a_a3: $tType ).
thf(type_def_22,type,
set_c_d_c_d_d: $tType ).
thf(type_def_23,type,
set_c_d_c_d_a2: $tType ).
thf(type_def_24,type,
set_a_a_c_d: $tType ).
thf(type_def_25,type,
set_a_a_a_a: $tType ).
thf(type_def_26,type,
set_a_c_d_a: $tType ).
thf(type_def_27,type,
set_a_a_a_a2: $tType ).
thf(type_def_28,type,
set_c_d_c_d: $tType ).
thf(type_def_29,type,
set_c_d_a_a: $tType ).
thf(type_def_30,type,
set_a_a_c_d2: $tType ).
thf(type_def_31,type,
set_a_a_a_a3: $tType ).
thf(type_def_32,type,
set_a_a_a_d: $tType ).
thf(type_def_33,type,
set_a_a_a_a4: $tType ).
thf(type_def_34,type,
set_d_c_d: $tType ).
thf(type_def_35,type,
set_c_c_d: $tType ).
thf(type_def_36,type,
set_a_c_d: $tType ).
thf(type_def_37,type,
set_a_a_a: $tType ).
thf(type_def_38,type,
set_c_d_d: $tType ).
thf(type_def_39,type,
set_c_d_a: $tType ).
thf(type_def_40,type,
set_a_a_d: $tType ).
thf(type_def_41,type,
set_a_a_a2: $tType ).
thf(type_def_42,type,
set_d_d: $tType ).
thf(type_def_43,type,
set_d_c: $tType ).
thf(type_def_44,type,
set_d_a: $tType ).
thf(type_def_45,type,
set_c_d: $tType ).
thf(type_def_46,type,
set_c_c: $tType ).
thf(type_def_47,type,
set_c_a: $tType ).
thf(type_def_48,type,
set_a_d: $tType ).
thf(type_def_49,type,
set_a_c: $tType ).
thf(type_def_50,type,
set_a_a: $tType ).
thf(type_def_51,type,
set_nat: $tType ).
thf(type_def_52,type,
set_d: $tType ).
thf(type_def_53,type,
set_c: $tType ).
thf(type_def_54,type,
set_a: $tType ).
thf(type_def_55,type,
nat: $tType ).
thf(type_def_56,type,
d: $tType ).
thf(type_def_57,type,
c: $tType ).
thf(type_def_58,type,
a: $tType ).
thf(type_def_59,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
carrie20288686t_unit: carrie1954260683t_unit > set_c_d ).
thf(func_def_1,type,
carrie867757212xt_a_b: carrie1105631105xt_a_b > set_a ).
thf(func_def_2,type,
carrie11369756_d_a_e: carrie1948989069_d_a_e > set_d ).
thf(func_def_3,type,
j_rad_a_b: carrie1105631105xt_a_b > set_a ).
thf(func_def_4,type,
ring_a_b: carrie1105631105xt_a_b > $o ).
thf(func_def_5,type,
tp_a_b: carrie1105631105xt_a_b > a > a > a ).
thf(func_def_6,type,
un_a_b: carrie1105631105xt_a_b > a ).
thf(func_def_7,type,
sr_a_b: carrie1105631105xt_a_b > set_a > carrie1105631105xt_a_b ).
thf(func_def_8,type,
subring_a_b_b: carrie1105631105xt_a_b > carrie1105631105xt_a_b > $o ).
thf(func_def_9,type,
unit_a_b: carrie1105631105xt_a_b > a > $o ).
thf(func_def_10,type,
aGroup2131905830t_unit: carrie1954260683t_unit > $o ).
thf(func_def_11,type,
aGroup2097840802xt_a_b: carrie1105631105xt_a_b > $o ).
thf(func_def_12,type,
aGroup1940521469_d_a_e: carrie1948989069_d_a_e > $o ).
thf(func_def_13,type,
mop_a_Ring_ext_a_b: carrie1105631105xt_a_b > a > a ).
thf(func_def_14,type,
pop_c_449750139t_unit: carrie1954260683t_unit > ( c > d ) > ( c > d ) > c > d ).
thf(func_def_15,type,
pop_a_Ring_ext_a_b: carrie1105631105xt_a_b > a > a > a ).
thf(func_def_16,type,
pop_d_261713874_d_a_e: carrie1948989069_d_a_e > d > d > d ).
thf(func_def_17,type,
aset_s1743553894xt_a_b: carrie1105631105xt_a_b > set_a > set_a > set_a ).
thf(func_def_18,type,
carr_d267359390xt_a_b: set_a > ( a > carrie1105631105xt_a_b ) > set_a_a ).
thf(func_def_19,type,
carr_d56066307_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > set_c_d ).
thf(func_def_20,type,
carr_p1617094073xt_a_b: set_c_d_c_d > ( ( ( c > d ) > c > d ) > carrie1105631105xt_a_b ) > set_c_d_c_d_a2 ).
thf(func_def_21,type,
carr_p428609062_d_a_e: set_c_d_c_d > ( ( ( c > d ) > c > d ) > carrie1948989069_d_a_e ) > set_c_d_c_d_d ).
thf(func_def_22,type,
carr_p1980447933_d_a_e: set_a_a_a_a_a > ( ( a > a > a > a > a ) > carrie1948989069_d_a_e ) > set_a_a_a_a_a_d ).
thf(func_def_23,type,
carr_p1850824937xt_a_b: set_a_a_a_a > ( ( a > a > a > a ) > carrie1105631105xt_a_b ) > set_a_a_a_a_a3 ).
thf(func_def_24,type,
carr_p305487606_d_a_e: set_a_a_a_a > ( ( a > a > a > a ) > carrie1948989069_d_a_e ) > set_a_a_a_a_d ).
thf(func_def_25,type,
carr_p109409832xt_a_b: set_a_a_c_d > ( ( a > a > c > d ) > carrie1105631105xt_a_b ) > set_a_a_c_d_a ).
thf(func_def_26,type,
carr_p577380087_d_a_e: set_a_a_c_d > ( ( a > a > c > d ) > carrie1948989069_d_a_e ) > set_a_a_c_d_d ).
thf(func_def_27,type,
carr_p1481099064xt_a_b: set_a_a_a > ( ( a > a > a ) > carrie1105631105xt_a_b ) > set_a_a_a_a4 ).
thf(func_def_28,type,
carr_p1364179431_d_a_e: set_a_a_a > ( ( a > a > a ) > carrie1948989069_d_a_e ) > set_a_a_a_d ).
thf(func_def_29,type,
carr_p740328767xt_a_b: set_a_a > ( ( a > a ) > carrie1105631105xt_a_b ) > set_a_a_a2 ).
thf(func_def_30,type,
carr_p1646427936_d_a_e: set_a_a > ( ( a > a ) > carrie1948989069_d_a_e ) > set_a_a_d ).
thf(func_def_31,type,
carr_p996491646xt_a_b: set_c_d > ( ( c > d ) > carrie1105631105xt_a_b ) > set_c_d_a ).
thf(func_def_32,type,
carr_p124510241_d_a_e: set_c_d > ( ( c > d ) > carrie1948989069_d_a_e ) > set_c_d_d ).
thf(func_def_33,type,
carr_p923087418t_unit: set_a > ( a > carrie1954260683t_unit ) > set_a_c_d ).
thf(func_def_34,type,
carr_p290614414xt_a_b: set_a > ( a > carrie1105631105xt_a_b ) > set_a_a ).
thf(func_def_35,type,
carr_p1084104977_d_a_e: set_a > ( a > carrie1948989069_d_a_e ) > set_a_d ).
thf(func_def_36,type,
carr_p1080792380t_unit: set_c > ( c > carrie1954260683t_unit ) > set_c_c_d ).
thf(func_def_37,type,
carr_p295160588xt_a_b: set_c > ( c > carrie1105631105xt_a_b ) > set_c_a ).
thf(func_def_38,type,
carr_p1636662547_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > set_c_d ).
thf(func_def_39,type,
carr_p1159644861t_unit: set_d > ( d > carrie1954260683t_unit ) > set_d_c_d ).
thf(func_def_40,type,
carr_p297433675xt_a_b: set_d > ( d > carrie1105631105xt_a_b ) > set_d_a ).
thf(func_def_41,type,
carr_p1912941332_d_a_e: set_d > ( d > carrie1948989069_d_a_e ) > set_d_d ).
thf(func_def_42,type,
local_ring_a_b: carrie1105631105xt_a_b > $o ).
thf(func_def_43,type,
maximal_ideal_a_b: carrie1105631105xt_a_b > set_a > $o ).
thf(func_def_44,type,
mul_closed_set_a_b: carrie1105631105xt_a_b > set_a > $o ).
thf(func_def_45,type,
nscal_a_b: carrie1105631105xt_a_b > a > nat > a ).
thf(func_def_46,type,
primary_ideal_a_b: carrie1105631105xt_a_b > set_a > $o ).
thf(func_def_47,type,
prod_m2022989242xt_a_b: set_a > ( a > carrie1105631105xt_a_b ) > ( a > a ) > a > a ).
thf(func_def_48,type,
prod_m854557927_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > ( c > d ) > c > d ).
thf(func_def_49,type,
prod_p1959959370xt_a_b: set_c_d_c_d > ( ( ( c > d ) > c > d ) > carrie1105631105xt_a_b ) > ( ( ( c > d ) > c > d ) > a ) > ( ( ( c > d ) > c > d ) > a ) > ( ( c > d ) > c > d ) > a ).
thf(func_def_50,type,
prod_p46206586xt_a_b: set_a_a_a_a > ( ( a > a > a > a ) > carrie1105631105xt_a_b ) > ( ( a > a > a > a ) > a ) > ( ( a > a > a > a ) > a ) > ( a > a > a > a ) > a ).
thf(func_def_51,type,
prod_p452275129xt_a_b: set_a_a_c_d > ( ( a > a > c > d ) > carrie1105631105xt_a_b ) > ( ( a > a > c > d ) > a ) > ( ( a > a > c > d ) > a ) > ( a > a > c > d ) > a ).
thf(func_def_52,type,
prod_p1460711911xt_a_b: set_a_a_a > ( ( a > a > a ) > carrie1105631105xt_a_b ) > ( ( a > a > a ) > a ) > ( ( a > a > a ) > a ) > ( a > a > a ) > a ).
thf(func_def_53,type,
prod_p1210452560xt_a_b: set_a_a > ( ( a > a ) > carrie1105631105xt_a_b ) > ( ( a > a ) > a ) > ( ( a > a ) > a ) > ( a > a ) > a ).
thf(func_def_54,type,
prod_p1466615439xt_a_b: set_c_d > ( ( c > d ) > carrie1105631105xt_a_b ) > ( ( c > d ) > a ) > ( ( c > d ) > a ) > ( c > d ) > a ).
thf(func_def_55,type,
prod_p704341949xt_a_b: set_a > ( a > carrie1105631105xt_a_b ) > ( a > a ) > ( a > a ) > a > a ).
thf(func_def_56,type,
prod_p708888123xt_a_b: set_c > ( c > carrie1105631105xt_a_b ) > ( c > a ) > ( c > a ) > c > a ).
thf(func_def_57,type,
prod_p131511076_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > ( c > d ) > ( c > d ) > c > d ).
thf(func_def_58,type,
prod_p711161210xt_a_b: set_d > ( d > carrie1105631105xt_a_b ) > ( d > a ) > ( d > a ) > d > a ).
thf(func_def_59,type,
prod_z851058290xt_a_b: set_a > ( a > carrie1105631105xt_a_b ) > a > a ).
thf(func_def_60,type,
prod_z1214987823_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > c > d ).
thf(func_def_61,type,
sr_a_b2: carrie1105631105xt_a_b > set_a > $o ).
thf(func_def_62,type,
zeroring_a_b: carrie1105631105xt_a_b > $o ).
thf(func_def_63,type,
sum_mult_a_b: carrie1105631105xt_a_b > set_a > set_a > set_a ).
thf(func_def_64,type,
module1440397025unit_b: carrie1954260683t_unit > carrie1105631105xt_a_b > $o ).
thf(func_def_65,type,
module_d_a_e_b: carrie1948989069_d_a_e > carrie1105631105xt_a_b > $o ).
thf(func_def_66,type,
sprod_1929599593t_unit: carrie1954260683t_unit > a > ( c > d ) > c > d ).
thf(func_def_67,type,
sprod_d_a_e: carrie1948989069_d_a_e > a > d > d ).
thf(func_def_68,type,
mHom_a1526663829t_unit: carrie1105631105xt_a_b > carrie1954260683t_unit > carrie1954260683t_unit > set_c_d_c_d ).
thf(func_def_69,type,
mHom_a764575953it_d_e: carrie1105631105xt_a_b > carrie1954260683t_unit > carrie1948989069_d_a_e > set_c_d_d ).
thf(func_def_70,type,
mHom_a_b_d_e_d_e: carrie1105631105xt_a_b > carrie1948989069_d_a_e > carrie1948989069_d_a_e > set_d_d ).
thf(func_def_71,type,
algebr1968153176_c_d_e: carrie1105631105xt_a_b > set_c > ( c > carrie1948989069_d_a_e ) > carrie1954260683t_unit ).
thf(func_def_72,type,
algebr828196337_d_d_e: carrie1105631105xt_a_b > set_c_d_c_d > ( ( ( c > d ) > c > d ) > carrie1948989069_d_a_e ) > a > ( ( ( c > d ) > c > d ) > d ) > ( ( c > d ) > c > d ) > d ).
thf(func_def_73,type,
algebr2122715238_a_d_e: carrie1105631105xt_a_b > set_a_a_a_a_a > ( ( a > a > a > a > a ) > carrie1948989069_d_a_e ) > a > ( ( a > a > a > a > a ) > d ) > ( a > a > a > a > a ) > d ).
thf(func_def_74,type,
algebr303206081_a_d_e: carrie1105631105xt_a_b > set_a_a_a_a > ( ( a > a > a > a ) > carrie1948989069_d_a_e ) > a > ( ( a > a > a > a ) > d ) > ( a > a > a > a ) > d ).
thf(func_def_75,type,
algebr1620716610_d_d_e: carrie1105631105xt_a_b > set_a_a_c_d > ( ( a > a > c > d ) > carrie1948989069_d_a_e ) > a > ( ( a > a > c > d ) > d ) > ( a > a > c > d ) > d ).
thf(func_def_76,type,
algebr1655014672_a_d_e: carrie1105631105xt_a_b > set_a_a_a > ( ( a > a > a ) > carrie1948989069_d_a_e ) > a > ( ( a > a > a ) > d ) > ( a > a > a ) > d ).
thf(func_def_77,type,
algebr137561451_a_d_e: carrie1105631105xt_a_b > set_a_a > ( ( a > a ) > carrie1948989069_d_a_e ) > a > ( ( a > a ) > d ) > ( a > a ) > d ).
thf(func_def_78,type,
algebr924632044_d_d_e: carrie1105631105xt_a_b > set_c_d > ( ( c > d ) > carrie1948989069_d_a_e ) > a > ( ( c > d ) > d ) > ( c > d ) > d ).
thf(func_def_79,type,
algebr2109842362_a_d_e: carrie1105631105xt_a_b > set_a > ( a > carrie1948989069_d_a_e ) > a > ( a > d ) > a > d ).
thf(func_def_80,type,
algebr1697692348_c_d_e: carrie1105631105xt_a_b > set_c > ( c > carrie1948989069_d_a_e ) > a > ( c > d ) > c > d ).
thf(func_def_81,type,
algebr417875517_d_d_e: carrie1105631105xt_a_b > set_d > ( d > carrie1948989069_d_a_e ) > a > ( d > d ) > d > d ).
thf(func_def_82,type,
pi_a_a_a_a_a: set_a_a_a > ( ( a > a > a ) > set_a_a ) > set_a_a_a_a_a2 ).
thf(func_def_83,type,
pi_a_a_a_c_d: set_a_a_a > ( ( a > a > a ) > set_c_d ) > set_a_a_a_c_d ).
thf(func_def_84,type,
pi_a_a_a_a: set_a_a_a > ( ( a > a > a ) > set_a ) > set_a_a_a_a4 ).
thf(func_def_85,type,
pi_a_a_a_a2: set_a_a > ( ( a > a ) > set_a_a ) > set_a_a_a_a3 ).
thf(func_def_86,type,
pi_a_a_c_d: set_a_a > ( ( a > a ) > set_c_d ) > set_a_a_c_d2 ).
thf(func_def_87,type,
pi_a_a_a: set_a_a > ( ( a > a ) > set_a ) > set_a_a_a2 ).
thf(func_def_88,type,
pi_c_d_a_a_a: set_c_d > ( ( c > d ) > set_a_a_a2 ) > set_c_d_a_a_a2 ).
thf(func_def_89,type,
pi_c_d_c_d_c_d: set_c_d > ( ( c > d ) > set_c_d_c_d ) > set_c_d_c_d_c_d ).
thf(func_def_90,type,
pi_c_d_c_d_a: set_c_d > ( ( c > d ) > set_c_d_a ) > set_c_d_c_d_a ).
thf(func_def_91,type,
pi_c_d_a_a_a2: set_c_d > ( ( c > d ) > set_a_a_a ) > set_c_d_a_a_a ).
thf(func_def_92,type,
pi_c_d_a_a: set_c_d > ( ( c > d ) > set_a_a ) > set_c_d_a_a ).
thf(func_def_93,type,
pi_c_d_c_d: set_c_d > ( ( c > d ) > set_c_d ) > set_c_d_c_d ).
thf(func_def_94,type,
pi_c_d_a: set_c_d > ( ( c > d ) > set_a ) > set_c_d_a ).
thf(func_def_95,type,
pi_a_a_a_a3: set_a > ( a > set_a_a_a2 ) > set_a_a_a_a2 ).
thf(func_def_96,type,
pi_a_c_d_a: set_a > ( a > set_c_d_a ) > set_a_c_d_a ).
thf(func_def_97,type,
pi_a_a_c_d_c_d: set_a > ( a > set_a_c_d_c_d ) > set_a_a_c_d_c_d ).
thf(func_def_98,type,
pi_a_a_a_a_a2: set_a > ( a > set_a_a_a_a ) > set_a_a_a_a_a ).
thf(func_def_99,type,
pi_a_a_a_a4: set_a > ( a > set_a_a_a ) > set_a_a_a_a ).
thf(func_def_100,type,
pi_a_a_c_d2: set_a > ( a > set_a_c_d ) > set_a_a_c_d ).
thf(func_def_101,type,
pi_a_a_a2: set_a > ( a > set_a_a ) > set_a_a_a ).
thf(func_def_102,type,
pi_a_c_d: set_a > ( a > set_c_d ) > set_a_c_d ).
thf(func_def_103,type,
pi_a_a: set_a > ( a > set_a ) > set_a_a ).
thf(func_def_104,type,
pi_a_c: set_a > ( a > set_c ) > set_a_c ).
thf(func_def_105,type,
pi_a_d: set_a > ( a > set_d ) > set_a_d ).
thf(func_def_106,type,
pi_c_a: set_c > ( c > set_a ) > set_c_a ).
thf(func_def_107,type,
pi_c_c: set_c > ( c > set_c ) > set_c_c ).
thf(func_def_108,type,
pi_c_d: set_c > ( c > set_d ) > set_c_d ).
thf(func_def_109,type,
pi_d_a: set_d > ( d > set_a ) > set_d_a ).
thf(func_def_110,type,
pi_d_c: set_d > ( d > set_c ) > set_d_c ).
thf(func_def_111,type,
pi_d_d: set_d > ( d > set_d ) > set_d_d ).
thf(func_def_112,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_113,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_114,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_115,type,
collect_c_d_c_d: ( ( ( c > d ) > c > d ) > $o ) > set_c_d_c_d ).
thf(func_def_116,type,
collect_a_a_a_a: ( ( a > a > a > a ) > $o ) > set_a_a_a_a ).
thf(func_def_117,type,
collect_a_a_c_d: ( ( a > a > c > d ) > $o ) > set_a_a_c_d ).
thf(func_def_118,type,
collect_a_a_a: ( ( a > a > a ) > $o ) > set_a_a_a ).
thf(func_def_119,type,
collect_a_a: ( ( a > a ) > $o ) > set_a_a ).
thf(func_def_120,type,
collect_c_d: ( ( c > d ) > $o ) > set_c_d ).
thf(func_def_121,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_122,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_123,type,
collect_c: ( c > $o ) > set_c ).
thf(func_def_124,type,
collect_d: ( d > $o ) > set_d ).
thf(func_def_125,type,
member_c_d_c_d_a: ( ( ( c > d ) > c > d ) > a ) > set_c_d_c_d_a2 > $o ).
thf(func_def_126,type,
member_c_d_c_d_d: ( ( ( c > d ) > c > d ) > d ) > set_c_d_c_d_d > $o ).
thf(func_def_127,type,
member_a_a_a_a_a_d: ( ( a > a > a > a > a ) > d ) > set_a_a_a_a_a_d > $o ).
thf(func_def_128,type,
member_a_a_a_a_a: ( ( a > a > a > a ) > a ) > set_a_a_a_a_a3 > $o ).
thf(func_def_129,type,
member_a_a_a_a_d: ( ( a > a > a > a ) > d ) > set_a_a_a_a_d > $o ).
thf(func_def_130,type,
member_a_a_c_d_a: ( ( a > a > c > d ) > a ) > set_a_a_c_d_a > $o ).
thf(func_def_131,type,
member_a_a_c_d_d: ( ( a > a > c > d ) > d ) > set_a_a_c_d_d > $o ).
thf(func_def_132,type,
member_a_a_a_a_a2: ( ( a > a > a ) > a > a ) > set_a_a_a_a_a2 > $o ).
thf(func_def_133,type,
member_a_a_a_c_d: ( ( a > a > a ) > c > d ) > set_a_a_a_c_d > $o ).
thf(func_def_134,type,
member_a_a_a_a: ( ( a > a > a ) > a ) > set_a_a_a_a4 > $o ).
thf(func_def_135,type,
member_a_a_a_d: ( ( a > a > a ) > d ) > set_a_a_a_d > $o ).
thf(func_def_136,type,
member_a_a_a_a2: ( ( a > a ) > a > a ) > set_a_a_a_a3 > $o ).
thf(func_def_137,type,
member_a_a_c_d: ( ( a > a ) > c > d ) > set_a_a_c_d2 > $o ).
thf(func_def_138,type,
member_a_a_a: ( ( a > a ) > a ) > set_a_a_a2 > $o ).
thf(func_def_139,type,
member_a_a_d: ( ( a > a ) > d ) > set_a_a_d > $o ).
thf(func_def_140,type,
member_c_d_a_a_a: ( ( c > d ) > ( a > a ) > a ) > set_c_d_a_a_a2 > $o ).
thf(func_def_141,type,
member_c_d_c_d_c_d: ( ( c > d ) > ( c > d ) > c > d ) > set_c_d_c_d_c_d > $o ).
thf(func_def_142,type,
member_c_d_c_d_a2: ( ( c > d ) > ( c > d ) > a ) > set_c_d_c_d_a > $o ).
thf(func_def_143,type,
member_c_d_a_a_a2: ( ( c > d ) > a > a > a ) > set_c_d_a_a_a > $o ).
thf(func_def_144,type,
member_c_d_a_a: ( ( c > d ) > a > a ) > set_c_d_a_a > $o ).
thf(func_def_145,type,
member_c_d_c_d: ( ( c > d ) > c > d ) > set_c_d_c_d > $o ).
thf(func_def_146,type,
member_c_d_a: ( ( c > d ) > a ) > set_c_d_a > $o ).
thf(func_def_147,type,
member_c_d_d: ( ( c > d ) > d ) > set_c_d_d > $o ).
thf(func_def_148,type,
member_a_a_a_a3: ( a > ( a > a ) > a ) > set_a_a_a_a2 > $o ).
thf(func_def_149,type,
member_a_c_d_c_d: ( a > ( c > d ) > c > d ) > set_a_c_d_c_d > $o ).
thf(func_def_150,type,
member_a_c_d_a: ( a > ( c > d ) > a ) > set_a_c_d_a > $o ).
thf(func_def_151,type,
member_a_a_c_d_c_d: ( a > a > ( c > d ) > c > d ) > set_a_a_c_d_c_d > $o ).
thf(func_def_152,type,
member_a_a_a_a_a3: ( a > a > a > a > a ) > set_a_a_a_a_a > $o ).
thf(func_def_153,type,
member_a_a_a_a4: ( a > a > a > a ) > set_a_a_a_a > $o ).
thf(func_def_154,type,
member_a_a_c_d2: ( a > a > c > d ) > set_a_a_c_d > $o ).
thf(func_def_155,type,
member_a_a_a2: ( a > a > a ) > set_a_a_a > $o ).
thf(func_def_156,type,
member_a_c_d: ( a > c > d ) > set_a_c_d > $o ).
thf(func_def_157,type,
member_a_a: ( a > a ) > set_a_a > $o ).
thf(func_def_158,type,
member_a_c: ( a > c ) > set_a_c > $o ).
thf(func_def_159,type,
member_a_d: ( a > d ) > set_a_d > $o ).
thf(func_def_160,type,
member_c_c_d: ( c > c > d ) > set_c_c_d > $o ).
thf(func_def_161,type,
member_c_a: ( c > a ) > set_c_a > $o ).
thf(func_def_162,type,
member_c_c: ( c > c ) > set_c_c > $o ).
thf(func_def_163,type,
member_c_d: ( c > d ) > set_c_d > $o ).
thf(func_def_164,type,
member_d_c_d: ( d > c > d ) > set_d_c_d > $o ).
thf(func_def_165,type,
member_d_a: ( d > a ) > set_d_a > $o ).
thf(func_def_166,type,
member_d_c: ( d > c ) > set_d_c > $o ).
thf(func_def_167,type,
member_d_d: ( d > d ) > set_d_d > $o ).
thf(func_def_168,type,
member_nat: nat > set_nat > $o ).
thf(func_def_169,type,
member_a: a > set_a > $o ).
thf(func_def_170,type,
member_c: c > set_c > $o ).
thf(func_def_171,type,
member_d: d > set_d > $o ).
thf(func_def_172,type,
i: set_c ).
thf(func_def_173,type,
m: c > carrie1948989069_d_a_e ).
thf(func_def_174,type,
r: carrie1105631105xt_a_b ).
thf(func_def_178,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_179,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_180,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_181,type,
vIMP: $o > $o > $o ).
thf(func_def_182,type,
sK0: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_183,type,
sK1: set_c > ( c > carrie1948989069_d_a_e ) > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_184,type,
sK2: set_a > ( a > set_c_d ) > ( a > c > d ) > a ).
thf(func_def_185,type,
sK3: ( c > d ) > set_c > ( c > d ) > c ).
thf(func_def_186,type,
sK4: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_187,type,
sK5: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_188,type,
sK6: c > d ).
thf(func_def_189,type,
sK7: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_190,type,
sK8: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_191,type,
sK9: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_192,type,
sK10: set_a > set_a > ( a > a ) > a ).
thf(func_def_193,type,
sK11: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_194,type,
sK12: ( a > set_a ) > ( a > a ) > set_a > a ).
thf(func_def_195,type,
sK13: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_196,type,
sK14: set_c_d > ( ( c > d ) > c > d ) > set_c_d > c > d ).
thf(func_def_197,type,
sK15: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_198,type,
sK16: ( c > carrie1948989069_d_a_e ) > ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_199,type,
sK17: ( ( c > d ) > ( c > d ) > c > d ) > set_c_d > ( ( c > d ) > ( c > d ) > c > d ) > c > d ).
thf(func_def_200,type,
sK18: ( c > carrie1948989069_d_a_e ) > set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_201,type,
sK19: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_202,type,
sK20: set_c > ( c > d ) > ( c > set_d ) > c ).
thf(func_def_203,type,
sK21: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_204,type,
sK22: set_a > ( a > a > a ) > set_a_a > a ).
thf(func_def_205,type,
sK23: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_206,type,
sK24: ( c > carrie1948989069_d_a_e ) > ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_207,type,
sK25: ( a > a > a ) > ( a > a > a ) > set_a > a ).
thf(func_def_208,type,
sK26: ( c > d ) > ( c > d ) > set_c > c ).
thf(func_def_209,type,
sK27: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_210,type,
sK28: ( a > a > a > a ) > set_a > ( a > a > a > a ) > a ).
thf(func_def_211,type,
sK29: ( c > set_d ) > set_c > ( c > d ) > c ).
thf(func_def_212,type,
sK30: set_c > ( c > d ) > set_d > c ).
thf(func_def_213,type,
sK31: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_214,type,
sK32: ( a > a > c > d ) > ( a > a > c > d ) > set_a > a ).
thf(func_def_215,type,
sK33: ( a > a ) > set_a > ( a > a ) > a ).
thf(func_def_216,type,
sK34: set_c > ( c > carrie1948989069_d_a_e ) > c ).
thf(func_def_217,type,
sK35: ( ( c > d ) > set_c_d ) > ( ( c > d ) > c > d ) > set_c_d > c > d ).
thf(func_def_218,type,
sK36: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_219,type,
sK37: ( a > a ) > set_a > ( a > set_a ) > a ).
thf(func_def_220,type,
sK38: ( c > carrie1948989069_d_a_e ) > set_c > c ).
thf(func_def_221,type,
sK39: set_a > ( a > set_a_a ) > ( a > a > a ) > a ).
thf(func_def_222,type,
sK40: ( a > a > a > a > a ) > ( a > a > a > a > a ) > set_a > a ).
thf(func_def_223,type,
sK41: ( ( c > d ) > c > d ) > set_c_d > ( ( c > d ) > c > d ) > c > d ).
thf(func_def_224,type,
sK42: ( a > c > d ) > set_a > ( a > c > d ) > a ).
thf(func_def_225,type,
sK43: set_c_d > set_a > ( a > c > d ) > a ).
thf(func_def_226,type,
vNOT: $o > $o ).
thf(func_def_227,type,
sK44: ( a > a > a > a ) > ( a > set_a_a_a ) > set_a > a ).
thf(func_def_228,type,
sK45: set_c_d > ( ( c > d ) > c > d ) > ( ( c > d ) > set_c_d ) > c > d ).
thf(func_def_229,type,
sK46: ( a > a > c > d ) > ( a > set_a_c_d ) > set_a > a ).
thf(func_def_230,type,
sK47: ( ( c > d ) > ( c > d ) > c > d ) > ( ( c > d ) > set_c_d_c_d ) > set_c_d > c > d ).
thf(func_def_231,type,
sK48: ( a > a > a > a > a ) > set_a > ( a > set_a_a_a_a ) > a ).
thf(func_def_232,type,
sK49: ( a > a ) > set_a > ( a > set_a ) > a ).
thf(func_def_233,type,
sK50: set_c > ( c > set_d ) > ( c > d ) > c ).
thf(func_def_234,type,
sK51: ( a > set_c_d ) > ( a > c > d ) > set_a > a ).
thf(func_def_235,type,
sK52: set_a > ( a > set_a_a ) > ( a > a > a ) > a ).
thf(func_def_236,type,
sK53: c ).
thf(f357,axiom,
( ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X4: c > d] :
( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) @ X4 )
= ( prod_p131511076_d_a_e @ i @ m @ X2 @ ( prod_p131511076_d_a_e @ i @ m @ X3 @ X4 ) ) ) ) ) )
& ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
& ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X3 @ X2 ) ) ) )
& ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X0: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) )
& ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X2 ) @ X2 )
= ( prod_z1214987823_d_a_e @ i @ m ) ) )
& ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X0: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
& ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(f358,conjecture,
! [X0: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X0 )
| ~ ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(f359,negated_conjecture,
~ ! [X0: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X0 )
| ~ ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f738,plain,
~ ! [X0: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X0 )
| ~ ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) ) ),
inference(rectify,[],[f359]) ).
thf(f739,plain,
~ ! [X0: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X0 )
| ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) ),
inference(fool_elimination,[],[f738]) ).
thf(f1016,plain,
( ! [X0: c > d] :
( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X0 @ X1 ) @ X2 )
= ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) ) ) ) ) )
& ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
& ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X4: c > d] :
( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X3 @ X4 )
= ( prod_p131511076_d_a_e @ i @ m @ X4 @ X3 ) ) ) )
& ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X5: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) )
& ! [X6: c > d] :
( ( member_c_d @ X6 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_z1214987823_d_a_e @ i @ m )
= ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X6 ) @ X6 ) ) )
& ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X7: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X8: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
& ! [X9: c > d] :
( ( member_c_d @ X9 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X9 )
= X9 ) ) ),
inference(rectify,[],[f357]) ).
thf(f1017,plain,
( ! [X0: c > d] :
( ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ! [X1: c > d] :
( ( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ! [X2: c > d] :
( ( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X0 @ X1 ) @ X2 )
= ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) ) ) ) ) )
& ( ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
& ! [X3: c > d] :
( ( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ! [X4: c > d] :
( ( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X3 @ X4 )
= ( prod_p131511076_d_a_e @ i @ m @ X4 @ X3 ) ) ) )
& ( ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) )
= $true )
& ! [X6: c > d] :
( ( $true
= ( member_c_d @ X6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) )
=> ( ( prod_z1214987823_d_a_e @ i @ m )
= ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X6 ) @ X6 ) ) )
& ( $true
= ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) ) )
& ! [X9: c > d] :
( ( ( member_c_d @ X9 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X9 )
= X9 ) ) ),
inference(fool_elimination,[],[f1016]) ).
thf(f1052,plain,
~ ! [X0: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X0 )
| ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) ),
inference(flattening,[],[f739]) ).
thf(f1053,plain,
( ( ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) )
= $true )
& ! [X3: c > d] :
( ( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ! [X4: c > d] :
( ( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X3 @ X4 )
= ( prod_p131511076_d_a_e @ i @ m @ X4 @ X3 ) ) ) )
& ! [X6: c > d] :
( ( $true
= ( member_c_d @ X6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X6 )
= X6 ) )
& ! [X5: c > d] :
( ( ( member_c_d @ X5 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ( ( prod_z1214987823_d_a_e @ i @ m )
= ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X5 ) @ X5 ) ) )
& ! [X0: c > d] :
( ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ! [X1: c > d] :
( ( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ! [X2: c > d] :
( ( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X0 @ X1 ) @ X2 )
= ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) ) ) ) ) )
& ( ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
& ( $true
= ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) ) ) ),
inference(rectify,[],[f1017]) ).
thf(f1057,plain,
( ( ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) )
= $true )
& ! [X0: c > d] :
( ! [X1: c > d] :
( ! [X2: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X0 @ X1 ) @ X2 )
= ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) ) )
| ( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
| ( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
| ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
& ! [X5: c > d] :
( ( ( prod_z1214987823_d_a_e @ i @ m )
= ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X5 ) @ X5 ) )
| ( ( member_c_d @ X5 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
& ( ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
& ( $true
= ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) ) )
& ! [X3: c > d] :
( ! [X4: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X3 @ X4 )
= ( prod_p131511076_d_a_e @ i @ m @ X4 @ X3 ) )
| ( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
| ( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
& ! [X6: c > d] :
( ( $true
!= ( member_c_d @ X6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) )
| ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X6 )
= X6 ) ) ),
inference(ennf_transformation,[],[f1053]) ).
thf(f1149,plain,
? [X0: c > d] :
( ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
& ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
!= X0 ) ),
inference(ennf_transformation,[],[f1052]) ).
thf(f1337,plain,
( ( $true
= ( member_c_d @ sK6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) )
& ( sK6
!= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f1149]) ).
thf(f1397,plain,
( ( ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) )
= $true )
& ! [X0: c > d] :
( ! [X1: c > d] :
( ! [X2: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X0 @ X1 ) @ X2 )
= ( prod_p131511076_d_a_e @ i @ m @ X0 @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) ) )
| ( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
| ( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
| ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
& ! [X3: c > d] :
( ( ( prod_z1214987823_d_a_e @ i @ m )
= ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X3 ) @ X3 ) )
| ( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
& ( ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true )
& ( $true
= ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y0: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [Y1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) ) )
& ! [X4: c > d] :
( ! [X5: c > d] :
( ( ( prod_p131511076_d_a_e @ i @ m @ X4 @ X5 )
= ( prod_p131511076_d_a_e @ i @ m @ X5 @ X4 ) )
| ( ( member_c_d @ X5 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
| ( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) )
& ! [X6: c > d] :
( ( $true
!= ( member_c_d @ X6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) )
| ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X6 )
= X6 ) ) ),
inference(rectify,[],[f1057]) ).
thf(f1517,plain,
( sK6
!= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ),
inference(cnf_transformation,[],[f1337]) ).
thf(f1518,plain,
( $true
= ( member_c_d @ sK6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) ),
inference(cnf_transformation,[],[f1337]) ).
thf(f1594,plain,
! [X6: c > d] :
( ( $true
!= ( member_c_d @ X6 @ ( carr_p1636662547_d_a_e @ i @ m ) ) )
| ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X6 )
= X6 ) ),
inference(cnf_transformation,[],[f1397]) ).
thf(f1595,plain,
! [X4: c > d,X5: c > d] :
( ( ( member_c_d @ X5 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true )
| ( ( prod_p131511076_d_a_e @ i @ m @ X4 @ X5 )
= ( prod_p131511076_d_a_e @ i @ m @ X5 @ X4 ) )
| ( ( member_c_d @ X4 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true ) ),
inference(cnf_transformation,[],[f1397]) ).
thf(f1597,plain,
( ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
= $true ),
inference(cnf_transformation,[],[f1397]) ).
thf(f1894,plain,
( ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ sK6 )
= sK6 )
| ( $true != $true ) ),
inference(superposition,[],[f1594,f1518]) ).
thf(f1899,plain,
( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ sK6 )
= sK6 ),
inference(trivial_inequality_removal,[],[f1894]) ).
thf(f1907,plain,
! [X0: c > d] :
( ( $true != $true )
| ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true )
| ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ sK6 )
= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ X0 ) ) ),
inference(superposition,[],[f1595,f1518]) ).
thf(f1911,plain,
! [X0: c > d] :
( ( ( member_c_d @ X0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
!= $true )
| ( ( prod_p131511076_d_a_e @ i @ m @ X0 @ sK6 )
= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1907]) ).
thf(f1920,plain,
( ( $true != $true )
| ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ sK6 )
= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ) ),
inference(superposition,[],[f1911,f1597]) ).
thf(f1922,plain,
( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ sK6 )
= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ),
inference(trivial_inequality_removal,[],[f1920]) ).
thf(f1924,plain,
( sK6
= ( prod_p131511076_d_a_e @ i @ m @ sK6 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ),
inference(forward_demodulation,[],[f1922,f1899]) ).
thf(f1925,plain,
$false,
inference(forward_subsumption_resolution,[],[f1924,f1517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP027^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n017.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 19:33:22 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.21/0.33 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
% 0.82/0.50 % (796057)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.82/0.50 % (796064)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1143186480:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.82/0.50 % (796064)Instruction limit reached!
% 0.82/0.50 % (796064)------------------------------
% 0.82/0.50 % (796064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.50 % (796064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.50 % (796064)CaDiCaL version: 2.1.3
% 0.82/0.50 % (796064)Termination reason: Instruction limit
% 0.82/0.50 % (796064)Termination phase: shuffling
% 0.82/0.50 % (796064)Time elapsed: 0.001 s
% 0.82/0.50 % (796064)Peak memory usage: 10 MB
% 0.82/0.50 % (796064)Instructions burned: 5 (million)
% 0.82/0.50 % (796068)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.82/0.50 % (796068)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
% 0.82/0.50 % (796063)lrs+10_16_si=on:nwc=1.5:random_seed=1429163397:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.82/0.50 % (796062)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=448860066:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.82/0.50 % (796065)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=3784706266: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)
% 0.82/0.50 % (796067)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3642955803:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.82/0.50 % (796066)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=316241189:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.82/0.50 % (796068)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=597403433:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.82/0.50 % (796063)Instruction limit reached!
% 0.82/0.50 % (796063)------------------------------
% 0.82/0.50 % (796063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.50 % (796063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.50 % (796063)CaDiCaL version: 2.1.3
% 0.82/0.50 % (796063)Termination reason: Instruction limit
% 0.82/0.50 % (796063)Termination phase: shuffling
% 0.82/0.50 % (796063)Time elapsed: 0.009 s
% 0.82/0.50 % (796063)Peak memory usage: 10 MB
% 0.82/0.50 % (796063)Instructions burned: 19 (million)
% 0.82/0.50 % (796066)Instruction limit reached!
% 0.82/0.50 % (796066)------------------------------
% 0.82/0.50 % (796066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.50 % (796066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.50 % (796066)CaDiCaL version: 2.1.3
% 0.82/0.50 % (796066)Termination reason: Instruction limit
% 0.82/0.50 % (796066)Termination phase: shuffling
% 0.82/0.50 % (796066)Time elapsed: 0.012 s
% 0.82/0.50 % (796066)Peak memory usage: 10 MB
% 0.82/0.50 % (796066)Instructions burned: 24 (million)
% 0.82/0.50 % (796070)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1650207864:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.82/0.50 % (796070)Instruction limit reached!
% 0.82/0.50 % (796070)------------------------------
% 0.82/0.50 % (796070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.50 % (796070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.50 % (796070)CaDiCaL version: 2.1.3
% 0.82/0.50 % (796070)Termination reason: Instruction limit
% 0.82/0.50 % (796070)Termination phase: shuffling
% 0.82/0.50 % (796070)Time elapsed: 0.002 s
% 0.82/0.50 % (796070)Peak memory usage: 10 MB
% 0.82/0.50 % (796070)Instructions burned: 4 (million)
% 0.82/0.50 % (796077)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3954666218:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.82/0.50 % (796077)Instruction limit reached!
% 0.82/0.54 % (796077)------------------------------
% 0.82/0.54 % (796077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796077)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796077)Termination reason: Instruction limit
% 0.82/0.54 % (796077)Termination phase: shuffling
% 0.82/0.54 % (796077)Time elapsed: 0.003 s
% 0.82/0.54 % (796077)Peak memory usage: 10 MB
% 0.82/0.54 % (796077)Instructions burned: 7 (million)
% 0.82/0.54 % (796078)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.82/0.54 % (796078)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3656433903:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.82/0.54 % (796062)Instruction limit reached!
% 0.82/0.54 % (796062)------------------------------
% 0.82/0.54 % (796062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796062)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796062)Termination reason: Instruction limit
% 0.82/0.54 % (796062)Termination phase: Property scanning
% 0.82/0.54 % (796062)Time elapsed: 0.038 s
% 0.82/0.54 % (796062)Peak memory usage: 11 MB
% 0.82/0.54 % (796062)Instructions burned: 89 (million)
% 0.82/0.54 % (796080)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1527702594:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.82/0.54 % (796068)Instruction limit reached!
% 0.82/0.54 % (796068)------------------------------
% 0.82/0.54 % (796068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796068)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796068)Termination reason: Instruction limit
% 0.82/0.54 % (796068)Termination phase: Property scanning
% 0.82/0.54 % (796068)Time elapsed: 0.038 s
% 0.82/0.54 % (796068)Peak memory usage: 13 MB
% 0.82/0.54 % (796068)Instructions burned: 161 (million)
% 0.82/0.54 % (796078)Instruction limit reached!
% 0.82/0.54 % (796078)------------------------------
% 0.82/0.54 % (796078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796078)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796078)Termination reason: Instruction limit
% 0.82/0.54 % (796078)Termination phase: shuffling
% 0.82/0.54 % (796078)Time elapsed: 0.005 s
% 0.82/0.54 % (796078)Peak memory usage: 10 MB
% 0.82/0.54 % (796078)Instructions burned: 8 (million)
% 0.82/0.54 % (796067)Instruction limit reached!
% 0.82/0.54 % (796067)------------------------------
% 0.82/0.54 % (796067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796067)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796067)Termination reason: Instruction limit
% 0.82/0.54 % (796067)Termination phase: Property scanning
% 0.82/0.54 % (796067)Time elapsed: 0.041 s
% 0.82/0.54 % (796067)Peak memory usage: 11 MB
% 0.82/0.54 % (796067)Instructions burned: 78 (million)
% 0.82/0.54 % (796080)Instruction limit reached!
% 0.82/0.54 % (796080)------------------------------
% 0.82/0.54 % (796080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796080)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796080)Termination reason: Instruction limit
% 0.82/0.54 % (796080)Termination phase: shuffling
% 0.82/0.54 % (796080)Time elapsed: 0.006 s
% 0.82/0.54 % (796080)Peak memory usage: 10 MB
% 0.82/0.54 % (796080)Instructions burned: 13 (million)
% 0.82/0.54 % (796082)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
% 0.82/0.54 % (796082)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.82/0.54 % (796086)lrs+10_1_si=on:cs=on:random_seed=2204529556:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.82/0.54 % (796086)Instruction limit reached!
% 0.82/0.54 % (796086)------------------------------
% 0.82/0.54 % (796086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796086)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796086)Termination reason: Instruction limit
% 0.82/0.54 % (796086)Termination phase: shuffling
% 0.82/0.54 % (796086)Time elapsed: 0.003 s
% 0.82/0.54 % (796086)Peak memory usage: 10 MB
% 0.82/0.54 % (796086)Instructions burned: 12 (million)
% 0.82/0.54 % (796082)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3475493651:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.82/0.54 % (796084)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=1473413480:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.82/0.54 % (796087)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.82/0.54 % (796089)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3911289136:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.82/0.54 % (796092)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=560955989:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.82/0.54 % (796087)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=1378448147:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.82/0.54 % (796082)Instruction limit reached!
% 0.82/0.54 % (796082)------------------------------
% 0.82/0.54 % (796082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796082)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796082)Termination reason: Instruction limit
% 0.82/0.54 % (796082)Termination phase: shuffling
% 0.82/0.54 % (796082)Time elapsed: 0.014 s
% 0.82/0.54 % (796082)Peak memory usage: 11 MB
% 0.82/0.54 % (796082)Instructions burned: 29 (million)
% 0.82/0.54 % (796087)Instruction limit reached!
% 0.82/0.54 % (796087)------------------------------
% 0.82/0.54 % (796087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796087)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796087)Termination reason: Instruction limit
% 0.82/0.54 % (796087)Termination phase: shuffling
% 0.82/0.54 % (796087)Time elapsed: 0.002 s
% 0.82/0.54 % (796087)Peak memory usage: 10 MB
% 0.82/0.54 % (796087)Instructions burned: 3 (million)
% 0.82/0.54 % (796092)Instruction limit reached!
% 0.82/0.54 % (796092)------------------------------
% 0.82/0.54 % (796092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796092)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796092)Termination reason: Instruction limit
% 0.82/0.54 % (796092)Termination phase: shuffling
% 0.82/0.54 % (796092)Time elapsed: 0.007 s
% 0.82/0.54 % (796092)Peak memory usage: 11 MB
% 0.82/0.54 % (796092)Instructions burned: 31 (million)
% 0.82/0.54 % (796088)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1685276659:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.82/0.54 % (796098)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3275214443:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.82/0.54 % (796097)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1667307705:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.82/0.54 % (796099)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3422893840:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.82/0.54 % (796088)Instruction limit reached!
% 0.82/0.54 % (796088)------------------------------
% 0.82/0.54 % (796088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796088)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796088)Termination reason: Instruction limit
% 0.82/0.54 % (796088)Termination phase: shuffling
% 0.82/0.54 % (796088)Time elapsed: 0.017 s
% 0.82/0.54 % (796088)Peak memory usage: 10 MB
% 0.82/0.54 % (796088)Instructions burned: 38 (million)
% 0.82/0.54 % (796084)Instruction limit reached!
% 0.82/0.54 % (796084)------------------------------
% 0.82/0.54 % (796084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796084)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796084)Termination reason: Instruction limit
% 0.82/0.54 % (796084)Termination phase: Property scanning
% 0.82/0.54 % (796084)Time elapsed: 0.039 s
% 0.82/0.54 % (796084)Peak memory usage: 12 MB
% 0.82/0.54 % (796084)Instructions burned: 87 (million)
% 0.82/0.54 % (796097)Instruction limit reached!
% 0.82/0.54 % (796097)------------------------------
% 0.82/0.54 % (796097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796097)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796097)Termination reason: Instruction limit
% 0.82/0.54 % (796097)Termination phase: shuffling
% 0.82/0.54 % (796097)Time elapsed: 0.009 s
% 0.82/0.54 % (796097)Peak memory usage: 10 MB
% 0.82/0.54 % (796097)Instructions burned: 15 (million)
% 0.82/0.54 % (796099)Instruction limit reached!
% 0.82/0.54 % (796099)------------------------------
% 0.82/0.54 % (796099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796099)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796099)Termination reason: Instruction limit
% 0.82/0.54 % (796099)Termination phase: shuffling
% 0.82/0.54 % (796099)Time elapsed: 0.007 s
% 0.82/0.54 % (796099)Peak memory usage: 10 MB
% 0.82/0.54 % (796099)Instructions burned: 16 (million)
% 0.82/0.54 % (796104)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=214302334:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.82/0.54 % (796105)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=300244235:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.82/0.54 % (796104)Instruction limit reached!
% 0.82/0.54 % (796104)------------------------------
% 0.82/0.54 % (796104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796104)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796104)Termination reason: Instruction limit
% 0.82/0.54 % (796104)Termination phase: shuffling
% 0.82/0.54 % (796104)Time elapsed: 0.002 s
% 0.82/0.54 % (796104)Peak memory usage: 10 MB
% 0.82/0.54 % (796104)Instructions burned: 2 (million)
% 0.82/0.54 % (796106)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1083152772:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.82/0.54 % (796107)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=576486144:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.82/0.54 % (796106)Instruction limit reached!
% 0.82/0.54 % (796106)------------------------------
% 0.82/0.54 % (796106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796098) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-796057-796098"...
% 0.82/0.54 % (796106)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796106)Termination reason: Instruction limit
% 0.82/0.54 % (796106)Termination phase: shuffling
% 0.82/0.54 % (796106)Time elapsed: 0.011 s
% 0.82/0.54 % (796106)Peak memory usage: 10 MB
% 0.82/0.54 % (796106)Instructions burned: 25 (million)
% 0.82/0.54 % (796105)Instruction limit reached!
% 0.82/0.54 % (796105)------------------------------
% 0.82/0.54 % (796105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796105)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796105)Termination reason: Instruction limit
% 0.82/0.54 % (796105)Termination phase: shuffling
% 0.82/0.54 % (796105)Time elapsed: 0.017 s
% 0.82/0.54 % (796105)Peak memory usage: 10 MB
% 0.82/0.54 % (796105)Instructions burned: 26 (million)
% 0.82/0.54 % (796098)...printing done.
% 0.82/0.54 % (796098)Refutation found. Thanks to Tanya!
% 0.82/0.54 % SZS status Theorem for theBenchmark
% 0.82/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.82/0.54 % (796098)------------------------------
% 0.82/0.54 % (796098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.54 % (796098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.54 % (796098)CaDiCaL version: 2.1.3
% 0.82/0.54 % (796098)Termination reason: Refutation
% 0.82/0.54 % (796098)Time elapsed: 0.047 s
% 0.82/0.54 % (796098)Peak memory usage: 14 MB
% 0.82/0.54 % (796098)Instructions burned: 198 (million)
% 0.82/0.54 % (796057)Success in time 0.205 s
% 0.82/0.54 % Vampire exiting
%------------------------------------------------------------------------------