%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP141^1 : 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 : n009.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 2.57s 0.70s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 30
% Syntax : Number of formulae : 661 ( 53 unt; 0 typ; 25 def)
% Number of atoms : 7860 (2347 equ; 0 cnn)
% Maximal formula atoms : 21 ( 11 avg)
% Number of connectives : 13295 ( 564 ~;1932 |; 434 &;9196 @)
% ( 25 <=>; 414 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 197 ( 192 usr; 50 con; 0-4 aty)
% ( 496 !!; 234 ??; 0 @@+; 0 @@-)
% Number of variables : 2155 ( 0 sgn1255 !; 2 ?;2155 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1702239303tate_o: $tType ).
thf(type_def_6,type,
produc1307154919tate_o: $tType ).
thf(type_def_7,type,
set_Pr1590995257tate_o: $tType ).
thf(type_def_8,type,
set_Pr778812871_state: $tType ).
thf(type_def_9,type,
produc696469763tate_o: $tType ).
thf(type_def_10,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_11,type,
produc1390548711_state: $tType ).
thf(type_def_12,type,
produc842455143at_nat: $tType ).
thf(type_def_13,type,
set_Pr1740974983tate_o: $tType ).
thf(type_def_14,type,
produc204914599tate_o: $tType ).
thf(type_def_15,type,
set_Pr795498619_state: $tType ).
thf(type_def_16,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_17,type,
produc1115495963_state: $tType ).
thf(type_def_18,type,
product_prod_nat_nat: $tType ).
thf(type_def_19,type,
set_state: $tType ).
thf(type_def_20,type,
set_nat: $tType ).
thf(type_def_21,type,
state: $tType ).
thf(type_def_22,type,
com: $tType ).
thf(type_def_23,type,
nat: $tType ).
thf(type_def_24,type,
a: $tType ).
thf(type_def_25,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
suc: nat > nat ).
thf(func_def_1,type,
order_aboveS_nat: set_Pr1986765409at_nat > nat > set_nat ).
thf(func_def_2,type,
order_aboveS_state: set_Pr795498619_state > state > set_state ).
thf(func_def_3,type,
order_1121016664tate_o: set_Pr1702239303tate_o > produc696469763tate_o > set_Pr1590995257tate_o ).
thf(func_def_4,type,
order_665764460at_nat: set_Pr1490359111at_nat > product_prod_nat_nat > set_Pr1986765409at_nat ).
thf(func_def_5,type,
order_2027321734_state: set_Pr778812871_state > produc1115495963_state > set_Pr795498619_state ).
thf(func_def_6,type,
order_130026331on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_7,type,
order_286167592_state: set_state > set_Pr795498619_state > $o ).
thf(func_def_8,type,
order_50454158tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_9,type,
order_721919926at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_10,type,
order_178668240_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
thf(func_def_11,type,
bot_bo2130564770te_o_o: ( a > state > $o ) > produc204914599tate_o > $o ).
thf(func_def_12,type,
bot_bot_nat_nat_o: nat > nat > $o ).
thf(func_def_13,type,
bot_bo935656620te_o_o: com > ( a > state > $o ) > $o ).
thf(func_def_14,type,
bot_bo51534648tate_o: state > state > $o ).
thf(func_def_15,type,
bot_bo250281208te_o_o: produc696469763tate_o > $o ).
thf(func_def_16,type,
bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
thf(func_def_17,type,
bot_bo446391478tate_o: produc1115495963_state > $o ).
thf(func_def_18,type,
bot_bot_set_nat: set_nat ).
thf(func_def_19,type,
bot_bot_set_state: set_state ).
thf(func_def_20,type,
bot_bo170732493tate_o: set_Pr1590995257tate_o ).
thf(func_def_21,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_22,type,
bot_bo1692783091tate_o: set_Pr1740974983tate_o ).
thf(func_def_23,type,
bot_bo1625160935_state: set_Pr795498619_state ).
thf(func_def_24,type,
bot_bo1714653363tate_o: set_Pr1702239303tate_o ).
thf(func_def_25,type,
bot_bo34127283at_nat: set_Pr1490359111at_nat ).
thf(func_def_26,type,
bot_bo1331673139_state: set_Pr778812871_state ).
thf(func_def_27,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_28,type,
pHoare382919414oare_a: set_Pr1590995257tate_o > ( a > state > $o ) > com > ( a > state > $o ) > $o ).
thf(func_def_29,type,
hoare_a: set_Pr1590995257tate_o > ( a > state > $o ) > com > ( a > state > $o ) > $o ).
thf(func_def_30,type,
body: com ).
thf(func_def_31,type,
call: com ).
thf(func_def_32,type,
semi: com > com > com ).
thf(func_def_33,type,
while: ( state > $o ) > com > com ).
thf(func_def_34,type,
exec: state > com > state > $o ).
thf(func_def_35,type,
execn: state > com > nat > state > $o ).
thf(func_def_36,type,
termi: com > state > $o ).
thf(func_def_37,type,
produc33908149tate_o: ( a > state > $o ) > produc204914599tate_o > produc696469763tate_o ).
thf(func_def_38,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_39,type,
produc1948644831tate_o: com > ( a > state > $o ) > produc204914599tate_o ).
thf(func_def_40,type,
produc64584659_state: state > state > produc1115495963_state ).
thf(func_def_41,type,
produc1684562079tate_o: produc696469763tate_o > produc696469763tate_o > produc1307154919tate_o ).
thf(func_def_42,type,
produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).
thf(func_def_43,type,
produc1964772951_state: produc1115495963_state > produc1115495963_state > produc1390548711_state ).
thf(func_def_44,type,
produc385877620_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_45,type,
produc938968666tate_o: ( state > state > $o ) > produc1115495963_state > $o ).
thf(func_def_46,type,
produc1271576886te_o_o: ( ( a > state > $o ) > produc204914599tate_o > $o ) > produc696469763tate_o > $o ).
thf(func_def_47,type,
produc949581770_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_48,type,
produc1610543495tate_o: ( nat > nat > set_Pr1590995257tate_o ) > product_prod_nat_nat > set_Pr1590995257tate_o ).
thf(func_def_49,type,
produc1915186323at_nat: ( nat > nat > set_Pr1986765409at_nat ) > product_prod_nat_nat > set_Pr1986765409at_nat ).
thf(func_def_50,type,
produc1654445_state: ( nat > nat > set_Pr795498619_state ) > product_prod_nat_nat > set_Pr795498619_state ).
thf(func_def_51,type,
produc281270436te_o_o: ( com > ( a > state > $o ) > $o ) > produc204914599tate_o > $o ).
thf(func_def_52,type,
produc789892016tate_o: ( state > state > $o ) > produc1115495963_state > $o ).
thf(func_def_53,type,
irrefl_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_54,type,
refl_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_55,type,
refl_on_state: set_state > set_Pr795498619_state > $o ).
thf(func_def_56,type,
refl_o489021252tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_57,type,
refl_o1619599232at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_58,type,
refl_o1438232218_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
thf(func_def_59,type,
total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_60,type,
total_on_state: set_state > set_Pr795498619_state > $o ).
thf(func_def_61,type,
total_795385983tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_62,type,
total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_63,type,
total_1316653983_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
thf(func_def_64,type,
trans_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_65,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_66,type,
collect_state: ( state > $o ) > set_state ).
thf(func_def_67,type,
collec1499596504tate_o: ( produc696469763tate_o > $o ) > set_Pr1590995257tate_o ).
thf(func_def_68,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_69,type,
collec496201222_state: ( produc1115495963_state > $o ) > set_Pr795498619_state ).
thf(func_def_70,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_71,type,
insert_state: state > set_state > set_state ).
thf(func_def_72,type,
insert2053719859tate_o: produc696469763tate_o > set_Pr1590995257tate_o > set_Pr1590995257tate_o ).
thf(func_def_73,type,
insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_74,type,
insert311944171_state: produc1115495963_state > set_Pr795498619_state > set_Pr795498619_state ).
thf(func_def_75,type,
insert1597128631tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > set_Pr1702239303tate_o ).
thf(func_def_76,type,
insert584009271at_nat: produc842455143at_nat > set_Pr1490359111at_nat > set_Pr1490359111at_nat ).
thf(func_def_77,type,
insert1616594103_state: produc1390548711_state > set_Pr778812871_state > set_Pr778812871_state ).
thf(func_def_78,type,
is_emp807847857tate_o: set_Pr1590995257tate_o > $o ).
thf(func_def_79,type,
is_emp825011411at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_80,type,
is_emp1062983149_state: set_Pr795498619_state > $o ).
thf(func_def_81,type,
is_sin1547905295tate_o: set_Pr1590995257tate_o > $o ).
thf(func_def_82,type,
is_sin1352690165at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_83,type,
is_sin1132515087_state: set_Pr795498619_state > $o ).
thf(func_def_84,type,
the_el1569055182tate_o: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_85,type,
the_el1949240438at_nat: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_86,type,
the_el1967402896_state: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_87,type,
less_than: set_Pr1986765409at_nat ).
thf(func_def_88,type,
measure_nat: ( nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_89,type,
measure_state: ( state > nat ) > set_Pr795498619_state ).
thf(func_def_90,type,
pred_nat: set_Pr1986765409at_nat ).
thf(func_def_91,type,
wf_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_92,type,
wf_state: set_Pr795498619_state > $o ).
thf(func_def_93,type,
wf_Pro309705690tate_o: set_Pr1702239303tate_o > $o ).
thf(func_def_94,type,
wf_Pro745352042at_nat: set_Pr1490359111at_nat > $o ).
thf(func_def_95,type,
wf_Pro1783588484_state: set_Pr778812871_state > $o ).
thf(func_def_96,type,
member_nat: nat > set_nat > $o ).
thf(func_def_97,type,
member_state: state > set_state > $o ).
thf(func_def_98,type,
member1838112666tate_o: produc696469763tate_o > set_Pr1590995257tate_o > $o ).
thf(func_def_99,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_100,type,
member221067728tate_o: produc204914599tate_o > set_Pr1740974983tate_o > $o ).
thf(func_def_101,type,
member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o ).
thf(func_def_102,type,
member1629320336tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_103,type,
member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_104,type,
member768948240_state: produc1390548711_state > set_Pr778812871_state > $o ).
thf(func_def_105,type,
pa: a > state > $o ).
thf(func_def_106,type,
qa: a > state > $o ).
thf(func_def_107,type,
r: set_Pr795498619_state ).
thf(func_def_108,type,
x: state ).
thf(func_def_110,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_111,type,
vIMP: $o > $o > $o ).
thf(func_def_112,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_113,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_114,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_115,type,
vAND: $o > $o > $o ).
thf(func_def_116,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_117,type,
vNOT: $o > $o ).
thf(func_def_118,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_122,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_123,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
vOR: $o > $o > $o ).
thf(func_def_125,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
sK1: state ).
thf(func_def_131,type,
sK2: a ).
thf(func_def_132,type,
sK3: state > state ).
thf(func_def_133,type,
sK4: state > state ).
thf(func_def_134,type,
sK5: state > state ).
thf(func_def_135,type,
sK6: state > a ).
thf(func_def_136,type,
sK7: state > a ).
thf(func_def_137,type,
sK8: state > nat ).
thf(func_def_138,type,
sK9: produc1115495963_state > state ).
thf(func_def_139,type,
sK10: produc1115495963_state > state ).
thf(func_def_140,type,
sK11: product_prod_nat_nat > nat ).
thf(func_def_141,type,
sK12: product_prod_nat_nat > nat ).
thf(func_def_142,type,
sK13: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_143,type,
sK14: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_144,type,
sK15: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_145,type,
sK16: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_146,type,
sK17: product_prod_nat_nat > nat ).
thf(func_def_147,type,
sK18: state ).
thf(func_def_148,type,
sK19: state ).
thf(func_def_149,type,
sK20: nat ).
thf(func_def_150,type,
sK21: a ).
thf(func_def_151,type,
sK22: product_prod_nat_nat > nat ).
thf(func_def_152,type,
sK23: produc1115495963_state > state ).
thf(func_def_153,type,
sK24: produc1115495963_state > state ).
thf(func_def_154,type,
sK25: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_155,type,
sK26: produc696469763tate_o > produc204914599tate_o ).
thf(func_def_156,type,
sK27: produc696469763tate_o > a > state > $o ).
thf(func_def_157,type,
sK28: produc204914599tate_o > com ).
thf(func_def_158,type,
sK29: produc204914599tate_o > a > state > $o ).
thf(func_def_159,type,
sK30: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_160,type,
sK31: produc696469763tate_o > produc204914599tate_o ).
thf(func_def_161,type,
sK32: produc696469763tate_o > a > state > $o ).
thf(func_def_162,type,
sK33: ( produc1115495963_state > $o ) > state ).
thf(func_def_163,type,
sK34: ( produc1115495963_state > $o ) > state ).
thf(func_def_164,type,
sK35: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_165,type,
sK36: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_166,type,
sK37: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_167,type,
sK38: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_168,type,
sK39: produc204914599tate_o > a > state > $o ).
thf(func_def_169,type,
sK40: produc204914599tate_o > com ).
thf(f86,axiom,
( insert2053719859tate_o
= ( ^ [X0: produc696469763tate_o,X1: set_Pr1590995257tate_o] :
( collec1499596504tate_o
@ ^ [X2: produc696469763tate_o] :
( ( member1838112666tate_o @ X2 @ X1 )
| ( X2 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_insert__compr) ).
thf(f342,axiom,
( exec
= ( ^ [X0: state,X1: com,X2: state] :
? [X3: nat] : ( execn @ X0 @ X1 @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_exec__iff__execn) ).
thf(f355,axiom,
! [X0: state] :
( ( ( ! [X4: state,X3: state] :
( ( exec @ X3 @ body @ X4 )
=> ! [X5: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ X3 @ X0 ) @ r )
& ( pa @ X5 @ X3 ) )
=> ( qa @ X5 @ X4 ) ) )
& ! [X5: a,X3: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ X3 @ X0 ) @ r )
& ( pa @ X5 @ X3 ) )
=> ( termi @ body @ X3 ) ) )
=> ( ! [X6: state,X7: state] :
( ( exec @ X6 @ body @ X7 )
=> ! [X8: a] :
( ( ( pa @ X8 @ X6 )
& ( X6 = X0 ) )
=> ( qa @ X8 @ X7 ) ) )
& ! [X6: state,X8: a] :
( ( ( pa @ X8 @ X6 )
& ( X6 = X0 ) )
=> ( termi @ body @ X6 ) ) ) )
& ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [X1: a,X2: state] :
( ( pa @ X1 @ X2 )
& ( member1389040324_state @ ( produc64584659_state @ X2 @ X0 ) @ r ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [X1: a,X2: state] :
( ( X2 = X0 )
& ( pa @ X1 @ X2 ) )
@ body
@ qa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f356,axiom,
! [X0: state] :
( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
=> ( ! [X1: state,X3: a] :
( ( ( pa @ X3 @ X1 )
& ( X1 = X0 ) )
=> ( termi @ body @ X1 ) )
& ! [X1: state,X2: state] :
( ( exec @ X1 @ body @ X2 )
=> ! [X3: a] :
( ( ( pa @ X3 @ X1 )
& ( X1 = X0 ) )
=> ( qa @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(f357,conjecture,
( ! [X1: state,X0: state] :
( ! [X2: a] :
( ( qa @ X2 @ X1 )
| ( X0 != x )
| ~ ( pa @ X2 @ X0 ) )
| ~ ( exec @ X0 @ body @ X1 ) )
& ! [X2: a,X0: state] :
( ~ ( pa @ X2 @ X0 )
| ( termi @ body @ X0 )
| ( X0 != x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(f358,negated_conjecture,
~ ( ! [X1: state,X0: state] :
( ! [X2: a] :
( ( qa @ X2 @ X1 )
| ( X0 != x )
| ~ ( pa @ X2 @ X0 ) )
| ~ ( exec @ X0 @ body @ X1 ) )
& ! [X2: a,X0: state] :
( ~ ( pa @ X2 @ X0 )
| ( termi @ body @ X0 )
| ( X0 != x ) ) ),
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f407,plain,
~ ( ! [X0: state,X1: state] :
( ! [X2: a] :
( ( qa @ X2 @ X0 )
| ( x != X1 )
| ~ ( pa @ X2 @ X1 ) )
| ~ ( exec @ X1 @ body @ X0 ) )
& ! [X3: a,X4: state] :
( ~ ( pa @ X3 @ X4 )
| ( termi @ body @ X4 )
| ( x != X4 ) ) ),
inference(rectify,[],[f358]) ).
thf(f408,plain,
( $true
= ( ~ ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( exec @ Y0 @ body @ Y1 )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f407]) ).
thf(f625,plain,
( exec
= ( ^ [X0: state,X1: com,X2: state] :
? [X3: nat] : ( execn @ X0 @ X1 @ X3 @ X2 ) ) ),
inference(rectify,[],[f342]) ).
thf(f626,plain,
( exec
= ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f625]) ).
thf(f843,plain,
( insert2053719859tate_o
= ( ^ [X0: produc696469763tate_o,X1: set_Pr1590995257tate_o] :
( collec1499596504tate_o
@ ^ [X2: produc696469763tate_o] :
( ( member1838112666tate_o @ X2 @ X1 )
| ( X2 = X0 ) ) ) ) ),
inference(rectify,[],[f86]) ).
thf(f844,plain,
( insert2053719859tate_o
= ( ^ [Y0: produc696469763tate_o,Y1: set_Pr1590995257tate_o] :
( collec1499596504tate_o
@ ^ [Y2: produc696469763tate_o] :
( ( Y0 = Y2 )
| ( member1838112666tate_o @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f843]) ).
thf(f855,plain,
! [X0: state] :
( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
=> ( ! [X1: state,X2: a] :
( ( ( pa @ X2 @ X1 )
& ( X1 = X0 ) )
=> ( termi @ body @ X1 ) )
& ! [X3: state,X4: state] :
( ( exec @ X3 @ body @ X4 )
=> ! [X5: a] :
( ( ( pa @ X5 @ X3 )
& ( X0 = X3 ) )
=> ( qa @ X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f356]) ).
thf(f856,plain,
( $true
= ( !! @ state
@ ^ [Y0: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y0 @ x ) @ r )
=> ( ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( exec @ Y2 @ body @ Y1 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f855]) ).
thf(f880,plain,
! [X0: state] :
( ( ( ! [X1: state,X2: state] :
( ( exec @ X2 @ body @ X1 )
=> ! [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ X2 @ X0 ) @ r )
& ( pa @ X3 @ X2 ) )
=> ( qa @ X3 @ X1 ) ) )
& ! [X4: a,X5: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r )
& ( pa @ X4 @ X5 ) )
=> ( termi @ body @ X5 ) ) )
=> ( ! [X6: state,X7: state] :
( ( exec @ X6 @ body @ X7 )
=> ! [X8: a] :
( ( ( pa @ X8 @ X6 )
& ( X6 = X0 ) )
=> ( qa @ X8 @ X7 ) ) )
& ! [X9: state,X10: a] :
( ( ( pa @ X10 @ X9 )
& ( X0 = X9 ) )
=> ( termi @ body @ X9 ) ) ) )
& ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [X11: a,X12: state] :
( ( pa @ X11 @ X12 )
& ( member1389040324_state @ ( produc64584659_state @ X12 @ X0 ) @ r ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [X13: a,X14: state] :
( ( X0 = X14 )
& ( pa @ X13 @ X14 ) )
@ body
@ qa ) ),
inference(rectify,[],[f355]) ).
thf(f881,plain,
( ( !! @ state
@ ^ [Y0: state] :
( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y1: a,Y2: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Y0 ) @ r )
& ( pa @ Y1 @ Y2 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y1: a,Y2: state] :
( ( pa @ Y1 @ Y2 )
& ( Y0 = Y2 ) )
@ body
@ qa )
& ( ( ( !! @ state
@ ^ [Y1: state] :
( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( exec @ Y1 @ body @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( pa @ Y3 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( qa @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( exec @ Y2 @ body @ Y1 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f880]) ).
thf(f1093,plain,
( $true
= ( !! @ state
@ ^ [Y0: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y0 @ x ) @ r )
=> ( ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( exec @ Y2 @ body @ Y1 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f856]) ).
thf(f1118,plain,
( insert2053719859tate_o
= ( ^ [Y0: produc696469763tate_o,Y1: set_Pr1590995257tate_o] :
( collec1499596504tate_o
@ ^ [Y2: produc696469763tate_o] :
( ( Y0 = Y2 )
| ( member1838112666tate_o @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f844]) ).
thf(f1153,plain,
( $true
= ( ~ ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( exec @ Y0 @ body @ Y1 )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f408]) ).
thf(f1189,plain,
( ( !! @ state
@ ^ [Y0: state] :
( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y1: a,Y2: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Y0 ) @ r )
& ( pa @ Y1 @ Y2 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y1: a,Y2: state] :
( ( pa @ Y1 @ Y2 )
& ( Y0 = Y2 ) )
@ body
@ qa )
& ( ( ( !! @ state
@ ^ [Y1: state] :
( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( exec @ Y1 @ body @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( pa @ Y3 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( qa @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( exec @ Y2 @ body @ Y1 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f881]) ).
thf(f1203,plain,
( exec
= ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f626]) ).
thf(f1422,plain,
( $true
= ( !! @ state
@ ^ [Y0: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y0 @ x ) @ r )
=> ( ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ^ [Y3: state,Y4: com,Y5: state] :
( ?? @ nat
@ ^ [Y6: nat] : ( execn @ Y3 @ Y4 @ Y6 @ Y5 ) )
@ Y2
@ body
@ Y1 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f1093,f1203]) ).
thf(f1459,plain,
( $true
= ( ~ ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ^ [Y2: state,Y3: com,Y4: state] :
( ?? @ nat
@ ^ [Y5: nat] : ( execn @ Y2 @ Y3 @ Y5 @ Y4 ) )
@ Y0
@ body
@ Y1 )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f1153,f1203]) ).
thf(f1479,plain,
( ( !! @ state
@ ^ [Y0: state] :
( ( pHoare382919414oare_a
@ ( ^ [Y1: produc696469763tate_o,Y2: set_Pr1590995257tate_o] :
( collec1499596504tate_o
@ ^ [Y3: produc696469763tate_o] :
( ( Y1 = Y3 )
| ( member1838112666tate_o @ Y3 @ Y2 ) ) )
@ ( produc33908149tate_o
@ ^ [Y1: a,Y2: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Y0 ) @ r )
& ( pa @ Y1 @ Y2 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y1: a,Y2: state] :
( ( pa @ Y1 @ Y2 )
& ( Y0 = Y2 ) )
@ body
@ qa )
& ( ( ( !! @ state
@ ^ [Y1: state] :
( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ^ [Y3: state,Y4: com,Y5: state] :
( ?? @ nat
@ ^ [Y6: nat] : ( execn @ Y3 @ Y4 @ Y6 @ Y5 ) )
@ Y1
@ body
@ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( pa @ Y3 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( qa @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ^ [Y3: state,Y4: com,Y5: state] :
( ?? @ nat
@ ^ [Y6: nat] : ( execn @ Y3 @ Y4 @ Y6 @ Y5 ) )
@ Y2
@ body
@ Y1 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f1189,f1118,f1203,f1203]) ).
thf(f1660,plain,
( ( !! @ state
@ ^ [Y0: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y0 @ x ) @ r )
=> ( ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y2 @ body @ Y3 @ Y1 ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1422]) ).
thf(f1701,plain,
( $true
= ( !! @ state
@ ^ [Y0: state] :
( ( pHoare382919414oare_a
@ ( collec1499596504tate_o
@ ^ [Y1: produc696469763tate_o] :
( ( ( produc33908149tate_o
@ ^ [Y2: a,Y3: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y3 @ Y0 ) @ r )
& ( pa @ Y2 @ Y3 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
= Y1 )
| ( member1838112666tate_o @ Y1 @ bot_bo170732493tate_o ) ) )
@ ^ [Y1: a,Y2: state] :
( ( pa @ Y1 @ Y2 )
& ( Y0 = Y2 ) )
@ body
@ qa )
& ( ( ( !! @ state
@ ^ [Y1: state] :
( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y1 @ body @ Y3 @ Y2 ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( pa @ Y3 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( qa @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y2 @ body @ Y3 @ Y1 ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1479]) ).
thf(f1742,plain,
( $true
= ( ~ ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1459]) ).
thf(f1746,plain,
( $false
= ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f1742]) ).
thf(f1747,plain,
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f1746]) ).
thf(f1749,definition,
( spl0_1
<=> ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f1751,plain,
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1749]) ).
thf(f1753,definition,
( spl0_2
<=> ( $false
= ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f1755,plain,
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1753]) ).
thf(f1756,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1747,f1753,f1749]) ).
thf(f1757,plain,
( ( $false
= ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( x != Y0 )
| ( termi @ body @ Y0 )
| ~ ( pa @ Y1 @ Y0 ) ) )
@ sK1 ) )
| ~ spl0_2 ),
inference(sigma_proxy_clausification,[],[f1755]) ).
thf(f1758,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( x != sK1 )
| ( termi @ body @ sK1 )
| ~ ( pa @ Y0 @ sK1 ) ) ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f1757]) ).
thf(f1759,plain,
( ( $false
= ( ^ [Y0: a] :
( ( x != sK1 )
| ( termi @ body @ sK1 )
| ~ ( pa @ Y0 @ sK1 ) )
@ sK2 ) )
| ~ spl0_2 ),
inference(sigma_proxy_clausification,[],[f1758]) ).
thf(f1760,plain,
( ( ( ( x != sK1 )
| ( termi @ body @ sK1 )
| ~ ( pa @ sK2 @ sK1 ) )
= $false )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f1759]) ).
thf(f1761,plain,
( ( $false
= ( ~ ( pa @ sK2 @ sK1 ) ) )
| ~ spl0_2 ),
inference(or_proxy_clausification,[],[f1760]) ).
thf(f1762,plain,
( ( $false
= ( ( x != sK1 )
| ( termi @ body @ sK1 ) ) )
| ~ spl0_2 ),
inference(or_proxy_clausification,[],[f1760]) ).
thf(f1763,plain,
( ( ( pa @ sK2 @ sK1 )
= $true )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f1761]) ).
thf(f1764,plain,
( ( $false
= ( termi @ body @ sK1 ) )
| ~ spl0_2 ),
inference(or_proxy_clausification,[],[f1762]) ).
thf(f1765,plain,
( ( $false
= ( x != sK1 ) )
| ~ spl0_2 ),
inference(or_proxy_clausification,[],[f1762]) ).
thf(f1766,plain,
( ( ( x = sK1 )
= $true )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f1765]) ).
thf(f1767,plain,
( ( x = sK1 )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f1766]) ).
thf(f1768,plain,
! [X1: state] :
( ( ^ [Y0: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y0 @ x ) @ r )
=> ( ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y2 @ body @ Y3 @ Y1 ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1660]) ).
thf(f1769,plain,
! [X1: state] :
( $true
= ( ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r )
=> ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1768]) ).
thf(f1770,plain,
! [X1: state] :
( ( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(imp_proxy_clausification,[],[f1769]) ).
thf(f1771,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(and_proxy_clausification,[],[f1770]) ).
thf(f1772,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(and_proxy_clausification,[],[f1770]) ).
thf(f1784,plain,
! [X1: state] :
( ( ^ [Y0: state] :
( ( pHoare382919414oare_a
@ ( collec1499596504tate_o
@ ^ [Y1: produc696469763tate_o] :
( ( ( produc33908149tate_o
@ ^ [Y2: a,Y3: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y3 @ Y0 ) @ r )
& ( pa @ Y2 @ Y3 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
= Y1 )
| ( member1838112666tate_o @ Y1 @ bot_bo170732493tate_o ) ) )
@ ^ [Y1: a,Y2: state] :
( ( pa @ Y1 @ Y2 )
& ( Y0 = Y2 ) )
@ body
@ qa )
& ( ( ( !! @ state
@ ^ [Y1: state] :
( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y1 @ body @ Y3 @ Y2 ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( pa @ Y3 @ Y1 )
& ( member1389040324_state @ ( produc64584659_state @ Y1 @ Y0 ) @ r ) )
=> ( qa @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ state
@ ^ [Y2: state] :
( ( ( Y0 = Y2 )
& ( pa @ Y1 @ Y2 ) )
=> ( termi @ body @ Y2 ) ) ) )
& ( !! @ state
@ ^ [Y1: state] :
( !! @ state
@ ^ [Y2: state] :
( ( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y2 @ body @ Y3 @ Y1 ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 = Y2 )
& ( pa @ Y3 @ Y2 ) )
=> ( qa @ Y3 @ Y1 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1701]) ).
thf(f1785,plain,
! [X1: state] :
( $true
= ( ( pHoare382919414oare_a
@ ( collec1499596504tate_o
@ ^ [Y0: produc696469763tate_o] :
( ( ( produc33908149tate_o
@ ^ [Y1: a,Y2: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y2 @ X1 ) @ r )
& ( pa @ Y1 @ Y2 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
= Y0 )
| ( member1838112666tate_o @ Y0 @ bot_bo170732493tate_o ) ) )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X1 = Y1 ) )
@ body
@ qa )
& ( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1784]) ).
thf(f1786,plain,
! [X1: state] :
( $true
= ( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1785]) ).
thf(f1788,plain,
! [X1: state] :
( ( $false
= ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1786]) ).
thf(f1789,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) )
& ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1788]) ).
thf(f1790,plain,
! [X1: state] :
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1789]) ).
thf(f1791,plain,
! [X1: state] :
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1789]) ).
thf(f1792,plain,
( ( ( pa @ sK2 @ x )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1763,f1767]) ).
thf(f1793,plain,
! [X2: a,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1771]) ).
thf(f1794,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(beta-eta_normalization,[],[f1793]) ).
thf(f1795,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1794]) ).
thf(f1796,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1795]) ).
thf(f1797,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1796]) ).
thf(f1798,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( X1 = X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f1797]) ).
thf(f1799,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f1798]) ).
thf(f1800,plain,
( ( $false
= ( termi @ body @ x ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1764,f1767]) ).
thf(f1805,plain,
! [X2: state,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1772]) ).
thf(f1806,plain,
! [X2: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ Y0 @ body @ Y1 @ X2 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( X1 = Y0 )
& ( pa @ Y1 @ Y0 ) )
=> ( qa @ Y1 @ X2 ) ) ) ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(beta-eta_normalization,[],[f1805]) ).
thf(f1807,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ Y0 @ body @ Y1 @ X2 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( X1 = Y0 )
& ( pa @ Y1 @ Y0 ) )
=> ( qa @ Y1 @ X2 ) ) ) )
@ X3 ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(pi_proxy_clausification,[],[f1806]) ).
thf(f1808,plain,
! [X2: state,X3: state,X1: state] :
( ( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(beta-eta_normalization,[],[f1807]) ).
thf(f1809,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(imp_proxy_clausification,[],[f1808]) ).
thf(f1810,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) ) ),
inference(pi_proxy_clausification,[],[f1809]) ).
thf(f1811,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1810]) ).
thf(f1812,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f1811]) ).
thf(f1813,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( X1 = X3 )
= $false )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f1812]) ).
thf(f1814,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f1813]) ).
thf(f1815,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1814]) ).
thf(f1818,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f1815]) ).
thf(f1821,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1791]) ).
thf(f1824,plain,
! [X1: state] :
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y1 @ Y0 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1821]) ).
thf(f1825,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y1 @ Y0 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y1 @ Y0 ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1824]) ).
thf(f1827,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1825]) ).
thf(f1829,plain,
! [X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1827]) ).
thf(f1830,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1827]) ).
thf(f1831,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( pa @ Y2 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( qa @ Y2 @ Y1 ) ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1790]) ).
thf(f1834,plain,
! [X1: state] :
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y1 @ Y0 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y1 @ Y0 ) ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1831]) ).
thf(f1835,plain,
! [X1: state] :
( ( $false
= ( ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y1 @ Y0 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y1 @ Y0 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1834]) ).
thf(f1838,plain,
! [X1: state] :
( ( $false
= ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1835]) ).
thf(f1839,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1838]) ).
thf(f1840,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1838]) ).
thf(f1841,plain,
! [X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1830]) ).
thf(f1843,plain,
! [X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1841]) ).
thf(f1845,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1843]) ).
thf(f1848,plain,
! [X1: state] :
( ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1845]) ).
thf(f1849,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1848]) ).
thf(f1850,plain,
! [X1: state] :
( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1848]) ).
thf(f1851,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f1850]) ).
thf(f1852,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1850]) ).
thf(f1854,plain,
! [X1: state] :
( ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) )
@ ( sK7 @ X1 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1829]) ).
thf(f1857,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1854]) ).
thf(f1858,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1857]) ).
thf(f1859,plain,
! [X1: state] :
( ( $true
= ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1857]) ).
thf(f1860,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1859]) ).
thf(f1861,plain,
! [X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1859]) ).
thf(f1862,plain,
! [X2: a,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1849]) ).
thf(f1863,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1862]) ).
thf(f1865,plain,
! [X2: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) )
@ X2 )
= $true )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f1840]) ).
thf(f1866,plain,
! [X2: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ Y0 @ body @ Y1 @ X2 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( X1 = Y0 )
& ( pa @ Y1 @ Y0 ) )
=> ( qa @ Y1 @ X2 ) ) ) ) )
= $true )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1865]) ).
thf(f1867,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ Y0 @ body @ Y1 @ X2 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( X1 = Y0 )
& ( pa @ Y1 @ Y0 ) )
=> ( qa @ Y1 @ X2 ) ) ) )
@ X3 ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1866]) ).
thf(f1868,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1867]) ).
thf(f1869,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1868]) ).
thf(f1871,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1863]) ).
thf(f1872,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1871]) ).
thf(f1873,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1872]) ).
thf(f1874,plain,
! [X2: a,X3: state,X1: state] :
( ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( X1 = X3 )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1873]) ).
thf(f1875,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f1874]) ).
thf(f1876,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1869]) ).
thf(f1878,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1876]) ).
thf(f1880,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1878]) ).
thf(f1883,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1880]) ).
thf(f1884,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1883]) ).
thf(f1885,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1883]) ).
thf(f1886,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f1885]) ).
thf(f1887,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1885]) ).
thf(f1888,plain,
! [X2: a,X3: state,X1: state] :
( ( X1 != X3 )
| ( ( ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) )
@ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1875]) ).
thf(f1889,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f1888]) ).
thf(f1890,plain,
! [X2: state,X1: state] :
( ( ( ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y1 @ body @ Y2 @ Y0 ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( ( X1 = Y1 )
& ( pa @ Y2 @ Y1 ) )
=> ( qa @ Y2 @ Y0 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f1839]) ).
thf(f1891,plain,
! [X2: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ Y0 @ body @ Y1 @ X2 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( X1 = Y0 )
& ( pa @ Y1 @ Y0 ) )
=> ( qa @ Y1 @ X2 ) ) ) ) )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1890]) ).
thf(f1895,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) )
| ( $true
= ( ^ [Y0: state] :
( ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ Y0 @ body @ Y1 @ X2 ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( ( X1 = Y0 )
& ( pa @ Y1 @ Y0 ) )
=> ( qa @ Y1 @ X2 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1891]) ).
thf(f1896,plain,
! [X2: state,X3: state,X1: state] :
( ( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
= $true )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1895]) ).
thf(f1897,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1896]) ).
thf(f1900,plain,
! [X2: state,X3: state,X0: state,X1: a,X4: a] :
( ( ( termi @ body @ X2 )
= $true )
| ( $false
= ( pa @ X4 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ X3 @ x ) @ r )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( pa @ X1 @ X2 )
= $false )
| ( X0 != X2 )
| ( $false = $true )
| ( ( qa @ X4 @ ( sK4 @ X0 ) )
= $true )
| ( ( sK3 @ X0 )
!= X3 ) ),
inference(superposition,[],[f1889,f1818]) ).
thf(f1902,plain,
! [X2: state,X3: state,X0: state,X1: a,X4: a] :
( ( ( sK3 @ X0 )
!= X3 )
| ( ( pa @ X1 @ X2 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ X3 @ x ) @ r )
= $false )
| ( $false
= ( pa @ X4 @ ( sK3 @ X0 ) ) )
| ( ( qa @ X4 @ ( sK4 @ X0 ) )
= $true )
| ( ( termi @ body @ X2 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( X0 != X2 ) ),
inference(trivial_inequality_removal,[],[f1900]) ).
thf(f1907,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ Y0 @ ( sK4 @ X1 ) ) )
@ ( sK7 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1897]) ).
thf(f1910,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
=> ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1907]) ).
thf(f1911,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1910]) ).
thf(f1912,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) )
| ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1910]) ).
thf(f1913,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(and_proxy_clausification,[],[f1912]) ).
thf(f1914,plain,
! [X2: state,X3: state,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1912]) ).
thf(f1917,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1884]) ).
thf(f1918,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1917]) ).
thf(f1919,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1918]) ).
thf(f1920,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( X1 = X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1919]) ).
thf(f1921,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f1920]) ).
thf(f1926,plain,
! [X2: state,X3: a,X0: a,X1: state] :
( ( $false
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X2 ) @ x ) @ r ) )
| ( $false
= ( pa @ X3 @ ( sK3 @ X2 ) ) )
| ( ( termi @ body @ ( sK5 @ X2 ) )
= $false )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( $true
= ( qa @ X3 @ ( sK4 @ X2 ) ) )
| ( ( termi @ body @ X1 )
= $true )
| ( X1 != X2 ) ),
inference(equality_resolution,[],[f1902]) ).
thf(f1929,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( pa @ X4 @ X3 ) )
| ( ( ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) )
@ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( X1 != X3 )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f1921]) ).
thf(f1930,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f1929]) ).
thf(f1931,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( X1 != X3 )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1930]) ).
thf(f1934,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f1931]) ).
thf(f1939,plain,
! [X2: state,X3: state,X0: state,X1: a,X6: a,X4: nat,X5: state] :
( ( ( sK3 @ X0 )
!= X5 )
| ( ( qa @ X1 @ X3 )
= $true )
| ( ( pa @ X1 @ X2 )
= $false )
| ( ( execn @ X2 @ body @ X4 @ X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( qa @ X6 @ ( sK4 @ X0 ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X5 @ x ) @ r ) )
| ( $false
= ( pa @ X6 @ ( sK3 @ X0 ) ) )
| ( X0 != X2 )
| ( $false = $true ) ),
inference(superposition,[],[f1934,f1818]) ).
thf(f1942,plain,
! [X2: state,X3: state,X0: state,X1: a,X6: a,X4: nat,X5: state] :
( ( ( sK3 @ X0 )
!= X5 )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X5 @ x ) @ r ) )
| ( $false
= ( pa @ X6 @ ( sK3 @ X0 ) ) )
| ( ( qa @ X6 @ ( sK4 @ X0 ) )
= $true )
| ( ( execn @ X2 @ body @ X4 @ X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( qa @ X1 @ X3 )
= $true )
| ( ( pa @ X1 @ X2 )
= $false )
| ( X0 != X2 ) ),
inference(trivial_inequality_removal,[],[f1939]) ).
thf(f1945,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1858]) ).
thf(f1947,plain,
! [X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1945]) ).
thf(f1950,plain,
! [X1: state] :
( ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1947]) ).
thf(f1952,plain,
! [X1: state] :
( ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1950]) ).
thf(f1954,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1952]) ).
thf(f1955,plain,
! [X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1952]) ).
thf(f1956,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f1955]) ).
thf(f1957,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1955]) ).
thf(f1958,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1911]) ).
thf(f1960,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1958]) ).
thf(f1962,plain,
! [X2: a,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1954]) ).
thf(f1963,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1962]) ).
thf(f1967,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1960]) ).
thf(f1969,plain,
! [X2: state,X3: state,X1: state] :
( ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1967]) ).
thf(f1971,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1969]) ).
thf(f1972,plain,
! [X2: state,X3: state,X1: state] :
( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1969]) ).
thf(f1973,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f1972]) ).
thf(f1974,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1972]) ).
thf(f1975,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1963]) ).
thf(f1976,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1975]) ).
thf(f1977,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1976]) ).
thf(f1978,plain,
! [X2: a,X3: state,X1: state] :
( ( ( X1 = X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f1977]) ).
thf(f1979,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f1978]) ).
thf(f1986,plain,
! [X2: state,X3: nat,X0: state,X1: a,X4: state,X5: a] :
( ( ( execn @ X2 @ body @ X3 @ X4 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( qa @ X5 @ X4 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X5 @ X2 )
= $false )
| ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( X0 != X2 ) ),
inference(equality_resolution,[],[f1942]) ).
thf(f1990,plain,
! [X2: a,X1: state] :
( ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1957]) ).
thf(f1991,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1990]) ).
thf(f1995,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1971]) ).
thf(f1996,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1995]) ).
thf(f1997,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1996]) ).
thf(f1998,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( X1 = X3 )
= $false )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f1997]) ).
thf(f1999,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f1998]) ).
thf(f2000,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1999]) ).
thf(f2003,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2000]) ).
thf(f2024,plain,
! [X2: a,X1: state] :
( ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1852]) ).
thf(f2025,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2024]) ).
thf(f2026,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2025]) ).
thf(f2027,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2026]) ).
thf(f2028,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2027]) ).
thf(f2029,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( X1 = X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f2028]) ).
thf(f2030,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2029]) ).
thf(f2033,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) )
@ ( sK8 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f2030]) ).
thf(f2034,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2033]) ).
thf(f2040,plain,
! [X2: a,X3: state,X0: state,X1: state,X4: a] :
( ( ( termi @ body @ X3 )
= $true )
| ( X0 != X3 )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( $false = $true )
| ( ( sK3 @ X0 )
!= X1 )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) ) ),
inference(superposition,[],[f1818,f2034]) ).
thf(f2043,plain,
! [X2: a,X3: state,X0: state,X1: state,X4: a] :
( ( ( sK3 @ X0 )
!= X1 )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( X0 != X3 ) ),
inference(trivial_inequality_removal,[],[f2040]) ).
thf(f2052,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1991]) ).
thf(f2053,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2052]) ).
thf(f2054,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f2053]) ).
thf(f2055,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( X1 = X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f2054]) ).
thf(f2056,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2055]) ).
thf(f2061,plain,
! [X2: a,X1: state] :
( ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f1851]) ).
thf(f2062,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2061]) ).
thf(f2068,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f2062]) ).
thf(f2069,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2068]) ).
thf(f2070,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2069]) ).
thf(f2071,plain,
! [X2: a,X3: state,X1: state] :
( ( ( X1 = X3 )
= $false )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f2070]) ).
thf(f2072,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2071]) ).
thf(f2075,plain,
! [X2: a,X3: state,X1: state] :
( ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) )
@ ( sK8 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(sigma_proxy_clausification,[],[f2072]) ).
thf(f2076,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2075]) ).
thf(f2084,plain,
! [X2: a,X3: state,X0: state,X1: state,X4: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( X0 != X3 )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( sK3 @ X0 )
!= X1 )
| ( $false = $true )
| ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false ) ),
inference(superposition,[],[f1818,f2076]) ).
thf(f2087,plain,
! [X2: a,X3: state,X0: state,X1: state,X4: a] :
( ( ( sK3 @ X0 )
!= X1 )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( X0 != X3 ) ),
inference(trivial_inequality_removal,[],[f2084]) ).
thf(f2089,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1887]) ).
thf(f2090,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2089]) ).
thf(f2091,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2090]) ).
thf(f2092,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( ( X1 = X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f2091]) ).
thf(f2093,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2092]) ).
thf(f2098,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) )
@ ( sK8 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f2093]) ).
thf(f2099,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2098]) ).
thf(f2106,plain,
! [X2: state,X3: a,X0: a,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ x ) @ r )
= $false )
| ( $false
= ( pa @ X3 @ X2 ) )
| ( ( qa @ X0 @ ( sK4 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X0 @ ( sK3 @ X1 ) ) )
| ( ( termi @ body @ X2 )
= $true )
| ( X1 != X2 ) ),
inference(equality_resolution,[],[f2043]) ).
thf(f2107,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 )
| ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2099]) ).
thf(f2115,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2107]) ).
thf(f2124,plain,
! [X2: a,X3: a,X0: state,X1: state,X6: nat,X4: state,X5: state] :
( ( X0 != X4 )
| ( $true
= ( qa @ X3 @ X5 ) )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( $false = $true )
| ( ( sK3 @ X0 )
!= X1 )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( $false
= ( execn @ X4 @ body @ X6 @ X5 ) )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( $false
= ( pa @ X3 @ X4 ) ) ),
inference(superposition,[],[f1818,f2115]) ).
thf(f2126,plain,
! [X2: a,X3: a,X0: state,X1: state,X6: nat,X4: state,X5: state] :
( ( ( sK3 @ X0 )
!= X1 )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( $true
= ( qa @ X3 @ X5 ) )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( $false
= ( execn @ X4 @ body @ X6 @ X5 ) )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r ) )
| ( X0 != X4 ) ),
inference(trivial_inequality_removal,[],[f2124]) ).
thf(f2137,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1886]) ).
thf(f2138,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(beta-eta_normalization,[],[f2137]) ).
thf(f2139,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2138]) ).
thf(f2140,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( X1 = X3 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2139]) ).
thf(f2141,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2140]) ).
thf(f2144,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( X1 != X3 )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( ^ [Y0: nat] : ( execn @ ( sK3 @ X1 ) @ body @ Y0 @ ( sK4 @ X1 ) )
@ ( sK8 @ X1 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f2141]) ).
thf(f2145,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2144]) ).
thf(f2154,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( X1 != X3 )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2145]) ).
thf(f2160,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( execn @ ( sK3 @ X1 ) @ body @ ( sK8 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2154]) ).
thf(f2167,plain,
! [X2: nat,X3: state,X0: state,X1: state,X6: a,X4: a,X5: state] :
( ( ( execn @ X1 @ body @ X2 @ X3 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( X0 != X1 )
| ( ( sK3 @ X0 )
!= X5 )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X5 @ x ) @ r ) )
| ( ( qa @ X6 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X4 @ X1 )
= $false )
| ( $false
= ( pa @ X6 @ ( sK3 @ X0 ) ) )
| ( $true
= ( qa @ X4 @ X3 ) )
| ( $false = $true ) ),
inference(superposition,[],[f2160,f1818]) ).
thf(f2171,plain,
! [X2: nat,X3: state,X0: state,X1: state,X6: a,X4: a,X5: state] :
( ( ( sK3 @ X0 )
!= X5 )
| ( $false
= ( member1389040324_state @ ( produc64584659_state @ X5 @ x ) @ r ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( $false
= ( pa @ X6 @ ( sK3 @ X0 ) ) )
| ( ( pa @ X4 @ X1 )
= $false )
| ( ( execn @ X1 @ body @ X2 @ X3 )
= $false )
| ( $true
= ( qa @ X4 @ X3 ) )
| ( ( qa @ X6 @ ( sK4 @ X0 ) )
= $true )
| ( X0 != X1 ) ),
inference(trivial_inequality_removal,[],[f2167]) ).
thf(f2181,plain,
! [X2: a,X3: state,X0: a,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X3 ) @ X3 ) @ r )
= $true )
| ( ( pa @ X2 @ ( sK3 @ X3 ) )
= $false )
| ( ( termi @ body @ X1 )
= $true )
| ( $true
= ( qa @ X2 @ ( sK4 @ X3 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X3 ) @ x ) @ r )
= $false )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( X1 != X3 ) ),
inference(equality_resolution,[],[f2087]) ).
thf(f2185,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1861]) ).
thf(f2187,plain,
! [X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2185]) ).
thf(f2193,plain,
! [X1: state] :
( ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2187]) ).
thf(f2195,plain,
! [X1: state] :
( ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2193]) ).
thf(f2197,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2195]) ).
thf(f2198,plain,
! [X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2195]) ).
thf(f2199,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f2198]) ).
thf(f2200,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2198]) ).
thf(f2206,plain,
! [X2: a,X1: state] :
( ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2197]) ).
thf(f2207,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2206]) ).
thf(f2208,plain,
! [X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1860]) ).
thf(f2211,plain,
! [X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2208]) ).
thf(f2214,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2211]) ).
thf(f2217,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f2214]) ).
thf(f2218,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(imp_proxy_clausification,[],[f2217]) ).
thf(f2219,plain,
! [X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2217]) ).
thf(f2220,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(and_proxy_clausification,[],[f2219]) ).
thf(f2221,plain,
! [X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2219]) ).
thf(f2227,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2207]) ).
thf(f2228,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2227]) ).
thf(f2229,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2228]) ).
thf(f2230,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( X1 = X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f2229]) ).
thf(f2231,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2230]) ).
thf(f2235,plain,
! [X2: state,X3: state,X1: state] :
( ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1914]) ).
thf(f2237,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2235]) ).
thf(f2246,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f2237]) ).
thf(f2249,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f2246]) ).
thf(f2250,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f2249]) ).
thf(f2251,plain,
! [X2: state,X3: state,X1: state] :
( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f2249]) ).
thf(f2252,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2251]) ).
thf(f2253,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2251]) ).
thf(f2266,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( ( ^ [Y0: state] :
( !! @ a
@ ^ [Y1: a] :
( ( ( pa @ Y1 @ Y0 )
& ( member1389040324_state @ ( produc64584659_state @ Y0 @ X1 ) @ r ) )
=> ( termi @ body @ Y0 ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1913]) ).
thf(f2269,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2266]) ).
thf(f2277,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( pa @ Y0 @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
@ ( sK6 @ X1 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(sigma_proxy_clausification,[],[f2269]) ).
thf(f2279,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
=> ( termi @ body @ ( sK5 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f2277]) ).
thf(f2281,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2279]) ).
thf(f2282,plain,
! [X2: state,X3: state,X1: state] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
& ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r ) )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2279]) ).
thf(f2283,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f2282]) ).
thf(f2284,plain,
! [X2: state,X3: state,X1: state] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2282]) ).
thf(f2295,plain,
! [X2: a,X3: state,X0: a,X1: state,X4: a] :
( ( ( termi @ body @ X1 )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false = $true )
| ( ( termi @ body @ X3 )
= $true )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( ( sK5 @ x )
!= X1 )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( x != X3 )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false ) ),
inference(superposition,[],[f1799,f2181]) ).
thf(f2297,plain,
! [X2: a,X3: state,X0: a,X1: state,X4: a] :
( ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( ( termi @ body @ X1 )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( ( sK5 @ x )
!= X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false )
| ( x != X3 )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f2295]) ).
thf(f2299,definition,
( spl0_3
<=> ! [X0: a] :
( ( ( qa @ X0 @ ( sK4 @ x ) )
= $true )
| ( ( pa @ X0 @ ( sK3 @ x ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f2300,plain,
( ! [X0: a] :
( ( ( qa @ X0 @ ( sK4 @ x ) )
= $true )
| ( ( pa @ X0 @ ( sK3 @ x ) )
= $false ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f2299]) ).
thf(f2302,definition,
( spl0_4
<=> ! [X2: a,X1: state] :
( ( ( termi @ body @ X1 )
= $true )
| ( x != X1 )
| ( $false
= ( pa @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f2303,plain,
( ! [X2: a,X1: state] :
( ( x != X1 )
| ( $false
= ( pa @ X2 @ X1 ) )
| ( ( termi @ body @ X1 )
= $true ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f2302]) ).
thf(f2305,definition,
( spl0_5
<=> ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f2307,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f2305]) ).
thf(f2309,definition,
( spl0_6
<=> ! [X4: state,X3: a] :
( ( ( sK5 @ x )
!= X4 )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( ( termi @ body @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f2310,plain,
( ! [X3: a,X4: state] :
( ( ( sK5 @ x )
!= X4 )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( ( termi @ body @ X4 )
= $true ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f2309]) ).
thf(f2312,plain,
( spl0_4
| spl0_3
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f2297,f2309,f2305,f2299,f2302]) ).
thf(f2322,plain,
! [X2: a,X1: state] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(pi_proxy_clausification,[],[f2218]) ).
thf(f2323,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2322]) ).
thf(f2340,definition,
( spl0_7
<=> ( $false
= ( termi @ body @ ( sK5 @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f2342,plain,
( ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f2340]) ).
thf(f2344,definition,
( spl0_8
<=> ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f2346,plain,
( ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f2344]) ).
thf(f2349,definition,
( spl0_9
<=> ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f2351,plain,
( ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f2349]) ).
thf(f2360,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2323]) ).
thf(f2361,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2360]) ).
thf(f2362,plain,
! [X2: a,X3: state,X1: state] :
( ( ( termi @ body @ X3 )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f2361]) ).
thf(f2363,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( X1 = X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f2362]) ).
thf(f2364,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2363]) ).
thf(f2369,plain,
! [X2: a,X3: a,X0: state,X1: a,X4: state] :
( ( x != X4 )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( ( termi @ body @ X4 )
= $true )
| ( $false = $true )
| ( x != X0 )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( pa @ X3 @ X4 ) ) ),
inference(superposition,[],[f2364,f1926]) ).
thf(f2376,plain,
! [X2: a,X3: a,X0: state,X1: a,X4: state] :
( ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( x != X0 )
| ( ( termi @ body @ X4 )
= $true )
| ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( x != X4 )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f2369]) ).
thf(f2377,plain,
! [X2: a,X3: a,X0: state,X1: a,X4: state] :
( ( $false
= ( pa @ X1 @ X0 ) )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( x != X0 )
| ( x != X4 )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( ( termi @ body @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f2376]) ).
thf(f2383,plain,
( spl0_3
| spl0_4
| spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f2377,f2340,f2302,f2302,f2299]) ).
thf(f2395,plain,
( ! [X2: a] :
( ( $true
= ( termi @ body @ x ) )
| ( x != x )
| ( $false
= ( pa @ X2 @ x ) ) )
| ~ spl0_4 ),
inference(imitation,[],[f2303]) ).
thf(f2397,plain,
( ! [X2: a] :
( ( $true
= ( termi @ body @ x ) )
| ( $false
= ( pa @ X2 @ x ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f2395]) ).
thf(f2398,plain,
( ! [X2: a] :
( ( $false
= ( pa @ X2 @ x ) )
| ( $false = $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f2397,f1800]) ).
thf(f2399,plain,
( ! [X2: a] :
( $false
= ( pa @ X2 @ x ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f2398]) ).
thf(f2404,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f1792,f2399]) ).
thf(f2408,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f2404]) ).
thf(f2409,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f2408]) ).
thf(f2429,plain,
( ( ( ^ [Y0: state] :
( !! @ state
@ ^ [Y1: state] :
( ~ ( ?? @ nat
@ ^ [Y2: nat] : ( execn @ Y0 @ body @ Y2 @ Y1 ) )
| ( !! @ a
@ ^ [Y2: a] :
( ~ ( pa @ Y2 @ Y0 )
| ( x != Y0 )
| ( qa @ Y2 @ Y1 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f1751]) ).
thf(f2432,plain,
( ( $false
= ( !! @ state
@ ^ [Y0: state] :
( ~ ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ sK18 @ body @ Y1 @ Y0 ) )
| ( !! @ a
@ ^ [Y1: a] :
( ~ ( pa @ Y1 @ sK18 )
| ( x != sK18 )
| ( qa @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f2429]) ).
thf(f2433,plain,
( ( ( ^ [Y0: state] :
( ~ ( ?? @ nat
@ ^ [Y1: nat] : ( execn @ sK18 @ body @ Y1 @ Y0 ) )
| ( !! @ a
@ ^ [Y1: a] :
( ~ ( pa @ Y1 @ sK18 )
| ( x != sK18 )
| ( qa @ Y1 @ Y0 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f2432]) ).
thf(f2436,plain,
( ( $false
= ( ~ ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ sK18 @ body @ Y0 @ sK19 ) )
| ( !! @ a
@ ^ [Y0: a] :
( ~ ( pa @ Y0 @ sK18 )
| ( x != sK18 )
| ( qa @ Y0 @ sK19 ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f2433]) ).
thf(f2437,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ~ ( pa @ Y0 @ sK18 )
| ( x != sK18 )
| ( qa @ Y0 @ sK19 ) ) ) )
| ~ spl0_1 ),
inference(or_proxy_clausification,[],[f2436]) ).
thf(f2438,plain,
( ( ( ~ ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ sK18 @ body @ Y0 @ sK19 ) ) )
= $false )
| ~ spl0_1 ),
inference(or_proxy_clausification,[],[f2436]) ).
thf(f2439,plain,
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ sK18 @ body @ Y0 @ sK19 ) )
= $true )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f2438]) ).
thf(f2440,plain,
( ( ( ^ [Y0: nat] : ( execn @ sK18 @ body @ Y0 @ sK19 )
@ sK20 )
= $true )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f2439]) ).
thf(f2441,plain,
( ( ( execn @ sK18 @ body @ sK20 @ sK19 )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f2440]) ).
thf(f2463,plain,
( ( $false
= ( ^ [Y0: a] :
( ~ ( pa @ Y0 @ sK18 )
| ( x != sK18 )
| ( qa @ Y0 @ sK19 ) )
@ sK21 ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f2437]) ).
thf(f2466,plain,
( ( $false
= ( ~ ( pa @ sK21 @ sK18 )
| ( x != sK18 )
| ( qa @ sK21 @ sK19 ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f2463]) ).
thf(f2467,plain,
( ( ( qa @ sK21 @ sK19 )
= $false )
| ~ spl0_1 ),
inference(or_proxy_clausification,[],[f2466]) ).
thf(f2468,plain,
( ( $false
= ( ~ ( pa @ sK21 @ sK18 )
| ( x != sK18 ) ) )
| ~ spl0_1 ),
inference(or_proxy_clausification,[],[f2466]) ).
thf(f2469,plain,
( ( $false
= ( x != sK18 ) )
| ~ spl0_1 ),
inference(or_proxy_clausification,[],[f2468]) ).
thf(f2470,plain,
( ( ( ~ ( pa @ sK21 @ sK18 ) )
= $false )
| ~ spl0_1 ),
inference(or_proxy_clausification,[],[f2468]) ).
thf(f2471,plain,
( ( ( x = sK18 )
= $true )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f2469]) ).
thf(f2472,plain,
( ( $true
= ( pa @ sK21 @ sK18 ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f2470]) ).
thf(f2473,plain,
( ( x = sK18 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[],[f2471]) ).
thf(f2482,plain,
( ( $true
= ( execn @ x @ body @ sK20 @ sK19 ) )
| ~ spl0_1 ),
inference(superposition,[],[f2441,f2473]) ).
thf(f2483,plain,
( ( ( pa @ sK21 @ x )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2472,f2473]) ).
thf(f2487,plain,
( ! [X0: state,X1: a] :
( ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( pa @ X1 @ x )
= $false )
| ( $false = $true )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( x != X0 ) )
| ~ spl0_1 ),
inference(superposition,[],[f2482,f2003]) ).
thf(f2494,plain,
( ! [X0: state,X1: a] :
( ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( pa @ X1 @ x )
= $false )
| ( x != X0 )
| ( ( qa @ X1 @ sK19 )
= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f2487]) ).
thf(f2496,definition,
( spl0_16
<=> ! [X1: a] :
( ( ( pa @ X1 @ x )
= $false )
| ( ( qa @ X1 @ sK19 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
thf(f2497,plain,
( ! [X1: a] :
( ( ( qa @ X1 @ sK19 )
= $true )
| ( ( pa @ X1 @ x )
= $false ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f2496]) ).
thf(f2499,definition,
( spl0_17
<=> ! [X0: state] :
( ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( x != X0 )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f2500,plain,
( ! [X0: state] :
( ( x != X0 )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f2499]) ).
thf(f2507,plain,
( spl0_17
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f2494,f1749,f2496,f2499]) ).
thf(f2514,plain,
( ( ( pa @ sK21 @ x )
= $false )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[],[f2497,f2467]) ).
thf(f2516,plain,
( ( ( pa @ sK21 @ x )
= $false )
| ~ spl0_1
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f2514]) ).
thf(f2528,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[],[f2483,f2516]) ).
thf(f2532,plain,
( $false
| ~ spl0_1
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f2528]) ).
thf(f2533,plain,
( ~ spl0_1
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f2532]) ).
thf(f2546,plain,
( ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ~ spl0_17 ),
inference(equality_resolution,[],[f2500]) ).
thf(f2549,definition,
( spl0_19
<=> ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
thf(f2551,plain,
( ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f2549]) ).
thf(f2553,plain,
( spl0_19
| spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f2546,f2499,f2340,f2549]) ).
thf(f2556,plain,
! [X2: a,X1: state] :
( ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f1956]) ).
thf(f2557,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2556]) ).
thf(f2560,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2557]) ).
thf(f2561,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(beta-eta_normalization,[],[f2560]) ).
thf(f2562,plain,
! [X2: a,X3: state,X1: state] :
( ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(imp_proxy_clausification,[],[f2561]) ).
thf(f2563,plain,
! [X2: a,X3: state,X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( X1 = X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(and_proxy_clausification,[],[f2562]) ).
thf(f2564,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2563]) ).
thf(f2569,plain,
! [X2: a,X3: state,X0: a,X1: state] :
( ( ( pa @ X2 @ X3 )
= $false )
| ( ( sK5 @ x )
!= X3 )
| ( $false = $true )
| ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ( ( termi @ body @ X1 )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( x != X1 )
| ( $false
= ( pa @ X0 @ X1 ) ) ),
inference(superposition,[],[f2564,f1799]) ).
thf(f2572,plain,
! [X2: a,X3: state,X0: a,X1: state] :
( ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ( ( sK5 @ x )
!= X3 )
| ( ( termi @ body @ X1 )
= $true )
| ( x != X1 )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( $false
= ( pa @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f2569]) ).
thf(f2577,plain,
! [X2: a,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2200]) ).
thf(f2578,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2577]) ).
thf(f2588,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2578]) ).
thf(f2589,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2588]) ).
thf(f2590,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2589]) ).
thf(f2591,plain,
! [X2: a,X3: state,X1: state] :
( ( ( X1 = X3 )
= $false )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2590]) ).
thf(f2592,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2591]) ).
thf(f2606,plain,
( ! [X2: a,X0: state,X1: a] :
( ( sK18 != X0 )
| ( $false = $true )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( $false
= ( pa @ X1 @ sK18 ) )
| ( ( qa @ X1 @ sK19 )
= $true ) )
| ~ spl0_1 ),
inference(superposition,[],[f1986,f2441]) ).
thf(f2640,plain,
( ! [X2: a,X0: state,X1: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( sK18 != X0 )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( $false
= ( pa @ X1 @ sK18 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f2606]) ).
thf(f2645,definition,
( spl0_20
<=> ! [X2: a,X0: state] :
( ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( x != X0 )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
thf(f2646,plain,
( ! [X2: a,X0: state] :
( ( x != X0 )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f2645]) ).
thf(f2649,plain,
( ! [X2: a,X0: state,X1: a] :
( ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true )
| ( x != X0 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( $false
= ( pa @ X1 @ sK18 ) )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2640,f2473]) ).
thf(f2651,plain,
( ! [X2: a,X0: state,X1: a] :
( ( ( pa @ X1 @ x )
= $false )
| ( x != X0 )
| ( ( pa @ X2 @ ( sK3 @ X0 ) )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( ( qa @ X2 @ ( sK4 @ X0 ) )
= $true ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2649,f2473]) ).
thf(f2653,plain,
( spl0_20
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f2651,f1749,f2496,f2645]) ).
thf(f2660,plain,
( ! [X0: a] :
( ( ( pa @ X0 @ ( sK3 @ x ) )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false )
| ( ( qa @ X0 @ ( sK4 @ x ) )
= $true ) )
| ~ spl0_20 ),
inference(equality_resolution,[],[f2646]) ).
thf(f2663,plain,
( spl0_5
| spl0_3
| spl0_7
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f2660,f2645,f2340,f2299,f2305]) ).
thf(f2665,plain,
! [X2: state,X3: a,X0: state,X1: a,X4: state,X5: nat] :
( ( ( execn @ X4 @ body @ X5 @ X2 )
= $false )
| ( ( qa @ X1 @ X2 )
= $true )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( $false
= ( pa @ X1 @ X4 ) )
| ( ( qa @ X3 @ ( sK4 @ X0 ) )
= $true )
| ( $false
= ( pa @ X3 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( X0 != X4 ) ),
inference(equality_resolution,[],[f2126]) ).
thf(f2706,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2250]) ).
thf(f2707,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2706]) ).
thf(f2708,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2707]) ).
thf(f2709,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( X1 = X3 )
= $false )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2708]) ).
thf(f2710,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2709]) ).
thf(f2713,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2710]) ).
thf(f2716,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2713]) ).
thf(f2781,definition,
( spl0_21
<=> ! [X1: state] :
( ( x != X1 )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
thf(f2782,plain,
( ! [X1: state] :
( ( x != X1 )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f2781]) ).
thf(f2809,plain,
( ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ~ spl0_21 ),
inference(equality_resolution,[],[f2782]) ).
thf(f2812,definition,
( spl0_22
<=> ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
thf(f2813,plain,
( ( $true
!= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| spl0_22 ),
inference(avatar_component_clause,[],[f2812]) ).
thf(f2814,plain,
( ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f2812]) ).
thf(f2817,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1974]) ).
thf(f2818,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2817]) ).
thf(f2819,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2818]) ).
thf(f2820,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( X1 = X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2819]) ).
thf(f2821,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2820]) ).
thf(f2829,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( X1 != X3 )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2821]) ).
thf(f2831,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2829]) ).
thf(f2849,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( pa @ X0 @ sK18 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false = $true )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( sK18 != X1 )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f2831,f2441]) ).
thf(f2879,plain,
( ! [X0: a,X1: state] :
( ( $true
= ( qa @ X0 @ sK19 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( sK18 != X1 )
| ( $false
= ( pa @ X0 @ sK18 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f2849]) ).
thf(f2887,definition,
( spl0_23
<=> ! [X1: state] :
( ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
thf(f2888,plain,
( ! [X1: state] :
( ( x != X1 )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f2887]) ).
thf(f2891,plain,
( ! [X0: a,X1: state] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( x != X1 )
| ( $false
= ( pa @ X0 @ sK18 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( qa @ X0 @ sK19 ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2879,f2473]) ).
thf(f2894,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( pa @ X0 @ x ) )
| ( x != X1 )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2891,f2473]) ).
thf(f2896,plain,
( spl0_16
| spl0_23
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f2894,f1749,f2887,f2496]) ).
thf(f2897,plain,
( ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( x != x )
| ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ~ spl0_23 ),
inference(imitation,[],[f2888]) ).
thf(f2899,plain,
( ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f2897]) ).
thf(f2901,plain,
! [X2: a,X3: state,X0: state,X1: a,X4: nat,X5: state] :
( ( ( execn @ X3 @ body @ X4 @ X5 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( $true
= ( qa @ X2 @ X5 ) )
| ( X0 != X3 ) ),
inference(equality_resolution,[],[f2171]) ).
thf(f2918,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2281]) ).
thf(f2919,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2918]) ).
thf(f2920,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2919]) ).
thf(f2921,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( X1 = X3 )
= $false )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2920]) ).
thf(f2922,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f2921]) ).
thf(f2926,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( X1 != X3 )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2922]) ).
thf(f2928,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f2926]) ).
thf(f2939,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false = $true )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( sK18 != X1 )
| ( $false
= ( pa @ X0 @ sK18 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f2928,f2441]) ).
thf(f2962,plain,
( ! [X0: a,X1: state] :
( ( $true
= ( qa @ X0 @ sK19 ) )
| ( $false
= ( pa @ X0 @ sK18 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( sK18 != X1 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f2939]) ).
thf(f2977,definition,
( spl0_24
<=> ! [X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
thf(f2978,plain,
( ! [X1: state] :
( ( x != X1 )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f2977]) ).
thf(f2981,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( sK18 != X1 )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( pa @ X0 @ x ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2962,f2473]) ).
thf(f2984,plain,
( ! [X0: a,X1: state] :
( ( x != X1 )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( $false
= ( pa @ X0 @ x ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2981,f2473]) ).
thf(f2986,plain,
( spl0_24
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f2984,f1749,f2496,f2977]) ).
thf(f2988,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ~ spl0_24 ),
inference(equality_resolution,[],[f2978]) ).
thf(f2990,plain,
( ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $false = $true )
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f2988,f2307]) ).
thf(f2991,plain,
( ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ~ spl0_5
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f2990]) ).
thf(f2994,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f2991,f2977,f2305,f2340]) ).
thf(f3001,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1973]) ).
thf(f3002,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f3001]) ).
thf(f3003,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3002]) ).
thf(f3004,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( X1 = X3 )
= $false )
| ( $false
= ( pa @ X4 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3003]) ).
thf(f3005,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f3004]) ).
thf(f3009,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( X1 != X3 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3005]) ).
thf(f3011,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $false
= ( qa @ ( sK7 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f3009]) ).
thf(f3056,plain,
( ! [X0: state,X1: a] :
( ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( sK18 != X0 )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( $false = $true )
| ( $false
= ( pa @ X1 @ sK18 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true ) )
| ~ spl0_1 ),
inference(superposition,[],[f3011,f2441]) ).
thf(f3079,plain,
( ! [X0: state,X1: a] :
( ( $false
= ( pa @ X1 @ sK18 ) )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( sK18 != X0 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f3056]) ).
thf(f3094,definition,
( spl0_26
<=> ! [X0: state] :
( ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( x != X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
thf(f3095,plain,
( ! [X0: state] :
( ( x != X0 )
| ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true ) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3094]) ).
thf(f3098,plain,
( ! [X0: state,X1: a] :
( ( ( pa @ X1 @ x )
= $false )
| ( sK18 != X0 )
| ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f3079,f2473]) ).
thf(f3101,plain,
( ! [X0: state,X1: a] :
( ( x != X0 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( pa @ X1 @ x )
= $false )
| ( $false
= ( qa @ ( sK7 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( qa @ X1 @ sK19 )
= $true ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f3098,f2473]) ).
thf(f3103,plain,
( spl0_26
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f3101,f1749,f2496,f3094]) ).
thf(f3109,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ( x != x )
| ~ spl0_26 ),
inference(imitation,[],[f3095]) ).
thf(f3111,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ( ( qa @ ( sK7 @ x ) @ ( sK4 @ x ) )
= $false )
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f3109]) ).
thf(f3158,plain,
! [X2: a,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2199]) ).
thf(f3159,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3158]) ).
thf(f3180,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3159]) ).
thf(f3181,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3180]) ).
thf(f3182,plain,
! [X2: a,X3: state,X1: state] :
( ( ( termi @ body @ X3 )
= $true )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(imp_proxy_clausification,[],[f3181]) ).
thf(f3183,plain,
! [X2: a,X3: state,X1: state] :
( ( ( X1 = X3 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3182]) ).
thf(f3184,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f3183]) ).
thf(f3203,plain,
! [X2: a,X3: state,X0: state,X1: a] :
( ( ( termi @ body @ X3 )
= $true )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( $false = $true )
| ( ( sK5 @ x )
!= X3 )
| ( ( pa @ X2 @ X3 )
= $false )
| ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ( ( termi @ body @ X0 )
= $true )
| ( x != X0 ) ),
inference(superposition,[],[f3184,f1799]) ).
thf(f3206,plain,
! [X2: a,X3: state,X0: state,X1: a] :
( ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( ( sK5 @ x )
!= X3 )
| ( x != X0 )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3203]) ).
thf(f3215,plain,
! [X2: a,X1: state] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(pi_proxy_clausification,[],[f2221]) ).
thf(f3216,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3215]) ).
thf(f3233,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3216]) ).
thf(f3234,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3233]) ).
thf(f3235,plain,
! [X2: a,X3: state,X1: state] :
( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( termi @ body @ X3 )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(imp_proxy_clausification,[],[f3234]) ).
thf(f3236,plain,
! [X2: a,X3: state,X1: state] :
( ( ( termi @ body @ X3 )
= $true )
| ( ( X1 = X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(and_proxy_clausification,[],[f3235]) ).
thf(f3237,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f3236]) ).
thf(f3277,plain,
! [X2: a,X3: a,X0: a,X1: state,X4: state] :
( ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( x != X4 )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( ( termi @ body @ X1 )
= $true )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( ( termi @ body @ X4 )
= $true )
| ( $false = $true )
| ( x != X1 )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) ) ),
inference(superposition,[],[f2106,f3237]) ).
thf(f3281,plain,
! [X2: a,X3: a,X0: a,X1: state,X4: state] :
( ( x != X4 )
| ( ( termi @ body @ X4 )
= $true )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( x != X1 )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( ( termi @ body @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( pa @ X3 @ X4 ) )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f3277]) ).
thf(f3282,plain,
! [X2: a,X3: a,X0: a,X1: state,X4: state] :
( ( x != X1 )
| ( $true
= ( qa @ X2 @ ( sK4 @ x ) ) )
| ( x != X4 )
| ( ( termi @ body @ X1 )
= $true )
| ( ( pa @ X2 @ ( sK3 @ x ) )
= $false )
| ( ( termi @ body @ X4 )
= $true )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( $false
= ( pa @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f3281]) ).
thf(f3334,plain,
! [X2: a,X1: state] :
( ( ( ^ [Y0: a] :
( !! @ state
@ ^ [Y1: state] :
( ( ( X1 = Y1 )
& ( pa @ Y0 @ Y1 ) )
=> ( termi @ body @ Y1 ) ) )
@ X2 )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f2220]) ).
thf(f3335,plain,
! [X2: a,X1: state] :
( ( ( !! @ state
@ ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(beta-eta_normalization,[],[f3334]) ).
thf(f3336,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( ^ [Y0: state] :
( ( ( X1 = Y0 )
& ( pa @ X2 @ Y0 ) )
=> ( termi @ body @ Y0 ) )
@ X3 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(pi_proxy_clausification,[],[f3335]) ).
thf(f3337,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
=> ( termi @ body @ X3 ) )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(beta-eta_normalization,[],[f3336]) ).
thf(f3338,plain,
! [X2: a,X3: state,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( ( X1 = X3 )
& ( pa @ X2 @ X3 ) )
= $false )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3337]) ).
thf(f3339,plain,
! [X2: a,X3: state,X1: state] :
( ( ( pa @ X2 @ X3 )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( X1 = X3 )
= $false )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( termi @ body @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f3338]) ).
thf(f3340,plain,
! [X2: a,X3: state,X1: state] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ X2 @ X3 )
= $false )
| ( ( termi @ body @ X3 )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f3339]) ).
thf(f3536,definition,
( spl0_30
<=> ! [X2: a,X1: state] :
( ( $false
= ( pa @ X2 @ ( sK3 @ X1 ) ) )
| ( $true
= ( qa @ X2 @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( x != X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ x ) @ r )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
thf(f3537,plain,
( ! [X2: a,X1: state] :
( ( x != X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ x ) @ r )
= $false )
| ( $false
= ( pa @ X2 @ ( sK3 @ X1 ) ) )
| ( $true
= ( qa @ X2 @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f3536]) ).
thf(f3553,plain,
( ! [X0: a] :
( ( ( qa @ X0 @ ( sK4 @ x ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false )
| ( ( pa @ X0 @ ( sK3 @ x ) )
= $false )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) ) )
| ~ spl0_30 ),
inference(equality_resolution,[],[f3537]) ).
thf(f3556,plain,
( spl0_9
| spl0_3
| spl0_5
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f3553,f3536,f2305,f2299,f2349]) ).
thf(f3566,plain,
( ! [X2: a,X0: state,X1: a] :
( ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( sK18 != X0 )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( qa @ X2 @ sK19 )
= $true )
| ( $false = $true )
| ( $false
= ( pa @ X2 @ sK18 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f2901,f2441]) ).
thf(f3585,plain,
( ! [X2: a,X0: state,X1: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( sK18 != X0 )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( $false
= ( pa @ X2 @ sK18 ) )
| ( ( qa @ X2 @ sK19 )
= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f3566]) ).
thf(f3604,plain,
( ! [X2: a,X0: state,X1: a] :
( ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( qa @ X2 @ sK19 )
= $true )
| ( $false
= ( pa @ X2 @ sK18 ) )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( x != X0 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f3585,f2473]) ).
thf(f3606,definition,
( spl0_31
<=> ! [X0: state,X1: a] :
( ( x != X0 )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false )
| ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
thf(f3607,plain,
( ! [X0: state,X1: a] :
( ( x != X0 )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false ) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3606]) ).
thf(f3611,plain,
( ! [X2: a,X0: state,X1: a] :
( ( ( qa @ X2 @ sK19 )
= $true )
| ( $false
= ( pa @ X1 @ ( sK3 @ X0 ) ) )
| ( x != X0 )
| ( ( qa @ X1 @ ( sK4 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( $false
= ( pa @ X2 @ x ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ x ) @ r )
= $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f3604,f2473]) ).
thf(f3613,plain,
( spl0_31
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f3611,f1749,f2496,f3606]) ).
thf(f3618,plain,
( ! [X0: a] :
( ( ( pa @ X0 @ ( sK3 @ x ) )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ( ( qa @ X0 @ ( sK4 @ x ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $false ) )
| ~ spl0_31 ),
inference(equality_resolution,[],[f3607]) ).
thf(f3621,definition,
( spl0_32
<=> ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
thf(f3622,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
!= $true )
| spl0_32 ),
inference(avatar_component_clause,[],[f3621]) ).
thf(f3623,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f3621]) ).
thf(f3625,plain,
( spl0_32
| spl0_3
| spl0_5
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f3618,f3606,f2305,f2299,f3621]) ).
thf(f3627,plain,
( ! [X0: a,X1: state] :
( ( ( termi @ body @ X1 )
= $true )
| ( ( sK5 @ x )
!= X1 )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( $false = $true ) )
| ~ spl0_32 ),
inference(superposition,[],[f1799,f3623]) ).
thf(f3628,plain,
( ! [X0: a,X1: state] :
( ( ( termi @ body @ X1 )
= $true )
| ( ( sK5 @ x )
!= X1 )
| ( $false
= ( pa @ X0 @ X1 ) ) )
| ~ spl0_32 ),
inference(trivial_inequality_removal,[],[f3627]) ).
thf(f3630,plain,
( spl0_6
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f3628,f3621,f2309]) ).
thf(f3631,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2253]) ).
thf(f3632,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3631]) ).
thf(f3633,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3632]) ).
thf(f3634,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( X1 = X3 )
= $false )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3633]) ).
thf(f3635,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f3634]) ).
thf(f3640,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $true
= ( qa @ X4 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3635]) ).
thf(f3642,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f3640]) ).
thf(f3651,plain,
( ! [X0: a] :
( ( $true
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ X0 @ ( sK5 @ x ) ) ) )
| ~ spl0_6 ),
inference(equality_resolution,[],[f2310]) ).
thf(f3652,plain,
( ! [X0: a] :
( ( $false
= ( pa @ X0 @ ( sK5 @ x ) ) )
| ( $false = $true ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f3651,f2342]) ).
thf(f3653,plain,
( ! [X0: a] :
( $false
= ( pa @ X0 @ ( sK5 @ x ) ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f3652]) ).
thf(f3656,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f2351,f3653]) ).
thf(f3660,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f3656]) ).
thf(f3661,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f3660]) ).
thf(f3707,plain,
( spl0_9
| spl0_3
| spl0_4
| spl0_4 ),
inference(avatar_split_clause,[],[f3282,f2302,f2302,f2299,f2349]) ).
thf(f3971,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f2346,f2814]) ).
thf(f3975,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f2814,f2346]) ).
thf(f3976,plain,
( ! [X0: state,X1: a] :
( ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( $false = $true )
| ( x != X0 ) )
| ~ spl0_8 ),
inference(superposition,[],[f2592,f2346]) ).
thf(f3979,plain,
( ! [X0: state,X1: a] :
( ( x != X0 )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( ( termi @ body @ X0 )
= $true ) )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f3976]) ).
thf(f3981,plain,
( $false
| ~ spl0_8
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f3975]) ).
thf(f3982,plain,
( ~ spl0_8
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f3981]) ).
thf(f3983,plain,
( $false
| ~ spl0_8
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f3971]) ).
thf(f3984,plain,
( ~ spl0_8
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f3983]) ).
thf(f3988,plain,
( spl0_9
| spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f3979,f2344,f2302,f2349]) ).
thf(f3990,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f2252]) ).
thf(f3991,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3990]) ).
thf(f3992,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3991]) ).
thf(f3993,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( qa @ X4 @ X2 ) )
| ( ( X1 = X3 )
= $false )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3992]) ).
thf(f3994,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f3993]) ).
thf(f3995,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f3994]) ).
thf(f3997,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f3995]) ).
thf(f4009,plain,
( ! [X0: state,X1: a] :
( ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( ( termi @ body @ X0 )
= $true )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( x != X0 )
| ( $false = $true ) )
| ~ spl0_3 ),
inference(superposition,[],[f2300,f2056]) ).
thf(f4010,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( x != X1 )
| ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ( $false = $true )
| ( ( termi @ body @ X1 )
= $true )
| ( $false
= ( pa @ X0 @ X1 ) ) )
| ~ spl0_3 ),
inference(superposition,[],[f2300,f1979]) ).
thf(f4011,plain,
( ( $false = $true )
| ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[],[f2551,f2300]) ).
thf(f4014,plain,
( ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ~ spl0_3
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f4011]) ).
thf(f4018,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( pa @ X0 @ X1 ) )
| ( x != X1 )
| ( ( termi @ body @ X1 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f4010]) ).
thf(f4019,plain,
( ! [X0: state,X1: a] :
( ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( x != X0 )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f4009]) ).
thf(f4020,plain,
( spl0_8
| ~ spl0_3
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f4014,f2549,f2299,f2344]) ).
thf(f4025,plain,
( spl0_19
| spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f2572,f2302,f2309,f2549]) ).
thf(f4033,plain,
( spl0_4
| spl0_22
| spl0_6 ),
inference(avatar_split_clause,[],[f3206,f2309,f2812,f2302]) ).
thf(f4038,plain,
( spl0_32
| spl0_19
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f3111,f3094,f2549,f3621]) ).
thf(f4039,plain,
( spl0_8
| spl0_4
| spl0_7
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f4018,f2299,f2340,f2302,f2344]) ).
thf(f4093,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2284]) ).
thf(f4094,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4093]) ).
thf(f4095,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(imp_proxy_clausification,[],[f4094]) ).
thf(f4096,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( X1 = X3 )
= $false )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(and_proxy_clausification,[],[f4095]) ).
thf(f4097,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f4096]) ).
thf(f4108,plain,
( ! [X0: state,X1: a] :
( ( ( termi @ body @ X0 )
= $true )
| ( x != X0 )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $true != $true )
| ( $false
= ( pa @ X1 @ X0 ) ) )
| spl0_22 ),
inference(superposition,[],[f2813,f2231]) ).
thf(f4110,plain,
( ! [X0: state,X1: a] :
( ( ( termi @ body @ X0 )
= $true )
| ( $false
= ( termi @ body @ ( sK5 @ x ) ) )
| ( $false
= ( pa @ X1 @ X0 ) )
| ( x != X0 ) )
| spl0_22 ),
inference(trivial_inequality_removal,[],[f4108]) ).
thf(f4113,plain,
( spl0_7
| spl0_4
| spl0_22 ),
inference(avatar_split_clause,[],[f4110,f2812,f2302,f2340]) ).
thf(f4227,plain,
( spl0_4
| spl0_8
| spl0_9
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f4019,f2299,f2349,f2344,f2302]) ).
thf(f4304,plain,
( ( $true
= ( execn @ x @ body @ sK20 @ sK19 ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2441,f2473]) ).
thf(f4313,plain,
( ! [X2: a,X0: a,X1: state] :
( ( $false = $true )
| ( $true
= ( qa @ X2 @ ( sK4 @ X1 ) ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ x ) @ r )
= $false )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( x != X1 )
| ( $false
= ( pa @ X0 @ x ) )
| ( $false
= ( pa @ X2 @ ( sK3 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f4304,f2665]) ).
thf(f4314,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( pa @ X0 @ x ) )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( $false = $true )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) )
| ( x != X1 )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) )
| ~ spl0_1 ),
inference(superposition,[],[f4304,f2716]) ).
thf(f4330,plain,
( ! [X0: a,X1: state] :
( ( $true
= ( qa @ X0 @ sK19 ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false = $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X0 @ x ) )
| ( x != X1 ) )
| ~ spl0_1 ),
inference(superposition,[],[f3642,f4304]) ).
thf(f4331,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( pa @ X0 @ x ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( x != X1 )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false = $true ) )
| ~ spl0_1 ),
inference(superposition,[],[f3997,f4304]) ).
thf(f4341,plain,
( ! [X2: a,X0: a,X1: state] :
( ( $true
= ( qa @ X0 @ sK19 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X0 @ x ) )
| ( $false
= ( pa @ X2 @ ( sK3 @ X1 ) ) )
| ( x != X1 )
| ( $true
= ( qa @ X2 @ ( sK4 @ X1 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ x ) @ r )
= $false ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f4313]) ).
thf(f4343,plain,
( ! [X0: a,X1: state] :
( ( $true
= ( qa @ X0 @ sK19 ) )
| ( $false
= ( pa @ X0 @ x ) )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( x != X1 )
| ( $false
= ( termi @ body @ ( sK5 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f4314]) ).
thf(f4348,plain,
( ! [X0: a,X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( pa @ X0 @ x ) )
| ( $true
= ( qa @ X0 @ sK19 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( x != X1 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f4330]) ).
thf(f4351,plain,
( ! [X0: a,X1: state] :
( ( $true
= ( qa @ X0 @ sK19 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( x != X1 )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( pa @ X0 @ x ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f4331]) ).
thf(f4355,definition,
( spl0_44
<=> ! [X1: state] :
( ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
thf(f4356,plain,
( ! [X1: state] :
( ( x != X1 )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true ) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f4355]) ).
thf(f4359,plain,
( spl0_16
| spl0_30
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4341,f1749,f3536,f2496]) ).
thf(f4361,plain,
( spl0_16
| spl0_21
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4343,f1749,f2781,f2496]) ).
thf(f4362,plain,
( spl0_16
| spl0_44
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4348,f1749,f4355,f2496]) ).
thf(f4364,definition,
( spl0_45
<=> ! [X1: state] :
( ( x != X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
thf(f4365,plain,
( ! [X1: state] :
( ( x != X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( ( pa @ ( sK7 @ X1 ) @ ( sK3 @ X1 ) )
= $true ) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f4364]) ).
thf(f4367,plain,
( spl0_45
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4351,f1749,f2496,f4364]) ).
thf(f4445,plain,
( ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ~ spl0_44 ),
inference(equality_resolution,[],[f4356]) ).
thf(f4462,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( X1 != X3 )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) ) ),
inference(pi_proxy_clausification,[],[f4097]) ).
thf(f4464,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( ( pa @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f4462]) ).
thf(f4495,plain,
( ! [X0: state,X1: a] :
( ( $false = $true )
| ( ( pa @ X1 @ x )
= $false )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true )
| ( x != X0 ) )
| ~ spl0_1 ),
inference(superposition,[],[f4464,f4304]) ).
thf(f4517,plain,
( ! [X0: state,X1: a] :
( ( x != X0 )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( ( pa @ X1 @ x )
= $false ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f4495]) ).
thf(f4529,definition,
( spl0_46
<=> ! [X0: state] :
( ( x != X0 )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
thf(f4530,plain,
( ! [X0: state] :
( ( x != X0 )
| ( ( pa @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true ) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f4529]) ).
thf(f4532,plain,
( spl0_46
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4517,f1749,f2496,f4529]) ).
thf(f4538,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ( x != x )
| ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ~ spl0_45 ),
inference(imitation,[],[f4365]) ).
thf(f4540,plain,
( ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ~ spl0_45 ),
inference(trivial_inequality_removal,[],[f4538]) ).
thf(f4541,plain,
( ( $true
= ( pa @ ( sK7 @ x ) @ ( sK3 @ x ) ) )
| spl0_32
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f4540,f3622]) ).
thf(f4552,plain,
( spl0_9
| spl0_19
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f2899,f2887,f2549,f2349]) ).
thf(f4557,plain,
( spl0_22
| spl0_7
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f2809,f2781,f2340,f2812]) ).
thf(f4559,plain,
( spl0_22
| spl0_9
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f4445,f4355,f2349,f2812]) ).
thf(f4563,plain,
( spl0_22
| spl0_32
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f4541,f4364,f3621,f2812]) ).
thf(f4632,plain,
( ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ( x != x )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $true )
| ~ spl0_46 ),
inference(imitation,[],[f4530]) ).
thf(f4634,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $true )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ~ spl0_46 ),
inference(trivial_inequality_removal,[],[f4632]) ).
thf(f4691,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X1 = X3 )
& ( pa @ Y0 @ X3 ) )
=> ( qa @ Y0 @ X2 ) )
@ X4 )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true ) ),
inference(pi_proxy_clausification,[],[f2283]) ).
thf(f4692,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) )
=> ( qa @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f4691]) ).
thf(f4693,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( $false
= ( ( X1 = X3 )
& ( pa @ X4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f4692]) ).
thf(f4694,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( ( X1 = X3 )
= $false )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f4693]) ).
thf(f4695,plain,
! [X2: state,X3: state,X1: state,X4: a] :
( ( $false
= ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f4694]) ).
thf(f4701,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( $false
= ( ^ [Y0: nat] : ( execn @ X3 @ body @ Y0 @ X2 )
@ X5 ) )
| ( X1 != X3 ) ),
inference(pi_proxy_clausification,[],[f4695]) ).
thf(f4703,plain,
! [X2: state,X3: state,X1: state,X4: a,X5: nat] :
( ( $false
= ( execn @ X3 @ body @ X5 @ X2 ) )
| ( $true
= ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X1 ) @ X1 ) @ r ) )
| ( $false
= ( pa @ X4 @ X3 ) )
| ( $true
= ( qa @ X4 @ X2 ) )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X1 ) @ X1 ) @ r )
= $true )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f4701]) ).
thf(f4718,plain,
( ! [X0: state,X1: a] :
( ( $false = $true )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( x != X0 )
| ( ( pa @ X1 @ x )
= $false )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true ) )
| ~ spl0_1 ),
inference(superposition,[],[f4703,f4304]) ).
thf(f4738,plain,
( ! [X0: state,X1: a] :
( ( x != X0 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( qa @ X1 @ sK19 )
= $true )
| ( ( pa @ X1 @ x )
= $false ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f4718]) ).
thf(f4752,definition,
( spl0_48
<=> ! [X0: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true )
| ( x != X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
thf(f4753,plain,
( ! [X0: state] :
( ( x != X0 )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ X0 ) @ X0 ) @ r )
= $true ) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f4752]) ).
thf(f4755,plain,
( spl0_16
| spl0_48
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4738,f1749,f4752,f2496]) ).
thf(f4763,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK3 @ x ) @ x ) @ r )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ~ spl0_48 ),
inference(equality_resolution,[],[f4753]) ).
thf(f4803,plain,
( ! [X0: a,X1: state] :
( ( $false
= ( pa @ X0 @ X1 ) )
| ( x != X1 )
| ( ( termi @ body @ X1 )
= $true )
| ( $false = $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true ) )
| ~ spl0_5 ),
inference(superposition,[],[f3340,f2307]) ).
thf(f4809,plain,
( ! [X0: a,X1: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ( $false
= ( pa @ X0 @ X1 ) )
| ( x != X1 )
| ( ( termi @ body @ X1 )
= $true ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f4803]) ).
thf(f4832,plain,
( ( $false = $true )
| ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ~ spl0_5
| ~ spl0_46 ),
inference(forward_demodulation,[],[f4634,f2307]) ).
thf(f4833,plain,
( ( $true
= ( pa @ ( sK6 @ x ) @ ( sK5 @ x ) ) )
| ~ spl0_5
| ~ spl0_46 ),
inference(trivial_inequality_removal,[],[f4832]) ).
thf(f4836,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ( $false = $true )
| ~ spl0_5
| ~ spl0_48 ),
inference(forward_demodulation,[],[f4763,f2307]) ).
thf(f4837,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK5 @ x ) @ x ) @ r )
= $true )
| ~ spl0_5
| ~ spl0_48 ),
inference(trivial_inequality_removal,[],[f4836]) ).
thf(f4842,plain,
( spl0_4
| spl0_32
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f4809,f2305,f3621,f2302]) ).
thf(f4843,plain,
( spl0_9
| ~ spl0_5
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f4833,f4529,f2305,f2349]) ).
thf(f4844,plain,
( spl0_32
| ~ spl0_5
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f4837,f4752,f2305,f3621]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1756]) ).
cnf(s3,plain,
( spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f2312]) ).
cnf(s10,plain,
( spl0_4
| spl0_3
| spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f2383]) ).
cnf(s11,plain,
( spl0_3
| spl0_4
| spl0_7 ),
inference(rat,[],[s10]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f2409]) ).
cnf(s29,plain,
( ~ spl0_1
| spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f2507]) ).
cnf(s32,plain,
( ~ spl0_1
| ~ spl0_16 ),
inference(sat_conversion,[],[f2533]) ).
cnf(s36,plain,
( spl0_7
| ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f2553]) ).
cnf(s40,plain,
( ~ spl0_1
| spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f2653]) ).
cnf(s42,plain,
( spl0_3
| spl0_5
| spl0_7
| ~ spl0_20 ),
inference(sat_conversion,[],[f2663]) ).
cnf(s52,plain,
( ~ spl0_1
| spl0_16
| spl0_23 ),
inference(sat_conversion,[],[f2896]) ).
cnf(s56,plain,
( ~ spl0_1
| spl0_16
| spl0_24 ),
inference(sat_conversion,[],[f2986]) ).
cnf(s57,plain,
( ~ spl0_5
| spl0_7
| ~ spl0_24 ),
inference(sat_conversion,[],[f2994]) ).
cnf(s64,plain,
( ~ spl0_1
| spl0_16
| spl0_26 ),
inference(sat_conversion,[],[f3103]) ).
cnf(s72,plain,
( spl0_3
| spl0_5
| spl0_9
| ~ spl0_30 ),
inference(sat_conversion,[],[f3556]) ).
cnf(s76,plain,
( ~ spl0_1
| spl0_16
| spl0_31 ),
inference(sat_conversion,[],[f3613]) ).
cnf(s78,plain,
( spl0_3
| spl0_5
| ~ spl0_31
| spl0_32 ),
inference(sat_conversion,[],[f3625]) ).
cnf(s79,plain,
( spl0_6
| ~ spl0_32 ),
inference(sat_conversion,[],[f3630]) ).
cnf(s82,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f3661]) ).
cnf(s98,plain,
( spl0_4
| spl0_3
| spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f3707]) ).
cnf(s99,plain,
( spl0_3
| spl0_4
| spl0_9 ),
inference(rat,[],[s98]) ).
cnf(s113,plain,
( ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f3982]) ).
cnf(s114,plain,
( ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f3984]) ).
cnf(s116,plain,
( spl0_4
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f3988]) ).
cnf(s117,plain,
( ~ spl0_3
| spl0_8
| ~ spl0_19 ),
inference(sat_conversion,[],[f4020]) ).
cnf(s122,plain,
( spl0_4
| spl0_6
| spl0_19 ),
inference(sat_conversion,[],[f4025]) ).
cnf(s129,plain,
( spl0_4
| spl0_6
| spl0_22 ),
inference(sat_conversion,[],[f4033]) ).
cnf(s137,plain,
( spl0_19
| ~ spl0_26
| spl0_32 ),
inference(sat_conversion,[],[f4038]) ).
cnf(s138,plain,
( ~ spl0_3
| spl0_4
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f4039]) ).
cnf(s141,plain,
( spl0_4
| spl0_7
| spl0_22 ),
inference(sat_conversion,[],[f4113]) ).
cnf(s171,plain,
( ~ spl0_3
| spl0_4
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f4227]) ).
cnf(s195,plain,
( ~ spl0_1
| spl0_16
| spl0_30 ),
inference(sat_conversion,[],[f4359]) ).
cnf(s197,plain,
( ~ spl0_1
| spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f4361]) ).
cnf(s198,plain,
( ~ spl0_1
| spl0_16
| spl0_44 ),
inference(sat_conversion,[],[f4362]) ).
cnf(s200,plain,
( ~ spl0_1
| spl0_16
| spl0_45 ),
inference(sat_conversion,[],[f4367]) ).
cnf(s212,plain,
( ~ spl0_1
| spl0_16
| spl0_46 ),
inference(sat_conversion,[],[f4532]) ).
cnf(s218,plain,
( spl0_9
| spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f4552]) ).
cnf(s223,plain,
( spl0_7
| ~ spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f4557]) ).
cnf(s225,plain,
( spl0_9
| spl0_22
| ~ spl0_44 ),
inference(sat_conversion,[],[f4559]) ).
cnf(s229,plain,
( spl0_22
| spl0_32
| ~ spl0_45 ),
inference(sat_conversion,[],[f4563]) ).
cnf(s256,plain,
( ~ spl0_1
| spl0_16
| spl0_48 ),
inference(sat_conversion,[],[f4755]) ).
cnf(s268,plain,
( spl0_4
| ~ spl0_5
| spl0_32 ),
inference(sat_conversion,[],[f4842]) ).
cnf(s269,plain,
( ~ spl0_5
| spl0_9
| ~ spl0_46 ),
inference(sat_conversion,[],[f4843]) ).
cnf(s271,plain,
( ~ spl0_5
| spl0_32
| ~ spl0_48 ),
inference(sat_conversion,[],[f4844]) ).
cnf(s273,plain,
( spl0_3
| spl0_4 ),
inference(rat,[],[s268,s3,s79,s82,s11,s99]) ).
cnf(s274,plain,
( spl0_7
| spl0_4 ),
inference(rat,[],[s113,s138,s141,s273]) ).
cnf(s276,plain,
( spl0_9
| spl0_4 ),
inference(rat,[],[s171,s116,s273]) ).
cnf(s277,plain,
spl0_4,
inference(rat,[],[s117,s114,s122,s129,s82,s276,s274,s273]) ).
cnf(s278,plain,
~ spl0_2,
inference(rat,[],[s19,s277]) ).
cnf(s279,plain,
spl0_1,
inference(rat,[],[s1,s278]) ).
cnf(s280,plain,
~ spl0_16,
inference(rat,[],[s32,s279]) ).
cnf(s282,plain,
spl0_48,
inference(rat,[],[s256,s279,s280]) ).
cnf(s284,plain,
spl0_46,
inference(rat,[],[s212,s279,s280]) ).
cnf(s285,plain,
spl0_45,
inference(rat,[],[s200,s279,s280]) ).
cnf(s286,plain,
spl0_44,
inference(rat,[],[s198,s279,s280]) ).
cnf(s287,plain,
spl0_21,
inference(rat,[],[s197,s279,s280]) ).
cnf(s288,plain,
spl0_30,
inference(rat,[],[s195,s279,s280]) ).
cnf(s289,plain,
spl0_31,
inference(rat,[],[s76,s279,s280]) ).
cnf(s290,plain,
spl0_26,
inference(rat,[],[s64,s279,s280]) ).
cnf(s291,plain,
spl0_24,
inference(rat,[],[s56,s279,s280]) ).
cnf(s292,plain,
spl0_23,
inference(rat,[],[s52,s279,s280]) ).
cnf(s293,plain,
spl0_20,
inference(rat,[],[s40,s279,s280]) ).
cnf(s294,plain,
spl0_17,
inference(rat,[],[s29,s279,s280]) ).
cnf(s305,plain,
( spl0_9
| spl0_5 ),
inference(rat,[],[s117,s114,s218,s225,s72,s288,s286,s292]) ).
cnf(s306,plain,
spl0_9,
inference(rat,[],[s305,s269,s284]) ).
cnf(s307,plain,
spl0_7,
inference(rat,[],[s117,s114,s42,s36,s223,s57,s293,s294,s287,s291]) ).
cnf(s308,plain,
~ spl0_6,
inference(rat,[],[s82,s306,s307]) ).
cnf(s309,plain,
~ spl0_32,
inference(rat,[],[s79,s308]) ).
cnf(s310,plain,
spl0_22,
inference(rat,[],[s229,s285,s309]) ).
cnf(s311,plain,
~ spl0_5,
inference(rat,[],[s271,s282,s309]) ).
cnf(s312,plain,
spl0_19,
inference(rat,[],[s137,s290,s309]) ).
cnf(s313,plain,
~ spl0_8,
inference(rat,[],[s114,s310]) ).
cnf(s315,plain,
spl0_3,
inference(rat,[],[s78,s309,s289,s311]) ).
cnf(s316,plain,
$false,
inference(rat,[],[s117,s315,s312,s313]) ).
thf(f4845,plain,
$false,
inference(avatar_sat_refutation,[],[s316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP141^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 19:59:45 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.21/0.27 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
% 0.50/0.42 % (279566)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.42 % (279572)lrs+10_16_si=on:nwc=1.5:random_seed=2814507993:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.42 % (279577)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.42 % (279577)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
% 0.50/0.42 % (279572)Instruction limit reached!
% 0.50/0.42 % (279572)------------------------------
% 0.50/0.42 % (279572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (279572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (279572)CaDiCaL version: 2.1.3
% 0.50/0.42 % (279572)Termination reason: Instruction limit
% 0.50/0.42 % (279572)Termination phase: shuffling
% 0.50/0.42 % (279572)Time elapsed: 0.005 s
% 0.50/0.42 % (279572)Peak memory usage: 10 MB
% 0.50/0.42 % (279572)Instructions burned: 19 (million)
% 0.50/0.42 % (279573)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2755655908:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.42 % (279574)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=2612952505: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)
% 0.50/0.42 % (279575)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3343215898:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.42 % (279576)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4143277593:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.42 % (279571)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1953450969:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.42 % (279577)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=3004809078:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.42 % (279573)Instruction limit reached!
% 0.50/0.42 % (279573)------------------------------
% 0.50/0.42 % (279573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (279573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (279573)CaDiCaL version: 2.1.3
% 0.50/0.42 % (279573)Termination reason: Instruction limit
% 0.50/0.42 % (279573)Termination phase: shuffling
% 0.50/0.42 % (279573)Time elapsed: 0.004 s
% 0.50/0.42 % (279573)Peak memory usage: 10 MB
% 0.50/0.42 % (279573)Instructions burned: 7 (million)
% 0.50/0.42 % (279575)Instruction limit reached!
% 0.50/0.42 % (279575)------------------------------
% 0.50/0.42 % (279575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (279575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (279575)CaDiCaL version: 2.1.3
% 0.50/0.42 % (279575)Termination reason: Instruction limit
% 0.50/0.42 % (279575)Termination phase: Property scanning
% 0.50/0.42 % (279575)Time elapsed: 0.012 s
% 0.50/0.42 % (279575)Peak memory usage: 11 MB
% 0.50/0.42 % (279575)Instructions burned: 25 (million)
% 0.50/0.42 % (279579)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3301914362:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.42 % (279579)Instruction limit reached!
% 0.50/0.42 % (279579)------------------------------
% 0.50/0.42 % (279579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (279579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (279579)CaDiCaL version: 2.1.3
% 0.50/0.42 % (279579)Termination reason: Instruction limit
% 0.50/0.42 % (279579)Termination phase: shuffling
% 0.50/0.42 % (279579)Time elapsed: 0.003 s
% 0.50/0.42 % (279579)Peak memory usage: 10 MB
% 0.50/0.42 % (279579)Instructions burned: 6 (million)
% 0.50/0.42 % (279571)Instruction limit reached!
% 0.50/0.42 % (279571)------------------------------
% 0.50/0.42 % (279571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (279571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (279571)CaDiCaL version: 2.1.3
% 0.50/0.45 % (279571)Termination reason: Instruction limit
% 0.50/0.45 % (279571)Termination phase: Property scanning
% 0.50/0.45 % (279571)Time elapsed: 0.022 s
% 0.50/0.45 % (279571)Peak memory usage: 12 MB
% 0.50/0.45 % (279571)Instructions burned: 88 (million)
% 0.50/0.45 % (279586)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2907609015:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.50/0.45 % (279586)Instruction limit reached!
% 0.50/0.45 % (279586)------------------------------
% 0.50/0.45 % (279586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (279586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (279586)CaDiCaL version: 2.1.3
% 0.50/0.45 % (279586)Termination reason: Instruction limit
% 0.50/0.45 % (279586)Termination phase: shuffling
% 0.50/0.45 % (279586)Time elapsed: 0.003 s
% 0.50/0.45 % (279586)Peak memory usage: 10 MB
% 0.50/0.45 % (279586)Instructions burned: 6 (million)
% 0.50/0.45 % (279587)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.45 % (279590)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
% 0.50/0.45 % (279590)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.45 % (279590)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3087239534:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.50/0.45 % (279587)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2845832880:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.50/0.45 % (279576)Instruction limit reached!
% 0.50/0.45 % (279576)------------------------------
% 0.50/0.45 % (279576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (279576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (279576)CaDiCaL version: 2.1.3
% 0.50/0.45 % (279576)Termination reason: Instruction limit
% 0.50/0.45 % (279576)Termination phase: Property scanning
% 0.50/0.45 % (279576)Time elapsed: 0.037 s
% 0.50/0.45 % (279576)Peak memory usage: 12 MB
% 0.50/0.45 % (279576)Instructions burned: 77 (million)
% 0.50/0.45 % (279589)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3038360220:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.50/0.45 % (279587)Instruction limit reached!
% 0.50/0.45 % (279587)------------------------------
% 0.50/0.45 % (279587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (279587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (279587)CaDiCaL version: 2.1.3
% 0.50/0.45 % (279587)Termination reason: Instruction limit
% 0.50/0.45 % (279587)Termination phase: shuffling
% 0.50/0.45 % (279587)Time elapsed: 0.004 s
% 0.50/0.45 % (279587)Peak memory usage: 10 MB
% 0.50/0.45 % (279587)Instructions burned: 7 (million)
% 0.50/0.45 % (279590)Instruction limit reached!
% 0.50/0.45 % (279590)------------------------------
% 0.50/0.45 % (279590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (279590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (279590)CaDiCaL version: 2.1.3
% 0.50/0.45 % (279590)Termination reason: Instruction limit
% 0.50/0.45 % (279590)Termination phase: shuffling
% 0.50/0.45 % (279590)Time elapsed: 0.007 s
% 0.50/0.45 % (279590)Peak memory usage: 11 MB
% 0.50/0.45 % (279590)Instructions burned: 31 (million)
% 0.50/0.45 % (279589)Instruction limit reached!
% 0.50/0.45 % (279589)------------------------------
% 0.50/0.45 % (279589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (279589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (279589)CaDiCaL version: 2.1.3
% 0.50/0.45 % (279589)Termination reason: Instruction limit
% 0.50/0.45 % (279589)Termination phase: shuffling
% 0.50/0.45 % (279589)Time elapsed: 0.006 s
% 0.50/0.45 % (279589)Peak memory usage: 10 MB
% 0.50/0.48 % (279589)Instructions burned: 12 (million)
% 0.50/0.48 % (279592)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=3525035269:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.50/0.48 % (279598)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=418180528:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.50/0.48 % (279597)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.50/0.48 % (279595)lrs+10_1_si=on:cs=on:random_seed=3419231843:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.50/0.48 % (279597)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=1986828452:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.48 % (279598)Instruction limit reached!
% 0.50/0.48 % (279598)------------------------------
% 0.50/0.48 % (279598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.48 % (279598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.48 % (279598)CaDiCaL version: 2.1.3
% 0.50/0.48 % (279598)Termination reason: Instruction limit
% 0.50/0.48 % (279598)Termination phase: Property scanning
% 0.50/0.48 % (279598)Time elapsed: 0.009 s
% 0.50/0.48 % (279598)Peak memory usage: 11 MB
% 0.50/0.48 % (279598)Instructions burned: 38 (million)
% 0.50/0.48 % (279597)Instruction limit reached!
% 0.50/0.48 % (279597)------------------------------
% 0.50/0.48 % (279597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.48 % (279597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.48 % (279597)CaDiCaL version: 2.1.3
% 0.50/0.48 % (279597)Termination reason: Instruction limit
% 0.50/0.48 % (279597)Termination phase: shuffling
% 0.50/0.48 % (279597)Time elapsed: 0.002 s
% 0.50/0.48 % (279597)Peak memory usage: 10 MB
% 0.50/0.48 % (279597)Instructions burned: 3 (million)
% 0.50/0.48 % (279595)Instruction limit reached!
% 0.50/0.48 % (279595)------------------------------
% 0.50/0.48 % (279595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.48 % (279595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.48 % (279595)CaDiCaL version: 2.1.3
% 0.50/0.48 % (279595)Termination reason: Instruction limit
% 0.50/0.48 % (279595)Termination phase: shuffling
% 0.50/0.48 % (279595)Time elapsed: 0.005 s
% 0.50/0.48 % (279595)Peak memory usage: 10 MB
% 0.50/0.48 % (279595)Instructions burned: 10 (million)
% 0.50/0.48 % (279599)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4030611883:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.50/0.48 % (279604)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2725596202:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.50/0.48 % (279604)Instruction limit reached!
% 0.50/0.48 % (279604)------------------------------
% 0.50/0.48 % (279604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.48 % (279604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.48 % (279604)CaDiCaL version: 2.1.3
% 0.50/0.48 % (279604)Termination reason: Instruction limit
% 0.50/0.48 % (279604)Termination phase: Property scanning
% 0.50/0.48 % (279604)Time elapsed: 0.006 s
% 0.50/0.48 % (279604)Peak memory usage: 11 MB
% 0.50/0.48 % (279604)Instructions burned: 26 (million)
% 0.50/0.48 % (279605)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3331656640:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.50/0.48 % (279606)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3800231844:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.50/0.48 % (279592)Instruction limit reached!
% 0.50/0.48 % (279592)------------------------------
% 0.50/0.48 % (279592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.48 % (279592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.48 % (279592)CaDiCaL version: 2.1.3
% 0.50/0.48 % (279592)Termination reason: Instruction limit
% 0.50/0.48 % (279592)Termination phase: Property scanning
% 1.39/0.54 % (279592)Time elapsed: 0.037 s
% 1.39/0.54 % (279592)Peak memory usage: 11 MB
% 1.39/0.54 % (279592)Instructions burned: 87 (million)
% 1.39/0.54 % (279609)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2883226772:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.39/0.54 % (279605)Instruction limit reached!
% 1.39/0.54 % (279605)------------------------------
% 1.39/0.54 % (279605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.54 % (279605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.54 % (279605)CaDiCaL version: 2.1.3
% 1.39/0.54 % (279605)Termination reason: Instruction limit
% 1.39/0.54 % (279605)Termination phase: shuffling
% 1.39/0.54 % (279605)Time elapsed: 0.008 s
% 1.39/0.54 % (279605)Peak memory usage: 10 MB
% 1.39/0.54 % (279605)Instructions burned: 16 (million)
% 1.39/0.54 % (279609)Instruction limit reached!
% 1.39/0.54 % (279609)------------------------------
% 1.39/0.54 % (279609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.54 % (279609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.55 % (279609)CaDiCaL version: 2.1.3
% 1.39/0.55 % (279609)Termination reason: Instruction limit
% 1.39/0.55 % (279609)Termination phase: shuffling
% 1.39/0.55 % (279609)Time elapsed: 0.004 s
% 1.39/0.55 % (279609)Peak memory usage: 10 MB
% 1.39/0.55 % (279609)Instructions burned: 17 (million)
% 1.39/0.55 % (279577)Instruction limit reached!
% 1.39/0.55 % (279577)------------------------------
% 1.39/0.55 % (279577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.55 % (279577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.55 % (279577)CaDiCaL version: 2.1.3
% 1.39/0.55 % (279577)Termination reason: Instruction limit
% 1.39/0.55 % (279577)Termination phase: Saturation
% 1.39/0.55 % (279577)Time elapsed: 0.099 s
% 1.39/0.55 % (279577)Peak memory usage: 13 MB
% 1.39/0.55 % (279577)Instructions burned: 158 (million)
% 1.39/0.55 % (279615)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2419977968:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.39/0.55 % (279612)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2051509699: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)
% 1.39/0.55 % (279612)Instruction limit reached!
% 1.39/0.55 % (279612)------------------------------
% 1.39/0.55 % (279612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.55 % (279612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.55 % (279612)CaDiCaL version: 2.1.3
% 1.39/0.55 % (279612)Termination reason: Instruction limit
% 1.39/0.55 % (279612)Termination phase: shuffling
% 1.39/0.55 % (279612)Time elapsed: 0.003 s
% 1.39/0.55 % (279612)Peak memory usage: 10 MB
% 1.39/0.55 % (279612)Instructions burned: 6 (million)
% 1.39/0.55 % (279614)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1788839295:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.39/0.55 % (279615)Instruction limit reached!
% 1.39/0.55 % (279615)------------------------------
% 1.39/0.55 % (279615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.55 % (279615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.55 % (279615)CaDiCaL version: 2.1.3
% 1.39/0.55 % (279615)Termination reason: Instruction limit
% 1.39/0.55 % (279615)Termination phase: shuffling
% 1.39/0.55 % (279615)Time elapsed: 0.006 s
% 1.39/0.55 % (279615)Peak memory usage: 10 MB
% 1.39/0.55 % (279615)Instructions burned: 24 (million)
% 1.39/0.55 % (279599)Refutation not found, incomplete strategy
% 1.39/0.55 % (279599)------------------------------
% 1.39/0.55 % (279599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.55 % (279599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.55 % (279599)CaDiCaL version: 2.1.3
% 1.39/0.55 % (279599)Termination reason: Refutation not found, incomplete strategy
% 1.39/0.55 % (279599)Time elapsed: 0.044 s
% 1.39/0.55 % (279599)Peak memory usage: 14 MB
% 1.39/0.55 % (279599)Instructions burned: 90 (million)
% 1.39/0.55 % (279599)------------------------------
% 1.39/0.55 % (279599)------------------------------
% 1.39/0.55 % (279621)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.19/0.64 % (279621)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=104267943:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.19/0.64 % (279614)Instruction limit reached!
% 2.19/0.64 % (279614)------------------------------
% 2.19/0.64 % (279614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.64 % (279614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.64 % (279614)CaDiCaL version: 2.1.3
% 2.19/0.64 % (279614)Termination reason: Instruction limit
% 2.19/0.64 % (279614)Termination phase: shuffling
% 2.19/0.64 % (279614)Time elapsed: 0.012 s
% 2.19/0.64 % (279614)Peak memory usage: 11 MB
% 2.19/0.64 % (279614)Instructions burned: 26 (million)
% 2.19/0.64 % (279616)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=257990282:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.19/0.64 % (279621)Instruction limit reached!
% 2.19/0.64 % (279621)------------------------------
% 2.19/0.64 % (279621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.64 % (279621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.64 % (279621)CaDiCaL version: 2.1.3
% 2.19/0.64 % (279621)Termination reason: Instruction limit
% 2.19/0.64 % (279621)Termination phase: shuffling
% 2.19/0.64 % (279621)Time elapsed: 0.003 s
% 2.19/0.64 % (279621)Peak memory usage: 10 MB
% 2.19/0.64 % (279621)Instructions burned: 12 (million)
% 2.19/0.64 % (279620)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 2.19/0.64 % (279620)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.19/0.64 % (279620)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1051867177:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.19/0.64 % (279622)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2591016691:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.19/0.64 % (279626)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2335603710:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.19/0.64 % (279620)Instruction limit reached!
% 2.19/0.64 % (279620)------------------------------
% 2.19/0.64 % (279620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.64 % (279620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.64 % (279620)CaDiCaL version: 2.1.3
% 2.19/0.64 % (279620)Termination reason: Instruction limit
% 2.19/0.64 % (279620)Termination phase: shuffling
% 2.19/0.64 % (279620)Time elapsed: 0.007 s
% 2.19/0.64 % (279620)Peak memory usage: 10 MB
% 2.19/0.64 % (279620)Instructions burned: 14 (million)
% 2.19/0.64 % (279626)Instruction limit reached!
% 2.19/0.64 % (279626)------------------------------
% 2.19/0.64 % (279626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.64 % (279626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.64 % (279626)CaDiCaL version: 2.1.3
% 2.19/0.64 % (279626)Termination reason: Instruction limit
% 2.19/0.64 % (279626)Termination phase: shuffling
% 2.19/0.64 % (279626)Time elapsed: 0.006 s
% 2.19/0.64 % (279626)Peak memory usage: 11 MB
% 2.19/0.64 % (279626)Instructions burned: 25 (million)
% 2.19/0.64 % (279625)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1672261099:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.19/0.64 % (279625)Instruction limit reached!
% 2.19/0.64 % (279625)------------------------------
% 2.19/0.64 % (279625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.64 % (279625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.64 % (279625)CaDiCaL version: 2.1.3
% 2.19/0.64 % (279625)Termination reason: Instruction limit
% 2.19/0.64 % (279625)Termination phase: shuffling
% 2.19/0.64 % (279625)Time elapsed: 0.004 s
% 2.19/0.64 % (279625)Peak memory usage: 10 MB
% 2.19/0.64 % (279625)Instructions burned: 8 (million)
% 2.45/0.70 % (279622)Instruction limit reached!
% 2.45/0.70 % (279622)------------------------------
% 2.45/0.70 % (279622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.45/0.70 % (279622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/0.70 % (279622)CaDiCaL version: 2.1.3
% 2.45/0.70 % (279622)Termination reason: Instruction limit
% 2.45/0.70 % (279622)Termination phase: shuffling
% 2.45/0.70 % (279622)Time elapsed: 0.015 s
% 2.45/0.70 % (279622)Peak memory usage: 11 MB
% 2.45/0.70 % (279622)Instructions burned: 33 (million)
% 2.45/0.70 % (279632)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2737710618:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.45/0.70 % (279616)Instruction limit reached!
% 2.45/0.70 % (279616)------------------------------
% 2.45/0.70 % (279616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.45/0.70 % (279616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/0.70 % (279616)CaDiCaL version: 2.1.3
% 2.45/0.70 % (279616)Termination reason: Instruction limit
% 2.45/0.70 % (279616)Termination phase: Clausification
% 2.45/0.70 % (279616)Time elapsed: 0.029 s
% 2.45/0.70 % (279616)Peak memory usage: 12 MB
% 2.45/0.70 % (279616)Instructions burned: 61 (million)
% 2.45/0.70 % (279630)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4220962850:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.45/0.70 % (279633)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=319072249:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.45/0.70 % (279630)Instruction limit reached!
% 2.45/0.70 % (279630)------------------------------
% 2.45/0.70 % (279630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.45/0.70 % (279630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/0.70 % (279630)CaDiCaL version: 2.1.3
% 2.45/0.70 % (279630)Termination reason: Instruction limit
% 2.45/0.70 % (279630)Termination phase: shuffling
% 2.45/0.70 % (279630)Time elapsed: 0.010 s
% 2.45/0.70 % (279630)Peak memory usage: 10 MB
% 2.45/0.70 % (279630)Instructions burned: 21 (million)
% 2.45/0.70 % (279634)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=411502442:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.45/0.70 % (279636)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=708678268:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.45/0.70 % (279639)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.45/0.70 % (279639)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1268693539:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.45/0.70 % (279639)Instruction limit reached!
% 2.45/0.70 % (279639)------------------------------
% 2.45/0.70 % (279639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.45/0.70 % (279639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/0.70 % (279639)CaDiCaL version: 2.1.3
% 2.45/0.70 % (279639)Termination reason: Instruction limit
% 2.45/0.70 % (279639)Termination phase: shuffling
% 2.45/0.70 % (279639)Time elapsed: 0.004 s
% 2.45/0.70 % (279639)Peak memory usage: 10 MB
% 2.45/0.70 % (279639)Instructions burned: 8 (million)
% 2.45/0.70 % (279636)Instruction limit reached!
% 2.45/0.70 % (279636)------------------------------
% 2.45/0.70 % (279636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.45/0.70 % (279636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/0.70 % (279636)CaDiCaL version: 2.1.3
% 2.45/0.70 % (279636)Termination reason: Instruction limit
% 2.45/0.70 % (279636)Termination phase: Preprocessing 1
% 2.45/0.70 % (279636)Time elapsed: 0.019 s
% 2.45/0.70 % (279636)Peak memory usage: 11 MB
% 2.45/0.70 % (279636)Instructions burned: 43 (million)
% 2.45/0.70 % (279643)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1086896642:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.45/0.70 % (279644)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3402942874:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.57/0.70 % (279633)Instruction limit reached!
% 2.57/0.70 % (279633)------------------------------
% 2.57/0.70 % (279633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279633)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279633)Termination reason: Instruction limit
% 2.57/0.70 % (279633)Termination phase: Saturation
% 2.57/0.70 % (279633)Time elapsed: 0.063 s
% 2.57/0.70 % (279633)Peak memory usage: 14 MB
% 2.57/0.70 % (279633)Instructions burned: 144 (million)
% 2.57/0.70 % (279647)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.57/0.70 % (279647)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1843526132:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.57/0.70 % (279647)Instruction limit reached!
% 2.57/0.70 % (279647)------------------------------
% 2.57/0.70 % (279647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279647)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279647)Termination reason: Instruction limit
% 2.57/0.70 % (279647)Termination phase: shuffling
% 2.57/0.70 % (279647)Time elapsed: 0.004 s
% 2.57/0.70 % (279647)Peak memory usage: 10 MB
% 2.57/0.70 % (279647)Instructions burned: 8 (million)
% 2.57/0.70 % (279634)Instruction limit reached!
% 2.57/0.70 % (279634)------------------------------
% 2.57/0.70 % (279634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279634)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279634)Termination reason: Instruction limit
% 2.57/0.70 % (279634)Termination phase: Saturation
% 2.57/0.70 % (279634)Time elapsed: 0.095 s
% 2.57/0.70 % (279634)Peak memory usage: 15 MB
% 2.57/0.70 % (279634)Instructions burned: 193 (million)
% 2.57/0.70 % (279649)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1008708507:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.57/0.70 % (279650)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2342677340:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.57/0.70 % (279649)Instruction limit reached!
% 2.57/0.70 % (279649)------------------------------
% 2.57/0.70 % (279649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279649)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279649)Termination reason: Instruction limit
% 2.57/0.70 % (279649)Termination phase: shuffling
% 2.57/0.70 % (279649)Time elapsed: 0.010 s
% 2.57/0.70 % (279649)Peak memory usage: 10 MB
% 2.57/0.70 % (279649)Instructions burned: 22 (million)
% 2.57/0.70 % (279644)Instruction limit reached!
% 2.57/0.70 % (279644)------------------------------
% 2.57/0.70 % (279644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279644)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279644)Termination reason: Instruction limit
% 2.57/0.70 % (279644)Termination phase: Saturation
% 2.57/0.70 % (279644)Time elapsed: 0.080 s
% 2.57/0.70 % (279644)Peak memory usage: 14 MB
% 2.57/0.70 % (279644)Instructions burned: 169 (million)
% 2.57/0.70 % (279650)Instruction limit reached!
% 2.57/0.70 % (279650)------------------------------
% 2.57/0.70 % (279650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279650)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279650)Termination reason: Instruction limit
% 2.57/0.70 % (279650)Termination phase: shuffling
% 2.57/0.70 % (279650)Time elapsed: 0.010 s
% 2.57/0.70 % (279650)Peak memory usage: 10 MB
% 2.57/0.70 % (279650)Instructions burned: 21 (million)
% 2.57/0.70 % (279653)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=936587169:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.57/0.70 % (279643)Instruction limit reached!
% 2.57/0.70 % (279643)------------------------------
% 2.57/0.70 % (279643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279643)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279643)Termination reason: Instruction limit
% 2.57/0.70 % (279643)Termination phase: Saturation
% 2.57/0.70 % (279643)Time elapsed: 0.095 s
% 2.57/0.70 % (279643)Peak memory usage: 14 MB
% 2.57/0.70 % (279643)Instructions burned: 182 (million)
% 2.57/0.70 % (279654)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3781637669:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.57/0.70 % (279655)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3064910085:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.57/0.70 % (279606)Instruction limit reached!
% 2.57/0.70 % (279606)------------------------------
% 2.57/0.70 % (279606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279606)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279606)Termination reason: Instruction limit
% 2.57/0.70 % (279606)Termination phase: Saturation
% 2.57/0.70 % (279606)Time elapsed: 0.228 s
% 2.57/0.70 % (279606)Peak memory usage: 15 MB
% 2.57/0.70 % (279606)Instructions burned: 327 (million)
% 2.57/0.70 % (279657)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=693546864:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.57/0.70 % (279655)Instruction limit reached!
% 2.57/0.70 % (279655)------------------------------
% 2.57/0.70 % (279655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279655)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279655)Termination reason: Instruction limit
% 2.57/0.70 % (279655)Termination phase: Property scanning
% 2.57/0.70 % (279655)Time elapsed: 0.021 s
% 2.57/0.70 % (279655)Peak memory usage: 11 MB
% 2.57/0.70 % (279655)Instructions burned: 47 (million)
% 2.57/0.70 % (279660)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=534359118:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.57/0.70 % (279574)Instruction limit reached!
% 2.57/0.70 % (279574)------------------------------
% 2.57/0.70 % (279574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279574)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279574)Termination reason: Instruction limit
% 2.57/0.70 % (279574)Termination phase: Saturation
% 2.57/0.70 % (279574)Time elapsed: 0.338 s
% 2.57/0.70 % (279574)Peak memory usage: 17 MB
% 2.57/0.70 % (279574)Instructions burned: 635 (million)
% 2.57/0.70 % (279660)Instruction limit reached!
% 2.57/0.70 % (279660)------------------------------
% 2.57/0.70 % (279660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279660)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279660)Termination reason: Instruction limit
% 2.57/0.70 % (279660)Termination phase: shuffling
% 2.57/0.70 % (279660)Time elapsed: 0.010 s
% 2.57/0.70 % (279660)Peak memory usage: 10 MB
% 2.57/0.70 % (279660)Instructions burned: 23 (million)
% 2.57/0.70 % (279662)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.57/0.70 % (279662)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2799008386:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.57/0.70 % (279632) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-279566-279632"...
% 2.57/0.70 % (279664)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2521407898:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.57/0.70 % (279665)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=766908596:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 2.57/0.70 % (279664)Instruction limit reached!
% 2.57/0.70 % (279664)------------------------------
% 2.57/0.70 % (279664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.70 % (279664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.70 % (279664)CaDiCaL version: 2.1.3
% 2.57/0.70 % (279664)Termination reason: Instruction limit
% 2.57/0.70 % (279664)Termination phase: shuffling
% 2.57/0.70 % (279664)Time elapsed: 0.007 s
% 2.57/0.70 % (279664)Peak memory usage: 10 MB
% 2.57/0.70 % (279664)Instructions burned: 15 (million)
% 2.57/0.70 % (279632)...printing done.
% 2.57/0.70 % (279632)Refutation found. Thanks to Tanya!
% 2.57/0.70 % SZS status Theorem for theBenchmark
% 2.57/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/0.71 % (279632)------------------------------
% 2.57/0.71 % (279632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.71 % (279632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.71 % (279632)CaDiCaL version: 2.1.3
% 2.57/0.71 % (279632)Termination reason: Refutation
% 2.57/0.71 % (279632)Time elapsed: 0.215 s
% 2.57/0.71 % (279632)Peak memory usage: 17 MB
% 2.57/0.71 % (279632)Instructions burned: 816 (million)
% 2.57/0.71 % (279566)Success in time 0.427 s
% 2.57/0.71 % Vampire exiting
%------------------------------------------------------------------------------