TSTP Solution File: ITP089^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP089^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:51:26 EDT 2024
% Result : Theorem 8.35s 1.53s
% Output : Refutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 217
% Syntax : Number of formulae : 307 ( 58 unt; 202 typ; 0 def)
% Number of atoms : 1577 ( 267 equ; 0 cnn)
% Maximal formula atoms : 11 ( 15 avg)
% Number of connectives : 299 ( 109 ~; 136 |; 20 &; 0 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 316 ( 315 >; 1 *; 0 +; 0 <<)
% Number of symbols : 181 ( 178 usr; 12 con; 0-6 aty)
% Number of variables : 121 ( 0 ^ 98 !; 8 ?; 121 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
secrecy_specID: $tType ).
thf(type_def_6,type,
set_Secrecy_KS: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
secrecy_KS: $tType ).
thf(type_def_9,type,
set_Secrecy_Keys: $tType ).
thf(type_def_10,type,
set_Secrecy_Secrets: $tType ).
thf(type_def_11,type,
set_Secrecy_chanID: $tType ).
thf(type_def_12,type,
set_Secrecy_specID: $tType ).
thf(type_def_13,type,
secrecy_Expression: $tType ).
thf(type_def_14,type,
list_S529945141ession: $tType ).
thf(type_def_15,type,
secrecy_Keys: $tType ).
thf(type_def_16,type,
secrecy_Secrets: $tType ).
thf(type_def_17,type,
secrecy_chanID: $tType ).
thf(type_def_18,type,
nat: $tType ).
thf(func_def_0,type,
list_S529945141ession: $tType ).
thf(func_def_1,type,
set_Secrecy_Secrets: $tType ).
thf(func_def_2,type,
set_Secrecy_specID: $tType ).
thf(func_def_3,type,
set_Secrecy_chanID: $tType ).
thf(func_def_4,type,
set_Secrecy_Keys: $tType ).
thf(func_def_5,type,
set_Secrecy_KS: $tType ).
thf(func_def_6,type,
secrecy_Expression: $tType ).
thf(func_def_7,type,
secrecy_Secrets: $tType ).
thf(func_def_8,type,
secrecy_specID: $tType ).
thf(func_def_9,type,
secrecy_chanID: $tType ).
thf(func_def_10,type,
secrecy_Keys: $tType ).
thf(func_def_11,type,
secrecy_KS: $tType ).
thf(func_def_12,type,
nat: $tType ).
thf(func_def_13,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_14,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(func_def_15,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(func_def_16,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_17,type,
sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_18,type,
sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_19,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_20,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_21,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_22,type,
bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
thf(func_def_23,type,
bot_bo2072920570Keys_o: secrecy_Keys > $o ).
thf(func_def_24,type,
bot_bo1909946299rets_o: secrecy_Secrets > $o ).
thf(func_def_25,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(func_def_26,type,
bot_bo1767780696ecID_o: secrecy_specID > $o ).
thf(func_def_27,type,
bot_bo1943466239ecy_KS: set_Secrecy_KS ).
thf(func_def_28,type,
bot_bo701486667y_Keys: set_Secrecy_Keys ).
thf(func_def_29,type,
bot_bo1124690338ecrets: set_Secrecy_Secrets ).
thf(func_def_30,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(func_def_31,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(func_def_32,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_33,type,
correctCompositionKS: secrecy_specID > $o ).
thf(func_def_34,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_35,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_36,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_37,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_38,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_39,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_40,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_41,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_42,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_43,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_44,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_45,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_46,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_47,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_48,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_49,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_50,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_51,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_52,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_53,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_54,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_55,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_56,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_57,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_58,type,
insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_59,type,
insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_60,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_61,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_62,type,
is_emp928984296chanID: set_Secrecy_chanID > $o ).
thf(func_def_63,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(func_def_64,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(func_def_65,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(func_def_66,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(func_def_67,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_68,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_69,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_70,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_71,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_72,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_73,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_74,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_75,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_76,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_77,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_78,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_79,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_80,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(func_def_81,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_82,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_83,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_84,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_85,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_86,type,
p: secrecy_specID ).
thf(func_def_87,type,
pq: secrecy_specID ).
thf(func_def_88,type,
q: secrecy_specID ).
thf(func_def_89,type,
m: secrecy_KS ).
thf(func_def_90,type,
secret: secrecy_Secrets ).
thf(func_def_94,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_95,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_96,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_97,type,
vAND: $o > $o > $o ).
thf(func_def_98,type,
vIMP: $o > $o > $o ).
thf(func_def_99,type,
vNOT: $o > $o ).
thf(func_def_100,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_101,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_102,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_103,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_104,type,
vOR: $o > $o > $o ).
thf(func_def_105,type,
sK0: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_106,type,
sK1: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_107,type,
sK2: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_108,type,
sK3: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_109,type,
sK4: set_Secrecy_KS > secrecy_KS ).
thf(func_def_110,type,
sK5: set_Secrecy_KS > secrecy_KS ).
thf(func_def_111,type,
sK6: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_112,type,
sK7: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_113,type,
sK8: set_Secrecy_specID > secrecy_specID ).
thf(func_def_114,type,
sK9: set_Secrecy_specID > secrecy_specID ).
thf(func_def_115,type,
sK10: secrecy_KS > secrecy_Secrets ).
thf(func_def_116,type,
sK11: secrecy_KS > secrecy_Keys ).
thf(func_def_117,type,
sK12: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_118,type,
sK13: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_119,type,
sK14: set_Secrecy_KS > secrecy_KS ).
thf(func_def_120,type,
sK15: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_121,type,
sK16: set_Secrecy_specID > secrecy_specID ).
thf(func_def_122,type,
sK17: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_123,type,
sK18: set_Secrecy_specID > secrecy_specID ).
thf(func_def_124,type,
sK19: ( secrecy_KS > $o ) > secrecy_Secrets ).
thf(func_def_125,type,
sK20: ( secrecy_KS > $o ) > secrecy_Keys ).
thf(func_def_126,type,
sK21: set_Secrecy_Keys > secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_127,type,
sK22: set_Secrecy_Keys > secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_128,type,
sK23: set_Secrecy_Secrets > secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_129,type,
sK24: set_Secrecy_Secrets > secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_130,type,
sK25: set_Secrecy_KS > secrecy_KS > set_Secrecy_KS ).
thf(func_def_131,type,
sK26: set_Secrecy_KS > secrecy_KS > set_Secrecy_KS ).
thf(func_def_132,type,
sK27: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_133,type,
sK28: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_134,type,
sK29: set_Secrecy_specID > secrecy_specID > set_Secrecy_specID ).
thf(func_def_135,type,
sK30: set_Secrecy_specID > secrecy_specID > set_Secrecy_specID ).
thf(func_def_136,type,
sK31: secrecy_Keys > secrecy_specID > secrecy_specID ).
thf(func_def_137,type,
sK32: secrecy_Secrets > secrecy_specID > secrecy_specID ).
thf(func_def_138,type,
sK33: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets ).
thf(func_def_139,type,
sK34: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys ).
thf(func_def_140,type,
sK35: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets ).
thf(func_def_141,type,
sK36: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys ).
thf(func_def_142,type,
sK37: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_143,type,
sK38: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_144,type,
sK39: secrecy_Secrets > secrecy_specID > secrecy_chanID ).
thf(func_def_145,type,
sK40: secrecy_Secrets > secrecy_specID > secrecy_chanID ).
thf(func_def_146,type,
sK41: secrecy_Expression > secrecy_specID > secrecy_chanID ).
thf(func_def_147,type,
sK42: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_148,type,
sK43: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_149,type,
sK44: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_150,type,
sK45: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_151,type,
sK46: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_152,type,
sK47: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_153,type,
sK48: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_154,type,
sK49: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_155,type,
sK50: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_156,type,
sK51: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_157,type,
sK52: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_158,type,
sK53: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_160,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_161,type,
sK55: set_Secrecy_specID > secrecy_specID > set_Secrecy_specID > secrecy_specID > set_Secrecy_specID ).
thf(func_def_162,type,
sK56: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_163,type,
sK57: set_Secrecy_KS > secrecy_KS > set_Secrecy_KS > secrecy_KS > set_Secrecy_KS ).
thf(func_def_164,type,
sK58: set_Secrecy_Secrets > secrecy_Secrets > set_Secrecy_Secrets > secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_165,type,
sK59: set_Secrecy_Keys > secrecy_Keys > set_Secrecy_Keys > secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_166,type,
sK60: set_Secrecy_chanID > ( secrecy_chanID > $o ) > secrecy_chanID ).
thf(func_def_167,type,
sK61: ( secrecy_chanID > $o ) > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_168,type,
sK62: set_Secrecy_chanID > set_Secrecy_chanID > ( secrecy_chanID > $o ) > secrecy_chanID ).
thf(func_def_169,type,
sK63: set_Secrecy_KS > ( secrecy_KS > $o ) > secrecy_KS ).
thf(func_def_170,type,
sK64: ( secrecy_KS > $o ) > set_Secrecy_KS > secrecy_KS ).
thf(func_def_171,type,
sK65: set_Secrecy_KS > set_Secrecy_KS > ( secrecy_KS > $o ) > secrecy_KS ).
thf(func_def_172,type,
sK66: set_Secrecy_chanID > set_Secrecy_chanID > ( secrecy_chanID > $o ) > secrecy_chanID ).
thf(func_def_173,type,
sK67: set_Secrecy_chanID > ( secrecy_chanID > $o ) > secrecy_chanID ).
thf(func_def_174,type,
sK68: ( secrecy_chanID > $o ) > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_175,type,
sK69: set_Secrecy_KS > set_Secrecy_KS > ( secrecy_KS > $o ) > secrecy_KS ).
thf(func_def_176,type,
sK70: set_Secrecy_KS > ( secrecy_KS > $o ) > secrecy_KS ).
thf(func_def_177,type,
sK71: ( secrecy_KS > $o ) > set_Secrecy_KS > secrecy_KS ).
thf(func_def_178,type,
sK72: set_Secrecy_specID > secrecy_specID ).
thf(func_def_179,type,
sK73: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_180,type,
sK74: set_Secrecy_KS > secrecy_KS ).
thf(func_def_181,type,
sK75: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_182,type,
sK76: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_183,type,
sK77: set_Secrecy_specID > secrecy_specID ).
thf(func_def_184,type,
sK78: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_185,type,
sK79: set_Secrecy_KS > secrecy_KS ).
thf(func_def_186,type,
sK80: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_187,type,
sK81: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_188,type,
sK82: ( secrecy_specID > $o ) > secrecy_specID ).
thf(func_def_189,type,
sK83: ( secrecy_specID > $o ) > secrecy_specID ).
thf(func_def_190,type,
sK84: ( secrecy_chanID > $o ) > secrecy_chanID ).
thf(func_def_191,type,
sK85: ( secrecy_chanID > $o ) > secrecy_chanID ).
thf(f12225,plain,
$false,
inference(trivial_inequality_removal,[],[f12224]) ).
thf(f12224,plain,
$true = $false,
inference(forward_demodulation,[],[f12223,f2996]) ).
thf(f2996,plain,
$false = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)),
inference(trivial_inequality_removal,[],[f2995]) ).
thf(f2995,plain,
( ( $true != $true )
| ( $false = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(superposition,[],[f2904,f359]) ).
thf(f359,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f2904,plain,
$true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)),
inference(forward_demodulation,[],[f1568,f1529]) ).
thf(f1529,plain,
vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret) = m,
inference(cnf_transformation,[],[f7]) ).
thf(f7,axiom,
vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret) = m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_a2) ).
thf(f1568,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) != $true,
inference(cnf_transformation,[],[f974]) ).
thf(f974,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) != $true,
inference(flattening,[],[f433]) ).
thf(f433,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) != $true,
inference(fool_elimination,[],[f432]) ).
thf(f432,plain,
~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_sg2b) ).
thf(f12223,plain,
$true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)),
inference(trivial_inequality_removal,[],[f12222]) ).
thf(f12222,plain,
( ( $true = $false )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12221,f3024]) ).
thf(f3024,plain,
$false = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)),
inference(trivial_inequality_removal,[],[f3023]) ).
thf(f3023,plain,
( ( $true != $true )
| ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)) ) ),
inference(superposition,[],[f2977,f359]) ).
thf(f2977,plain,
$true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)),
inference(backward_demodulation,[],[f1565,f2974]) ).
thf(f2974,plain,
vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m),
inference(superposition,[],[f1587,f1529]) ).
thf(f1587,plain,
! [X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)) ),
inference(cnf_transformation,[],[f993]) ).
thf(f993,plain,
! [X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X0) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X3: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X3) = vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_KS2Expression_Osimps_I2_J) ).
thf(f1565,plain,
vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) != $true,
inference(cnf_transformation,[],[f971]) ).
thf(f971,plain,
vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) != $true,
inference(flattening,[],[f427]) ).
thf(f427,plain,
vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) != $true,
inference(fool_elimination,[],[f426]) ).
thf(f426,plain,
~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_sg1a) ).
thf(f12221,plain,
( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12220,f2974]) ).
thf(f12220,plain,
( ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) = $true )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12219,f11688]) ).
thf(f11688,plain,
secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p),
inference(trivial_inequality_removal,[],[f11687]) ).
thf(f11687,plain,
( ( $true = $false )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p) ) ),
inference(forward_demodulation,[],[f11686,f2996]) ).
thf(f11686,plain,
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p) ) ),
inference(trivial_inequality_removal,[],[f11685]) ).
thf(f11685,plain,
( ( $true = $false )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p) ) ),
inference(forward_demodulation,[],[f11682,f3002]) ).
thf(f3002,plain,
$false = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)),
inference(trivial_inequality_removal,[],[f3001]) ).
thf(f3001,plain,
( ( $true != $true )
| ( $false = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) ) ),
inference(superposition,[],[f2905,f359]) ).
thf(f2905,plain,
$true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)),
inference(forward_demodulation,[],[f1569,f1529]) ).
thf(f1569,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) != $true,
inference(cnf_transformation,[],[f975]) ).
thf(f975,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) != $true,
inference(flattening,[],[f435]) ).
thf(f435,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) != $true,
inference(fool_elimination,[],[f434]) ).
thf(f434,plain,
~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sg1b) ).
thf(f11682,plain,
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p) ) ),
inference(trivial_inequality_removal,[],[f11675]) ).
thf(f11675,plain,
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p) ) ),
inference(superposition,[],[f11658,f1532]) ).
thf(f1532,plain,
vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) = vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,p),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,q),bot_bo1785112429specID)),
inference(cnf_transformation,[],[f6]) ).
thf(f6,axiom,
vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) = vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,p),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,q),bot_bo1785112429specID)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_subPQ) ).
thf(f11658,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1) ) ),
inference(trivial_inequality_removal,[],[f11655]) ).
thf(f11655,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( m != m )
| ( secret = vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(superposition,[],[f2987,f10466]) ).
thf(f10466,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( m = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(subsumption_resolution,[],[f10465,f1962]) ).
thf(f1962,plain,
vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) = $true,
inference(cnf_transformation,[],[f963]) ).
thf(f963,plain,
vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) = $true,
inference(fool_elimination,[],[f962]) ).
thf(f962,plain,
vAPP(secrecy_specID,$o,correc965049635ionLoc,pq),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(secrecy_specID,$o,correc965049635ionLoc,pq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_cCompLoc) ).
thf(f10465,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( m = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1)) )
| ( vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) != $true )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(subsumption_resolution,[],[f10464,f2942]) ).
thf(f2942,plain,
! [X0: secrecy_Keys] : ( m != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) ),
inference(superposition,[],[f1652,f1529]) ).
thf(f1652,plain,
! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) ),
inference(cnf_transformation,[],[f1012]) ).
thf(f1012,plain,
! [X0: secrecy_Keys,X1: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X0) ),
inference(rectify,[],[f282]) ).
thf(f282,axiom,
! [X42: secrecy_Keys,X0: secrecy_Secrets] : ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_KS_Odistinct_I1_J) ).
thf(f10464,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( m = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1)) )
| ( m = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,m),X0),X1)) )
| ( vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) != $true )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(trivial_inequality_removal,[],[f10454]) ).
thf(f10454,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( $true != $true )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( m = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1)) )
| ( m = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,m),X0),X1)) )
| ( vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) != $true )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(superposition,[],[f1845,f2901]) ).
thf(f2901,plain,
$true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)),
inference(backward_demodulation,[],[f1528,f1529]) ).
thf(f1528,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)) = $true,
inference(cnf_transformation,[],[f966]) ).
thf(f966,plain,
vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)) = $true,
inference(flattening,[],[f361]) ).
thf(f361,plain,
~ ( ( vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)) != $true ) ),
inference(fool_elimination,[],[f360]) ).
thf(f360,plain,
~ ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)),
inference(rectify,[],[f357]) ).
thf(f357,negated_conjecture,
~ ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)),
inference(negated_conjecture,[],[f356]) ).
thf(f356,conjecture,
~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,secret)),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,pq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1845,plain,
! [X2: secrecy_specID,X3: secrecy_KS,X0: secrecy_specID,X1: secrecy_specID] :
( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1)) = X3 )
| ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1)) = X3 )
| ( $true != vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) ) ),
inference(cnf_transformation,[],[f1489]) ).
thf(f1489,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1))) ) )
& ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1)) = X3 ) )
| ( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1))) ) )
& ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1)) = X3 ) )
| ( $true != vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f1486,f1488,f1487]) ).
thf(f1487,plain,
! [X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ? [X4: secrecy_Secrets] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X4)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X4)) ) )
& ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X4) = X3 ) )
=> ( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1))) ) )
& ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1488,plain,
! [X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ? [X5: secrecy_Keys] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X5)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X5)) ) )
& ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X5) = X3 ) )
=> ( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1))) ) )
& ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1486,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ? [X4: secrecy_Secrets] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X4)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X4)) ) )
& ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X4) = X3 ) )
| ? [X5: secrecy_Keys] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X5)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X5)) ) )
& ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X5) = X3 ) )
| ( $true != vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) ) ),
inference(rectify,[],[f1294]) ).
thf(f1294,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ? [X5: secrecy_Secrets] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) ) )
& ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5) = X3 ) )
| ? [X4: secrecy_Keys] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) ) )
& ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X4) = X3 ) )
| ( $true != vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) ) ),
inference(flattening,[],[f1293]) ).
thf(f1293,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ? [X5: secrecy_Secrets] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) ) )
& ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5) = X3 ) )
| ? [X4: secrecy_Keys] :
( ( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) ) )
& ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X4) = X3 ) )
| ( $true != vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) ) ),
inference(ennf_transformation,[],[f1085]) ).
thf(f1085,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) = vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) )
=> ( ( $true = vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
=> ( ! [X4: secrecy_Keys] :
( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X4) = X3 )
=> ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) )
& ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) ) ) )
=> ( ! [X5: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5) = X3 )
=> ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) )
& ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) ) ) )
=> ( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
=> ( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
=> ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) ) ) ) ) ) ) ),
inference(flattening,[],[f825]) ).
thf(f825,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) = vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) )
=> ( ( $true = vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
=> ( ! [X4: secrecy_Keys] :
( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X4) = X3 )
=> ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) )
& ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) ) ) )
=> ( ! [X5: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5) = X3 )
=> ( ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) )
& ( $true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) ) ) )
=> ( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
=> ( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
=> ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f824]) ).
thf(f824,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) = vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) )
=> ( vAPP(secrecy_specID,$o,correc965049635ionLoc,X0)
=> ( ! [X4: secrecy_Keys] :
( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X4) = X3 )
=> ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4))
& ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X4)) ) )
=> ( ! [X5: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X5) = X3 )
=> ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5))
& ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X5)) ) )
=> ( ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1))
=> ( ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2))
=> ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) ) ) ) ) ) ),
inference(rectify,[],[f302]) ).
thf(f302,axiom,
! [X5: secrecy_specID,X6: secrecy_specID,X7: secrecy_specID,X39: secrecy_KS] :
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X5) = vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X6),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X7),bot_bo1785112429specID)) )
=> ( vAPP(secrecy_specID,$o,correc965049635ionLoc,X5)
=> ( ! [X52: secrecy_Keys] :
( ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,X52) = X39 )
=> ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X7),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X52))
& ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X6),vAPP(secrecy_Keys,secrecy_Expression,secrecy_kE,X52)) ) )
=> ( ! [X52: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X52) = X39 )
=> ( ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X7),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X52))
& ~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X6),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,X52)) ) )
=> ( ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X39),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X6))
=> ( ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X39),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X7))
=> ~ vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X39),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X5)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_LocalSecretsComposition__neg1) ).
thf(f2987,plain,
! [X0: secrecy_Secrets] :
( ( m != vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) )
| ( secret = X0 ) ),
inference(superposition,[],[f2770,f1529]) ).
thf(f2770,plain,
! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2769]) ).
thf(f2769,plain,
! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) != vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
| ( $true = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2768]) ).
thf(f2768,plain,
! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
( ( $false = vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) )
| ( $true = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1667]) ).
thf(f1667,plain,
! [X0: secrecy_Secrets,X1: secrecy_Secrets] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ),
inference(cnf_transformation,[],[f542]) ).
thf(f542,plain,
! [X0: secrecy_Secrets,X1: secrecy_Secrets] : ( vAPP(secrecy_KS,$o,vAPP(secrecy_KS,sTfun(secrecy_KS,$o),vEQ(secrecy_KS),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0)),vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1)) = vAPP(secrecy_Secrets,$o,vAPP(secrecy_Secrets,sTfun(secrecy_Secrets,$o),vEQ(secrecy_Secrets),X0),X1) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,axiom,
! [X0: secrecy_Secrets,X1: secrecy_Secrets] :
( ( vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X0) = vAPP(secrecy_Secrets,secrecy_KS,secrecy_sKS,X1) )
= ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_KS_Oinject_I2_J) ).
thf(f12219,plain,
( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(trivial_inequality_removal,[],[f12218]) ).
thf(f12218,plain,
( ( $true = $false )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12217,f3007]) ).
thf(f3007,plain,
$false = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)),
inference(trivial_inequality_removal,[],[f3006]) ).
thf(f3006,plain,
( ( $true != $true )
| ( $false = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)) ) ),
inference(superposition,[],[f2975,f359]) ).
thf(f2975,plain,
$true != vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)),
inference(backward_demodulation,[],[f1567,f2974]) ).
thf(f1567,plain,
vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) != $true,
inference(cnf_transformation,[],[f973]) ).
thf(f973,plain,
vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) != $true,
inference(flattening,[],[f431]) ).
thf(f431,plain,
vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) != $true,
inference(fool_elimination,[],[f430]) ).
thf(f430,plain,
~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
~ vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sg2a) ).
thf(f12217,plain,
( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_KS,secrecy_Expression,secrec1016742679ession,m)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12216,f2974]) ).
thf(f12216,plain,
( ( vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,secret)) = $true )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12215,f11688]) ).
thf(f12215,plain,
( ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(trivial_inequality_removal,[],[f12214]) ).
thf(f12214,plain,
( ( $true = $false )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(forward_demodulation,[],[f12211,f3002]) ).
thf(f12211,plain,
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(trivial_inequality_removal,[],[f12204]) ).
thf(f12204,plain,
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,p)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,q),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,p),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),q),p))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,q)) ) ),
inference(superposition,[],[f11793,f1532]) ).
thf(f11793,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) ) ),
inference(subsumption_resolution,[],[f11792,f1962]) ).
thf(f11792,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) != $true )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(subsumption_resolution,[],[f11791,f2942]) ).
thf(f11791,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( m = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,m),X0),X1)) )
| ( vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) != $true )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(trivial_inequality_removal,[],[f11780]) ).
thf(f11780,plain,
! [X0: secrecy_specID,X1: secrecy_specID] :
( ( $true != $true )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,m),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X0),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,m),X0),X1))) )
| ( m = vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,m),X0),X1)) )
| ( vAPP(secrecy_specID,$o,correc965049635ionLoc,pq) != $true )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,pq) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X0),bot_bo1785112429specID)) ) ),
inference(superposition,[],[f1847,f2901]) ).
thf(f1847,plain,
! [X2: secrecy_specID,X3: secrecy_KS,X0: secrecy_specID,X1: secrecy_specID] :
( ( $true != vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X0)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X2)) )
| ( $true = vAPP(set_Secrecy_KS,$o,vAPP(secrecy_KS,sTfun(set_Secrecy_KS,$o),member_Secrecy_KS,X3),vAPP(secrecy_specID,set_Secrecy_KS,localSecrets,X1)) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X2),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1))) )
| ( $true = vAPP(secrecy_Expression,$o,vAPP(secrecy_specID,sTfun(secrecy_Expression,$o),ine,X1),vAPP(secrecy_Secrets,secrecy_Expression,secrecy_sE,vAPP(secrecy_specID,secrecy_Secrets,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Secrets)),sK33,X3),X2),X1))) )
| ( vAPP(secrecy_Keys,secrecy_KS,secrecy_kKS,vAPP(secrecy_specID,secrecy_Keys,vAPP(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys),vAPP(secrecy_KS,sTfun(secrecy_specID,sTfun(secrecy_specID,secrecy_Keys)),sK34,X3),X2),X1)) = X3 )
| ( $true != vAPP(secrecy_specID,$o,correc965049635ionLoc,X0) )
| ( vAPP(secrecy_specID,set_Secrecy_specID,subcomponents,X0) != vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X1),vAPP(set_Secrecy_specID,set_Secrecy_specID,vAPP(secrecy_specID,sTfun(set_Secrecy_specID,set_Secrecy_specID),insert1671894227specID,X2),bot_bo1785112429specID)) ) ),
inference(cnf_transformation,[],[f1489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ITP089^1 : TPTP v8.2.0. Released v7.5.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat May 18 17:59:22 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % (11890)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (11893)WARNING: value z3 for option sas not known
% 0.12/0.36 % (11894)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36 % (11892)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36 % (11893)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.36 % (11895)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.36 % (11891)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.36 % (11896)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.36 % (11897)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.41 % (11897)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.42 % Exception at run slice level
% 0.17/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.42 % Exception at run slice level
% 0.17/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.42 % Exception at run slice level
% 0.17/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.44 % (11898)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.44 % (11899)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.17/0.44 % (11900)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.17/0.49 % (11898)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.49 % (11899)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.50 % Exception at run slice level
% 0.17/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.51 % (11901)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 7.82/1.52 % (11900)First to succeed.
% 7.82/1.53 % (11900)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11890"
% 8.35/1.53 % (11900)Refutation found. Thanks to Tanya!
% 8.35/1.53 % SZS status Theorem for theBenchmark
% 8.35/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 8.35/1.53 % (11900)------------------------------
% 8.35/1.53 % (11900)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 8.35/1.53 % (11900)Termination reason: Refutation
% 8.35/1.53
% 8.35/1.53 % (11900)Memory used [KB]: 9199
% 8.35/1.53 % (11900)Time elapsed: 1.082 s
% 8.35/1.53 % (11900)Instructions burned: 2649 (million)
% 8.35/1.53 % (11890)Success in time 1.194 s
%------------------------------------------------------------------------------