TSTP Solution File: ITP060^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP060^1 : 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 : n006.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 22:50:01 EDT 2024
% Result : Theorem 23.47s 3.75s
% Output : Refutation 23.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 160
% Syntax : Number of formulae : 180 ( 15 unt; 155 typ; 0 def)
% Number of atoms : 243 ( 27 equ; 0 cnn)
% Maximal formula atoms : 3 ( 9 avg)
% Number of connectives : 25 ( 10 ~; 6 |; 0 &; 0 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 730 ( 729 >; 1 *; 0 +; 0 <<)
% Number of symbols : 149 ( 146 usr; 15 con; 0-6 aty)
% Number of variables : 49 ( 0 ^ 35 !; 0 ?; 49 :)
% ( 14 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
config256849571t_unit: $tType ).
thf(type_def_6,type,
message_p_v: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
list_c1059388851t_unit: $tType ).
thf(type_def_9,type,
list_message_p_v: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(func_def_0,type,
list_c1059388851t_unit: $tType ).
thf(func_def_1,type,
config256849571t_unit: $tType ).
thf(func_def_2,type,
list_message_p_v: $tType ).
thf(func_def_3,type,
message_p_v: $tType ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(func_def_6,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(func_def_7,type,
fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
thf(func_def_8,type,
fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
thf(func_def_9,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_10,type,
one_one_nat: nat ).
thf(func_def_11,type,
zero_zero_nat: nat ).
thf(func_def_12,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_13,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_14,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_15,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(func_def_16,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_17,type,
nil_message_p_v: list_message_p_v ).
thf(func_def_18,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(func_def_19,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(func_def_20,type,
suc: nat > nat ).
thf(func_def_21,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_22,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(func_def_23,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_24,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_25,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_26,type,
ft: nat > list_message_p_v ).
thf(func_def_27,type,
index: nat ).
thf(func_def_28,type,
msgInSet: message_p_v ).
thf(func_def_29,type,
msg: message_p_v ).
thf(func_def_30,type,
n0: nat ).
thf(func_def_31,type,
n1: nat ).
thf(func_def_32,type,
nMsg: nat ).
thf(func_def_33,type,
n: nat ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_42,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_43,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
sP0: nat > ( nat > $o ) > $o ).
thf(func_def_48,type,
sP1: ( nat > nat > $o ) > $o ).
thf(func_def_49,type,
sP2: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > $o ).
thf(func_def_50,type,
sP3: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > $o ).
thf(func_def_51,type,
sK4: nat ).
thf(func_def_52,type,
sK5: nat ).
thf(func_def_53,type,
sK6: nat > nat ).
thf(func_def_54,type,
sK7: nat > nat ).
thf(func_def_55,type,
sK8: ( nat > $o ) > nat ).
thf(func_def_56,type,
sK9: ( nat > $o ) > nat ).
thf(func_def_57,type,
sK10: nat > nat ).
thf(func_def_58,type,
sK11: nat > list_c1059388851t_unit ).
thf(func_def_59,type,
sK12: nat > list_message_p_v ).
thf(func_def_60,type,
sK13: list_c1059388851t_unit > list_c1059388851t_unit > nat ).
thf(func_def_61,type,
sK14: list_message_p_v > list_message_p_v > nat ).
thf(func_def_62,type,
sK15: ( nat > $o ) > nat ).
thf(func_def_63,type,
sK16: ( nat > $o ) > nat ).
thf(func_def_64,type,
sK17: ( nat > $o ) > nat ).
thf(func_def_65,type,
sK18: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_66,type,
sK19: ( list_message_p_v > $o ) > list_message_p_v ).
thf(func_def_67,type,
sK20: ( nat > $o ) > nat ).
thf(func_def_68,type,
sK21: ( nat > $o ) > nat ).
thf(func_def_69,type,
sK22: ( nat > $o ) > nat ).
thf(func_def_70,type,
sK23: nat > ( nat > $o ) > nat ).
thf(func_def_71,type,
sK24: nat > ( nat > $o ) > nat ).
thf(func_def_72,type,
sK25: ( nat > $o ) > nat ).
thf(func_def_73,type,
sK26: ( nat > $o ) > nat ).
thf(func_def_74,type,
sK27: ( nat > $o ) > nat > nat ).
thf(func_def_75,type,
sK28: nat > nat > nat ).
thf(func_def_76,type,
sK29: nat > nat ).
thf(func_def_77,type,
sK30: nat > nat > nat ).
thf(func_def_78,type,
sK31: ( nat > $o ) > ( nat > $o ) > nat > nat ).
thf(func_def_79,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_80,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_81,type,
sK34: ( nat > nat > $o ) > nat ).
thf(func_def_82,type,
sK35: ( nat > nat > $o ) > nat ).
thf(func_def_83,type,
sK36: ( nat > nat ) > nat ).
thf(func_def_84,type,
sK37: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK38: ( nat > nat ) > nat ).
thf(func_def_86,type,
sK39: ( nat > nat ) > nat ).
thf(func_def_87,type,
sK40: ( nat > nat ) > nat ).
thf(func_def_88,type,
sK41: ( nat > nat ) > nat ).
thf(func_def_89,type,
sK42: ( nat > $o ) > nat ).
thf(func_def_90,type,
sK43: nat > ( nat > $o ) > nat ).
thf(func_def_91,type,
sK44: ( nat > $o ) > nat ).
thf(func_def_92,type,
sK45: ( nat > nat > $o ) > nat ).
thf(func_def_93,type,
sK46: ( nat > nat > $o ) > nat ).
thf(func_def_94,type,
sK47: ( nat > nat > $o ) > nat ).
thf(func_def_95,type,
sK48: ( nat > nat > $o ) > nat ).
thf(func_def_96,type,
sK49: ( nat > nat > $o ) > nat ).
thf(func_def_97,type,
sK50: ( nat > $o ) > nat > nat ).
thf(func_def_98,type,
sK51: ( nat > $o ) > nat > nat > nat ).
thf(func_def_99,type,
sK52: ( nat > $o ) > nat > nat > nat ).
thf(func_def_100,type,
sK53: nat > ( nat > $o ) > nat ).
thf(func_def_101,type,
sK54: ( nat > $o ) > nat > nat ).
thf(func_def_102,type,
sK55: ( nat > nat > $o ) > nat ).
thf(func_def_103,type,
sK56: ( nat > nat > $o ) > nat ).
thf(func_def_104,type,
sK57: ( nat > nat > $o ) > nat ).
thf(func_def_105,type,
sK58: ( nat > nat > $o ) > nat ).
thf(func_def_106,type,
sK59: message_p_v > nat > nat > nat ).
thf(func_def_107,type,
sK60: list_message_p_v > nat > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > config256849571t_unit > nat ).
thf(func_def_108,type,
sK61: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_109,type,
sK62: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_110,type,
sK63: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_111,type,
sK64: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_112,type,
sK65: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_113,type,
sK66: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_114,type,
sK67: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_115,type,
sK68: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_116,type,
sK69: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_117,type,
sK70: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_118,type,
sK71: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_119,type,
sK72: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_120,type,
sK73: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_121,type,
sK74: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_122,type,
sK75: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_123,type,
sK76: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_124,type,
sK77: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_125,type,
sK78: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_126,type,
sK79: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_127,type,
sK80: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_128,type,
sK81: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_129,type,
sK82: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_130,type,
sK83: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_131,type,
sK84: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_132,type,
sK85: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_133,type,
sK86: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_134,type,
sK87: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_135,type,
sK88: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_136,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_137,type,
sK89: nat > nat > nat ).
thf(func_def_138,type,
sK90: nat > nat > nat ).
thf(func_def_139,type,
sK91: ( nat > $o ) > nat > nat ).
thf(func_def_140,type,
sK92: ( nat > $o ) > nat > nat ).
thf(func_def_141,type,
sK93: ( nat > $o ) > nat > nat ).
thf(func_def_142,type,
sK94: ( nat > $o ) > nat > nat ).
thf(func_def_143,type,
sK95: ( nat > $o ) > nat > nat ).
thf(func_def_144,type,
sK96: ( nat > $o ) > nat > nat ).
thf(func_def_145,type,
sK97: ( nat > $o ) > nat > nat ).
thf(func_def_146,type,
sK98: ( nat > $o ) > nat > nat ).
thf(func_def_147,type,
sK99: ( nat > config256849571t_unit > $o ) > nat > nat ).
thf(func_def_148,type,
sK100: ( nat > config256849571t_unit > $o ) > nat > list_c1059388851t_unit ).
thf(func_def_149,type,
sK101: ( nat > message_p_v > $o ) > nat > nat ).
thf(func_def_150,type,
sK102: ( nat > message_p_v > $o ) > nat > list_message_p_v ).
thf(func_def_151,type,
sK103: nat > nat ).
thf(f94235,plain,
$false,
inference(subsumption_resolution,[],[f94228,f32401]) ).
thf(f32401,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),X0)),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))) ),
inference(unit_resulting_resolution,[],[f1304,f1273]) ).
thf(f1273,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) ) ),
inference(cnf_transformation,[],[f867]) ).
thf(f867,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f574]) ).
thf(f574,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) ) ),
inference(fool_elimination,[],[f573]) ).
thf(f573,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) ),
inference(rectify,[],[f155]) ).
thf(f155,axiom,
! [X24: nat,X3: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X24),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X24),X1)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_less__imp__diff__less) ).
thf(f1304,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))) = $true,
inference(cnf_transformation,[],[f600]) ).
thf(f600,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))) = $true,
inference(fool_elimination,[],[f599]) ).
thf(f599,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Occ3_H) ).
thf(f94228,plain,
$true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(unit_resulting_resolution,[],[f1102,f1009,f1179]) ).
thf(f1179,plain,
! [X2: nat,X0: list_c1059388851t_unit,X1: list_c1059388851t_unit] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,X0)) )
| ( vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X0),X2) = vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X1),X2) )
| ( $true != vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,X0),X1) ) ),
inference(cnf_transformation,[],[f777]) ).
thf(f777,plain,
! [X0: list_c1059388851t_unit,X1: list_c1059388851t_unit] :
( ! [X2: nat] :
( ( vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X0),X2) = vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,X0)) ) )
| ( $true != vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,X0),X1) ) ),
inference(ennf_transformation,[],[f452]) ).
thf(f452,plain,
! [X0: list_c1059388851t_unit,X1: list_c1059388851t_unit] :
( ( $true = vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,X0),X1) )
=> ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,X0)) )
=> ( vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X0),X2) = vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X1),X2) ) ) ),
inference(fool_elimination,[],[f451]) ).
thf(f451,plain,
! [X0: list_c1059388851t_unit,X1: list_c1059388851t_unit] :
( vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,X0),X1)
=> ! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,X0))
=> ( vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X0),X2) = vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X1),X2) ) ) ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X60: list_c1059388851t_unit,X61: list_c1059388851t_unit] :
( vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,X60),X61)
=> ! [X62: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X62),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,X60))
=> ( vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X60),X62) = vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,X61),X62) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_PrefixSameOnLow) ).
thf(f1009,plain,
vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,index)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)) != vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,index))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)),
inference(cnf_transformation,[],[f639]) ).
thf(f639,plain,
vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,index)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)) != vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,index))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)),
inference(flattening,[],[f246]) ).
thf(f246,negated_conjecture,
vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,index)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)) != vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,index))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)),
inference(negated_conjecture,[],[f245]) ).
thf(f245,conjecture,
vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,index)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)) = vAPP(nat,config256849571t_unit,vAPP(list_c1059388851t_unit,sTfun(nat,config256849571t_unit),nth_co1649820636t_unit,vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,index))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,n1),one_one_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1102,plain,
! [X0: nat] : ( vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,vAPP(nat,list_c1059388851t_unit,fe,X0)),vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,X0))) = $true ),
inference(cnf_transformation,[],[f368]) ).
thf(f368,plain,
! [X0: nat] : ( vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,vAPP(nat,list_c1059388851t_unit,fe,X0)),vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,X0))) = $true ),
inference(fool_elimination,[],[f367]) ).
thf(f367,plain,
! [X0: nat] : vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,vAPP(nat,list_c1059388851t_unit,fe,X0)),vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,X0))),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X0: nat] : vAPP(list_c1059388851t_unit,$o,vAPP(list_c1059388851t_unit,sTfun(list_c1059388851t_unit,$o),prefix1615116500t_unit,vAPP(nat,list_c1059388851t_unit,fe,X0)),vAPP(nat,list_c1059388851t_unit,fe,vAPP(nat,nat,suc,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_IPrefixListEx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP060^1 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.31 % Computer : n006.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sat May 18 17:40:53 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % (15414)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (15415)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.34 % (15417)WARNING: value z3 for option sas not known
% 0.16/0.34 % (15420)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)
% 0.16/0.34 % (15417)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)
% 0.16/0.34 % (15421)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)
% 0.16/0.34 % (15418)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34 % (15419)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)
% 0.16/0.34 % (15416)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.35 % Exception at run slice level
% 0.16/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.36 % (15421)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.37 % (15422)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.37 % Exception at run slice level
% 0.16/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.37 % Exception at run slice level
% 0.16/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.38 % (15423)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)
% 0.16/0.39 % (15424)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)
% 0.16/0.39 % (15422)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.39 % (15423)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.39 % Exception at run slice level
% 0.16/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.42 % (15425)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)
% 23.47/3.74 % (15423)First to succeed.
% 23.47/3.75 % (15423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15414"
% 23.47/3.75 % (15423)Refutation found. Thanks to Tanya!
% 23.47/3.75 % SZS status Theorem for theBenchmark
% 23.47/3.75 % SZS output start Proof for theBenchmark
% See solution above
% 23.47/3.75 % (15423)------------------------------
% 23.47/3.75 % (15423)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 23.47/3.75 % (15423)Termination reason: Refutation
% 23.47/3.75
% 23.47/3.75 % (15423)Memory used [KB]: 14744
% 23.47/3.75 % (15423)Time elapsed: 3.363 s
% 23.47/3.75 % (15423)Instructions burned: 8962 (million)
% 23.47/3.75 % (15414)Success in time 3.419 s
%------------------------------------------------------------------------------