TSTP Solution File: ITP054^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP054^1 : 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 : n004.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 22:49:37 EDT 2024
% Result : Theorem 7.92s 1.52s
% Output : Refutation 7.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 186
% Syntax : Number of formulae : 258 ( 30 unt; 172 typ; 0 def)
% Number of atoms : 695 ( 146 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 168 ( 66 ~; 57 |; 9 &; 0 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 748 ( 747 >; 1 *; 0 +; 0 <<)
% Number of symbols : 165 ( 162 usr; 17 con; 0-6 aty)
% Number of variables : 145 ( 0 ^ 120 !; 11 ?; 145 :)
% ( 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,
nat: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_9,type,
list_c1059388851t_unit: $tType ).
thf(type_def_10,type,
list_message_p_v: $tType ).
thf(type_def_11,type,
set_message_p_v: $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,
set_message_p_v: $tType ).
thf(func_def_4,type,
message_p_v: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
thf(func_def_7,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(func_def_8,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(func_def_9,type,
minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
thf(func_def_10,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_11,type,
one_one_nat: nat ).
thf(func_def_12,type,
zero_zero_nat: nat ).
thf(func_def_13,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_14,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_15,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_16,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_17,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(func_def_18,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_19,type,
nil_message_p_v: list_message_p_v ).
thf(func_def_20,type,
tl_con485597044t_unit: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_21,type,
tl_message_p_v: list_message_p_v > list_message_p_v ).
thf(func_def_22,type,
list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(func_def_23,type,
list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(func_def_24,type,
list_e581556831t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(func_def_25,type,
list_ex_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(func_def_26,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(func_def_27,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(func_def_28,type,
remdup949903207t_unit: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_29,type,
remdup74979931ge_p_v: list_message_p_v > list_message_p_v ).
thf(func_def_30,type,
suc: nat > nat ).
thf(func_def_31,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_32,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(func_def_33,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_34,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_35,type,
collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
thf(func_def_36,type,
member_message_p_v: message_p_v > set_message_p_v > $o ).
thf(func_def_37,type,
consumedMsg: message_p_v ).
thf(func_def_38,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_39,type,
firstOccSet: nat > set_message_p_v ).
thf(func_def_40,type,
ft: nat > list_message_p_v ).
thf(func_def_41,type,
index: nat ).
thf(func_def_42,type,
msg: message_p_v ).
thf(func_def_43,type,
n0: nat ).
thf(func_def_44,type,
n1: nat ).
thf(func_def_45,type,
nMsg: nat ).
thf(func_def_46,type,
n: nat ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_55,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_56,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_57,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
vOR: $o > $o > $o ).
thf(func_def_59,type,
vNOT: $o > $o ).
thf(func_def_60,type,
sP0: nat > ( nat > $o ) > $o ).
thf(func_def_61,type,
sP1: ( nat > nat > $o ) > $o ).
thf(func_def_62,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_63,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_64,type,
sK4: nat ).
thf(func_def_65,type,
sK5: nat ).
thf(func_def_66,type,
sK6: nat ).
thf(func_def_67,type,
sK7: nat ).
thf(func_def_68,type,
sK8: nat > nat ).
thf(func_def_69,type,
sK9: nat > nat ).
thf(func_def_70,type,
sK10: ( nat > $o ) > nat ).
thf(func_def_71,type,
sK11: ( nat > $o ) > nat ).
thf(func_def_72,type,
sK12: nat > nat ).
thf(func_def_73,type,
sK13: message_p_v > nat ).
thf(func_def_74,type,
sK14: nat > list_c1059388851t_unit ).
thf(func_def_75,type,
sK15: nat > list_message_p_v ).
thf(func_def_76,type,
sK16: list_c1059388851t_unit > list_c1059388851t_unit > nat ).
thf(func_def_77,type,
sK17: list_message_p_v > list_message_p_v > nat ).
thf(func_def_78,type,
sK18: ( message_p_v > $o ) > ( message_p_v > $o ) > message_p_v ).
thf(func_def_79,type,
sK19: ( nat > $o ) > nat ).
thf(func_def_80,type,
sK20: ( nat > $o ) > nat ).
thf(func_def_81,type,
sK21: ( nat > $o ) > nat ).
thf(func_def_82,type,
sK22: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_83,type,
sK23: ( list_message_p_v > $o ) > list_message_p_v ).
thf(func_def_84,type,
sK24: ( nat > $o ) > nat ).
thf(func_def_85,type,
sK25: ( nat > $o ) > nat ).
thf(func_def_86,type,
sK26: ( nat > $o ) > nat ).
thf(func_def_87,type,
sK27: nat > ( nat > $o ) > nat ).
thf(func_def_88,type,
sK28: nat > ( nat > $o ) > nat ).
thf(func_def_89,type,
sK29: ( nat > $o ) > nat ).
thf(func_def_90,type,
sK30: ( nat > $o ) > nat ).
thf(func_def_91,type,
sK31: ( nat > $o ) > nat > nat ).
thf(func_def_92,type,
sK32: nat > nat > nat ).
thf(func_def_93,type,
sK33: nat > nat ).
thf(func_def_94,type,
sK34: nat > nat > nat ).
thf(func_def_95,type,
sK35: ( nat > $o ) > ( nat > $o ) > nat > nat ).
thf(func_def_96,type,
sK36: ( nat > nat > $o ) > nat ).
thf(func_def_97,type,
sK37: ( nat > nat > $o ) > nat ).
thf(func_def_98,type,
sK38: ( nat > nat > $o ) > nat ).
thf(func_def_99,type,
sK39: ( nat > nat > $o ) > nat ).
thf(func_def_100,type,
sK40: ( nat > nat ) > nat ).
thf(func_def_101,type,
sK41: ( nat > nat ) > nat ).
thf(func_def_102,type,
sK42: ( nat > nat ) > nat ).
thf(func_def_103,type,
sK43: ( nat > nat ) > nat ).
thf(func_def_104,type,
sK44: ( nat > nat ) > nat ).
thf(func_def_105,type,
sK45: ( nat > nat ) > nat ).
thf(func_def_106,type,
sK46: ( nat > $o ) > nat ).
thf(func_def_107,type,
sK47: nat > ( nat > $o ) > nat ).
thf(func_def_108,type,
sK48: ( nat > $o ) > nat ).
thf(func_def_109,type,
sK49: ( nat > nat > $o ) > nat ).
thf(func_def_110,type,
sK50: ( nat > nat > $o ) > nat ).
thf(func_def_111,type,
sK51: ( nat > nat > $o ) > nat ).
thf(func_def_112,type,
sK52: ( nat > nat > $o ) > nat ).
thf(func_def_113,type,
sK53: ( nat > nat > $o ) > nat ).
thf(func_def_114,type,
sK54: ( nat > $o ) > nat > nat ).
thf(func_def_115,type,
sK55: ( nat > $o ) > nat > nat > nat ).
thf(func_def_116,type,
sK56: ( nat > $o ) > nat > nat > nat ).
thf(func_def_117,type,
sK57: nat > ( nat > $o ) > nat ).
thf(func_def_118,type,
sK58: ( nat > $o ) > nat > nat ).
thf(func_def_119,type,
sK59: ( nat > nat > $o ) > nat ).
thf(func_def_120,type,
sK60: ( nat > nat > $o ) > nat ).
thf(func_def_121,type,
sK61: ( nat > nat > $o ) > nat ).
thf(func_def_122,type,
sK62: ( nat > nat > $o ) > nat ).
thf(func_def_123,type,
sK63: message_p_v > nat > nat > nat ).
thf(func_def_124,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 ) > config256849571t_unit ).
thf(func_def_125,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 ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_126,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_message_p_v ).
thf(func_def_127,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 ) > nat ).
thf(func_def_128,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 ) > config256849571t_unit ).
thf(func_def_129,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 > ( 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_130,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 ) > ( 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_131,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 ) > ( 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_132,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_133,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_134,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_135,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 ).
thf(func_def_136,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 ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_137,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 ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_138,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 ) > config256849571t_unit ).
thf(func_def_139,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 ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_140,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_message_p_v ).
thf(func_def_141,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 ) > nat ).
thf(func_def_142,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 ) > config256849571t_unit ).
thf(func_def_143,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 > ( 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_144,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 ) > ( 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_145,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 ) > ( 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_146,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_147,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_148,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_149,type,
sK89: ( 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_150,type,
sK90: ( 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_151,type,
sK91: ( 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_152,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_153,type,
sK92: nat > nat > nat ).
thf(func_def_154,type,
sK93: nat > nat > nat ).
thf(func_def_155,type,
sK94: ( nat > $o ) > nat > nat ).
thf(func_def_156,type,
sK95: ( nat > $o ) > nat > nat ).
thf(func_def_157,type,
sK96: ( nat > $o ) > nat > nat ).
thf(func_def_158,type,
sK97: ( nat > $o ) > nat > nat ).
thf(func_def_159,type,
sK98: ( nat > $o ) > nat > nat ).
thf(func_def_160,type,
sK99: ( nat > $o ) > nat > nat ).
thf(func_def_161,type,
sK100: ( nat > $o ) > nat > nat ).
thf(func_def_162,type,
sK101: ( nat > $o ) > nat > nat ).
thf(func_def_163,type,
sK102: ( nat > message_p_v > $o ) > nat > nat ).
thf(func_def_164,type,
sK103: ( nat > message_p_v > $o ) > nat > list_message_p_v ).
thf(func_def_165,type,
sK104: ( nat > config256849571t_unit > $o ) > nat > nat ).
thf(func_def_166,type,
sK105: ( nat > config256849571t_unit > $o ) > nat > list_c1059388851t_unit ).
thf(func_def_167,type,
sK106: nat > nat ).
thf(f43040,plain,
$false,
inference(subsumption_resolution,[],[f42952,f1101]) ).
thf(f1101,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),n1) != $true,
inference(cnf_transformation,[],[f680]) ).
thf(f680,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),n1) != $true,
inference(flattening,[],[f299]) ).
thf(f299,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),n1) != $true,
inference(fool_elimination,[],[f298]) ).
thf(f298,plain,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),n1),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_AssumpGreaterOccurrence_I1_J) ).
thf(f42952,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),n1) = $true,
inference(superposition,[],[f1394,f42849]) ).
thf(f42849,plain,
n1 = vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index)),
inference(unit_resulting_resolution,[],[f1068,f42680,f1284]) ).
thf(f1284,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f835]) ).
thf(f835,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f834]) ).
thf(f834,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f528]) ).
thf(f528,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( X0 != X1 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(fool_elimination,[],[f527]) ).
thf(f527,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ( X0 != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(rectify,[],[f166]) ).
thf(f166,axiom,
! [X9: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X5)
=> ( ( X5 != X9 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__neq__implies__less) ).
thf(f42680,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(unit_resulting_resolution,[],[f33272,f7666,f1357]) ).
thf(f1357,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f908]) ).
thf(f908,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f907]) ).
thf(f907,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f628]) ).
thf(f628,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f627]) ).
thf(f627,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X16: nat,X17: nat,X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X16),X17)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X17),X21)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X16),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_le__trans) ).
thf(f7666,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,nMsg),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(unit_resulting_resolution,[],[f1394,f1237]) ).
thf(f1237,plain,
! [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_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f796]) ).
thf(f796,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
inference(ennf_transformation,[],[f474]) ).
thf(f474,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f473]) ).
thf(f473,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f167]) ).
thf(f167,axiom,
! [X9: nat,X5: nat] :
( ( ( X5 = X9 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X5) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_less__or__eq__imp__le) ).
thf(f33272,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,n1),nMsg),
inference(subsumption_resolution,[],[f33267,f29500]) ).
thf(f29500,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( X0 != X2 ) ),
inference(forward_demodulation,[],[f29497,f2422]) ).
thf(f2422,plain,
! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0 ),
inference(leibniz_equality_elimination,[],[f1155]) ).
thf(f1155,plain,
! [X3: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,X3) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ),
inference(cnf_transformation,[],[f954]) ).
thf(f954,plain,
! [X0: nat > $o] :
( ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,sK11,X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X2) ) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) )
| ! [X3: nat] : ( $true != vAPP(nat,$o,X0,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f952,f953]) ).
thf(f953,plain,
! [X0: nat > $o] :
( ? [X1: nat] :
( ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,X0,X2) ) )
& ( $true = vAPP(nat,$o,X0,X1) ) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,sK11,X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X2) ) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK11,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f952,plain,
! [X0: nat > $o] :
( ? [X1: nat] :
( ! [X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,X0,X2) ) )
& ( $true = vAPP(nat,$o,X0,X1) ) )
| ! [X3: nat] : ( $true != vAPP(nat,$o,X0,X3) ) ),
inference(rectify,[],[f763]) ).
thf(f763,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,X0,X3) ) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ! [X1: nat] : ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f352]) ).
thf(f352,plain,
! [X0: nat > $o] :
( ? [X1: nat] : ( $true = vAPP(nat,$o,X0,X1) )
=> ? [X2: nat] :
( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) )
& ( $true = vAPP(nat,$o,X0,X2) ) ) ),
inference(fool_elimination,[],[f351]) ).
thf(f351,plain,
! [X0: nat > $o] :
( ? [X1: nat] : vAPP(nat,$o,X0,X1)
=> ? [X2: nat] :
( ! [X3: nat] :
( vAPP(nat,$o,X0,X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
& vAPP(nat,$o,X0,X2) ) ),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X0: nat > $o] :
( ? [X82: nat] : vAPP(nat,$o,X0,X82)
=> ? [X83: nat] :
( ! [X53: nat] :
( vAPP(nat,$o,X0,X53)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X83),X53) )
& vAPP(nat,$o,X0,X83) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_MinPredicate) ).
thf(f29497,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))),X1) )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f29496]) ).
thf(f29496,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f29358]) ).
thf(f29358,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,sK11,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
inference(primitive_instantiation,[],[f1156]) ).
thf(f1156,plain,
! [X2: nat,X3: nat,X0: nat > $o] :
( ( $true != vAPP(nat,$o,X0,X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,sK11,X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X3) ) ),
inference(cnf_transformation,[],[f954]) ).
thf(f33267,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,n1),nMsg) )
| ( nMsg = n1 ) ),
inference(trivial_inequality_removal,[],[f33254]) ).
thf(f33254,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,n1),nMsg) )
| ( nMsg = n1 ) ),
inference(superposition,[],[f1237,f33029]) ).
thf(f33029,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),nMsg) )
| ( nMsg = n1 ) ),
inference(trivial_inequality_removal,[],[f33006]) ).
thf(f33006,plain,
( ( $true != $true )
| ( nMsg = n1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),nMsg) ) ),
inference(superposition,[],[f1240,f32517]) ).
thf(f32517,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(nat,nat,suc,nMsg)),
inference(unit_resulting_resolution,[],[f25759,f31257,f1284]) ).
thf(f31257,plain,
n1 != vAPP(nat,nat,suc,nMsg),
inference(unit_resulting_resolution,[],[f1793,f23756,f29500]) ).
thf(f23756,plain,
$true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,nMsg)),n1),
inference(unit_resulting_resolution,[],[f1101,f1305]) ).
thf(f1305,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f860]) ).
thf(f860,plain,
! [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_eq_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
inference(ennf_transformation,[],[f568]) ).
thf(f568,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(fool_elimination,[],[f567]) ).
thf(f567,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X0)),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
inference(rectify,[],[f176]) ).
thf(f176,axiom,
! [X9: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,suc,X9)),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Suc__le__lessD) ).
thf(f1793,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK8,vAPP(nat,nat,suc,X0))) ),
inference(unit_resulting_resolution,[],[f1103,f1145]) ).
thf(f1145,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK8,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f946]) ).
thf(f946,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK8,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f756,f945]) ).
thf(f945,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK8,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f756,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f701]) ).
thf(f701,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(rectify,[],[f100]) ).
thf(f100,axiom,
! [X8: nat] :
( ( zero_zero_nat != X8 )
=> ~ ! [X56: nat] : ( vAPP(nat,nat,suc,X56) != X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_old_Onat_Oexhaust) ).
thf(f1103,plain,
! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ),
inference(cnf_transformation,[],[f682]) ).
thf(f682,plain,
! [X0: nat] : ( zero_zero_nat != vAPP(nat,nat,suc,X0) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X9: nat] : ( vAPP(nat,nat,suc,X9) != zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Zero__not__Suc) ).
thf(f25759,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,n1),vAPP(nat,nat,suc,nMsg)),
inference(unit_resulting_resolution,[],[f23756,f1223]) ).
thf(f1223,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f464]) ).
thf(f464,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f463]) ).
thf(f463,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X9: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X9)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_nat__le__linear) ).
thf(f1240,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f799]) ).
thf(f799,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(flattening,[],[f798]) ).
thf(f798,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f737]) ).
thf(f737,plain,
! [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,X0),vAPP(nat,nat,suc,X1)) )
=> ( X0 = X1 ) ) ),
inference(flattening,[],[f478]) ).
thf(f478,plain,
! [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,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1)) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f477]) ).
thf(f477,plain,
! [X0: nat,X1: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,suc,X1))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X5: nat,X9: nat] :
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),vAPP(nat,nat,suc,X9))
=> ( X5 = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__antisym) ).
thf(f1068,plain,
vAPP(nat,$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))) != $true,
inference(cnf_transformation,[],[f679]) ).
thf(f679,plain,
vAPP(nat,$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))) != $true,
inference(flattening,[],[f267]) ).
thf(f267,plain,
vAPP(nat,$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))) != $true,
inference(fool_elimination,[],[f266]) ).
thf(f266,plain,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(rectify,[],[f263]) ).
thf(f263,negated_conjecture,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(negated_conjecture,[],[f262]) ).
thf(f262,conjecture,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,n1),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1394,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))) = $true,
inference(cnf_transformation,[],[f660]) ).
thf(f660,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))) = $true,
inference(fool_elimination,[],[f659]) ).
thf(f659,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,nMsg),vAPP(list_c1059388851t_unit,nat,size_s1406904903t_unit,vAPP(nat,list_c1059388851t_unit,fe,index))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP054^1 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 16:02:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (30037)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (30039)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (30042)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)
% 0.15/0.39 % (30043)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)
% 0.15/0.39 % (30041)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (30044)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)
% 0.15/0.40 % (30040)WARNING: value z3 for option sas not known
% 0.15/0.40 % (30040)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)
% 0.15/0.41 % (30038)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.42 % (30044)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44 % Exception at run slice level
% 0.21/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44 % (30046)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)
% 0.21/0.44 % (30045)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.46 % (30047)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)
% 0.21/0.47 % (30046)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.47 % (30045)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.47 % Exception at run slice level
% 0.21/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.49 % (30049)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)
% 7.92/1.51 % (30046)First to succeed.
% 7.92/1.51 % (30046)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30037"
% 7.92/1.52 % (30046)Refutation found. Thanks to Tanya!
% 7.92/1.52 % SZS status Theorem for theBenchmark
% 7.92/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 7.92/1.52 % (30046)------------------------------
% 7.92/1.52 % (30046)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.92/1.52 % (30046)Termination reason: Refutation
% 7.92/1.52
% 7.92/1.52 % (30046)Memory used [KB]: 8848
% 7.92/1.52 % (30046)Time elapsed: 1.073 s
% 7.92/1.52 % (30046)Instructions burned: 4223 (million)
% 7.92/1.52 % (30037)Success in time 1.146 s
%------------------------------------------------------------------------------