TSTP Solution File: DAT133^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT133^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 19:51:35 EDT 2024
% Result : Theorem 48.50s 7.32s
% Output : Refutation 48.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 146
% Syntax : Number of formulae : 180 ( 31 unt; 138 typ; 0 def)
% Number of atoms : 878 ( 44 equ; 0 cnn)
% Maximal formula atoms : 3 ( 20 avg)
% Number of connectives : 42 ( 30 ~; 8 |; 0 &; 0 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 332 ( 331 >; 1 *; 0 +; 0 <<)
% Number of symbols : 144 ( 141 usr; 7 con; 0-6 aty)
% Number of variables : 185 ( 24 ^ 35 !; 2 ?; 185 :)
% ( 124 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
itself: $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
coindu1593790203_llist: $tType > $tType ).
thf(type_def_9,type,
extended_enat: $tType ).
thf(type_def_10,type,
set: $tType > $tType ).
thf(type_def_11,type,
a: $tType ).
thf(func_def_0,type,
coindu1593790203_llist: $tType > $tType ).
thf(func_def_1,type,
extended_enat: $tType ).
thf(func_def_2,type,
set: $tType > $tType ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
itself: $tType > $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
type:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_7,type,
one:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_8,type,
neg_numeral:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_9,type,
group_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_10,type,
lattice:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_11,type,
finite_finite:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_12,type,
semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_13,type,
linordered_idom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_14,type,
ab_semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_15,type,
semilattice_inf:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_16,type,
linordered_semidom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_17,type,
cancel_semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_18,type,
ordere779506340up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_19,type,
ordere236663937imp_le:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_20,type,
ordere223160158up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_21,type,
strict2144017051up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_22,type,
coindu493225792length:
!>[X0: $tType] : ( nat > coindu1593790203_llist(X0) > extended_enat ) ).
thf(func_def_23,type,
coindu191418589_ldrop:
!>[X0: $tType] : ( extended_enat > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_24,type,
coindu438612276pWhile:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_25,type,
coindu531130065ldropn:
!>[X0: $tType] : ( nat > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_26,type,
coindu1889960678filter:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_27,type,
coindu1213758845finite:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > $o ) ).
thf(func_def_28,type,
coindu2000965700_llast:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_29,type,
coindu1018505716length:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > extended_enat ) ).
thf(func_def_30,type,
coindu1046438764le_lhd:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_31,type,
coindu335574135_lnull:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > $o ) ).
thf(func_def_32,type,
coindu1112613586e_lset:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > set(X0) ) ).
thf(func_def_33,type,
coindu1047225960le_ltl:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_34,type,
coindu749330388e_lnth:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > nat > X0 ) ).
thf(func_def_35,type,
coindu721411036eWhile:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_36,type,
coindu1491768222unfold:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > X0 ) > X0 > extended_enat ) ).
thf(func_def_37,type,
extended_enat2: nat > extended_enat ).
thf(func_def_38,type,
extended_rec_enat:
!>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).
thf(func_def_39,type,
extended_the_enat: extended_enat > nat ).
thf(func_def_40,type,
finite_finite2:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_41,type,
one_one:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
plus_plus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_43,type,
inf_inf:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_44,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
type2:
!>[X0: $tType] : itself(X0) ).
thf(func_def_47,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_48,type,
image:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > set(X0) > set(X1) ) ).
thf(func_def_49,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_50,type,
p: a > $o ).
thf(func_def_51,type,
n: nat ).
thf(func_def_52,type,
xs: coindu1593790203_llist(a) ).
thf(func_def_53,type,
xsa: coindu1593790203_llist(a) ).
thf(func_def_57,type,
vNOT: $o > $o ).
thf(func_def_58,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_59,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_60,type,
vIMP: $o > $o > $o ).
thf(func_def_61,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_62,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_63,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_64,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_65,type,
vAND: $o > $o > $o ).
thf(func_def_66,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_67,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_68,type,
vOR: $o > $o > $o ).
thf(func_def_69,type,
sP0:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > $o ) > $o ) ).
thf(func_def_70,type,
sP1:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o ) ).
thf(func_def_71,type,
sP2:
!>[X0: $tType] : ( ( X0 > coindu1593790203_llist(X0) > $o ) > $o ) ).
thf(func_def_72,type,
sK3: nat ).
thf(func_def_73,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_74,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_75,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_76,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_77,type,
sK8:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_78,type,
sK9:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_79,type,
sK10:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_80,type,
sK11:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_81,type,
sK12: ( nat > $o ) > nat ).
thf(func_def_82,type,
sK13: ( extended_enat > $o ) > extended_enat ).
thf(func_def_83,type,
sK14: ( nat > $o ) > nat ).
thf(func_def_84,type,
sK15: set(nat) > nat > nat ).
thf(func_def_85,type,
sK16: nat > set(nat) > nat ).
thf(func_def_86,type,
sK17: extended_enat > extended_enat > nat ).
thf(func_def_87,type,
sK18:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > nat ) ).
thf(func_def_88,type,
sK19: nat > extended_enat > nat ).
thf(func_def_89,type,
sK20: extended_enat > nat ).
thf(func_def_90,type,
sK21:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_91,type,
sK22:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_92,type,
sK23:
!>[X0: $tType] : ( nat > ( X0 > extended_enat ) > X0 ) ).
thf(func_def_93,type,
sK24:
!>[X0: $tType] : ( ( X0 > extended_enat ) > X0 ) ).
thf(func_def_94,type,
sK25:
!>[X0: $tType] : ( ( set(X0) > $o ) > set(X0) ) ).
thf(func_def_95,type,
sK26:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_96,type,
sK27:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_97,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > set(X1) > X1 ) ).
thf(func_def_98,type,
sK29:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_99,type,
sK30:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_100,type,
sK31:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_101,type,
sK32:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_102,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X1) > X1 > X0 ) ).
thf(func_def_103,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X1) > X1 ) ).
thf(func_def_104,type,
sK35:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_105,type,
sK36:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_106,type,
sK37:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_107,type,
sK38:
!>[X0: $tType] : ( ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_108,type,
sK39:
!>[X0: $tType] : ( ( X0 > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_109,type,
sK40:
!>[X0: $tType] : ( ( X0 > coindu1593790203_llist(X0) > $o ) > X0 ) ).
thf(func_def_110,type,
sK41:
!>[X0: $tType] : ( ( X0 > coindu1593790203_llist(X0) > $o ) > coindu1593790203_llist(X0) ) ).
thf(func_def_111,type,
sK42:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_112,type,
sK43:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_113,type,
sK44:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_114,type,
sK45:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X0) > set(X1) > X0 ) ).
thf(func_def_115,type,
sK46:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X0) > set(X1) > X1 ) ).
thf(func_def_116,type,
sK47:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > set(X1) > ( X1 > X0 ) > X0 ) ).
thf(func_def_117,type,
sK48:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > set(X1) > ( X1 > X0 ) > X1 ) ).
thf(func_def_118,type,
sK49:
!>[X0: $tType,X1: $tType] : ( set(X1) > ( X1 > X0 ) > X0 > X1 ) ).
thf(func_def_119,type,
sK50:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > set(X1) > X1 ) ).
thf(func_def_120,type,
sK51:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat > X0 > X0 ) ).
thf(func_def_121,type,
sK52:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).
thf(func_def_122,type,
sK53:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).
thf(func_def_123,type,
sK54:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > X0 ) ).
thf(func_def_124,type,
sK55: a ).
thf(func_def_126,type,
sK57:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > set(X1) > X0 > X1 ) ).
thf(func_def_127,type,
sK58:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > $o ) > ( X1 > $o ) > X1 ) ).
thf(func_def_128,type,
sK59:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_129,type,
sK60:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_130,type,
sK61:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_131,type,
sK62:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_132,type,
sK63:
!>[X0: $tType] : ( ( X0 > $o ) > coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_133,type,
sK64:
!>[X0: $tType] : ( X0 > coindu1593790203_llist(X0) > nat ) ).
thf(func_def_134,type,
sK65: set(nat) > nat ).
thf(f96220,plain,
$false,
inference(trivial_inequality_removal,[],[f96219]) ).
thf(f96219,plain,
$true = $false,
inference(backward_demodulation,[],[f1517,f96216]) ).
thf(f96216,plain,
$false = vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa))))))),
inference(trivial_inequality_removal,[],[f96179]) ).
thf(f96179,plain,
( ( $true = $false )
| ( $false = vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa))))))) ) ),
inference(superposition,[],[f9957,f5703]) ).
thf(f5703,plain,
! [X0: $tType,X2: $tType,X3: X0 > X2,X1: set(X0)] :
( ( $true = vAPP(set(X2),$o,finite_finite2(X2),vAPP(set(X0),set(X2),vAPP(sTfun(X0,X2),sTfun(set(X0),set(X2)),image(X0,X2),X3),X1)) )
| ( $false = vAPP(set(X0),$o,finite_finite2(X0),X1) ) ),
inference(trivial_inequality_removal,[],[f5702]) ).
thf(f5702,plain,
! [X0: $tType,X2: $tType,X3: X0 > X2,X1: set(X0)] :
( ( $true != $true )
| ( $true = vAPP(set(X2),$o,finite_finite2(X2),vAPP(set(X0),set(X2),vAPP(sTfun(X0,X2),sTfun(set(X0),set(X2)),image(X0,X2),X3),X1)) )
| ( $false = vAPP(set(X0),$o,finite_finite2(X0),X1) ) ),
inference(superposition,[],[f1425,f284]) ).
thf(f284,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1425,plain,
! [X1: $tType,X0: $tType,X2: set(X1),X3: X1 > X0] :
( ( $true != vAPP(set(X1),$o,finite_finite2(X1),X2) )
| ( $true = vAPP(set(X0),$o,finite_finite2(X0),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X3),X2)) ) ),
inference(cnf_transformation,[],[f1025]) ).
thf(f1025,plain,
! [X0: $tType,X1: $tType,X2: set(X1),X3: X1 > X0] :
( ( $true = vAPP(set(X0),$o,finite_finite2(X0),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X3),X2)) )
| ( $true != vAPP(set(X1),$o,finite_finite2(X1),X2) ) ),
inference(ennf_transformation,[],[f668]) ).
thf(f668,plain,
! [X0: $tType,X1: $tType,X2: set(X1),X3: X1 > X0] :
( ( $true = vAPP(set(X1),$o,finite_finite2(X1),X2) )
=> ( $true = vAPP(set(X0),$o,finite_finite2(X0),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X3),X2)) ) ),
inference(fool_elimination,[],[f667]) ).
thf(f667,plain,
! [X0: $tType,X1: $tType,X2: set(X1),X3: X1 > X0] :
( vAPP(set(X1),$o,finite_finite2(X1),X2)
=> vAPP(set(X0),$o,finite_finite2(X0),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X3),X2)) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X2: $tType,X0: $tType,X5: set(X0),X7: X0 > X2] :
( vAPP(set(X0),$o,finite_finite2(X0),X5)
=> vAPP(set(X2),$o,finite_finite2(X2),vAPP(set(X0),set(X2),vAPP(sTfun(X0,X2),sTfun(set(X0),set(X2)),image(X0,X2),X7),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__imageI) ).
thf(f9957,plain,
$false = vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),sK3),one_one(nat)))),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))))),
inference(trivial_inequality_removal,[],[f9956]) ).
thf(f9956,plain,
( ( $true != $true )
| ( $false = vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),sK3),one_one(nat)))),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))))) ) ),
inference(superposition,[],[f1820,f284]) ).
thf(f1820,plain,
$true != vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),sK3),one_one(nat)))),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))))),
inference(backward_demodulation,[],[f1177,f1819]) ).
thf(f1819,plain,
n = sK3,
inference(forward_demodulation,[],[f1818,f1185]) ).
thf(f1185,plain,
! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ),
inference(cnf_transformation,[],[f801]) ).
thf(f801,plain,
! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X27: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X27)) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_the__enat_Osimps) ).
thf(f1818,plain,
n = vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,sK3)),
inference(superposition,[],[f1185,f1762]) ).
thf(f1762,plain,
vAPP(nat,extended_enat,extended_enat2,n) = vAPP(nat,extended_enat,extended_enat2,sK3),
inference(backward_demodulation,[],[f1180,f1181]) ).
thf(f1181,plain,
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)) = vAPP(nat,extended_enat,extended_enat2,sK3),
inference(cnf_transformation,[],[f1085]) ).
thf(f1085,plain,
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)) = vAPP(nat,extended_enat,extended_enat2,sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f863,f1084]) ).
thf(f1084,plain,
( ? [X0: nat] : ( vAPP(nat,extended_enat,extended_enat2,X0) = vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)) )
=> ( vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)) = vAPP(nat,extended_enat,extended_enat2,sK3) ) ),
introduced(choice_axiom,[]) ).
thf(f863,plain,
? [X0: nat] : ( vAPP(nat,extended_enat,extended_enat2,X0) = vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)) ),
inference(ennf_transformation,[],[f292]) ).
thf(f292,plain,
~ ! [X0: nat] : ( vAPP(nat,extended_enat,extended_enat2,X0) != vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)) ),
inference(fool_elimination,[],[f291]) ).
thf(f291,plain,
~ ! [X0: nat] :
( vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),
^ [X1: a] : ~ vAPP(a,$o,p,X1)),
xsa)) != vAPP(nat,extended_enat,extended_enat2,X0) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
~ ! [X11: nat] :
( vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa)) != vAPP(nat,extended_enat,extended_enat2,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_A_IltakeWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(f1180,plain,
vAPP(nat,extended_enat,extended_enat2,n) = vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)),
inference(cnf_transformation,[],[f290]) ).
thf(f290,plain,
vAPP(nat,extended_enat,extended_enat2,n) = vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)),
inference(fool_elimination,[],[f289]) ).
thf(f289,plain,
( vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),
^ [X0: a] : ~ vAPP(a,$o,p,X0)),
xsa)) = vAPP(nat,extended_enat,extended_enat2,n) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
( vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu721411036eWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa)) = vAPP(nat,extended_enat,extended_enat2,n) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_n) ).
thf(f1177,plain,
$true != vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),n),one_one(nat)))),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))))),
inference(cnf_transformation,[],[f797]) ).
thf(f797,plain,
$true != vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),n),one_one(nat)))),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))))),
inference(flattening,[],[f286]) ).
thf(f286,plain,
$true != vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),n),one_one(nat)))),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))))),
inference(fool_elimination,[],[f285]) ).
thf(f285,plain,
~ vAPP(set(nat),$o,finite_finite2(nat),
vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),n),one_one(nat)))),
vAPP(set(nat),set(nat),
vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X0: nat] :
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,X0)),
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X1: a] : ~ vAPP(a,$o,p,X1)),
xsa)))))),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X2: nat] :
vAPP(a,$o,p,
vAPP(nat,a,
vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X3: a] : ~ vAPP(a,$o,p,X3)),
xsa))),
X2)))))),
inference(rectify,[],[f282]) ).
thf(f282,negated_conjecture,
~ vAPP(set(nat),$o,finite_finite2(nat),
vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),n),one_one(nat)))),
vAPP(set(nat),set(nat),
vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X3: nat] :
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,X3)),
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa)))))),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X3: nat] :
vAPP(a,$o,p,
vAPP(nat,a,
vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa))),
X3)))))),
inference(negated_conjecture,[],[f281]) ).
thf(f281,conjecture,
vAPP(set(nat),$o,finite_finite2(nat),
vAPP(set(nat),set(nat),vAPP(sTfun(nat,nat),sTfun(set(nat),set(nat)),image(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),n),one_one(nat)))),
vAPP(set(nat),set(nat),
vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X3: nat] :
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,X3)),
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa)))))),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X3: nat] :
vAPP(a,$o,p,
vAPP(nat,a,
vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa))),
X3)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1517,plain,
$true = vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa))))))),
inference(cnf_transformation,[],[f796]) ).
thf(f796,plain,
$true = vAPP(set(nat),$o,finite_finite2(nat),vAPP(set(nat),set(nat),vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(extended_enat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(extended_enat,$o)),sTfun(extended_enat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o)),vAPP(sTfun(extended_enat,sTfun(extended_enat,$o)),sTfun(sTfun(nat,extended_enat),sTfun(nat,sTfun(extended_enat,$o))),bCOMB,ord_less(extended_enat)),extended_enat2)),vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa)))))),vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(sTfun(nat,a),sTfun(nat,$o),vAPP(sTfun(a,$o),sTfun(sTfun(nat,a),sTfun(nat,$o)),bCOMB,p),vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),vAPP(sTfun(a,$o),sTfun(a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(a,$o),sTfun(a,$o)),bCOMB,vNOT),p)),xsa))))))),
inference(fool_elimination,[],[f795]) ).
thf(f795,plain,
vAPP(set(nat),$o,finite_finite2(nat),
vAPP(set(nat),set(nat),
vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X0: nat] :
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,X0)),
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X1: a] : ~ vAPP(a,$o,p,X1)),
xsa)))))),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X2: nat] :
vAPP(a,$o,p,
vAPP(nat,a,
vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X3: a] : ~ vAPP(a,$o,p,X3)),
xsa))),
X2))))),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(set(nat),$o,finite_finite2(nat),
vAPP(set(nat),set(nat),
vAPP(set(nat),sTfun(set(nat),set(nat)),inf_inf(set(nat)),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X3: nat] :
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,X3)),
vAPP(coindu1593790203_llist(a),extended_enat,coindu1018505716length(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa)))))),
vAPP(sTfun(nat,$o),set(nat),collect(nat),
^ [X3: nat] :
vAPP(a,$o,p,
vAPP(nat,a,
vAPP(coindu1593790203_llist(a),sTfun(nat,a),coindu749330388e_lnth(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),
vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),
vAPP(sTfun(a,$o),sTfun(coindu1593790203_llist(a),coindu1593790203_llist(a)),coindu438612276pWhile(a),
^ [X4: a] : ~ vAPP(a,$o,p,X4)),
xsa))),
X3))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_I_123n_O_Aenat_An_A_060_Allength_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_125_A_092_060inter_062_A_123n_O_AP_A_Ilnth_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_An_J_125_J_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT133^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 23:17:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (23485)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (23486)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.39 % (23489)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39 % (23490)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)
% 0.21/0.39 % (23492)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)
% 0.21/0.39 % (23491)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)
% 0.21/0.39 % (23487)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (23488)WARNING: value z3 for option sas not known
% 0.21/0.40 % (23488)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)
% 0.21/0.42 % (23492)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
% 0.21/0.44 % 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 % (23493)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 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
% 0.21/0.46 % (23494)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)
% 0.21/0.46 % (23495)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)
% 0.21/0.48 % (23493)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.50 % Exception at run slice level
% 0.21/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.50 % (23494)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.51 % (23496)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)
% 47.65/7.19 % (23495)First to succeed.
% 48.29/7.28 % (23495)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23485"
% 48.50/7.32 % (23495)Refutation found. Thanks to Tanya!
% 48.50/7.32 % SZS status Theorem for theBenchmark
% 48.50/7.32 % SZS output start Proof for theBenchmark
% See solution above
% 48.50/7.32 % (23495)------------------------------
% 48.50/7.32 % (23495)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 48.50/7.32 % (23495)Termination reason: Refutation
% 48.50/7.32
% 48.50/7.32 % (23495)Memory used [KB]: 108317
% 48.50/7.32 % (23495)Time elapsed: 6.816 s
% 48.50/7.32 % (23495)Instructions burned: 24496 (million)
% 48.50/7.32 % (23485)Success in time 6.937 s
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