TSTP Solution File: DAT183^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT183^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 : Sun May 5 05:06:10 EDT 2024
% Result : Theorem 1.90s 0.67s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 177
% Syntax : Number of formulae : 216 ( 20 unt; 169 typ; 0 def)
% Number of atoms : 319 ( 64 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 78 ( 43 ~; 20 |; 0 &; 0 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 358 ( 357 >; 1 *; 0 +; 0 <<)
% Number of symbols : 171 ( 168 usr; 3 con; 0-6 aty)
% Number of variables : 248 ( 0 ^ 73 !; 4 ?; 248 :)
% ( 171 !>; 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,
coinductive_llist: $tType > $tType ).
thf(type_def_8,type,
set: $tType > $tType ).
thf(type_def_9,type,
nat: $tType ).
thf(type_def_10,type,
a: $tType ).
thf(func_def_0,type,
coinductive_llist: $tType > $tType ).
thf(func_def_1,type,
set: $tType > $tType ).
thf(func_def_2,type,
nat: $tType ).
thf(func_def_3,type,
itself: $tType > $tType ).
thf(func_def_4,type,
a: $tType ).
thf(func_def_5,type,
bounded_lattice:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_6,type,
type:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_7,type,
ord:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_8,type,
top:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_9,type,
order:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_10,type,
no_bot:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_11,type,
no_top:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_12,type,
linorder:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_13,type,
preorder:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_14,type,
order_top:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_15,type,
wellorder:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_16,type,
dense_order:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_17,type,
linordered_idom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_18,type,
linordered_field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_19,type,
bounded_lattice_top:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_20,type,
condit1656338222tinuum:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_21,type,
coindu328551480prefix:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > $o ) ).
thf(func_def_22,type,
coinductive_lappend:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_23,type,
coinductive_lfinite:
!>[X0: $tType] : ( coinductive_llist(X0) > $o ) ).
thf(func_def_24,type,
coinductive_llast:
!>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).
thf(func_def_25,type,
coinductive_LCons:
!>[X0: $tType] : ( X0 > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_26,type,
coinductive_LNil:
!>[X0: $tType] : coinductive_llist(X0) ).
thf(func_def_27,type,
coinductive_lnull:
!>[X0: $tType] : ( coinductive_llist(X0) > $o ) ).
thf(func_def_28,type,
coinductive_lmember:
!>[X0: $tType] : ( X0 > coinductive_llist(X0) > $o ) ).
thf(func_def_29,type,
coindu1478340336prefix:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > $o ) ).
thf(func_def_30,type,
minus_minus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_31,type,
undefined:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
lList2435255213lllsts:
!>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).
thf(func_def_33,type,
lList21511617539llstsp:
!>[X0: $tType] : ( ( X0 > $o ) > coinductive_llist(X0) > $o ) ).
thf(func_def_34,type,
lList2236698231inlsts:
!>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).
thf(func_def_35,type,
lList21916056377ts_rec:
!>[X0: $tType,X1: $tType] : ( X0 > ( X1 > coinductive_llist(X1) > X0 > X0 ) > coinductive_llist(X1) > X0 ) ).
thf(func_def_36,type,
lList2860480441nlstsp:
!>[X0: $tType] : ( ( X0 > $o ) > coinductive_llist(X0) > $o ) ).
thf(func_def_37,type,
lList22096119349pslsts:
!>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).
thf(func_def_38,type,
lList21612149805nflsts:
!>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).
thf(func_def_39,type,
lList2370560421utlast:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_40,type,
lList2508575361_ldrop:
!>[X0: $tType] : ( coinductive_llist(X0) > nat > coinductive_llist(X0) ) ).
thf(func_def_41,type,
lList2170638824_llast:
!>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).
thf(func_def_42,type,
lList21232602520length:
!>[X0: $tType] : ( coinductive_llist(X0) > nat ) ).
thf(func_def_43,type,
lList2281150353e_lrev:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_44,type,
lList22119844313_ltake:
!>[X0: $tType] : ( coinductive_llist(X0) > nat > coinductive_llist(X0) ) ).
thf(func_def_45,type,
lList21148268032oslsts:
!>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).
thf(func_def_46,type,
sup_sup:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_47,type,
suc: nat > nat ).
thf(func_def_48,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
top_top:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
type2:
!>[X0: $tType] : itself(X0) ).
thf(func_def_51,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_52,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_53,type,
r: coinductive_llist(a) ).
thf(func_def_57,type,
vOR: $o > $o > $o ).
thf(func_def_58,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_59,type,
vAND: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_62,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_63,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_64,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_65,type,
vNOT: $o > $o ).
thf(func_def_66,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_67,type,
vIMP: $o > $o > $o ).
thf(func_def_68,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_69,type,
sP0:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > $o ) ).
thf(func_def_70,type,
sP1:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > $o ) ).
thf(func_def_71,type,
sP2:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > $o ) ).
thf(func_def_72,type,
sK3:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_73,type,
sK4:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_74,type,
sK5:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_75,type,
sK6:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_76,type,
sK7:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_77,type,
sK8:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_78,type,
sK9:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_79,type,
sK10:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_80,type,
sK11:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_81,type,
sK12:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_82,type,
sK13:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_83,type,
sK14:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_84,type,
sK15:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_85,type,
sK16:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_86,type,
sK17:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_87,type,
sK18:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_88,type,
sK19:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_89,type,
sK20:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_90,type,
sK21:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_91,type,
sK22:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_92,type,
sK23:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_93,type,
sK24:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_94,type,
sK25:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_95,type,
sK26:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_96,type,
sK27:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_97,type,
sK28:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_98,type,
sK29:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_99,type,
sK30:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_100,type,
sK31:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_101,type,
sK32:
!>[X0: $tType] : X0 ).
thf(func_def_102,type,
sK33:
!>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).
thf(func_def_103,type,
sK34:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_104,type,
sK35:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_105,type,
sK36:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_106,type,
sK37:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_107,type,
sK38:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_108,type,
sK39:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_109,type,
sK40:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_110,type,
sK41:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_111,type,
sK42:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_112,type,
sK43:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_113,type,
sK44:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_114,type,
sK45:
!>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).
thf(func_def_115,type,
sK46:
!>[X0: $tType,X1: $tType] : ( X1 > X0 ) ).
thf(func_def_116,type,
sK47:
!>[X0: $tType,X1: $tType] : ( X1 > X0 ) ).
thf(func_def_117,type,
sK48:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_118,type,
sK49:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_119,type,
sK50:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).
thf(func_def_120,type,
sK51:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_121,type,
sK52:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_122,type,
sK53:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).
thf(func_def_123,type,
sK54:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).
thf(func_def_124,type,
sK55:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_125,type,
sK56:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_126,type,
sK57:
!>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > coinductive_llist(X0) ) ).
thf(func_def_127,type,
sK58:
!>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_128,type,
sK59:
!>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > coinductive_llist(X0) ) ).
thf(func_def_129,type,
sK60:
!>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_130,type,
sK61:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).
thf(func_def_131,type,
sK62:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_132,type,
sK63:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_133,type,
sK64:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).
thf(func_def_134,type,
sK65:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).
thf(func_def_135,type,
sK66:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_136,type,
sK67:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_137,type,
sK68:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).
thf(func_def_138,type,
sK69:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).
thf(func_def_139,type,
sK70:
!>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_140,type,
sK71:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_141,type,
sK72:
!>[X0: $tType] : ( ( X0 > $o ) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_142,type,
sK73:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_143,type,
sK74:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > ( X0 > $o ) > coinductive_llist(X0) ) ).
thf(func_def_144,type,
sK75:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_145,type,
sK76:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > X0 ) ).
thf(func_def_146,type,
sK77:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_147,type,
sK78:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).
thf(func_def_148,type,
sK79:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > X0 ) ).
thf(func_def_149,type,
sK80:
!>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_150,type,
sK81:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).
thf(func_def_151,type,
sK82:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > coinductive_llist(X0) ) ).
thf(func_def_152,type,
sK83:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).
thf(func_def_153,type,
sK84:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).
thf(func_def_154,type,
sK85:
!>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > coinductive_llist(X0) ) ).
thf(func_def_155,type,
sK86:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > X0 > coinductive_llist(X0) ) ).
thf(func_def_156,type,
sK87:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_157,type,
sK88:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_158,type,
sK89:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > set(X0) > X0 ) ).
thf(func_def_159,type,
sK90:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > set(X0) > X0 ) ).
thf(func_def_160,type,
sK91:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_161,type,
sK92:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_162,type,
sK93:
!>[X0: $tType] : ( coinductive_llist(X0) > set(X0) > X0 ) ).
thf(func_def_163,type,
sK94:
!>[X0: $tType] : ( coinductive_llist(X0) > set(X0) > X0 ) ).
thf(func_def_164,type,
sK95:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(func_def_165,type,
sK96:
!>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).
thf(f9125,plain,
$false,
inference(trivial_inequality_removal,[],[f9124]) ).
thf(f9124,plain,
$true = $false,
inference(forward_demodulation,[],[f9122,f2357]) ).
thf(f2357,plain,
! [X0: $tType,X1: coinductive_llist(X0)] : ( $false = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),X1),X1) ),
inference(trivial_inequality_removal,[],[f2350]) ).
thf(f2350,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ( $true != $true )
| ( $false = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),X1),X1) ) ),
inference(superposition,[],[f2342,f1308]) ).
thf(f1308,plain,
! [X0: $tType] : ( $true = vAPP(itself(coinductive_llist(X0)),$o,preorder(coinductive_llist(X0)),type2(coinductive_llist(X0))) ),
inference(cnf_transformation,[],[f433]) ).
thf(f433,plain,
! [X0: $tType] : ( $true = vAPP(itself(coinductive_llist(X0)),$o,preorder(coinductive_llist(X0)),type2(coinductive_llist(X0))) ),
inference(fool_elimination,[],[f432]) ).
thf(f432,plain,
! [X0: $tType] : vAPP(itself(coinductive_llist(X0)),$o,preorder(coinductive_llist(X0)),type2(coinductive_llist(X0))),
inference(rectify,[],[f283]) ).
thf(f283,axiom,
! [X66: $tType] : vAPP(itself(coinductive_llist(X66)),$o,preorder(coinductive_llist(X66)),type2(coinductive_llist(X66))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Opreorder_19) ).
thf(f2342,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true )
| ( $false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
inference(trivial_inequality_removal,[],[f2341]) ).
thf(f2341,plain,
! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true )
| ( $false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
inference(superposition,[],[f1245,f289]) ).
thf(f289,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1245,plain,
! [X0: $tType,X1: X0] :
( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) )
| ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f870]) ).
thf(f870,plain,
! [X0: $tType] :
( ! [X1: X0] : ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) )
| ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f784]) ).
thf(f784,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
inference(flattening,[],[f331]) ).
thf(f331,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
inference(fool_elimination,[],[f330]) ).
thf(f330,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,preorder(X0),type2(X0))
=> ! [X1: X0] : ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,preorder(X0),type2(X0))
=> ! [X31: X0] : ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X31),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__irrefl) ).
thf(f9122,plain,
$true = vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),r),
inference(backward_demodulation,[],[f1217,f9120]) ).
thf(f9120,plain,
r = coinductive_LNil(a),
inference(trivial_inequality_removal,[],[f9116]) ).
thf(f9116,plain,
( ( $true != $true )
| ( r = coinductive_LNil(a) ) ),
inference(superposition,[],[f9108,f7870]) ).
thf(f7870,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ( $true = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),X1) )
| ( coinductive_LNil(X0) = X1 ) ),
inference(superposition,[],[f1462,f1327]) ).
thf(f1327,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),vAPP(coinductive_llist(X0),X0,sK33(X0),X1)),vAPP(coinductive_llist(X0),coinductive_llist(X0),sK34(X0),X1)) = X1 )
| ( coinductive_LNil(X0) = X1 ) ),
inference(cnf_transformation,[],[f1146]) ).
thf(f1146,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),vAPP(coinductive_llist(X0),X0,sK33(X0),X1)),vAPP(coinductive_llist(X0),coinductive_llist(X0),sK34(X0),X1)) = X1 )
| ( coinductive_LNil(X0) = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f922,f1145]) ).
thf(f1145,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ? [X2: X0,X3: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3) = X1 )
=> ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),vAPP(coinductive_llist(X0),X0,sK33(X0),X1)),vAPP(coinductive_llist(X0),coinductive_llist(X0),sK34(X0),X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f922,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ? [X2: X0,X3: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3) = X1 )
| ( coinductive_LNil(X0) = X1 ) ),
inference(ennf_transformation,[],[f807]) ).
thf(f807,plain,
! [X0: $tType,X1: coinductive_llist(X0)] :
( ( coinductive_LNil(X0) != X1 )
=> ~ ! [X2: X0,X3: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3) != X1 ) ),
inference(rectify,[],[f13]) ).
thf(f13,axiom,
! [X0: $tType,X15: coinductive_llist(X0)] :
( ( coinductive_LNil(X0) != X15 )
=> ~ ! [X16: X0,X17: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X16),X17) != X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_llistE) ).
thf(f1462,plain,
! [X0: $tType,X2: coinductive_llist(X0),X1: X0] : ( $true = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X1),X2)) ),
inference(cnf_transformation,[],[f625]) ).
thf(f625,plain,
! [X0: $tType,X1: X0,X2: coinductive_llist(X0)] : ( $true = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X1),X2)) ),
inference(fool_elimination,[],[f624]) ).
thf(f624,plain,
! [X0: $tType,X1: X0,X2: coinductive_llist(X0)] : vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X1),X2)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0,X3: coinductive_llist(X0)] : vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LNil__less__LCons) ).
thf(f9108,plain,
$true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r),
inference(trivial_inequality_removal,[],[f9107]) ).
thf(f9107,plain,
( ( $true != $true )
| ( $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r) ) ),
inference(forward_demodulation,[],[f9075,f1308]) ).
thf(f9075,plain,
( ( $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r) )
| ( $true != vAPP(itself(coinductive_llist(a)),$o,preorder(coinductive_llist(a)),type2(coinductive_llist(a))) ) ),
inference(trivial_inequality_removal,[],[f9058]) ).
thf(f9058,plain,
( ( $true != $true )
| ( $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r) )
| ( $true != vAPP(itself(coinductive_llist(a)),$o,preorder(coinductive_llist(a)),type2(coinductive_llist(a))) ) ),
inference(superposition,[],[f1246,f1217]) ).
thf(f1246,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) )
| ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
| ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f871]) ).
thf(f871,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) )
| ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) ) )
| ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f785]) ).
thf(f785,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
=> ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ),
inference(flattening,[],[f333]) ).
thf(f333,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
=> ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ),
inference(fool_elimination,[],[f332]) ).
thf(f332,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,preorder(X0),type2(X0))
=> ! [X1: X0,X2: X0] :
( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)
=> ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,preorder(X0),type2(X0))
=> ! [X31: X0,X15: X0] :
( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X31),X15)
=> ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X15),X31) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_less__not__sym) ).
thf(f1217,plain,
vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)) = $true,
inference(cnf_transformation,[],[f780]) ).
thf(f780,plain,
vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)) = $true,
inference(flattening,[],[f291]) ).
thf(f291,plain,
vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)) != $true,
inference(fool_elimination,[],[f290]) ).
thf(f290,plain,
~ ~ vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)),
inference(rectify,[],[f287]) ).
thf(f287,negated_conjecture,
~ ~ vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)),
inference(negated_conjecture,[],[f286]) ).
thf(f286,conjecture,
~ vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT183^1 : TPTP v8.1.2. Released v7.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 13:06:01 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (26375)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (26380)WARNING: value z3 for option sas not known
% 0.21/0.40 % (26378)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (26379)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 % (26381)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (26380)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)
% 0.21/0.40 % (26382)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)
% 0.21/0.40 % (26383)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)
% 0.21/0.40 % (26384)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)
% 0.21/0.43 % (26384)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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 % 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 % Exception at run slice level
% 0.21/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % (26385)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.45 % (26386)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 % (26387)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 % (26385)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.48 % (26386)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.49 % Exception at run slice level
% 0.21/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.50 % (26388)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)
% 1.90/0.67 % (26383)First to succeed.
% 1.90/0.67 % (26383)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26375"
% 1.90/0.67 % (26383)Refutation found. Thanks to Tanya!
% 1.90/0.67 % SZS status Theorem for theBenchmark
% 1.90/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 1.90/0.67 % (26383)------------------------------
% 1.90/0.67 % (26383)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.90/0.67 % (26383)Termination reason: Refutation
% 1.90/0.67
% 1.90/0.67 % (26383)Memory used [KB]: 3961
% 1.90/0.67 % (26383)Time elapsed: 0.273 s
% 1.90/0.67 % (26383)Instructions burned: 877 (million)
% 1.90/0.67 % (26375)Success in time 0.295 s
%------------------------------------------------------------------------------