TSTP Solution File: ITP071^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP071^2 : 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 : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:50:24 EDT 2024
% Result : Theorem 5.09s 1.08s
% Output : Refutation 5.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 302
% Syntax : Number of formulae : 330 ( 20 unt; 296 typ; 0 def)
% Number of atoms : 262 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 7 avg)
% Number of connectives : 26 ( 12 ~; 8 |; 0 &; 0 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 708 ( 705 >; 3 *; 0 +; 0 <<)
% Number of symbols : 298 ( 295 usr; 4 con; 0-9 aty)
% Number of variables : 648 ( 0 ^ 30 !; 0 ?; 648 :)
% ( 618 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
set: $tType > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
tree: $tType > $tType ).
thf(type_def_9,type,
list: $tType > $tType ).
thf(type_def_10,type,
multiset: $tType > $tType ).
thf(type_def_11,type,
a: $tType ).
thf(func_def_0,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
multiset: $tType > $tType ).
thf(func_def_2,type,
list: $tType > $tType ).
thf(func_def_3,type,
tree: $tType > $tType ).
thf(func_def_4,type,
set: $tType > $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_7,type,
ord:
!>[X0: $tType] : $o ).
thf(func_def_8,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_9,type,
linorder:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
preorder:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
bNF_Ca1785829860lChain:
!>[X0: $tType,X1: $tType] : ( set(product_prod(X0,X0)) > ( X0 > X1 ) > $o ) ).
thf(func_def_12,type,
bNF_csquare:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( set(X0) > ( X1 > X2 ) > ( X3 > X2 ) > ( X0 > X1 ) > ( X0 > X3 ) > $o ) ).
thf(func_def_13,type,
bNF_fstOp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > $o ) > ( X1 > X2 > $o ) > product_prod(X0,X2) > product_prod(X0,X1) ) ).
thf(func_def_14,type,
bNF_pick_middlep:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > $o ) > ( X1 > X2 > $o ) > X0 > X2 > X1 ) ).
thf(func_def_15,type,
bNF_sndOp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > $o ) > ( X1 > X2 > $o ) > product_prod(X0,X2) > product_prod(X1,X2) ) ).
thf(func_def_16,type,
bNF_Greatest_image2:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(X0) > ( X0 > X1 ) > ( X0 > X2 ) > set(product_prod(X1,X2)) ) ).
thf(func_def_17,type,
comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > ( X2 > X0 ) > X2 > X1 ) ).
thf(func_def_18,type,
heapIm818251801eapify:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_19,type,
heapIm721255937_empty:
!>[X0: $tType] : ( tree(X0) > $o ) ).
thf(func_def_20,type,
heapIm1542349758ve_max:
!>[X0: $tType] : ( tree(X0) > product_prod(X0,tree(X0)) ) ).
thf(func_def_21,type,
heapIm1271749598e_left:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_22,type,
heapIm970386777veLeaf:
!>[X0: $tType] : ( tree(X0) > product_prod(X0,tree(X0)) ) ).
thf(func_def_23,type,
heapIm1434396069_right:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_24,type,
heapIm748920189ftDown:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_25,type,
heap:
!>[X0: $tType,X1: $tType] : ( X0 > ( X0 > $o ) > ( list(X1) > X0 ) > ( X0 > multiset(X1) ) > ( X0 > tree(X1) ) > ( X0 > product_prod(X1,X0) ) > $o ) ).
thf(func_def_26,type,
heap_axioms:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( list(X1) > X0 ) > ( X0 > multiset(X1) ) > ( X0 > tree(X1) ) > ( X0 > product_prod(X1,X0) ) > $o ) ).
thf(func_def_27,type,
e:
!>[X0: $tType] : tree(X0) ).
thf(func_def_28,type,
t:
!>[X0: $tType] : ( X0 > tree(X0) > tree(X0) > tree(X0) ) ).
thf(func_def_29,type,
in_tree:
!>[X0: $tType] : ( X0 > tree(X0) > $o ) ).
thf(func_def_30,type,
is_heap:
!>[X0: $tType] : ( tree(X0) > $o ) ).
thf(func_def_31,type,
multiset2:
!>[X0: $tType] : ( tree(X0) > multiset(X0) ) ).
thf(func_def_32,type,
val:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_33,type,
if:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_34,type,
lattic929149872er_Max:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_35,type,
add_mset:
!>[X0: $tType] : ( X0 > multiset(X0) > multiset(X0) ) ).
thf(func_def_36,type,
set_mset:
!>[X0: $tType] : ( multiset(X0) > set(X0) ) ).
thf(func_def_37,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
order_Greatest:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_39,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).
thf(func_def_40,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > product_prod(X0,X2) > product_prod(X1,X2) ) ).
thf(func_def_41,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > product_prod(X2,X0) > product_prod(X2,X1) ) ).
thf(func_def_42,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X1) > X2 ) > X0 > X1 > X2 ) ).
thf(func_def_43,type,
produc2004651681e_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_44,type,
product_rec_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_45,type,
product_case_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_46,type,
product_fst:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_47,type,
product_snd:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_48,type,
product_swap:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > product_prod(X1,X0) ) ).
thf(func_def_49,type,
product_scomp:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( X0 > product_prod(X1,X2) ) > ( X1 > X2 > X3 ) > X0 > X3 ) ).
thf(func_def_50,type,
powp:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > $o ) ).
thf(func_def_51,type,
relcompp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > $o ) > ( X1 > X2 > $o ) > X0 > X2 > $o ) ).
thf(func_def_52,type,
collection:
!>[X0: $tType,X1: $tType] : ( X0 > ( X0 > $o ) > ( list(X1) > X0 ) > ( X0 > multiset(X1) ) > $o ) ).
thf(func_def_53,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_54,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_55,type,
t2: tree(a) ).
thf(func_def_56,type,
v: a ).
thf(func_def_60,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_62,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_63,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_64,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_65,type,
vIMP: $o > $o > $o ).
thf(func_def_66,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_67,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_68,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_69,type,
vNOT: $o > $o ).
thf(func_def_70,type,
vOR: $o > $o > $o ).
thf(func_def_71,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_72,type,
sP0:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_73,type,
sP1:
!>[X0: $tType] : ( ( tree(X0) > $o ) > $o ) ).
thf(func_def_74,type,
sP2:
!>[X0: $tType] : ( ( tree(X0) > $o ) > $o ) ).
thf(func_def_75,type,
sP3:
!>[X0: $tType] : ( ( tree(X0) > $o ) > $o ) ).
thf(func_def_76,type,
sP4:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_77,type,
sP5:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_78,type,
sP6:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_79,type,
sP7:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_80,type,
sP8:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > tree(X0) ) > $o ) ).
thf(func_def_81,type,
sP9:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > multiset(X0) ) > $o ) ).
thf(func_def_82,type,
sK10:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_83,type,
sK11:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_84,type,
sK12:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_85,type,
sK13:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_86,type,
sK14:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_87,type,
sK15:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_88,type,
sK16:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_89,type,
sK17:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_90,type,
sK18:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_91,type,
sK19:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_92,type,
sK20:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_93,type,
sK21:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_94,type,
sK22:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_95,type,
sK23:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_96,type,
sK24:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_97,type,
sK25:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_98,type,
sK26:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_99,type,
sK27:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_100,type,
sK28:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_101,type,
sK29:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_102,type,
sK30:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_103,type,
sK31:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_104,type,
sK32:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_105,type,
sK33:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_106,type,
sK34:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_107,type,
sK35:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_108,type,
sK36:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_109,type,
sK37:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_110,type,
sK38:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_111,type,
sK39:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_112,type,
sK40:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_113,type,
sK41:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_114,type,
sK42:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_115,type,
sK43:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_116,type,
sK44:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_117,type,
sK45:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_118,type,
sK46:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_119,type,
sK47:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_120,type,
sK48:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_121,type,
sK49:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_122,type,
sK50:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_123,type,
sK51:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_124,type,
sK52:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_125,type,
sK53:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_126,type,
sK54:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_127,type,
sK55:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_128,type,
sK56:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_129,type,
sK57:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_130,type,
sK58:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_131,type,
sK59:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_132,type,
sK60:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_133,type,
sK61:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_134,type,
sK62:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_135,type,
sK63:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_136,type,
sK64:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_137,type,
sK65:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_138,type,
sK66:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_139,type,
sK67:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_140,type,
sK68:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_141,type,
sK69:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_142,type,
sK70:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_143,type,
sK71:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_144,type,
sK72:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_145,type,
sK73:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_146,type,
sK74:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_147,type,
sK75:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_148,type,
sK76:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_149,type,
sK77:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_150,type,
sK78:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_151,type,
sK79:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_152,type,
sK80:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_153,type,
sK81:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_154,type,
sK82:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_155,type,
sK83:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_156,type,
sK84:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_157,type,
sK85:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_158,type,
sK86:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_159,type,
sK87:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_160,type,
sK88:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_161,type,
sK89:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_162,type,
sK90:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_163,type,
sK91:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_164,type,
sK92:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_165,type,
sK93:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_166,type,
sK94:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_167,type,
sK95:
!>[X0: $tType] : ( X0 > tree(X0) > tree(X0) ) ).
thf(func_def_168,type,
sK96:
!>[X0: $tType] : ( X0 > tree(X0) > X0 ) ).
thf(func_def_169,type,
sK97:
!>[X0: $tType] : ( X0 > tree(X0) > tree(X0) ) ).
thf(func_def_170,type,
sK98:
!>[X0: $tType] : ( tree(X0) > X0 ) ).
thf(func_def_171,type,
sK99:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_172,type,
sK100:
!>[X0: $tType] : ( tree(X0) > tree(X0) ) ).
thf(func_def_173,type,
sK101:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_174,type,
sK102:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_175,type,
sK103:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_176,type,
sK104:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_177,type,
sK105:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_178,type,
sK106:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_179,type,
sK107:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_180,type,
sK108:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_181,type,
sK109:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_182,type,
sK110:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_183,type,
sK111:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > multiset(X0) ) > X1 ) ).
thf(func_def_184,type,
sK112:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > multiset(X0) ) > X0 ) ).
thf(func_def_185,type,
sK113:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > multiset(X0) ) > X1 ) ).
thf(func_def_186,type,
sK114:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > tree(X0) ) > X1 ) ).
thf(func_def_187,type,
sK115:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > tree(X0) ) > X0 ) ).
thf(func_def_188,type,
sK116:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > product_prod(X0,X1) ) > ( X1 > tree(X0) ) > X1 ) ).
thf(func_def_189,type,
sK117:
!>[X0: $tType,X1: $tType] : ( ( X1 > product_prod(X0,X1) ) > ( X1 > $o ) > ( X1 > tree(X0) ) > X1 ) ).
thf(func_def_190,type,
sK118:
!>[X0: $tType,X1: $tType] : ( ( X1 > product_prod(X0,X1) ) > ( X1 > $o ) > ( X1 > tree(X0) ) > X0 ) ).
thf(func_def_191,type,
sK119:
!>[X0: $tType,X1: $tType] : ( ( X1 > product_prod(X0,X1) ) > ( X1 > $o ) > ( X1 > tree(X0) ) > X1 ) ).
thf(func_def_192,type,
sK120:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > tree(X0) ) > X1 ) ).
thf(func_def_193,type,
sK121:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > X1 ) > ( X1 > tree(X0) ) > list(X0) ) ).
thf(func_def_194,type,
sK122:
!>[X0: $tType,X1: $tType] : ( ( X1 > tree(X0) ) > ( X1 > multiset(X0) ) > X1 ) ).
thf(func_def_195,type,
sK123:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_196,type,
sK124:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_197,type,
sK125:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_198,type,
sK126:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_199,type,
sK127:
!>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).
thf(func_def_200,type,
sK128:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_201,type,
sK129:
!>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).
thf(func_def_202,type,
sK130:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_203,type,
sK131:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_204,type,
sK132:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_205,type,
sK133:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_206,type,
sK134:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_207,type,
sK135:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > product_prod(X1,X0) > X1 ) ).
thf(func_def_208,type,
sK136:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > product_prod(X1,X0) > X0 ) ).
thf(func_def_209,type,
sK137:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > ( X1 > X0 > $o ) > X1 ) ).
thf(func_def_210,type,
sK138:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > ( X1 > X0 > $o ) > X0 ) ).
thf(func_def_211,type,
sK139:
!>[X0: $tType,X1: $tType] : ( set(product_prod(X1,X0)) > set(product_prod(X1,X0)) > X1 ) ).
thf(func_def_212,type,
sK140:
!>[X0: $tType,X1: $tType] : ( set(product_prod(X1,X0)) > set(product_prod(X1,X0)) > X0 ) ).
thf(func_def_213,type,
sK141:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_214,type,
sK142:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_215,type,
sK143:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_216,type,
sK144:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_217,type,
sK145:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > ( X0 > X1 > $o ) > X0 ) ).
thf(func_def_218,type,
sK146:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > ( X0 > X1 > $o ) > X1 ) ).
thf(func_def_219,type,
sK147:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > $o ) > X1 ) ).
thf(func_def_220,type,
sK148:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > $o ) > X0 ) ).
thf(func_def_221,type,
sK149:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
thf(func_def_222,type,
sK150:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
thf(func_def_223,type,
sK151:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
thf(func_def_224,type,
sK152:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,X1) > X0 ) > ( X2 > X1 > X0 ) > X2 ) ).
thf(func_def_225,type,
sK153:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,X1) > X0 ) > ( X2 > X1 > X0 ) > X1 ) ).
thf(func_def_226,type,
sK154:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).
thf(func_def_227,type,
sK155:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).
thf(func_def_228,type,
sK156:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).
thf(func_def_229,type,
sK157:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_230,type,
sK158:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
thf(func_def_231,type,
sK159:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
thf(func_def_232,type,
sK160:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
thf(func_def_233,type,
sK161:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
thf(func_def_234,type,
sK162:
!>[X0: $tType,X1: $tType,X2: $tType] : ( X2 > ( X0 > X1 > X2 > $o ) > product_prod(X0,X1) > X0 ) ).
thf(func_def_235,type,
sK163:
!>[X0: $tType,X1: $tType,X2: $tType] : ( X2 > ( X0 > X1 > X2 > $o ) > product_prod(X0,X1) > X1 ) ).
thf(func_def_236,type,
sK164:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > set(X0) ) > X0 > product_prod(X2,X1) > X2 ) ).
thf(func_def_237,type,
sK165:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > set(X0) ) > X0 > product_prod(X2,X1) > X1 ) ).
thf(func_def_238,type,
sK166:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).
thf(func_def_239,type,
sK167:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).
thf(func_def_240,type,
sK168:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).
thf(func_def_241,type,
sK169:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).
thf(func_def_242,type,
sK170:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,X2) > ( X0 > X2 > X1 ) > ( X1 > $o ) > X0 ) ).
thf(func_def_243,type,
sK171:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,X2) > ( X0 > X2 > X1 ) > ( X1 > $o ) > X2 ) ).
thf(func_def_244,type,
sK172:
!>[X0: $tType,X1: $tType,X2: $tType] : ( X2 > product_prod(X1,X0) > ( X1 > X0 > X2 > $o ) > X1 ) ).
thf(func_def_245,type,
sK173:
!>[X0: $tType,X1: $tType,X2: $tType] : ( X2 > product_prod(X1,X0) > ( X1 > X0 > X2 > $o ) > X0 ) ).
thf(func_def_246,type,
sK174:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,X2) > ( X0 > X2 > set(X1) ) > X1 > X0 ) ).
thf(func_def_247,type,
sK175:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,X2) > ( X0 > X2 > set(X1) ) > X1 > X2 ) ).
thf(func_def_248,type,
sK176:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
thf(func_def_249,type,
sK177:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).
thf(func_def_250,type,
sK178:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
thf(func_def_251,type,
sK179:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
thf(func_def_252,type,
sK180:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
thf(func_def_253,type,
sK181:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > X0 ) > ( X2 > X1 > X0 ) > product_prod(X2,X1) > X2 ) ).
thf(func_def_254,type,
sK182:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > X0 ) > ( X2 > X1 > X0 ) > product_prod(X2,X1) > X1 ) ).
thf(func_def_255,type,
sK183:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X4 ) ).
thf(func_def_256,type,
sK184:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X3 ) ).
thf(func_def_257,type,
sK185:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X2 ) ).
thf(func_def_258,type,
sK186:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X1 ) ).
thf(func_def_259,type,
sK187:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X0 ) ).
thf(func_def_260,type,
sK188:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > X0 ) > ( X0 > $o ) > ( X1 > X2 > $o ) > X2 ) ).
thf(func_def_261,type,
sK189:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > X0 ) > ( X0 > $o ) > ( X1 > X2 > $o ) > X1 ) ).
thf(func_def_262,type,
sK190:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
thf(func_def_263,type,
sK191:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
thf(func_def_264,type,
sK192:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
thf(func_def_265,type,
sK193:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
thf(func_def_266,type,
sK194:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
thf(func_def_267,type,
sK195:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
thf(func_def_268,type,
sK196:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X5 ) ).
thf(func_def_269,type,
sK197:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X4 ) ).
thf(func_def_270,type,
sK198:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X3 ) ).
thf(func_def_271,type,
sK199:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X2 ) ).
thf(func_def_272,type,
sK200:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X1 ) ).
thf(func_def_273,type,
sK201:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X0 ) ).
thf(func_def_274,type,
sK202:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X0 ) ).
thf(func_def_275,type,
sK203:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X1 ) ).
thf(func_def_276,type,
sK204:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X2 ) ).
thf(func_def_277,type,
sK205:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X3 ) ).
thf(func_def_278,type,
sK206:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X4 ) ).
thf(func_def_279,type,
sK207:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X5 ) ).
thf(func_def_280,type,
sK208:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X6 ) ).
thf(func_def_281,type,
sK209:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X6 ) ).
thf(func_def_282,type,
sK210:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X5 ) ).
thf(func_def_283,type,
sK211:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X4 ) ).
thf(func_def_284,type,
sK212:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X3 ) ).
thf(func_def_285,type,
sK213:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X2 ) ).
thf(func_def_286,type,
sK214:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X1 ) ).
thf(func_def_287,type,
sK215:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X0 ) ).
thf(func_def_288,type,
sK216:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_289,type,
sK217:
!>[X0: $tType,X1: $tType] : ( product_prod(X1,X0) > X0 > X1 ) ).
thf(func_def_290,type,
sK218:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 > X1 ) ).
thf(func_def_291,type,
sK219:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(f7663,plain,
$false,
inference(trivial_inequality_removal,[],[f7662]) ).
thf(f7662,plain,
$true = $false,
inference(backward_demodulation,[],[f2101,f7661]) ).
thf(f7661,plain,
$false = vAPP(tree(a),$o,is_heap(a),e(a)),
inference(forward_demodulation,[],[f7660,f1382]) ).
thf(f1382,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)) = X3 ),
inference(cnf_transformation,[],[f737]) ).
thf(f737,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( vAPP(product_prod(X0,X1),X1,product_snd(X0,X1),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)) = X3 ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X46: $tType,X0: $tType,X36: X46,X37: X0] : ( vAPP(product_prod(X46,X0),X0,product_snd(X46,X0),vAPP(X0,product_prod(X46,X0),vAPP(X46,sTfun(X0,product_prod(X46,X0)),product_Pair(X46,X0),X36),X37)) = X37 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_snd__conv) ).
thf(f7660,plain,
$false = vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),vAPP(a,sTfun(tree(a),product_prod(a,tree(a))),product_Pair(a,tree(a)),v),e(a)))),
inference(backward_demodulation,[],[f3229,f7659]) ).
thf(f7659,plain,
! [X0: a] : ( vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),X0),e(a)),e(a))) = vAPP(tree(a),product_prod(a,tree(a)),vAPP(a,sTfun(tree(a),product_prod(a,tree(a))),product_Pair(a,tree(a)),X0),e(a)) ),
inference(trivial_inequality_removal,[],[f7654]) ).
thf(f7654,plain,
! [X0: a] :
( ( $true != $true )
| ( vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),X0),e(a)),e(a))) = vAPP(tree(a),product_prod(a,tree(a)),vAPP(a,sTfun(tree(a),product_prod(a,tree(a))),product_Pair(a,tree(a)),X0),e(a)) ) ),
inference(superposition,[],[f1214,f1174]) ).
thf(f1174,plain,
linorder(a) = $true,
inference(cnf_transformation,[],[f285]) ).
thf(f285,plain,
linorder(a) = $true,
inference(fool_elimination,[],[f284]) ).
thf(f284,plain,
linorder(a),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
linorder(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(f1214,plain,
! [X0: $tType,X1: X0] :
( ( linorder(X0) != $true )
| ( vAPP(tree(X0),product_prod(X0,tree(X0)),heapIm970386777veLeaf(X0),vAPP(tree(X0),tree(X0),vAPP(tree(X0),sTfun(tree(X0),tree(X0)),vAPP(X0,sTfun(tree(X0),sTfun(tree(X0),tree(X0))),t(X0),X1),e(X0)),e(X0))) = vAPP(tree(X0),product_prod(X0,tree(X0)),vAPP(X0,sTfun(tree(X0),product_prod(X0,tree(X0))),product_Pair(X0,tree(X0)),X1),e(X0)) ) ),
inference(cnf_transformation,[],[f826]) ).
thf(f826,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(tree(X0),product_prod(X0,tree(X0)),heapIm970386777veLeaf(X0),vAPP(tree(X0),tree(X0),vAPP(tree(X0),sTfun(tree(X0),tree(X0)),vAPP(X0,sTfun(tree(X0),sTfun(tree(X0),tree(X0))),t(X0),X1),e(X0)),e(X0))) = vAPP(tree(X0),product_prod(X0,tree(X0)),vAPP(X0,sTfun(tree(X0),product_prod(X0,tree(X0))),product_Pair(X0,tree(X0)),X1),e(X0)) )
| ( linorder(X0) != $true ) ),
inference(ennf_transformation,[],[f351]) ).
thf(f351,plain,
! [X0: $tType] :
( ( linorder(X0) = $true )
=> ! [X1: X0] : ( vAPP(tree(X0),product_prod(X0,tree(X0)),heapIm970386777veLeaf(X0),vAPP(tree(X0),tree(X0),vAPP(tree(X0),sTfun(tree(X0),tree(X0)),vAPP(X0,sTfun(tree(X0),sTfun(tree(X0),tree(X0))),t(X0),X1),e(X0)),e(X0))) = vAPP(tree(X0),product_prod(X0,tree(X0)),vAPP(X0,sTfun(tree(X0),product_prod(X0,tree(X0))),product_Pair(X0,tree(X0)),X1),e(X0)) ) ),
inference(fool_elimination,[],[f350]) ).
thf(f350,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0] : ( vAPP(tree(X0),product_prod(X0,tree(X0)),heapIm970386777veLeaf(X0),vAPP(tree(X0),tree(X0),vAPP(tree(X0),sTfun(tree(X0),tree(X0)),vAPP(X0,sTfun(tree(X0),sTfun(tree(X0),tree(X0))),t(X0),X1),e(X0)),e(X0))) = vAPP(tree(X0),product_prod(X0,tree(X0)),vAPP(X0,sTfun(tree(X0),product_prod(X0,tree(X0))),product_Pair(X0,tree(X0)),X1),e(X0)) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X15: X0] : ( vAPP(tree(X0),product_prod(X0,tree(X0)),heapIm970386777veLeaf(X0),vAPP(tree(X0),tree(X0),vAPP(tree(X0),sTfun(tree(X0),tree(X0)),vAPP(X0,sTfun(tree(X0),sTfun(tree(X0),tree(X0))),t(X0),X15),e(X0)),e(X0))) = vAPP(tree(X0),product_prod(X0,tree(X0)),vAPP(X0,sTfun(tree(X0),product_prod(X0,tree(X0))),product_Pair(X0,tree(X0)),X15),e(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_removeLeaf_Osimps_I1_J) ).
thf(f3229,plain,
vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))) = $false,
inference(trivial_inequality_removal,[],[f3228]) ).
thf(f3228,plain,
( ( $true != $true )
| ( vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))) = $false ) ),
inference(superposition,[],[f1173,f281]) ).
thf(f281,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1173,plain,
vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))) != $true,
inference(cnf_transformation,[],[f710]) ).
thf(f710,plain,
vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))) != $true,
inference(flattening,[],[f283]) ).
thf(f283,plain,
vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))) != $true,
inference(fool_elimination,[],[f282]) ).
thf(f282,plain,
~ vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))),
inference(rectify,[],[f279]) ).
thf(f279,negated_conjecture,
~ vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))),
inference(negated_conjecture,[],[f278]) ).
thf(f278,conjecture,
vAPP(tree(a),$o,is_heap(a),vAPP(product_prod(a,tree(a)),tree(a),product_snd(a,tree(a)),vAPP(tree(a),product_prod(a,tree(a)),heapIm970386777veLeaf(a),vAPP(tree(a),tree(a),vAPP(tree(a),sTfun(tree(a),tree(a)),vAPP(a,sTfun(tree(a),sTfun(tree(a),tree(a))),t(a),v),e(a)),e(a))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f2101,plain,
$true = vAPP(tree(a),$o,is_heap(a),e(a)),
inference(trivial_inequality_removal,[],[f2096]) ).
thf(f2096,plain,
( ( $true != $true )
| ( $true = vAPP(tree(a),$o,is_heap(a),e(a)) ) ),
inference(superposition,[],[f1284,f1174]) ).
thf(f1284,plain,
! [X0: $tType] :
( ( linorder(X0) != $true )
| ( vAPP(tree(X0),$o,is_heap(X0),e(X0)) = $true ) ),
inference(cnf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: $tType] :
( ( vAPP(tree(X0),$o,is_heap(X0),e(X0)) = $true )
| ( linorder(X0) != $true ) ),
inference(ennf_transformation,[],[f423]) ).
thf(f423,plain,
! [X0: $tType] :
( ( linorder(X0) = $true )
=> ( vAPP(tree(X0),$o,is_heap(X0),e(X0)) = $true ) ),
inference(fool_elimination,[],[f422]) ).
thf(f422,plain,
! [X0: $tType] :
( linorder(X0)
=> vAPP(tree(X0),$o,is_heap(X0),e(X0)) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X0: $tType] :
( linorder(X0)
=> vAPP(tree(X0),$o,is_heap(X0),e(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_is__heap_Osimps_I1_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP071^2 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat May 18 17:59:37 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % (16078)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (16079)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.36 % (16081)WARNING: value z3 for option sas not known
% 0.16/0.36 % (16080)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.36 % (16085)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.37 % (16084)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.37 % (16083)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.37 % (16082)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.37 % (16081)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.41 % (16085)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.43 % Exception at run slice level
% 0.16/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.44 % Exception at run slice level
% 0.16/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.44 % (16086)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.45 % (16087)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.16/0.47 % Exception at run slice level
% 0.16/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.48 % (16088)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.16/0.49 % (16086)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.49 % (16087)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.50 % Exception at run slice level
% 0.16/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.51 % (16089)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)
% 4.78/1.07 % (16084)First to succeed.
% 4.78/1.07 % (16084)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16078"
% 5.09/1.08 % (16084)Refutation found. Thanks to Tanya!
% 5.09/1.08 % SZS status Theorem for theBenchmark
% 5.09/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 5.09/1.08 % (16084)------------------------------
% 5.09/1.08 % (16084)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.09/1.08 % (16084)Termination reason: Refutation
% 5.09/1.08
% 5.09/1.08 % (16084)Memory used [KB]: 10170
% 5.09/1.08 % (16084)Time elapsed: 0.715 s
% 5.09/1.08 % (16084)Instructions burned: 1794 (million)
% 5.09/1.08 % (16078)Success in time 0.751 s
%------------------------------------------------------------------------------