TSTP Solution File: ITP071^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------