TSTP Solution File: DAT214^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT214^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 05:06:13 EDT 2024

% Result   : Theorem 63.19s 9.41s
% Output   : Refutation 63.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  198
% Syntax   : Number of formulae    :  231 (  22 unt; 191 typ;   0 def)
%            Number of atoms       :  418 (  67 equ;   0 cnn)
%            Maximal formula atoms :    3 (  10 avg)
%            Number of connectives :   62 (  28   ~;  22   |;   0   &;   0   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  330 ( 325   >;   5   *;   0   +;   0  <<)
%            Number of symbols     :  187 ( 184 usr;  13 con; 0-6 aty)
%            Number of variables   :  216 (   0   ^  63   !;   0   ?; 216   :)
%                                         ( 153  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    itself: $tType > $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    code_natural: $tType ).

thf(type_def_8,type,
    nat: $tType ).

thf(type_def_9,type,
    tree: $tType > $tType ).

thf(type_def_10,type,
    real: $tType ).

thf(type_def_11,type,
    a: $tType ).

thf(type_def_12,type,
    splay_2011811431op_s_t: $tType > $tType ).

thf(type_def_13,type,
    product_prod: ( $tType * $tType ) > $tType ).

thf(type_def_14,type,
    sum_sum: ( $tType * $tType ) > $tType ).

thf(func_def_0,type,
    splay_2011811431op_s_t: $tType > $tType ).

thf(func_def_1,type,
    code_natural: $tType ).

thf(func_def_2,type,
    product_prod: ( $tType * $tType ) > $tType ).

thf(func_def_3,type,
    sum_sum: ( $tType * $tType ) > $tType ).

thf(func_def_4,type,
    tree: $tType > $tType ).

thf(func_def_5,type,
    real: $tType ).

thf(func_def_6,type,
    nat: $tType ).

thf(func_def_7,type,
    itself: $tType > $tType ).

thf(func_def_8,type,
    a: $tType ).

thf(func_def_9,type,
    type: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_10,type,
    size: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_11,type,
    one: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_12,type,
    zero: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_13,type,
    neg_numeral: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_14,type,
    group_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_15,type,
    monoid_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_16,type,
    ln: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_17,type,
    linorder: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_18,type,
    zero_neq_one: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_19,type,
    zero_less_one: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_20,type,
    semigroup_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_21,type,
    comm_semiring_1: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_22,type,
    linordered_idom: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_23,type,
    comm_monoid_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_24,type,
    linordered_field: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_25,type,
    ab_semigroup_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_26,type,
    linordered_semidom: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_27,type,
    cancel_semigroup_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_28,type,
    cancel1352612707id_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_29,type,
    linord219039673up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_30,type,
    ordere216010020id_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_31,type,
    ordere779506340up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_32,type,
    linord1659791738miring: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_33,type,
    canoni770627133id_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_34,type,
    strict797366125id_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_35,type,
    ordere236663937imp_le: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_36,type,
    ordere223160158up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_37,type,
    strict2144017051up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_38,type,
    ordere516151231imp_le: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_39,type,
    semiri456707255roduct: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_40,type,
    code_case_natural: 
      !>[X0: $tType] : ( X0 > ( code_natural > X0 ) > code_natural > X0 ) ).

thf(func_def_41,type,
    code_rec_natural: 
      !>[X0: $tType] : ( X0 > ( code_natural > X0 > X0 ) > code_natural > X0 ) ).

thf(func_def_42,type,
    code_size_natural: code_natural > nat ).

thf(func_def_43,type,
    one_one: 
      !>[X0: $tType] : X0 ).

thf(func_def_44,type,
    plus_plus: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_45,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

thf(func_def_46,type,
    size_bool: $o > nat ).

thf(func_def_47,type,
    if: 
      !>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).

thf(func_def_48,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

thf(func_def_49,type,
    neg_numeral_dbl_dec: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_50,type,
    neg_numeral_dbl_inc: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_51,type,
    ord_less: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_52,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_53,type,
    product_rec_bool: 
      !>[X0: $tType] : ( X0 > X0 > $o > X0 ) ).

thf(func_def_54,type,
    type2: 
      !>[X0: $tType] : itself(X0) ).

thf(func_def_55,type,
    set_fo292404081st_nat: 
      !>[X0: $tType] : ( ( nat > X0 > X0 ) > nat > nat > X0 > X0 ) ).

thf(func_def_56,type,
    splay_splay: 
      !>[X0: $tType] : ( X0 > tree(X0) > tree(X0) ) ).

thf(func_def_57,type,
    splay_splay_max: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_58,type,
    splay_914434265_splay: 
      !>[X0: $tType] : ( X0 > tree(X0) > nat ) ).

thf(func_def_59,type,
    splay_878424299ay_max: 
      !>[X0: $tType] : ( tree(X0) > nat ) ).

thf(func_def_60,type,
    splay_1816415694ax_rel: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) > $o ) ).

thf(func_def_61,type,
    splay_266122055elle_A: 
      !>[X0: $tType] : ( X0 > tree(X0) > real ) ).

thf(func_def_62,type,
    ln_ln: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_63,type,
    powr: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_64,type,
    linorder_bst: 
      !>[X0: $tType] : ( tree(X0) > $o ) ).

thf(func_def_65,type,
    path_len: 
      !>[X0: $tType] : ( tree(X0) > nat ) ).

thf(func_def_66,type,
    path_len_rel: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) > $o ) ).

thf(func_def_67,type,
    size1: 
      !>[X0: $tType] : ( tree(X0) > nat ) ).

thf(func_def_68,type,
    leaf: 
      !>[X0: $tType] : tree(X0) ).

thf(func_def_69,type,
    node: 
      !>[X0: $tType] : ( tree(X0) > X0 > tree(X0) > tree(X0) ) ).

thf(func_def_70,type,
    size_tree: 
      !>[X0: $tType] : ( ( X0 > nat ) > tree(X0) > nat ) ).

thf(func_def_71,type,
    accp: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 > $o ) ).

thf(func_def_72,type,
    b: a ).

thf(func_def_73,type,
    c: a ).

thf(func_def_74,type,
    l: tree(a) ).

thf(func_def_75,type,
    l2: tree(a) ).

thf(func_def_76,type,
    r: tree(a) ).

thf(func_def_77,type,
    rl: tree(a) ).

thf(func_def_78,type,
    rr: tree(a) ).

thf(func_def_79,type,
    u: a ).

thf(func_def_83,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_84,type,
    vOR: $o > $o > $o ).

thf(func_def_85,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_86,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_87,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_88,type,
    vNOT: $o > $o ).

thf(func_def_89,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_90,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_91,type,
    vAND: $o > $o > $o ).

thf(func_def_92,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_93,type,
    sP0: 
      !>[X0: $tType] : ( tree(X0) > nat > $o ) ).

thf(func_def_94,type,
    sP1: 
      !>[X0: $tType] : ( tree(X0) > nat > $o ) ).

thf(func_def_95,type,
    sP2: 
      !>[X0: $tType] : ( tree(X0) > nat > $o ) ).

thf(func_def_96,type,
    sP3: 
      !>[X0: $tType] : ( tree(X0) > nat > $o ) ).

thf(func_def_97,type,
    sP4: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).

thf(func_def_98,type,
    sK5: tree(a) ).

thf(func_def_99,type,
    sK6: a ).

thf(func_def_100,type,
    sK7: tree(a) ).

thf(func_def_101,type,
    sK8: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_102,type,
    sK9: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_103,type,
    sK10: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_104,type,
    sK11: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_105,type,
    sK12: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_106,type,
    sK13: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_107,type,
    sK14: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_108,type,
    sK15: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_109,type,
    sK16: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_110,type,
    sK17: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_111,type,
    sK18: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_112,type,
    sK19: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_113,type,
    sK20: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_114,type,
    sK21: 
      !>[X0: $tType] : ( X0 > tree(X0) > tree(X0) ) ).

thf(func_def_115,type,
    sK22: 
      !>[X0: $tType] : ( X0 > tree(X0) > X0 ) ).

thf(func_def_116,type,
    sK23: 
      !>[X0: $tType] : ( X0 > tree(X0) > tree(X0) ) ).

thf(func_def_117,type,
    sK24: 
      !>[X0: $tType] : ( tree(X0) > nat > tree(X0) ) ).

thf(func_def_118,type,
    sK25: 
      !>[X0: $tType] : ( tree(X0) > nat > X0 ) ).

thf(func_def_119,type,
    sK26: 
      !>[X0: $tType] : ( tree(X0) > nat > tree(X0) ) ).

thf(func_def_120,type,
    sK27: 
      !>[X0: $tType] : ( tree(X0) > nat > X0 ) ).

thf(func_def_121,type,
    sK28: 
      !>[X0: $tType] : ( tree(X0) > nat > tree(X0) ) ).

thf(func_def_122,type,
    sK29: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_123,type,
    sK30: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_124,type,
    sK31: 
      !>[X0: $tType] : ( tree(X0) > nat > tree(X0) ) ).

thf(func_def_125,type,
    sK32: 
      !>[X0: $tType] : ( tree(X0) > nat > X0 ) ).

thf(func_def_126,type,
    sK33: 
      !>[X0: $tType] : ( tree(X0) > nat > tree(X0) ) ).

thf(func_def_127,type,
    sK34: 
      !>[X0: $tType] : ( tree(X0) > nat > X0 ) ).

thf(func_def_128,type,
    sK35: 
      !>[X0: $tType] : ( tree(X0) > nat > tree(X0) ) ).

thf(func_def_129,type,
    sK36: 
      !>[X0: $tType] : ( nat > tree(X0) > tree(X0) ) ).

thf(func_def_130,type,
    sK37: 
      !>[X0: $tType] : ( nat > tree(X0) > X0 ) ).

thf(func_def_131,type,
    sK38: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_132,type,
    sK39: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_133,type,
    sK40: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_134,type,
    sK41: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_135,type,
    sK42: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_136,type,
    sK43: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_137,type,
    sK44: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_138,type,
    sK45: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_139,type,
    sK46: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_140,type,
    sK47: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_141,type,
    sK48: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_142,type,
    sK49: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_143,type,
    sK50: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_144,type,
    sK51: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_145,type,
    sK52: 
      !>[X0: $tType] : ( tree(X0) > X0 ) ).

thf(func_def_146,type,
    sK53: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(func_def_147,type,
    sK54: ( nat > $o ) > nat ).

thf(func_def_148,type,
    sK55: ( nat > $o ) > nat ).

thf(func_def_149,type,
    sK56: ( nat > $o ) > nat ).

thf(func_def_150,type,
    sK57: nat > nat > nat ).

thf(func_def_151,type,
    sK58: real > real > real ).

thf(func_def_152,type,
    sK59: 
      !>[X0: $tType] : ( nat > tree(X0) > tree(X0) ) ).

thf(func_def_153,type,
    sK60: 
      !>[X0: $tType] : ( nat > tree(X0) > X0 ) ).

thf(func_def_154,type,
    sK61: 
      !>[X0: $tType] : ( nat > tree(X0) > tree(X0) ) ).

thf(func_def_155,type,
    sK62: 
      !>[X0: $tType] : ( nat > tree(X0) > tree(X0) ) ).

thf(func_def_156,type,
    sK63: 
      !>[X0: $tType] : ( nat > tree(X0) > X0 ) ).

thf(func_def_157,type,
    sK64: 
      !>[X0: $tType] : ( nat > tree(X0) > tree(X0) ) ).

thf(func_def_158,type,
    sK65: ( nat > nat > $o ) > nat ).

thf(func_def_159,type,
    sK66: ( nat > nat > $o ) > nat ).

thf(func_def_160,type,
    sK67: ( nat > nat > $o ) > nat ).

thf(func_def_161,type,
    sK68: ( nat > nat > $o ) > nat ).

thf(func_def_162,type,
    sK69: ( nat > nat > $o ) > nat ).

thf(func_def_163,type,
    sK70: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_164,type,
    sK71: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_165,type,
    sK72: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_166,type,
    sK73: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_167,type,
    sK74: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_168,type,
    sK75: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_169,type,
    sK76: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_170,type,
    sK77: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > X0 ) ).

thf(func_def_171,type,
    sK78: 
      !>[X0: $tType] : ( ( tree(X0) > $o ) > tree(X0) ) ).

thf(func_def_172,type,
    sK79: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_173,type,
    sK80: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_174,type,
    sK81: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_175,type,
    sK82: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_176,type,
    sK83: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_177,type,
    sK84: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_178,type,
    sK85: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat > X0 > X0 ) ).

thf(func_def_179,type,
    sK86: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).

thf(func_def_180,type,
    sK87: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).

thf(func_def_181,type,
    sK88: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > X0 ) ).

thf(func_def_182,type,
    vIMP: $o > $o > $o ).

thf(func_def_183,type,
    sK89: 
      !>[X0: $tType] : ( tree(X0) > tree(X0) ) ).

thf(f271109,plain,
    $false,
    inference(trivial_inequality_removal,[],[f270970]) ).

thf(f270970,plain,
    vAPP(tree(a),nat,size_size(tree(a)),rr) != vAPP(tree(a),nat,size_size(tree(a)),rr),
    inference(superposition,[],[f21798,f270968]) ).

thf(f270968,plain,
    vAPP(tree(a),nat,size_size(tree(a)),rr) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),one_one(nat)),
    inference(equality_resolution,[],[f74237]) ).

thf(f74237,plain,
    ! [X0: tree(a)] :
      ( ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( vAPP(tree(a),nat,size_size(tree(a)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),one_one(nat)) ) ),
    inference(trivial_inequality_removal,[],[f74236]) ).

thf(f74236,plain,
    ! [X0: tree(a)] :
      ( ( $true != $true )
      | ( vAPP(tree(a),nat,size_size(tree(a)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),one_one(nat)) )
      | ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) ) ),
    inference(forward_demodulation,[],[f74235,f1326]) ).

thf(f1326,plain,
    vAPP(itself(a),$o,linorder(a),type2(a)) = $true,
    inference(cnf_transformation,[],[f341]) ).

thf(f341,plain,
    vAPP(itself(a),$o,linorder(a),type2(a)) = $true,
    inference(fool_elimination,[],[f340]) ).

thf(f340,plain,
    vAPP(itself(a),$o,linorder(a),type2(a)),
    inference(rectify,[],[f335]) ).

thf(f335,axiom,
    vAPP(itself(a),$o,linorder(a),type2(a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

thf(f74235,plain,
    ! [X0: tree(a)] :
      ( ( vAPP(tree(a),nat,size_size(tree(a)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),one_one(nat)) )
      | ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( vAPP(itself(a),$o,linorder(a),type2(a)) != $true ) ),
    inference(forward_demodulation,[],[f74234,f1347]) ).

thf(f1347,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
    inference(cnf_transformation,[],[f946]) ).

thf(f946,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
    inference(rectify,[],[f88]) ).

thf(f88,axiom,
    ! [X15: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X15),zero_zero(nat)) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Nat_Oadd__0__right) ).

thf(f74234,plain,
    ! [X0: tree(a)] :
      ( ( vAPP(tree(a),nat,size_size(tree(a)),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),zero_zero(nat))),one_one(nat)) )
      | ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( vAPP(itself(a),$o,linorder(a),type2(a)) != $true ) ),
    inference(forward_demodulation,[],[f74230,f21772]) ).

thf(f21772,plain,
    zero_zero(nat) = vAPP(tree(a),nat,size_size(tree(a)),r),
    inference(superposition,[],[f1346,f21748]) ).

thf(f21748,plain,
    r = leaf(a),
    inference(equality_resolution,[],[f21743]) ).

thf(f21743,plain,
    ! [X0: tree(a)] :
      ( ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( r = leaf(a) ) ),
    inference(trivial_inequality_removal,[],[f21742]) ).

thf(f21742,plain,
    ! [X0: tree(a)] :
      ( ( $true != $true )
      | ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( r = leaf(a) ) ),
    inference(forward_demodulation,[],[f21740,f1326]) ).

thf(f21740,plain,
    ! [X0: tree(a)] :
      ( ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( r = leaf(a) )
      | ( vAPP(itself(a),$o,linorder(a),type2(a)) != $true ) ),
    inference(superposition,[],[f1499,f1335]) ).

thf(f1335,plain,
    vAPP(tree(a),tree(a),splay_splay_max(a),rr) = vAPP(tree(a),tree(a),vAPP(a,sTfun(tree(a),tree(a)),vAPP(tree(a),sTfun(a,sTfun(tree(a),tree(a))),node(a),l),u),r),
    inference(cnf_transformation,[],[f2]) ).

thf(f2,axiom,
    vAPP(tree(a),tree(a),splay_splay_max(a),rr) = vAPP(tree(a),tree(a),vAPP(a,sTfun(tree(a),tree(a)),vAPP(tree(a),sTfun(a,sTfun(tree(a),tree(a))),node(a),l),u),r),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_sp) ).

thf(f1499,plain,
    ! [X0: $tType,X2: tree(X0),X3: X0,X1: tree(X0),X4: tree(X0)] :
      ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) != vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) )
      | ( leaf(X0) = X4 )
      | ( vAPP(itself(X0),$o,linorder(X0),type2(X0)) != $true ) ),
    inference(cnf_transformation,[],[f1126]) ).

thf(f1126,plain,
    ! [X0: $tType] :
      ( ! [X1: tree(X0),X2: tree(X0),X3: X0,X4: tree(X0)] :
          ( ( leaf(X0) = X4 )
          | ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) != vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) ) )
      | ( vAPP(itself(X0),$o,linorder(X0),type2(X0)) != $true ) ),
    inference(ennf_transformation,[],[f613]) ).

thf(f613,plain,
    ! [X0: $tType] :
      ( ( vAPP(itself(X0),$o,linorder(X0),type2(X0)) = $true )
     => ! [X1: tree(X0),X2: tree(X0),X3: X0,X4: tree(X0)] :
          ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) = vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) )
         => ( leaf(X0) = X4 ) ) ),
    inference(fool_elimination,[],[f612]) ).

thf(f612,plain,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,linorder(X0),type2(X0))
     => ! [X1: tree(X0),X2: tree(X0),X3: X0,X4: tree(X0)] :
          ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) = vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) )
         => ( leaf(X0) = X4 ) ) ),
    inference(rectify,[],[f19]) ).

thf(f19,axiom,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,linorder(X0),type2(X0))
     => ! [X8: tree(X0),X9: tree(X0),X5: X0,X11: tree(X0)] :
          ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X8) = vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X9),X5),X11) )
         => ( leaf(X0) = X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_splay__max__Leaf) ).

thf(f1346,plain,
    ! [X0: $tType] : ( zero_zero(nat) = vAPP(tree(X0),nat,size_size(tree(X0)),leaf(X0)) ),
    inference(cnf_transformation,[],[f155]) ).

thf(f155,axiom,
    ! [X0: $tType] : ( zero_zero(nat) = vAPP(tree(X0),nat,size_size(tree(X0)),leaf(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_tree_Osize_I3_J) ).

thf(f74230,plain,
    ! [X0: tree(a)] :
      ( ( vAPP(tree(a),tree(a),splay_splay_max(a),rr) != vAPP(tree(a),tree(a),splay_splay_max(a),X0) )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),vAPP(tree(a),nat,size_size(tree(a)),r))),one_one(nat)) = vAPP(tree(a),nat,size_size(tree(a)),X0) )
      | ( vAPP(itself(a),$o,linorder(a),type2(a)) != $true ) ),
    inference(superposition,[],[f1500,f1335]) ).

thf(f1500,plain,
    ! [X0: $tType,X2: tree(X0),X3: X0,X1: tree(X0),X4: tree(X0)] :
      ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) != vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) )
      | ( vAPP(tree(X0),nat,size_size(tree(X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(X0),nat,size_size(tree(X0)),X2)),vAPP(tree(X0),nat,size_size(tree(X0)),X4))),one_one(nat)) )
      | ( vAPP(itself(X0),$o,linorder(X0),type2(X0)) != $true ) ),
    inference(cnf_transformation,[],[f1127]) ).

thf(f1127,plain,
    ! [X0: $tType] :
      ( ! [X1: tree(X0),X2: tree(X0),X3: X0,X4: tree(X0)] :
          ( ( vAPP(tree(X0),nat,size_size(tree(X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(X0),nat,size_size(tree(X0)),X2)),vAPP(tree(X0),nat,size_size(tree(X0)),X4))),one_one(nat)) )
          | ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) != vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) ) )
      | ( vAPP(itself(X0),$o,linorder(X0),type2(X0)) != $true ) ),
    inference(ennf_transformation,[],[f615]) ).

thf(f615,plain,
    ! [X0: $tType] :
      ( ( vAPP(itself(X0),$o,linorder(X0),type2(X0)) = $true )
     => ! [X1: tree(X0),X2: tree(X0),X3: X0,X4: tree(X0)] :
          ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) = vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) )
         => ( vAPP(tree(X0),nat,size_size(tree(X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(X0),nat,size_size(tree(X0)),X2)),vAPP(tree(X0),nat,size_size(tree(X0)),X4))),one_one(nat)) ) ) ),
    inference(fool_elimination,[],[f614]) ).

thf(f614,plain,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,linorder(X0),type2(X0))
     => ! [X1: tree(X0),X2: tree(X0),X3: X0,X4: tree(X0)] :
          ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X1) = vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X2),X3),X4) )
         => ( vAPP(tree(X0),nat,size_size(tree(X0)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(X0),nat,size_size(tree(X0)),X2)),vAPP(tree(X0),nat,size_size(tree(X0)),X4))),one_one(nat)) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,linorder(X0),type2(X0))
     => ! [X8: tree(X0),X9: tree(X0),X10: X0,X11: tree(X0)] :
          ( ( vAPP(tree(X0),tree(X0),splay_splay_max(X0),X8) = vAPP(tree(X0),tree(X0),vAPP(X0,sTfun(tree(X0),tree(X0)),vAPP(tree(X0),sTfun(X0,sTfun(tree(X0),tree(X0))),node(X0),X9),X10),X11) )
         => ( vAPP(tree(X0),nat,size_size(tree(X0)),X8) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(X0),nat,size_size(tree(X0)),X9)),vAPP(tree(X0),nat,size_size(tree(X0)),X11))),one_one(nat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_size__if__splay__max) ).

thf(f21798,plain,
    vAPP(tree(a),nat,size_size(tree(a)),rr) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),one_one(nat)),
    inference(forward_demodulation,[],[f21797,f1347]) ).

thf(f21797,plain,
    vAPP(tree(a),nat,size_size(tree(a)),rr) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),zero_zero(nat))),one_one(nat)),
    inference(backward_demodulation,[],[f1325,f21772]) ).

thf(f1325,plain,
    vAPP(tree(a),nat,size_size(tree(a)),rr) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),vAPP(tree(a),nat,size_size(tree(a)),r))),one_one(nat)),
    inference(cnf_transformation,[],[f944]) ).

thf(f944,plain,
    vAPP(tree(a),nat,size_size(tree(a)),rr) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),vAPP(tree(a),nat,size_size(tree(a)),r))),one_one(nat)),
    inference(flattening,[],[f337]) ).

thf(f337,negated_conjecture,
    vAPP(tree(a),nat,size_size(tree(a)),rr) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),vAPP(tree(a),nat,size_size(tree(a)),r))),one_one(nat)),
    inference(negated_conjecture,[],[f336]) ).

thf(f336,conjecture,
    vAPP(tree(a),nat,size_size(tree(a)),rr) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(tree(a),nat,size_size(tree(a)),l)),vAPP(tree(a),nat,size_size(tree(a)),r))),one_one(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : DAT214^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n026.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 13:19:06 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  % (7265)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.40  % (7268)WARNING: value z3 for option sas not known
% 0.16/0.40  % (7266)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.40  % (7267)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.40  % (7269)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.40  % (7268)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)
% 0.16/0.40  % (7271)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)
% 0.16/0.40  % (7270)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)
% 0.16/0.40  % (7272)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)
% 0.22/0.43  % (7272)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.44  % Exception at run slice level
% 0.22/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.44  % Exception at run slice level
% 0.22/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.44  % Exception at run slice level
% 0.22/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.46  % (7274)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.46  % (7275)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)
% 0.22/0.46  % (7276)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)
% 0.22/0.49  % (7274)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.49  % (7275)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.49  % Exception at run slice level
% 0.22/0.49  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.52  % (7286)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)
% 63.19/9.38  % (7271)First to succeed.
% 63.19/9.40  % (7271)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7265"
% 63.19/9.41  % (7271)Refutation found. Thanks to Tanya!
% 63.19/9.41  % SZS status Theorem for theBenchmark
% 63.19/9.41  % SZS output start Proof for theBenchmark
% See solution above
% 63.19/9.41  % (7271)------------------------------
% 63.19/9.41  % (7271)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 63.19/9.41  % (7271)Termination reason: Refutation
% 63.19/9.41  
% 63.19/9.41  % (7271)Memory used [KB]: 41804
% 63.19/9.41  % (7271)Time elapsed: 9.001 s
% 63.19/9.41  % (7271)Instructions burned: 35730 (million)
% 63.19/9.41  % (7265)Success in time 8.863 s
%------------------------------------------------------------------------------