TSTP Solution File: ITP187^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP187^2 : 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 : n028.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 22:55:34 EDT 2024

% Result   : Theorem 21.48s 3.43s
% Output   : Refutation 21.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  351
% Syntax   : Number of formulae    :  377 (  14 unt; 345 typ;   0 def)
%            Number of atoms       :  625 (  37 equ;   0 cnn)
%            Maximal formula atoms :    3 (  19 avg)
%            Number of connectives :   38 (  18   ~;  13   |;   4   &;   0   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  912 ( 909   >;   3   *;   0   +;   0  <<)
%            Number of symbols     :  338 ( 335 usr;  16 con; 0-8 aty)
%            Number of variables   :  474 (   0   ^  28   !;   4   ?; 474   :)
%                                         ( 442  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

thf(type_def_9,type,
    late_subject: $tType ).

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

thf(type_def_11,type,
    noption: $tType > $tType ).

thf(type_def_12,type,
    product_prod: ( $tType * $tType ) > $tType ).

thf(type_def_13,type,
    set: $tType > $tType ).

thf(func_def_0,type,
    late_residual: $tType ).

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

thf(func_def_2,type,
    late_freeRes: $tType ).

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

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

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

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

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

thf(func_def_8,type,
    fs_name: 
      !>[X0: $tType] : $o ).

thf(func_def_9,type,
    bang: pi > pi ).

thf(func_def_10,type,
    input: name > name > pi > pi ).

thf(func_def_11,type,
    match: name > name > pi > pi ).

thf(func_def_12,type,
    mismatch: name > name > pi > pi ).

thf(func_def_13,type,
    output: name > name > pi > pi ).

thf(func_def_14,type,
    par: pi > pi > pi ).

thf(func_def_15,type,
    piNil: pi ).

thf(func_def_16,type,
    res: name > pi > pi ).

thf(func_def_17,type,
    sum: pi > pi > pi ).

thf(func_def_18,type,
    tau: pi > pi ).

thf(func_def_19,type,
    subs: pi > name > name > pi ).

thf(func_def_20,type,
    subst_name: name > name > name > name ).

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

thf(func_def_22,type,
    late_OutputR: name > name > late_freeRes ).

thf(func_def_23,type,
    late_TauR: late_freeRes ).

thf(func_def_24,type,
    late_freeRes_rec: 
      !>[X0: $tType] : ( ( name > name > X0 ) > X0 > late_freeRes > X0 ) ).

thf(func_def_25,type,
    late_BoundR: late_subject > name > pi > late_residual ).

thf(func_def_26,type,
    late_FreeR: late_freeRes > pi > late_residual ).

thf(func_def_27,type,
    late_BoundOutputS: name > late_subject ).

thf(func_def_28,type,
    late_InputS: name > late_subject ).

thf(func_def_29,type,
    late_subject_rec: 
      !>[X0: $tType] : ( ( name > X0 ) > ( name > X0 ) > late_subject > X0 ) ).

thf(func_def_30,type,
    late_transitions: pi > late_residual > $o ).

thf(func_def_31,type,
    abs_fun: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 > noption(X1) ) ).

thf(func_def_32,type,
    fresh: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > $o ) ).

thf(func_def_33,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).

thf(func_def_34,type,
    produc2004651681e_prod: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).

thf(func_def_35,type,
    product_rec_prod: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).

thf(func_def_36,type,
    eqvt: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > $o ) ).

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

thf(func_def_38,type,
    strong2129052853vative: pi > pi > late_subject > name > set(product_prod(pi,pi)) > $o ).

thf(func_def_39,type,
    strong743114133lation: pi > set(product_prod(pi,pi)) > pi > $o ).

thf(func_def_40,type,
    member: 
      !>[X0: $tType] : ( X0 > set(X0) > $o ) ).

thf(func_def_41,type,
    p: pi ).

thf(func_def_42,type,
    pqr: pi ).

thf(func_def_43,type,
    p2: pi ).

thf(func_def_44,type,
    q: pi ).

thf(func_def_45,type,
    qr: pi ).

thf(func_def_46,type,
    q2: pi ).

thf(func_def_47,type,
    r: pi ).

thf(func_def_48,type,
    rel: set(product_prod(pi,pi)) ).

thf(func_def_49,type,
    alpha: late_freeRes ).

thf(func_def_50,type,
    a: name ).

thf(func_def_51,type,
    x: name ).

thf(func_def_52,type,
    y: name ).

thf(func_def_56,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_57,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_58,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_59,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_60,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_61,type,
    vAND: $o > $o > $o ).

thf(func_def_62,type,
    vIMP: $o > $o > $o ).

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

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

thf(func_def_65,type,
    vNOT: $o > $o ).

thf(func_def_66,type,
    vOR: $o > $o > $o ).

thf(func_def_67,type,
    sP0: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_68,type,
    sP1: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_69,type,
    sP2: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_70,type,
    sP3: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_71,type,
    sP4: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_72,type,
    sP5: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_73,type,
    sP6: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_74,type,
    sP7: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_75,type,
    sP8: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_76,type,
    sP9: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_77,type,
    sP10: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_78,type,
    sP11: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_79,type,
    sP12: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_80,type,
    sP13: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > $o ) ).

thf(func_def_81,type,
    sP14: 
      !>[X0: $tType] : ( pi > X0 > pi > set(product_prod(pi,pi)) > $o ) ).

thf(func_def_82,type,
    sP15: 
      !>[X0: $tType] : ( pi > X0 > pi > name > set(product_prod(pi,pi)) > $o ) ).

thf(func_def_83,type,
    sP16: pi > pi > name > set(product_prod(pi,pi)) > $o ).

thf(func_def_84,type,
    sP17: pi > pi > set(product_prod(pi,pi)) > $o ).

thf(func_def_85,type,
    sP18: name > pi > late_residual > $o ).

thf(func_def_86,type,
    sP19: name > pi > late_residual > $o ).

thf(func_def_87,type,
    sP20: name > name > pi > late_residual > $o ).

thf(func_def_88,type,
    sP21: name > pi > late_subject > name > pi > $o ).

thf(func_def_89,type,
    sP22: pi > pi > late_subject > name > pi > $o ).

thf(func_def_90,type,
    sP23: pi > pi > late_subject > name > pi > $o ).

thf(func_def_91,type,
    sK24: late_subject > name ).

thf(func_def_92,type,
    sK25: late_subject > name ).

thf(func_def_93,type,
    sK26: late_freeRes > name ).

thf(func_def_94,type,
    sK27: late_freeRes > name ).

thf(func_def_95,type,
    sK28: 
      !>[X0: $tType] : ( X0 > name ) ).

thf(func_def_96,type,
    sK29: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_97,type,
    sK30: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_98,type,
    sK31: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_99,type,
    sK32: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_100,type,
    sK33: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_101,type,
    sK34: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_102,type,
    sK35: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_103,type,
    sK36: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_104,type,
    sK37: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_105,type,
    sK38: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_106,type,
    sK39: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_107,type,
    sK40: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_108,type,
    sK41: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_109,type,
    sK42: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_110,type,
    sK43: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_111,type,
    sK44: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_112,type,
    sK45: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_113,type,
    sK46: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_114,type,
    sK47: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_115,type,
    sK48: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_116,type,
    sK49: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_117,type,
    sK50: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_118,type,
    sK51: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_119,type,
    sK52: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_120,type,
    sK53: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_121,type,
    sK54: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_122,type,
    sK55: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_123,type,
    sK56: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_124,type,
    sK57: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_125,type,
    sK58: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_126,type,
    sK59: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_127,type,
    sK60: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_128,type,
    sK61: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_129,type,
    sK62: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_130,type,
    sK63: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_131,type,
    sK64: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_132,type,
    sK65: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_133,type,
    sK66: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_134,type,
    sK67: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_135,type,
    sK68: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_136,type,
    sK69: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_137,type,
    sK70: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_138,type,
    sK71: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_139,type,
    sK72: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_140,type,
    sK73: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_141,type,
    sK74: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_142,type,
    sK75: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_143,type,
    sK76: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_144,type,
    sK77: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_145,type,
    sK78: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_146,type,
    sK79: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_147,type,
    sK80: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_148,type,
    sK81: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_149,type,
    sK82: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_150,type,
    sK83: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_151,type,
    sK84: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_152,type,
    sK85: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > name ) ).

thf(func_def_153,type,
    sK86: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > pi ) ).

thf(func_def_154,type,
    sK87: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_155,type,
    sK88: 
      !>[X0: $tType] : ( ( X0 > pi > $o ) > X0 ) ).

thf(func_def_156,type,
    sK89: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > late_freeRes ) ).

thf(func_def_157,type,
    sK90: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > pi ) ).

thf(func_def_158,type,
    sK91: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > X0 ) ).

thf(func_def_159,type,
    sK92: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > late_subject ) ).

thf(func_def_160,type,
    sK93: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > name ) ).

thf(func_def_161,type,
    sK94: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > pi ) ).

thf(func_def_162,type,
    sK95: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > X0 ) ).

thf(func_def_163,type,
    sK96: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > late_freeRes ) ).

thf(func_def_164,type,
    sK97: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > pi ) ).

thf(func_def_165,type,
    sK98: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > X0 ) ).

thf(func_def_166,type,
    sK99: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > late_subject ) ).

thf(func_def_167,type,
    sK100: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > name ) ).

thf(func_def_168,type,
    sK101: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > pi ) ).

thf(func_def_169,type,
    sK102: 
      !>[X0: $tType] : ( ( X0 > late_residual > $o ) > X0 ) ).

thf(func_def_170,type,
    sK103: 
      !>[X0: $tType] : ( pi > X0 > pi > set(product_prod(pi,pi)) > late_subject ) ).

thf(func_def_171,type,
    sK104: 
      !>[X0: $tType] : ( pi > X0 > pi > set(product_prod(pi,pi)) > name ) ).

thf(func_def_172,type,
    sK105: 
      !>[X0: $tType] : ( pi > X0 > pi > set(product_prod(pi,pi)) > pi ) ).

thf(func_def_173,type,
    sK106: pi > pi > set(product_prod(pi,pi)) > late_freeRes ).

thf(func_def_174,type,
    sK107: pi > pi > set(product_prod(pi,pi)) > pi ).

thf(func_def_175,type,
    sK108: pi > pi > name > set(product_prod(pi,pi)) > pi ).

thf(func_def_176,type,
    sK109: pi > pi > name > set(product_prod(pi,pi)) > name ).

thf(func_def_177,type,
    sK110: 
      !>[X0: $tType] : ( pi > X0 > pi > name > set(product_prod(pi,pi)) > pi ) ).

thf(func_def_178,type,
    sK111: 
      !>[X0: $tType] : ( pi > X0 > pi > name > set(product_prod(pi,pi)) > late_subject ) ).

thf(func_def_179,type,
    sK112: 
      !>[X0: $tType] : ( pi > X0 > pi > name > set(product_prod(pi,pi)) > name ) ).

thf(func_def_180,type,
    sK113: pi > name > pi > set(product_prod(pi,pi)) > pi ).

thf(func_def_181,type,
    sK114: pi > name > pi > set(product_prod(pi,pi)) > late_freeRes ).

thf(func_def_182,type,
    sK115: ( late_subject > $o ) > name ).

thf(func_def_183,type,
    sK116: ( late_subject > $o ) > name ).

thf(func_def_184,type,
    sK117: set(product_prod(pi,pi)) > pi ).

thf(func_def_185,type,
    sK118: set(product_prod(pi,pi)) > pi ).

thf(func_def_186,type,
    sK119: ( late_freeRes > $o ) > name ).

thf(func_def_187,type,
    sK120: ( late_freeRes > $o ) > name ).

thf(func_def_188,type,
    sK121: ( late_residual > $o ) > late_freeRes ).

thf(func_def_189,type,
    sK122: ( late_residual > $o ) > pi ).

thf(func_def_190,type,
    sK123: ( late_residual > $o ) > late_subject ).

thf(func_def_191,type,
    sK124: ( late_residual > $o ) > name ).

thf(func_def_192,type,
    sK125: ( late_residual > $o ) > pi ).

thf(func_def_193,type,
    sK126: late_residual > pi > pi ).

thf(func_def_194,type,
    sK127: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_195,type,
    sK128: set(product_prod(pi,pi)) > pi ).

thf(func_def_196,type,
    sK129: set(product_prod(pi,pi)) > pi ).

thf(func_def_197,type,
    sK130: set(product_prod(pi,pi)) > name ).

thf(func_def_198,type,
    sK131: set(product_prod(pi,pi)) > pi ).

thf(func_def_199,type,
    sK132: set(product_prod(pi,pi)) > pi ).

thf(func_def_200,type,
    sK133: pi > pi > set(product_prod(pi,pi)) > late_subject ).

thf(func_def_201,type,
    sK134: pi > pi > set(product_prod(pi,pi)) > name ).

thf(func_def_202,type,
    sK135: pi > pi > set(product_prod(pi,pi)) > pi ).

thf(func_def_203,type,
    sK136: set(product_prod(pi,pi)) > pi > pi > late_freeRes ).

thf(func_def_204,type,
    sK137: set(product_prod(pi,pi)) > pi > pi > pi ).

thf(func_def_205,type,
    sK138: name > pi > late_residual > pi ).

thf(func_def_206,type,
    sK139: name > pi > late_residual > name ).

thf(func_def_207,type,
    sK140: name > pi > late_residual > name ).

thf(func_def_208,type,
    sK141: name > pi > late_residual > pi ).

thf(func_def_209,type,
    sK142: name > pi > late_residual > pi ).

thf(func_def_210,type,
    sK143: name > pi > late_residual > late_subject ).

thf(func_def_211,type,
    sK144: name > pi > late_residual > name ).

thf(func_def_212,type,
    sK145: name > pi > late_residual > pi ).

thf(func_def_213,type,
    sK146: name > pi > late_residual > name ).

thf(func_def_214,type,
    sK147: late_residual > pi > name > pi ).

thf(func_def_215,type,
    sK148: late_residual > pi > name > late_freeRes ).

thf(func_def_216,type,
    sK149: late_residual > pi > name > pi ).

thf(func_def_217,type,
    sK150: late_residual > pi > name > name ).

thf(func_def_218,type,
    sK151: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

thf(func_def_219,type,
    sK152: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

thf(func_def_220,type,
    sK153: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

thf(func_def_221,type,
    sK154: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

thf(func_def_222,type,
    sK155: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > name ) ).

thf(func_def_223,type,
    sK156: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > X0 ) ).

thf(func_def_224,type,
    sK157: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > name ) ).

thf(func_def_225,type,
    sK158: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > X0 ) ).

thf(func_def_226,type,
    sK159: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > name ) ).

thf(func_def_227,type,
    sK160: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > X0 ) ).

thf(func_def_228,type,
    sK161: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > name ) ).

thf(func_def_229,type,
    sK162: 
      !>[X0: $tType] : ( ( X0 > late_subject > $o ) > X0 ) ).

thf(func_def_230,type,
    sK163: 
      !>[X0: $tType] : ( ( name > name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_231,type,
    sK164: 
      !>[X0: $tType] : ( ( name > name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_232,type,
    sK165: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).

thf(func_def_233,type,
    sK166: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).

thf(func_def_234,type,
    sK167: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).

thf(func_def_235,type,
    sK168: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).

thf(func_def_236,type,
    sK169: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > X0 ) ).

thf(func_def_237,type,
    sK170: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > name ) ).

thf(func_def_238,type,
    sK171: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > name ) ).

thf(func_def_239,type,
    sK172: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > X0 ) ).

thf(func_def_240,type,
    sK173: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > X0 ) ).

thf(func_def_241,type,
    sK174: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > name ) ).

thf(func_def_242,type,
    sK175: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > name ) ).

thf(func_def_243,type,
    sK176: 
      !>[X0: $tType] : ( ( X0 > late_freeRes > $o ) > X0 ) ).

thf(func_def_244,type,
    sK177: late_residual > pi > name > name > pi ).

thf(func_def_245,type,
    sK178: name > name > pi > late_residual > pi ).

thf(func_def_246,type,
    sK179: name > name > pi > late_residual > name ).

thf(func_def_247,type,
    sK180: name > name > pi > late_residual > name ).

thf(func_def_248,type,
    sK181: late_residual > pi > name > name > name ).

thf(func_def_249,type,
    sK182: late_residual > pi > name > name > name ).

thf(func_def_250,type,
    sK183: late_residual > pi > name > name > pi ).

thf(func_def_251,type,
    sK184: late_residual > pi > name > name > name ).

thf(func_def_252,type,
    sK185: late_residual > pi > name > name > name ).

thf(func_def_253,type,
    sK186: late_residual > pi > name > name > pi ).

thf(func_def_254,type,
    sK187: pi > late_freeRes > pi > name > pi ).

thf(func_def_255,type,
    sK188: pi > late_freeRes > pi > name > late_freeRes ).

thf(func_def_256,type,
    sK189: pi > late_freeRes > pi > name > pi ).

thf(func_def_257,type,
    sK190: pi > late_freeRes > pi > name > name ).

thf(func_def_258,type,
    sK191: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

thf(func_def_259,type,
    sK192: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

thf(func_def_260,type,
    sK193: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

thf(func_def_261,type,
    sK194: 
      !>[X0: $tType] : ( ( name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_262,type,
    sK195: 
      !>[X0: $tType] : ( ( name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_263,type,
    sK196: 
      !>[X0: $tType] : ( ( name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_264,type,
    sK197: 
      !>[X0: $tType] : ( ( name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_265,type,
    sK198: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).

thf(func_def_266,type,
    sK199: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).

thf(func_def_267,type,
    sK200: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).

thf(func_def_268,type,
    sK201: pi > late_freeRes > set(product_prod(pi,pi)) > pi > pi ).

thf(func_def_269,type,
    sK202: ( pi > $o ) > late_freeRes > pi > name > pi ).

thf(func_def_270,type,
    sK203: name > pi > late_subject > name > pi > pi ).

thf(func_def_271,type,
    sK204: name > pi > late_subject > name > pi > late_subject ).

thf(func_def_272,type,
    sK205: name > pi > late_subject > name > pi > name ).

thf(func_def_273,type,
    sK206: name > pi > late_subject > name > pi > pi ).

thf(func_def_274,type,
    sK207: name > pi > late_subject > name > pi > name ).

thf(func_def_275,type,
    sK208: pi > name > late_subject > pi > name > pi ).

thf(func_def_276,type,
    sK209: pi > name > late_subject > pi > name > name ).

thf(func_def_277,type,
    sK210: pi > name > late_subject > pi > name > name ).

thf(func_def_278,type,
    sK211: pi > name > late_subject > pi > name > pi ).

thf(func_def_279,type,
    sK212: pi > pi > late_subject > name > pi > pi ).

thf(func_def_280,type,
    sK213: pi > pi > late_subject > name > pi > late_subject ).

thf(func_def_281,type,
    sK214: pi > pi > late_subject > name > pi > name ).

thf(func_def_282,type,
    sK215: pi > pi > late_subject > name > pi > pi ).

thf(func_def_283,type,
    sK216: pi > pi > late_subject > name > pi > pi ).

thf(func_def_284,type,
    sK217: pi > pi > late_subject > name > pi > pi ).

thf(func_def_285,type,
    sK218: pi > pi > late_subject > name > pi > late_subject ).

thf(func_def_286,type,
    sK219: pi > pi > late_subject > name > pi > name ).

thf(func_def_287,type,
    sK220: pi > pi > late_subject > name > pi > pi ).

thf(func_def_288,type,
    sK221: pi > pi > late_subject > name > pi > pi ).

thf(func_def_289,type,
    sK222: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

thf(func_def_290,type,
    sK223: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

thf(func_def_291,type,
    sK224: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

thf(func_def_292,type,
    sK225: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

thf(func_def_293,type,
    sK226: 
      !>[X0: $tType] : ( ( name > name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_294,type,
    sK227: 
      !>[X0: $tType] : ( ( name > name > X0 ) > ( X0 > $o ) > name ) ).

thf(func_def_295,type,
    sK228: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).

thf(func_def_296,type,
    sK229: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).

thf(func_def_297,type,
    sK230: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).

thf(func_def_298,type,
    sK231: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).

thf(func_def_299,type,
    sK232: pi > name > late_subject > set(product_prod(pi,pi)) > pi > pi ).

thf(func_def_300,type,
    sK233: ( pi > $o ) > name > late_subject > pi > pi > pi ).

thf(func_def_301,type,
    sK234: ( pi > $o ) > name > late_subject > pi > pi > pi ).

thf(func_def_302,type,
    sK235: 
      !>[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_303,type,
    sK236: 
      !>[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_304,type,
    sK237: 
      !>[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_305,type,
    sK238: 
      !>[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_306,type,
    sK239: 
      !>[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_307,type,
    sK240: 
      !>[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_308,type,
    sK241: 
      !>[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_309,type,
    sK242: 
      !>[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_310,type,
    sK243: 
      !>[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_311,type,
    sK244: 
      !>[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_312,type,
    sK245: 
      !>[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_313,type,
    sK246: 
      !>[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_314,type,
    sK247: 
      !>[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_315,type,
    sK248: 
      !>[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_316,type,
    sK249: 
      !>[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_317,type,
    sK250: 
      !>[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_318,type,
    sK251: 
      !>[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_319,type,
    sK252: 
      !>[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_320,type,
    sK253: 
      !>[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_321,type,
    sK254: 
      !>[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_322,type,
    sK255: 
      !>[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_323,type,
    sK256: 
      !>[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_324,type,
    sK257: 
      !>[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_325,type,
    sK258: 
      !>[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_326,type,
    sK259: 
      !>[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_327,type,
    sK260: 
      !>[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_328,type,
    sK261: 
      !>[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_329,type,
    sK262: 
      !>[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_330,type,
    sK263: 
      !>[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_331,type,
    sK264: 
      !>[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_332,type,
    sK265: 
      !>[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_333,type,
    sK266: 
      !>[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_334,type,
    sK267: 
      !>[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_335,type,
    sK268: 
      !>[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_336,type,
    sK269: 
      !>[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_337,type,
    sK270: 
      !>[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_339,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(f20666,plain,
    $false,
    inference(trivial_inequality_removal,[],[f20665]) ).

thf(f20665,plain,
    $true = $false,
    inference(backward_demodulation,[],[f1598,f20663]) ).

thf(f20663,plain,
    vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y)))),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) = $false,
    inference(trivial_inequality_removal,[],[f20656]) ).

thf(f20656,plain,
    ( ( $true != $true )
    | ( vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y)))),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) = $false ) ),
    inference(superposition,[],[f20432,f1911]) ).

thf(f1911,plain,
    $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y))))),
    inference(forward_demodulation,[],[f1596,f1196]) ).

thf(f1196,plain,
    alpha = late_TauR,
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    alpha = late_TauR,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_cClose2_Ohyps_I14_J) ).

thf(f1596,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y))))) = $true,
    inference(cnf_transformation,[],[f638]) ).

thf(f638,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y))))) = $true,
    inference(fool_elimination,[],[f637]) ).

thf(f637,plain,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y))))),
    inference(rectify,[],[f11]) ).

thf(f11,axiom,
    vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062) ).

thf(f20432,plain,
    ! [X0: pi] :
      ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),X0)) )
      | ( $false = vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) ) ),
    inference(trivial_inequality_removal,[],[f20423]) ).

thf(f20423,plain,
    ! [X0: pi] :
      ( ( $true != $true )
      | ( $false = vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),X0)) ) ),
    inference(superposition,[],[f1979,f1416]) ).

thf(f1416,plain,
    ! [X2: pi,X3: pi,X0: pi,X1: late_freeRes] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(cnf_transformation,[],[f833]) ).

thf(f833,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) ) ),
    inference(ennf_transformation,[],[f452]) ).

thf(f452,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2)) )
     => ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) ) ),
    inference(fool_elimination,[],[f451]) ).

thf(f451,plain,
    ! [X0: pi,X1: late_freeRes,X2: pi,X3: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X0),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),X2))
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X0),X3)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X1),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X2),X3))) ),
    inference(rectify,[],[f23]) ).

thf(f23,axiom,
    ! [X11: pi,X13: late_freeRes,X14: pi,X12: pi] :
      ( vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,X11),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),X14))
     => vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X11),X12)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,X13),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,X14),X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Par1F) ).

thf(f1979,plain,
    ! [X0: pi] :
      ( ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),X0)) )
      | ( $false = vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) ) ),
    inference(trivial_inequality_removal,[],[f1978]) ).

thf(f1978,plain,
    ! [X0: pi] :
      ( ( $true != $true )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),X0)) )
      | ( $false = vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) ) ),
    inference(superposition,[],[f1882,f270]) ).

thf(f270,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f1882,plain,
    ! [X0: pi] :
      ( ( $true != vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,alpha),X0)) ) ),
    inference(backward_demodulation,[],[f1192,f1196]) ).

thf(f1192,plain,
    ! [X0: pi] :
      ( ( $true != vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X0)) ) ),
    inference(cnf_transformation,[],[f752]) ).

thf(f752,plain,
    ! [X0: pi] :
      ( ( $true != vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) )
      | ( $true != vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X0)) ) ),
    inference(ennf_transformation,[],[f272]) ).

thf(f272,plain,
    ~ ? [X0: pi] :
        ( ( $true = vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) )
        & ( $true = vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X0)) ) ),
    inference(fool_elimination,[],[f271]) ).

thf(f271,plain,
    ~ ? [X0: pi] :
        ( vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X0),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel)
        & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X0)) ),
    inference(rectify,[],[f268]) ).

thf(f268,negated_conjecture,
    ~ ? [X97: pi] :
        ( vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X97),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel)
        & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X97)) ),
    inference(negated_conjecture,[],[f267]) ).

thf(f267,conjecture,
    ? [X97: pi] :
      ( vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),X97),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel)
      & vAPP(late_residual,$o,vAPP(pi,sTfun(late_residual,$o),late_transitions,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p),q)),r)),vAPP(pi,late_residual,vAPP(late_freeRes,sTfun(pi,late_residual),late_FreeR,late_TauR),X97)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f1598,plain,
    vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y)))),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) = $true,
    inference(cnf_transformation,[],[f642]) ).

thf(f642,plain,
    vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y)))),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel) = $true,
    inference(fool_elimination,[],[f641]) ).

thf(f641,plain,
    vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y)))),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    vAPP(set(product_prod(pi,pi)),$o,vAPP(product_prod(pi,pi),sTfun(set(product_prod(pi,pi)),$o),member(product_prod(pi,pi)),vAPP(pi,product_prod(pi,pi),vAPP(pi,sTfun(pi,product_prod(pi,pi)),product_Pair(pi,pi),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,q2),x),y)))),r)),vAPP(pi,pi,vAPP(name,sTfun(pi,pi),res,y),vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,p2),vAPP(name,pi,vAPP(name,sTfun(name,pi),vAPP(pi,sTfun(name,sTfun(name,pi)),subs,vAPP(pi,pi,vAPP(pi,sTfun(pi,pi),par,q2),r)),x),y))))),rel),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : ITP187^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31  % Computer : n028.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sat May 18 16:48:22 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.11/0.32  % (22925)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35  % (22928)WARNING: value z3 for option sas not known
% 0.11/0.35  % (22926)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35  % (22932)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)
% 0.11/0.35  % (22931)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)
% 0.11/0.35  % (22927)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35  % (22928)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)
% 0.11/0.35  % (22929)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35  % (22930)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  % (22932)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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
% 0.16/0.49  % (22934)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.54  % (22934)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.63/0.57  % Exception at run slice level
% 1.63/0.57  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.63/0.58  % (22935)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)
% 2.06/0.63  % (22935)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.11/1.79  % Exception at run slice level
% 10.11/1.79  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 10.11/1.80  % (22944)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)
% 10.44/1.84  % Exception at run slice level
% 10.44/1.84  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 10.44/1.86  % (22945)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)
% 21.48/3.42  % (22944)First to succeed.
% 21.48/3.42  % (22944)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22925"
% 21.48/3.43  % (22944)Refutation found. Thanks to Tanya!
% 21.48/3.43  % SZS status Theorem for theBenchmark
% 21.48/3.43  % SZS output start Proof for theBenchmark
% See solution above
% 21.48/3.43  % (22944)------------------------------
% 21.48/3.43  % (22944)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 21.48/3.43  % (22944)Termination reason: Refutation
% 21.48/3.43  
% 21.48/3.43  % (22944)Memory used [KB]: 7993
% 21.48/3.43  % (22944)Time elapsed: 1.618 s
% 21.48/3.43  % (22944)Instructions burned: 3589 (million)
% 21.48/3.43  % (22925)Success in time 3.102 s
%------------------------------------------------------------------------------