TSTP Solution File: ITP156^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP156^2 : 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 : n006.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 22:54:11 EDT 2024

% Result   : Theorem 32.80s 5.07s
% Output   : Refutation 32.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :  195
% Syntax   : Number of formulae    :  354 (  61 unt; 169 typ;   0 def)
%            Number of atoms       : 1642 ( 270 equ;   0 cnn)
%            Maximal formula atoms :    4 (   8 avg)
%            Number of connectives :  302 ( 118   ~; 126   |;   3   &;   0   @)
%                                         (   3 <=>;  52  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  235 ( 232   >;   3   *;   0   +;   0  <<)
%            Number of symbols     :  176 ( 173 usr;  10 con; 0-8 aty)
%            Number of variables   :  592 (   0   ^ 194   !;   0   ?; 592   :)
%                                         ( 398  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(type_def_7,type,
    set: $tType > $tType ).

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

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

thf(func_def_0,type,
    product_prod: ( $tType * $tType ) > $tType ).

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

thf(func_def_2,type,
    set: $tType > $tType ).

thf(func_def_3,type,
    a: $tType ).

thf(func_def_4,type,
    ordere890947078_space: 
      !>[X0: $tType] : $o ).

thf(func_def_5,type,
    type: 
      !>[X0: $tType] : $o ).

thf(func_def_6,type,
    one: 
      !>[X0: $tType] : $o ).

thf(func_def_7,type,
    plus: 
      !>[X0: $tType] : $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_25,type,
    cancel1352612707id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_26,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

thf(func_def_27,type,
    ordere216010020id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_28,type,
    real_V1076094709vector: 
      !>[X0: $tType] : $o ).

thf(func_def_29,type,
    ordere779506340up_add: 
      !>[X0: $tType] : $o ).

thf(func_def_30,type,
    linord1659791738miring: 
      !>[X0: $tType] : $o ).

thf(func_def_31,type,
    canoni770627133id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_32,type,
    ordere1818651114id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_33,type,
    strict797366125id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_34,type,
    real_V55928688vector: 
      !>[X0: $tType] : $o ).

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

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

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

thf(func_def_38,type,
    real_V1587248058vector: 
      !>[X0: $tType] : $o ).

thf(func_def_39,type,
    unique1598680935umeral: 
      !>[X0: $tType] : $o ).

thf(func_def_40,type,
    ordere516151231imp_le: 
      !>[X0: $tType] : $o ).

thf(func_def_41,type,
    unique455577585es_aux: 
      !>[X0: $tType] : ( product_prod(X0,X0) > $o ) ).

thf(func_def_42,type,
    one_one: 
      !>[X0: $tType] : X0 ).

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

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

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

thf(func_def_46,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_47,type,
    prefer1289595409x_pref: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > $o ) ).

thf(func_def_48,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).

thf(func_def_49,type,
    product_rec_prod: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).

thf(func_def_50,type,
    real_V1908273582scaleR: 
      !>[X0: $tType] : ( real > X0 > X0 ) ).

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

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

thf(func_def_53,type,
    relation: set(product_prod(a,a)) ).

thf(func_def_54,type,
    u: real ).

thf(func_def_55,type,
    v: real ).

thf(func_def_56,type,
    x: a ).

thf(func_def_57,type,
    y: a ).

thf(func_def_61,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

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

thf(func_def_63,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_64,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_65,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

thf(func_def_67,type,
    vOR: $o > $o > $o ).

thf(func_def_68,type,
    vIMP: $o > $o > $o ).

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

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

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

thf(func_def_72,type,
    sP0: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_73,type,
    sP1: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_74,type,
    sP2: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_75,type,
    sP3: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_76,type,
    sP4: 
      !>[X0: $tType] : ( X0 > X0 > set(product_prod(X0,X0)) > $o ) ).

thf(func_def_77,type,
    sP5: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > $o ) ).

thf(func_def_78,type,
    sK6: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_79,type,
    sK7: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_80,type,
    sK8: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_81,type,
    sK9: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_82,type,
    sK10: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_83,type,
    sK11: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 > X0 ) ).

thf(func_def_84,type,
    sK12: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 > X0 ) ).

thf(func_def_85,type,
    sK13: 
      !>[X0: $tType] : ( X0 > X0 > set(product_prod(X0,X0)) > real ) ).

thf(func_def_86,type,
    sK14: 
      !>[X0: $tType] : ( X0 > X0 > set(product_prod(X0,X0)) > real ) ).

thf(func_def_87,type,
    sK15: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).

thf(func_def_88,type,
    sK16: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).

thf(func_def_89,type,
    sK17: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).

thf(func_def_90,type,
    sK18: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).

thf(func_def_91,type,
    sK19: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > real ) ).

thf(func_def_92,type,
    sK20: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > real ) ).

thf(func_def_93,type,
    sK21: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_94,type,
    sK22: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_95,type,
    sK23: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_96,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_97,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_98,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_99,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_100,type,
    sK28: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_101,type,
    sK29: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_102,type,
    sK30: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_103,type,
    sK31: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_104,type,
    sK32: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_105,type,
    sK33: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

thf(func_def_106,type,
    sK34: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

thf(func_def_107,type,
    sK35: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

thf(func_def_108,type,
    sK36: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

thf(func_def_109,type,
    sK37: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).

thf(func_def_110,type,
    sK38: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).

thf(func_def_111,type,
    sK39: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).

thf(func_def_112,type,
    sK40: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).

thf(func_def_113,type,
    sK41: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

thf(func_def_114,type,
    sK42: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

thf(func_def_115,type,
    sK43: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

thf(func_def_116,type,
    sK44: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).

thf(func_def_117,type,
    sK45: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).

thf(func_def_118,type,
    sK46: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).

thf(func_def_119,type,
    sK47: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

thf(func_def_120,type,
    sK48: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

thf(func_def_121,type,
    sK49: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

thf(func_def_122,type,
    sK50: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

thf(func_def_123,type,
    sK51: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).

thf(func_def_124,type,
    sK52: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).

thf(func_def_125,type,
    sK53: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).

thf(func_def_126,type,
    sK54: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).

thf(func_def_127,type,
    sK55: 
      !>[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_128,type,
    sK56: 
      !>[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_129,type,
    sK57: 
      !>[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_130,type,
    sK58: 
      !>[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_131,type,
    sK59: 
      !>[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_132,type,
    sK60: 
      !>[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_133,type,
    sK61: 
      !>[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_134,type,
    sK62: 
      !>[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_135,type,
    sK63: 
      !>[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_136,type,
    sK64: 
      !>[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_137,type,
    sK65: 
      !>[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_138,type,
    sK66: 
      !>[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_139,type,
    sK67: 
      !>[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_140,type,
    sK68: 
      !>[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_141,type,
    sK69: 
      !>[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_142,type,
    sK70: 
      !>[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_143,type,
    sK71: 
      !>[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_144,type,
    sK72: 
      !>[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_145,type,
    sK73: 
      !>[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_146,type,
    sK74: 
      !>[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_147,type,
    sK75: 
      !>[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_148,type,
    sK76: 
      !>[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_149,type,
    sK77: 
      !>[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_150,type,
    sK78: 
      !>[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_151,type,
    sK79: 
      !>[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_152,type,
    sK80: 
      !>[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_153,type,
    sK81: 
      !>[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_154,type,
    sK82: 
      !>[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_155,type,
    sK83: 
      !>[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_156,type,
    sK84: 
      !>[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_157,type,
    sK85: 
      !>[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_158,type,
    sK86: 
      !>[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_159,type,
    sK87: 
      !>[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_160,type,
    sK88: 
      !>[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_161,type,
    sK89: 
      !>[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_162,type,
    sK90: 
      !>[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_164,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_165,type,
    sK92: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > real ) > real ) ).

thf(func_def_166,type,
    sK93: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > real ) > real ) ).

thf(func_def_167,type,
    sK94: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(f83855,plain,
    $false,
    inference(avatar_sat_refutation,[],[f81580,f81704,f81722,f83852]) ).

thf(f83852,plain,
    ~ spl91_223,
    inference(avatar_contradiction_clause,[],[f83851]) ).

thf(f83851,plain,
    ( $false
    | ~ spl91_223 ),
    inference(trivial_inequality_removal,[],[f83850]) ).

thf(f83850,plain,
    ( ( $true = $false )
    | ~ spl91_223 ),
    inference(backward_demodulation,[],[f1870,f83849]) ).

thf(f83849,plain,
    ( ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),x),y)),relation) = $false )
    | ~ spl91_223 ),
    inference(forward_demodulation,[],[f83842,f4560]) ).

thf(f4560,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),X0),zero_zero(a)) = X0 ),
    inference(trivial_inequality_removal,[],[f4557]) ).

thf(f4557,plain,
    ! [X0: a] :
      ( ( $true != $true )
      | ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),X0),zero_zero(a)) = X0 ) ),
    inference(superposition,[],[f1546,f2281]) ).

thf(f2281,plain,
    $true = monoid_add(a),
    inference(trivial_inequality_removal,[],[f2276]) ).

thf(f2276,plain,
    ( ( $true != $true )
    | ( $true = monoid_add(a) ) ),
    inference(superposition,[],[f1722,f1493]) ).

thf(f1493,plain,
    real_V1076094709vector(a) = $true,
    inference(cnf_transformation,[],[f348]) ).

thf(f348,plain,
    real_V1076094709vector(a) = $true,
    inference(fool_elimination,[],[f347]) ).

thf(f347,plain,
    real_V1076094709vector(a),
    inference(rectify,[],[f340]) ).

thf(f340,axiom,
    real_V1076094709vector(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).

thf(f1722,plain,
    ! [X0: $tType] :
      ( ( real_V1076094709vector(X0) != $true )
      | ( monoid_add(X0) = $true ) ),
    inference(cnf_transformation,[],[f1277]) ).

thf(f1277,plain,
    ! [X0: $tType] :
      ( ( monoid_add(X0) = $true )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(ennf_transformation,[],[f750]) ).

thf(f750,plain,
    ! [X0: $tType] :
      ( ( real_V1076094709vector(X0) = $true )
     => ( monoid_add(X0) = $true ) ),
    inference(fool_elimination,[],[f749]) ).

thf(f749,plain,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => monoid_add(X0) ),
    inference(rectify,[],[f259]) ).

thf(f259,axiom,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => monoid_add(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Oreal__vector___Groups_Omonoid__add) ).

thf(f1546,plain,
    ! [X0: $tType,X1: X0] :
      ( ( monoid_add(X0) != $true )
      | ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
    inference(cnf_transformation,[],[f1067]) ).

thf(f1067,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
      | ( monoid_add(X0) != $true ) ),
    inference(ennf_transformation,[],[f428]) ).

thf(f428,plain,
    ! [X0: $tType] :
      ( ( monoid_add(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
    inference(fool_elimination,[],[f427]) ).

thf(f427,plain,
    ! [X0: $tType] :
      ( monoid_add(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
    inference(rectify,[],[f32]) ).

thf(f32,axiom,
    ! [X0: $tType] :
      ( monoid_add(X0)
     => ! [X7: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),zero_zero(X0)) = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add_Oright__neutral) ).

thf(f83842,plain,
    ( ( $false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),x),zero_zero(a))),y)),relation) )
    | ~ spl91_223 ),
    inference(backward_demodulation,[],[f2585,f83806]) ).

thf(f83806,plain,
    ( ! [X0: a] : ( zero_zero(a) = vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),X0) )
    | ~ spl91_223 ),
    inference(trivial_inequality_removal,[],[f83803]) ).

thf(f83803,plain,
    ( ! [X0: a] :
        ( ( $true != $true )
        | ( zero_zero(a) = vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),X0) ) )
    | ~ spl91_223 ),
    inference(superposition,[],[f81733,f1493]) ).

thf(f81733,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ( real_V1076094709vector(X0) != $true )
        | ( zero_zero(X0) = vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),v),X1) ) )
    | ~ spl91_223 ),
    inference(backward_demodulation,[],[f1693,f28709]) ).

thf(f28709,plain,
    ( ( zero_zero(real) = v )
    | ~ spl91_223 ),
    inference(avatar_component_clause,[],[f28707]) ).

thf(f28707,plain,
    ( spl91_223
  <=> ( zero_zero(real) = v ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_223])]) ).

thf(f1693,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),zero_zero(real)),X1) )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(cnf_transformation,[],[f1252]) ).

thf(f1252,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( zero_zero(X0) = vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),zero_zero(real)),X1) )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(ennf_transformation,[],[f712]) ).

thf(f712,plain,
    ! [X0: $tType] :
      ( ( real_V1076094709vector(X0) = $true )
     => ! [X1: X0] : ( zero_zero(X0) = vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),zero_zero(real)),X1) ) ),
    inference(fool_elimination,[],[f711]) ).

thf(f711,plain,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => ! [X1: X0] : ( zero_zero(X0) = vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),zero_zero(real)),X1) ) ),
    inference(rectify,[],[f115]) ).

thf(f115,axiom,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => ! [X3: X0] : ( zero_zero(X0) = vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),zero_zero(real)),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_scale__zero__left) ).

thf(f2585,plain,
    $false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),x),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation),
    inference(trivial_inequality_removal,[],[f2584]) ).

thf(f2584,plain,
    ( ( $true != $true )
    | ( $false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),x),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) ) ),
    inference(superposition,[],[f2205,f344]) ).

thf(f344,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f2205,plain,
    $true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),x),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation),
    inference(backward_demodulation,[],[f1492,f2204]) ).

thf(f2204,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),X0) = X0 ),
    inference(trivial_inequality_removal,[],[f2203]) ).

thf(f2203,plain,
    ! [X0: a] :
      ( ( $true != $true )
      | ( vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),X0) = X0 ) ),
    inference(superposition,[],[f2197,f1493]) ).

thf(f2197,plain,
    ! [X0: $tType,X1: X0] :
      ( ( real_V1076094709vector(X0) != $true )
      | ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),u),X1) = X1 ) ),
    inference(forward_demodulation,[],[f1692,f2190]) ).

thf(f2190,plain,
    u = one_one(real),
    inference(subsumption_resolution,[],[f2189,f2188]) ).

thf(f2188,plain,
    u != zero_zero(real),
    inference(subsumption_resolution,[],[f1495,f1492]) ).

thf(f1495,plain,
    ( ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true )
    | ( u != zero_zero(real) ) ),
    inference(cnf_transformation,[],[f1026]) ).

thf(f1026,plain,
    ( ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true )
    | ( u != zero_zero(real) ) ),
    inference(ennf_transformation,[],[f350]) ).

thf(f350,plain,
    ( ( u = zero_zero(real) )
   => ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true ) ),
    inference(fool_elimination,[],[f349]) ).

thf(f349,plain,
    ( ( u = zero_zero(real) )
   => vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) ),
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    ( ( u = zero_zero(real) )
   => vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_u__0) ).

thf(f2189,plain,
    ( ( u = one_one(real) )
    | ( u = zero_zero(real) ) ),
    inference(subsumption_resolution,[],[f1496,f1492]) ).

thf(f1496,plain,
    ( ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true )
    | ( u = one_one(real) )
    | ( u = zero_zero(real) ) ),
    inference(cnf_transformation,[],[f1028]) ).

thf(f1028,plain,
    ( ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true )
    | ( u = one_one(real) )
    | ( u = zero_zero(real) ) ),
    inference(flattening,[],[f1027]) ).

thf(f1027,plain,
    ( ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true )
    | ( u = one_one(real) )
    | ( u = zero_zero(real) ) ),
    inference(ennf_transformation,[],[f352]) ).

thf(f352,plain,
    ( ( ( u != one_one(real) )
      & ( u != zero_zero(real) ) )
   => ( vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) = $true ) ),
    inference(fool_elimination,[],[f351]) ).

thf(f351,plain,
    ( ( ( u != one_one(real) )
      & ( u != zero_zero(real) ) )
   => vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ( ( ( u != one_one(real) )
      & ( u != zero_zero(real) ) )
   => vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062) ).

thf(f1692,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(cnf_transformation,[],[f1251]) ).

thf(f1251,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(ennf_transformation,[],[f710]) ).

thf(f710,plain,
    ! [X0: $tType] :
      ( ( real_V1076094709vector(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 ) ),
    inference(fool_elimination,[],[f709]) ).

thf(f709,plain,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 ) ),
    inference(rectify,[],[f117]) ).

thf(f117,axiom,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => ! [X3: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X3) = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_scaleR__one) ).

thf(f1492,plain,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) != $true,
    inference(cnf_transformation,[],[f1003]) ).

thf(f1003,plain,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) != $true,
    inference(flattening,[],[f346]) ).

thf(f346,plain,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation) != $true,
    inference(fool_elimination,[],[f345]) ).

thf(f345,plain,
    ~ vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation),
    inference(rectify,[],[f342]) ).

thf(f342,negated_conjecture,
    ~ vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation),
    inference(negated_conjecture,[],[f341]) ).

thf(f341,conjecture,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus(a),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),u),x)),vAPP(a,a,vAPP(real,sTfun(a,a),real_V1908273582scaleR(a),v),y))),y)),relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f1870,plain,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),x),y)),relation) = $true,
    inference(cnf_transformation,[],[f1002]) ).

thf(f1002,plain,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),x),y)),relation) = $true,
    inference(fool_elimination,[],[f1001]) ).

thf(f1001,plain,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),x),y)),relation),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),x),y)),relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_assms_I2_J) ).

thf(f81722,plain,
    ( spl91_223
    | spl91_413
    | spl91_410 ),
    inference(avatar_split_clause,[],[f81677,f81434,f81625,f28707]) ).

thf(f81625,plain,
    ( spl91_413
  <=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),zero_zero(real)),v) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_413])]) ).

thf(f81434,plain,
    ( spl91_410
  <=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),v),zero_zero(real)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_410])]) ).

thf(f81677,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),zero_zero(real)),v) )
    | ( zero_zero(real) = v )
    | spl91_410 ),
    inference(trivial_inequality_removal,[],[f81652]) ).

thf(f81652,plain,
    ( ( $true = $false )
    | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),zero_zero(real)),v) )
    | ( zero_zero(real) = v )
    | spl91_410 ),
    inference(superposition,[],[f81619,f6435]) ).

thf(f6435,plain,
    ! [X0: real,X1: real] :
      ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),X0),X1) )
      | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),X1),X0) )
      | ( X0 = X1 ) ),
    inference(trivial_inequality_removal,[],[f6432]) ).

thf(f6432,plain,
    ! [X0: real,X1: real] :
      ( ( $true != $true )
      | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),X0),X1) )
      | ( X0 = X1 )
      | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),X1),X0) ) ),
    inference(superposition,[],[f1509,f1835]) ).

thf(f1835,plain,
    linordered_idom(real) = $true,
    inference(cnf_transformation,[],[f932]) ).

thf(f932,plain,
    linordered_idom(real) = $true,
    inference(fool_elimination,[],[f931]) ).

thf(f931,plain,
    linordered_idom(real),
    inference(rectify,[],[f303]) ).

thf(f303,axiom,
    linordered_idom(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom) ).

thf(f1509,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( linordered_idom(X0) != $true )
      | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
      | ( X1 = X2 )
      | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ),
    inference(cnf_transformation,[],[f1036]) ).

thf(f1036,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) )
          | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
          | ( X1 = X2 ) )
      | ( linordered_idom(X0) != $true ) ),
    inference(flattening,[],[f1035]) ).

thf(f1035,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) )
          | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
          | ( X1 = X2 ) )
      | ( linordered_idom(X0) != $true ) ),
    inference(ennf_transformation,[],[f1004]) ).

thf(f1004,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0) = $true )
     => ! [X1: X0,X2: X0] :
          ( ( X1 != X2 )
         => ( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
           => ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ) ),
    inference(flattening,[],[f378]) ).

thf(f378,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0) = $true )
     => ! [X1: X0,X2: X0] :
          ( ( X1 != X2 )
         => ( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
           => ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ) ),
    inference(fool_elimination,[],[f377]) ).

thf(f377,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0,X2: X0] :
          ( ( X1 != X2 )
         => ( ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)
           => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ),
    inference(rectify,[],[f161]) ).

thf(f161,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X3: X0,X4: X0] :
          ( ( X3 != X4 )
         => ( ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)
           => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_linorder__neqE__linordered__idom) ).

thf(f81619,plain,
    ( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),v),zero_zero(real)) )
    | spl91_410 ),
    inference(trivial_inequality_removal,[],[f81618]) ).

thf(f81618,plain,
    ( ( $true != $true )
    | ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),v),zero_zero(real)) )
    | spl91_410 ),
    inference(superposition,[],[f81435,f344]) ).

thf(f81435,plain,
    ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),v),zero_zero(real)) )
    | spl91_410 ),
    inference(avatar_component_clause,[],[f81434]) ).

thf(f81704,plain,
    ~ spl91_413,
    inference(avatar_contradiction_clause,[],[f81703]) ).

thf(f81703,plain,
    ( $false
    | ~ spl91_413 ),
    inference(trivial_inequality_removal,[],[f81702]) ).

thf(f81702,plain,
    ( ( $true = $false )
    | ~ spl91_413 ),
    inference(backward_demodulation,[],[f1854,f81701]) ).

thf(f81701,plain,
    ( ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(trivial_inequality_removal,[],[f81700]) ).

thf(f81700,plain,
    ( ( $true = $false )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(forward_demodulation,[],[f81699,f4875]) ).

thf(f4875,plain,
    $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),u),u),
    inference(trivial_inequality_removal,[],[f4874]) ).

thf(f4874,plain,
    ( ( $true != $true )
    | ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),u),u) ) ),
    inference(superposition,[],[f4873,f344]) ).

thf(f4873,plain,
    $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),u),u),
    inference(forward_demodulation,[],[f4872,f2190]) ).

thf(f4872,plain,
    $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),one_one(real)),one_one(real)),
    inference(trivial_inequality_removal,[],[f4869]) ).

thf(f4869,plain,
    ( ( $true != $true )
    | ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),one_one(real)),one_one(real)) ) ),
    inference(superposition,[],[f1588,f1854]) ).

thf(f1588,plain,
    ! [X0: $tType] :
      ( ( linord1659791738miring(X0) != $true )
      | ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),one_one(X0)),one_one(X0)) != $true ) ),
    inference(cnf_transformation,[],[f1114]) ).

thf(f1114,plain,
    ! [X0: $tType] :
      ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),one_one(X0)),one_one(X0)) != $true )
      | ( linord1659791738miring(X0) != $true ) ),
    inference(ennf_transformation,[],[f1007]) ).

thf(f1007,plain,
    ! [X0: $tType] :
      ( ( linord1659791738miring(X0) = $true )
     => ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),one_one(X0)),one_one(X0)) != $true ) ),
    inference(flattening,[],[f512]) ).

thf(f512,plain,
    ! [X0: $tType] :
      ( ( linord1659791738miring(X0) = $true )
     => ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),one_one(X0)),one_one(X0)) != $true ) ),
    inference(fool_elimination,[],[f511]) ).

thf(f511,plain,
    ! [X0: $tType] :
      ( linord1659791738miring(X0)
     => ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),one_one(X0)),one_one(X0)) ),
    inference(rectify,[],[f235]) ).

thf(f235,axiom,
    ! [X0: $tType] :
      ( linord1659791738miring(X0)
     => ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),one_one(X0)),one_one(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_less__numeral__extra_I4_J) ).

thf(f81699,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),u),u) )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(forward_demodulation,[],[f81698,f4561]) ).

thf(f4561,plain,
    ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),zero_zero(real)) = X0 ),
    inference(trivial_inequality_removal,[],[f4556]) ).

thf(f4556,plain,
    ! [X0: real] :
      ( ( $true != $true )
      | ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),zero_zero(real)) = X0 ) ),
    inference(superposition,[],[f1546,f1844]) ).

thf(f1844,plain,
    monoid_add(real) = $true,
    inference(cnf_transformation,[],[f950]) ).

thf(f950,plain,
    monoid_add(real) = $true,
    inference(fool_elimination,[],[f949]) ).

thf(f949,plain,
    monoid_add(real),
    inference(rectify,[],[f309]) ).

thf(f309,axiom,
    monoid_add(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_13) ).

thf(f81698,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),u),zero_zero(real))),u) )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(forward_demodulation,[],[f81697,f2577]) ).

thf(f2577,plain,
    ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X1),X0) ),
    inference(forward_demodulation,[],[f2576,f2207]) ).

thf(f2207,plain,
    ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X0) = X0 ),
    inference(trivial_inequality_removal,[],[f2206]) ).

thf(f2206,plain,
    ! [X0: real] :
      ( ( $true != $true )
      | ( vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X0) = X0 ) ),
    inference(superposition,[],[f2195,f1865]) ).

thf(f1865,plain,
    real_V55928688vector(real) = $true,
    inference(cnf_transformation,[],[f992]) ).

thf(f992,plain,
    real_V55928688vector(real) = $true,
    inference(fool_elimination,[],[f991]) ).

thf(f991,plain,
    real_V55928688vector(real),
    inference(rectify,[],[f289]) ).

thf(f289,axiom,
    real_V55928688vector(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector) ).

thf(f2195,plain,
    ! [X0: $tType,X1: X0] :
      ( ( real_V55928688vector(X0) != $true )
      | ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),u),X1) = X1 ) ),
    inference(forward_demodulation,[],[f1672,f2190]) ).

thf(f1672,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 )
      | ( real_V55928688vector(X0) != $true ) ),
    inference(cnf_transformation,[],[f1231]) ).

thf(f1231,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 )
      | ( real_V55928688vector(X0) != $true ) ),
    inference(ennf_transformation,[],[f670]) ).

thf(f670,plain,
    ! [X0: $tType] :
      ( ( real_V55928688vector(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 ) ),
    inference(fool_elimination,[],[f669]) ).

thf(f669,plain,
    ! [X0: $tType] :
      ( real_V55928688vector(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X1) = X1 ) ),
    inference(rectify,[],[f72]) ).

thf(f72,axiom,
    ! [X0: $tType] :
      ( real_V55928688vector(X0)
     => ! [X3: X0] : ( vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),one_one(real)),X3) = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_pth__1) ).

thf(f2576,plain,
    ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X1),X0) ),
    inference(forward_demodulation,[],[f2572,f2207]) ).

thf(f2572,plain,
    ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X1),vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X0)) ),
    inference(trivial_inequality_removal,[],[f2559]) ).

thf(f2559,plain,
    ! [X0: real,X1: real] :
      ( ( $true != $true )
      | ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X1),vAPP(real,real,vAPP(real,sTfun(real,real),real_V1908273582scaleR(real),u),X0)) ) ),
    inference(superposition,[],[f2557,f1866]) ).

thf(f1866,plain,
    real_V1076094709vector(real) = $true,
    inference(cnf_transformation,[],[f994]) ).

thf(f994,plain,
    real_V1076094709vector(real) = $true,
    inference(fool_elimination,[],[f993]) ).

thf(f993,plain,
    real_V1076094709vector(real),
    inference(rectify,[],[f294]) ).

thf(f294,axiom,
    real_V1076094709vector(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector) ).

thf(f2557,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( real_V1076094709vector(X0) != $true )
      | ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),u),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),u),X1)) ) ),
    inference(equality_resolution,[],[f2200]) ).

thf(f2200,plain,
    ! [X0: $tType,X2: real,X3: X0,X1: X0] :
      ( ( u != X2 )
      | ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1)) )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(forward_demodulation,[],[f1940,f2190]) ).

thf(f1940,plain,
    ! [X0: $tType,X2: real,X3: X0,X1: X0] :
      ( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1)) )
      | ( real_V1076094709vector(X0) != $true )
      | ( one_one(real) != X2 ) ),
    inference(equality_proxy_clausification,[],[f1937]) ).

thf(f1937,plain,
    ! [X0: $tType,X2: real,X3: X0,X1: X0] :
      ( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1)) )
      | ( real_V1076094709vector(X0) != $true )
      | ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),one_one(real)),X2) ) ),
    inference(binary_proxy_clausification,[],[f1936]) ).

thf(f1936,plain,
    ! [X0: $tType,X2: real,X3: X0,X1: X0] :
      ( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1)) )
      | ( real_V1076094709vector(X0) != $true )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),one_one(real)),X2)) ) ),
    inference(equality_proxy_clausification,[],[f1930]) ).

thf(f1930,plain,
    ! [X0: $tType,X2: real,X3: X0,X1: X0] :
      ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1))) )
      | ( real_V1076094709vector(X0) != $true )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),one_one(real)),X2)) ) ),
    inference(binary_proxy_clausification,[],[f1714]) ).

thf(f1714,plain,
    ! [X0: $tType,X2: real,X3: X0,X1: X0] :
      ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),one_one(real)),X2)) )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(cnf_transformation,[],[f1265]) ).

thf(f1265,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: real,X3: X0] : ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),one_one(real)),X2)) )
      | ( real_V1076094709vector(X0) != $true ) ),
    inference(ennf_transformation,[],[f734]) ).

thf(f734,plain,
    ! [X0: $tType] :
      ( ( real_V1076094709vector(X0) = $true )
     => ! [X1: X0,X2: real,X3: X0] : ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1))) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)),vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),one_one(real)),X2)) ) ),
    inference(fool_elimination,[],[f733]) ).

thf(f733,plain,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => ! [X1: X0,X2: real,X3: X0] :
          ( ( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X2),X1)) )
            = ( one_one(real) = X2 ) )
          | ( X1 = X3 ) ) ),
    inference(rectify,[],[f114]) ).

thf(f114,axiom,
    ! [X0: $tType] :
      ( real_V1076094709vector(X0)
     => ! [X8: X0,X52: real,X7: X0] :
          ( ( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X52),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),vAPP(X0,X0,vAPP(real,sTfun(X0,X0),real_V1908273582scaleR(X0),X52),X8)) )
            = ( one_one(real) = X52 ) )
          | ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_scaleR__eq__iff) ).

thf(f81697,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),zero_zero(real)),u)),u) )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(forward_demodulation,[],[f81696,f2580]) ).

thf(f2580,plain,
    u = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),v),u),
    inference(superposition,[],[f2577,f2191]) ).

thf(f2191,plain,
    u = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),u),v),
    inference(backward_demodulation,[],[f1494,f2190]) ).

thf(f1494,plain,
    one_one(real) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),u),v),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,axiom,
    one_one(real) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),u),v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_assms_I5_J) ).

thf(f81696,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),zero_zero(real)),u)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),v),u)) )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(forward_demodulation,[],[f81689,f2190]) ).

thf(f81689,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),zero_zero(real)),one_one(real))),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),v),one_one(real))) )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(trivial_inequality_removal,[],[f81682]) ).

thf(f81682,plain,
    ( ( $true != $true )
    | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),zero_zero(real)),one_one(real))),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),v),one_one(real))) )
    | ( linord1659791738miring(real) = $false )
    | ~ spl91_413 ),
    inference(superposition,[],[f8392,f81627]) ).

thf(f81627,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),zero_zero(real)),v) )
    | ~ spl91_413 ),
    inference(avatar_component_clause,[],[f81625]) ).

thf(f8392,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
      | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),one_one(X0))) )
      | ( linord1659791738miring(X0) = $false ) ),
    inference(trivial_inequality_removal,[],[f8391]) ).

thf(f8391,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( $true != $true )
      | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
      | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),one_one(X0))) )
      | ( linord1659791738miring(X0) = $false ) ),
    inference(superposition,[],[f1592,f344]) ).

thf(f1592,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( linord1659791738miring(X0) != $true )
      | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
      | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),one_one(X0))) ) ),
    inference(cnf_transformation,[],[f1118]) ).

thf(f1118,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),one_one(X0))) )
          | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) ) )
      | ( linord1659791738miring(X0) != $true ) ),
    inference(ennf_transformation,[],[f520]) ).

thf(f520,plain,
    ! [X0: $tType] :
      ( ( linord1659791738miring(X0) = $true )
     => ! [X1: X0,X2: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
         => ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),one_one(X0))) ) ) ),
    inference(fool_elimination,[],[f519]) ).

thf(f519,plain,
    ! [X0: $tType] :
      ( linord1659791738miring(X0)
     => ! [X1: X0,X2: X0] :
          ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)
         => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),one_one(X0))) ) ),
    inference(rectify,[],[f185]) ).

thf(f185,axiom,
    ! [X0: $tType] :
      ( linord1659791738miring(X0)
     => ! [X7: X0,X8: X0] :
          ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X8)
         => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),one_one(X0))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),one_one(X0))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_add__mono1) ).

thf(f1854,plain,
    linord1659791738miring(real) = $true,
    inference(cnf_transformation,[],[f970]) ).

thf(f970,plain,
    linord1659791738miring(real) = $true,
    inference(fool_elimination,[],[f969]) ).

thf(f969,plain,
    linord1659791738miring(real),
    inference(rectify,[],[f292]) ).

thf(f292,axiom,
    linord1659791738miring(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring) ).

thf(f81580,plain,
    ~ spl91_410,
    inference(avatar_contradiction_clause,[],[f81579]) ).

thf(f81579,plain,
    ( $false
    | ~ spl91_410 ),
    inference(trivial_inequality_removal,[],[f81578]) ).

thf(f81578,plain,
    ( ( $true = $false )
    | ~ spl91_410 ),
    inference(forward_demodulation,[],[f81527,f4875]) ).

thf(f81527,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),u),u) )
    | ~ spl91_410 ),
    inference(superposition,[],[f81518,f2191]) ).

thf(f81518,plain,
    ( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),v)),X0) )
    | ~ spl91_410 ),
    inference(forward_demodulation,[],[f81517,f4561]) ).

thf(f81517,plain,
    ( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),v)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),zero_zero(real))) )
    | ~ spl91_410 ),
    inference(trivial_inequality_removal,[],[f81504]) ).

thf(f81504,plain,
    ( ! [X0: real] :
        ( ( $true != $true )
        | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),v)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X0),zero_zero(real))) ) )
    | ~ spl91_410 ),
    inference(superposition,[],[f8162,f81436]) ).

thf(f81436,plain,
    ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),v),zero_zero(real)) )
    | ~ spl91_410 ),
    inference(avatar_component_clause,[],[f81434]) ).

thf(f8162,plain,
    ! [X2: real,X0: real,X1: real] :
      ( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),X0),X1) )
      | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X2),X1)) ) ),
    inference(trivial_inequality_removal,[],[f8157]) ).

thf(f8157,plain,
    ! [X2: real,X0: real,X1: real] :
      ( ( $true != $true )
      | ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),X0),X1) )
      | ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus(real),X2),X1)) ) ),
    inference(superposition,[],[f1594,f1855]) ).

thf(f1855,plain,
    ordere223160158up_add(real) = $true,
    inference(cnf_transformation,[],[f972]) ).

thf(f972,plain,
    ordere223160158up_add(real) = $true,
    inference(fool_elimination,[],[f971]) ).

thf(f971,plain,
    ordere223160158up_add(real),
    inference(rectify,[],[f287]) ).

thf(f287,axiom,
    ordere223160158up_add(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add) ).

thf(f1594,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ( ordere223160158up_add(X0) != $true )
      | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
      | ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) ) ),
    inference(cnf_transformation,[],[f1120]) ).

thf(f1120,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) )
          | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) ) )
      | ( ordere223160158up_add(X0) != $true ) ),
    inference(ennf_transformation,[],[f524]) ).

thf(f524,plain,
    ! [X0: $tType] :
      ( ( ordere223160158up_add(X0) = $true )
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
         => ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) ) ) ),
    inference(fool_elimination,[],[f523]) ).

thf(f523,plain,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)
         => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) ) ),
    inference(rectify,[],[f165]) ).

thf(f165,axiom,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X7: X0,X8: X0,X9: X0] :
          ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X8)
         => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X7)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X9),X8)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_add__strict__left__mono) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ITP156^2 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n006.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat May 18 16:06:23 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (16406)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (16422)WARNING: value z3 for option sas not known
% 0.15/0.39  % (16425)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40  % (16420)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40  % (16422)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.40  % (16424)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.40  % (16421)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40  % (16426)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.40  % (16423)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.43  % (16426)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.44  % Exception at run slice level
% 0.21/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44  % Exception at run slice level
% 0.21/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44  % Exception at run slice level
% 0.21/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.46  % (16449)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.46  % (16450)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.46  % (16451)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.49  % (16449)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.49  % (16450)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.50  % Exception at run slice level
% 0.21/0.50  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.51  % (16475)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)
% 32.80/5.05  % (16451)First to succeed.
% 32.80/5.06  % (16451)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16406"
% 32.80/5.07  % (16451)Refutation found. Thanks to Tanya!
% 32.80/5.07  % SZS status Theorem for theBenchmark
% 32.80/5.07  % SZS output start Proof for theBenchmark
% See solution above
% 32.80/5.07  % (16451)------------------------------
% 32.80/5.07  % (16451)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 32.80/5.07  % (16451)Termination reason: Refutation
% 32.80/5.07  
% 32.80/5.07  % (16451)Memory used [KB]: 28195
% 32.80/5.07  % (16451)Time elapsed: 4.607 s
% 32.80/5.07  % (16451)Instructions burned: 17287 (million)
% 32.80/5.07  % (16406)Success in time 4.69 s
%------------------------------------------------------------------------------