TSTP Solution File: ITP151^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP151^2 : 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 : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:53:49 EDT 2024

% Result   : Theorem 3.92s 0.91s
% Output   : Refutation 3.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  170
% Syntax   : Number of formulae    :  203 (  25 unt; 160 typ;   0 def)
%            Number of atoms       :  200 (  53 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :   44 (  21   ~;  10   |;   0   &;   0   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  302 ( 301   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  160 ( 157 usr;   4 con; 0-6 aty)
%            Number of variables   :  172 (   0   ^  35   !;   7   ?; 172   :)
%                                         ( 130  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    nat: $tType ).

thf(type_def_7,type,
    polyno1783536151e_poly: $tType > $tType ).

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

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

thf(func_def_0,type,
    polyno1783536151e_poly: $tType > $tType ).

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

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

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

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

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

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

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

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

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

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

thf(func_def_11,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

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

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

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

thf(func_def_15,type,
    semiring_char_0: 
      !>[X0: $tType] : $o ).

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

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

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

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

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

thf(func_def_21,type,
    semiring_1_cancel: 
      !>[X0: $tType] : $o ).

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

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

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

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

thf(func_def_26,type,
    cancel146912293up_add: 
      !>[X0: $tType] : $o ).

thf(func_def_27,type,
    linord1659791738miring: 
      !>[X0: $tType] : $o ).

thf(func_def_28,type,
    semiri134348788visors: 
      !>[X0: $tType] : $o ).

thf(func_def_29,type,
    archim1804426504_field: 
      !>[X0: $tType] : $o ).

thf(func_def_30,type,
    canoni770627133id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_31,type,
    condit1656338222tinuum: 
      !>[X0: $tType] : $o ).

thf(func_def_32,type,
    condit1037483654norder: 
      !>[X0: $tType] : $o ).

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

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

thf(func_def_35,type,
    suc: nat > nat ).

thf(func_def_36,type,
    semiring_1_of_nat: 
      !>[X0: $tType] : ( nat > X0 ) ).

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

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

thf(func_def_39,type,
    polyno498386536degree: 
      !>[X0: $tType] : ( polyno1783536151e_poly(X0) > nat ) ).

thf(func_def_40,type,
    polyno367318022egreen: 
      !>[X0: $tType] : ( polyno1783536151e_poly(X0) > nat > nat ) ).

thf(func_def_41,type,
    polyno2122670676snpoly: 
      !>[X0: $tType] : ( polyno1783536151e_poly(X0) > $o ) ).

thf(func_def_42,type,
    polyno86455060npolyh: 
      !>[X0: $tType] : ( polyno1783536151e_poly(X0) > nat > $o ) ).

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

thf(func_def_44,type,
    n: nat ).

thf(func_def_45,type,
    p: polyno1783536151e_poly(a) ).

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

thf(func_def_50,type,
    vNOT: $o > $o ).

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

thf(func_def_52,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_53,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_54,type,
    vAND: $o > $o > $o ).

thf(func_def_55,type,
    vIMP: $o > $o > $o ).

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

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

thf(func_def_58,type,
    vOR: $o > $o > $o ).

thf(func_def_59,type,
    sP0: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).

thf(func_def_60,type,
    sP1: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_61,type,
    sP2: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_62,type,
    sP3: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_63,type,
    sP4: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_64,type,
    sP5: nat > ( nat > $o ) > $o ).

thf(func_def_65,type,
    sP6: ( nat > nat > $o ) > $o ).

thf(func_def_66,type,
    sP7: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).

thf(func_def_67,type,
    sK8: nat > nat ).

thf(func_def_68,type,
    sK9: nat > nat ).

thf(func_def_69,type,
    sK10: nat > nat ).

thf(func_def_70,type,
    sK11: ( nat > $o ) > nat ).

thf(func_def_71,type,
    sK12: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_72,type,
    sK13: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_73,type,
    sK14: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_74,type,
    sK15: 
      !>[X0: $tType] : ( X0 > nat ) ).

thf(func_def_75,type,
    sK16: 
      !>[X0: $tType] : ( X0 > nat ) ).

thf(func_def_76,type,
    sK17: 
      !>[X0: $tType] : ( X0 > X0 > X0 > X0 ) ).

thf(func_def_77,type,
    sK18: 
      !>[X0: $tType] : ( X0 > X0 > X0 > X0 ) ).

thf(func_def_78,type,
    sK19: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_79,type,
    sK20: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_80,type,
    sK21: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_81,type,
    sK22: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_82,type,
    sK23: 
      !>[X0: $tType] : ( X0 > X0 > ( X0 > $o ) > X0 ) ).

thf(func_def_83,type,
    sK24: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > X0 ) ).

thf(func_def_84,type,
    sK25: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_85,type,
    sK26: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_86,type,
    sK27: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_87,type,
    sK28: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_88,type,
    sK29: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_89,type,
    sK30: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_90,type,
    sK31: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_91,type,
    sK32: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_92,type,
    sK33: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_93,type,
    sK34: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_94,type,
    sK35: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_95,type,
    sK36: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_96,type,
    sK37: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_97,type,
    sK38: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_98,type,
    sK39: int > nat ).

thf(func_def_99,type,
    sK40: int > nat ).

thf(func_def_100,type,
    sK41: int > nat ).

thf(func_def_101,type,
    sK42: int > nat ).

thf(func_def_102,type,
    sK43: nat > nat ).

thf(func_def_103,type,
    sK44: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_104,type,
    sK45: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_105,type,
    sK46: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_106,type,
    sK47: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_107,type,
    sK48: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_108,type,
    sK49: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_109,type,
    sK50: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_110,type,
    sK51: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_111,type,
    sK52: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_112,type,
    sK53: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_113,type,
    sK54: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_114,type,
    sK55: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_115,type,
    sK56: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_116,type,
    sK57: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_117,type,
    sK58: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_118,type,
    sK59: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_119,type,
    sK60: ( nat > $o ) > nat ).

thf(func_def_120,type,
    sK61: ( nat > $o ) > nat ).

thf(func_def_121,type,
    sK62: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_122,type,
    sK63: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_123,type,
    sK64: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_124,type,
    sK65: ( nat > $o ) > nat ).

thf(func_def_125,type,
    sK66: ( nat > $o ) > nat ).

thf(func_def_126,type,
    sK67: ( nat > $o ) > nat ).

thf(func_def_127,type,
    sK68: ( nat > $o ) > nat ).

thf(func_def_128,type,
    sK69: nat > nat > nat ).

thf(func_def_129,type,
    sK70: nat > nat > nat ).

thf(func_def_130,type,
    sK71: ( nat > nat > $o ) > nat ).

thf(func_def_131,type,
    sK72: ( nat > nat > $o ) > nat ).

thf(func_def_132,type,
    sK73: ( nat > nat > $o ) > nat ).

thf(func_def_133,type,
    sK74: ( nat > nat > $o ) > nat ).

thf(func_def_134,type,
    sK75: 
      !>[X0: $tType] : ( ( nat > X0 > X0 > $o ) > ( nat > X0 > $o ) > nat > X0 ) ).

thf(func_def_135,type,
    sK76: 
      !>[X0: $tType] : ( ( nat > X0 > X0 > $o ) > ( nat > X0 > $o ) > X0 ) ).

thf(func_def_136,type,
    sK77: 
      !>[X0: $tType] : ( ( nat > X0 > X0 > $o ) > ( nat > X0 > $o ) > nat ) ).

thf(func_def_137,type,
    sK78: nat > ( nat > $o ) > nat ).

thf(func_def_138,type,
    sK79: ( nat > $o ) > nat > nat ).

thf(func_def_139,type,
    sK80: ( nat > nat > $o ) > nat ).

thf(func_def_140,type,
    sK81: ( nat > nat > $o ) > nat ).

thf(func_def_141,type,
    sK82: ( nat > nat > $o ) > nat ).

thf(func_def_142,type,
    sK83: ( nat > nat > $o ) > nat ).

thf(func_def_143,type,
    sK84: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_144,type,
    sK85: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_145,type,
    sK86: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_146,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_147,type,
    sK87: nat > nat > nat ).

thf(func_def_148,type,
    sK88: nat > nat > nat ).

thf(func_def_149,type,
    sK89: ( nat > $o ) > nat > nat ).

thf(func_def_150,type,
    sK90: ( nat > $o ) > nat > nat ).

thf(func_def_151,type,
    sK91: ( nat > $o ) > nat > nat ).

thf(func_def_152,type,
    sK92: ( nat > $o ) > nat > nat ).

thf(func_def_153,type,
    sK93: ( nat > $o ) > nat > nat ).

thf(func_def_154,type,
    sK94: ( nat > $o ) > nat > nat ).

thf(func_def_155,type,
    sK95: ( nat > $o ) > nat > nat ).

thf(func_def_156,type,
    sK96: ( nat > $o ) > nat > nat ).

thf(func_def_157,type,
    sK97: nat > nat ).

thf(f17145,plain,
    $false,
    inference(subsumption_resolution,[],[f17133,f1355]) ).

thf(f1355,plain,
    vAPP(nat,$o,vAPP(polyno1783536151e_poly(a),sTfun(nat,$o),polyno86455060npolyh(a),p),n) = $true,
    inference(cnf_transformation,[],[f313]) ).

thf(f313,plain,
    vAPP(nat,$o,vAPP(polyno1783536151e_poly(a),sTfun(nat,$o),polyno86455060npolyh(a),p),n) = $true,
    inference(fool_elimination,[],[f312]) ).

thf(f312,plain,
    vAPP(nat,$o,vAPP(polyno1783536151e_poly(a),sTfun(nat,$o),polyno86455060npolyh(a),p),n),
    inference(rectify,[],[f303]) ).

thf(f303,axiom,
    vAPP(nat,$o,vAPP(polyno1783536151e_poly(a),sTfun(nat,$o),polyno86455060npolyh(a),p),n),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(f17133,plain,
    vAPP(nat,$o,vAPP(polyno1783536151e_poly(a),sTfun(nat,$o),polyno86455060npolyh(a),p),n) != $true,
    inference(superposition,[],[f17087,f6575]) ).

thf(f6575,plain,
    n = vAPP(nat,nat,suc,vAPP(nat,nat,sK8,n)),
    inference(superposition,[],[f2297,f6523]) ).

thf(f6523,plain,
    n = vAPP(nat,nat,suc,vAPP(nat,nat,sK43,n)),
    inference(unit_resulting_resolution,[],[f1354,f1554]) ).

thf(f1554,plain,
    ! [X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
      | ( vAPP(nat,nat,suc,vAPP(nat,nat,sK43,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1284]) ).

thf(f1284,plain,
    ! [X0: nat] :
      ( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK43,X0)) = X0 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f1109,f1283]) ).

thf(f1283,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
     => ( vAPP(nat,nat,suc,vAPP(nat,nat,sK43,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1109,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) ) ),
    inference(ennf_transformation,[],[f613]) ).

thf(f613,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
     => ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
    inference(fool_elimination,[],[f612]) ).

thf(f612,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)
     => ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
    inference(rectify,[],[f94]) ).

thf(f94,axiom,
    ! [X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X1)
     => ? [X34: nat] : ( vAPP(nat,nat,suc,X34) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_gr0__implies__Suc) ).

thf(f1354,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),n) = $true,
    inference(cnf_transformation,[],[f311]) ).

thf(f311,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),n) = $true,
    inference(fool_elimination,[],[f310]) ).

thf(f310,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),n),
    inference(rectify,[],[f302]) ).

thf(f302,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),n),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f2297,plain,
    ! [X0: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,vAPP(nat,nat,sK8,vAPP(nat,nat,suc,X0))) ),
    inference(unit_resulting_resolution,[],[f1360,f1374]) ).

thf(f1374,plain,
    ! [X0: nat] :
      ( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK8,X0)) = X0 )
      | ( zero_zero(nat) = X0 ) ),
    inference(cnf_transformation,[],[f1211]) ).

thf(f1211,plain,
    ! [X0: nat] :
      ( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK8,X0)) = X0 )
      | ( zero_zero(nat) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f924,f1210]) ).

thf(f1210,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
     => ( vAPP(nat,nat,suc,vAPP(nat,nat,sK8,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f924,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
      | ( zero_zero(nat) = X0 ) ),
    inference(ennf_transformation,[],[f878]) ).

thf(f878,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) != X0 )
     => ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
    inference(rectify,[],[f66]) ).

thf(f66,axiom,
    ! [X13: nat] :
      ( ( zero_zero(nat) != X13 )
     => ~ ! [X33: nat] : ( vAPP(nat,nat,suc,X33) != X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_old_Onat_Oexhaust) ).

thf(f1360,plain,
    ! [X0: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X0) ),
    inference(cnf_transformation,[],[f869]) ).

thf(f869,plain,
    ! [X0: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X0) ),
    inference(rectify,[],[f65]) ).

thf(f65,axiom,
    ! [X3: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Zero__not__Suc) ).

thf(f17087,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(polyno1783536151e_poly(a),sTfun(nat,$o),polyno86455060npolyh(a),p),vAPP(nat,nat,suc,X0)) ),
    inference(unit_resulting_resolution,[],[f1353,f1352,f1437]) ).

thf(f1437,plain,
    ! [X0: $tType,X2: nat,X1: polyno1783536151e_poly(X0)] :
      ( ( $true != vAPP(nat,$o,vAPP(polyno1783536151e_poly(X0),sTfun(nat,$o),polyno86455060npolyh(X0),X1),vAPP(nat,nat,suc,X2)) )
      | ( zero_zero(nat) = vAPP(polyno1783536151e_poly(X0),nat,polyno498386536degree(X0),X1) )
      | ( zero(X0) != $true ) ),
    inference(cnf_transformation,[],[f978]) ).

thf(f978,plain,
    ! [X0: $tType] :
      ( ! [X1: polyno1783536151e_poly(X0),X2: nat] :
          ( ( zero_zero(nat) = vAPP(polyno1783536151e_poly(X0),nat,polyno498386536degree(X0),X1) )
          | ( $true != vAPP(nat,$o,vAPP(polyno1783536151e_poly(X0),sTfun(nat,$o),polyno86455060npolyh(X0),X1),vAPP(nat,nat,suc,X2)) ) )
      | ( zero(X0) != $true ) ),
    inference(ennf_transformation,[],[f417]) ).

thf(f417,plain,
    ! [X0: $tType] :
      ( ( zero(X0) = $true )
     => ! [X1: polyno1783536151e_poly(X0),X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(polyno1783536151e_poly(X0),sTfun(nat,$o),polyno86455060npolyh(X0),X1),vAPP(nat,nat,suc,X2)) )
         => ( zero_zero(nat) = vAPP(polyno1783536151e_poly(X0),nat,polyno498386536degree(X0),X1) ) ) ),
    inference(fool_elimination,[],[f416]) ).

thf(f416,plain,
    ! [X0: $tType] :
      ( zero(X0)
     => ! [X1: polyno1783536151e_poly(X0),X2: nat] :
          ( vAPP(nat,$o,vAPP(polyno1783536151e_poly(X0),sTfun(nat,$o),polyno86455060npolyh(X0),X1),vAPP(nat,nat,suc,X2))
         => ( zero_zero(nat) = vAPP(polyno1783536151e_poly(X0),nat,polyno498386536degree(X0),X1) ) ) ),
    inference(rectify,[],[f34]) ).

thf(f34,axiom,
    ! [X0: $tType] :
      ( zero(X0)
     => ! [X20: polyno1783536151e_poly(X0),X1: nat] :
          ( vAPP(nat,$o,vAPP(polyno1783536151e_poly(X0),sTfun(nat,$o),polyno86455060npolyh(X0),X20),vAPP(nat,nat,suc,X1))
         => ( zero_zero(nat) = vAPP(polyno1783536151e_poly(X0),nat,polyno498386536degree(X0),X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_degree__isnpolyh__Suc) ).

thf(f1352,plain,
    zero_zero(nat) != vAPP(polyno1783536151e_poly(a),nat,polyno498386536degree(a),p),
    inference(cnf_transformation,[],[f866]) ).

thf(f866,plain,
    zero_zero(nat) != vAPP(polyno1783536151e_poly(a),nat,polyno498386536degree(a),p),
    inference(flattening,[],[f305]) ).

thf(f305,negated_conjecture,
    zero_zero(nat) != vAPP(polyno1783536151e_poly(a),nat,polyno498386536degree(a),p),
    inference(negated_conjecture,[],[f304]) ).

thf(f304,conjecture,
    zero_zero(nat) = vAPP(polyno1783536151e_poly(a),nat,polyno498386536degree(a),p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(f1353,plain,
    zero(a) = $true,
    inference(cnf_transformation,[],[f309]) ).

thf(f309,plain,
    zero(a) = $true,
    inference(fool_elimination,[],[f308]) ).

thf(f308,plain,
    zero(a),
    inference(rectify,[],[f301]) ).

thf(f301,axiom,
    zero(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : ITP151^2 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34  % Computer : n026.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Sat May 18 18:02:23 EDT 2024
% 0.15/0.34  % CPUTime    : 
% 0.15/0.35  % (9237)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (9240)WARNING: value z3 for option sas not known
% 0.15/0.38  % (9241)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (9242)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)
% 0.15/0.38  % (9238)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (9243)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)
% 0.15/0.38  % (9239)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (9240)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)
% 0.15/0.38  % (9244)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)
% 0.15/0.41  % (9244)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.41  % Exception at run slice level
% 0.15/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41  % Exception at run slice level
% 0.21/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41  % Exception at run slice level
% 0.21/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43  % (9245)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.43  % (9246)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)
% 0.21/0.43  % (9247)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)
% 0.21/0.45  % (9245)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.45  % (9246)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46  % Exception at run slice level
% 0.21/0.46  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.48  % (9248)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)
% 3.92/0.91  % (9246)First to succeed.
% 3.92/0.91  % (9246)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9237"
% 3.92/0.91  % (9246)Refutation found. Thanks to Tanya!
% 3.92/0.91  % SZS status Theorem for theBenchmark
% 3.92/0.91  % SZS output start Proof for theBenchmark
% See solution above
% 3.92/0.91  % (9246)------------------------------
% 3.92/0.91  % (9246)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.92/0.91  % (9246)Termination reason: Refutation
% 3.92/0.91  
% 3.92/0.91  % (9246)Memory used [KB]: 5044
% 3.92/0.91  % (9246)Time elapsed: 0.484 s
% 3.92/0.91  % (9246)Instructions burned: 1662 (million)
% 3.92/0.91  % (9237)Success in time 0.552 s
%------------------------------------------------------------------------------