TSTP Solution File: DAT137^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT137^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 19:51:36 EDT 2024

% Result   : Theorem 11.68s 1.98s
% Output   : Refutation 11.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  199
% Syntax   : Number of formulae    :  218 (  18 unt; 194 typ;   0 def)
%            Number of atoms       :  314 (  25 equ;   0 cnn)
%            Maximal formula atoms :    2 (  13 avg)
%            Number of connectives :   16 (  10   ~;   3   |;   0   &;   0   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  395 ( 394   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  193 ( 190 usr;   5 con; 0-6 aty)
%            Number of variables   :  199 (   0   ^  30   !;   0   ?; 199   :)
%                                         ( 169  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

thf(type_def_8,type,
    coindu1593790203_llist: $tType > $tType ).

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

thf(type_def_10,type,
    list: $tType > $tType ).

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

thf(func_def_0,type,
    coindu1593790203_llist: $tType > $tType ).

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

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

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

thf(func_def_4,type,
    nat: $tType ).

thf(func_def_5,type,
    itself: $tType > $tType ).

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

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

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

thf(func_def_9,type,
    ring_1: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

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

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

thf(func_def_12,type,
    ring_char_0: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

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

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

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

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

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

thf(func_def_18,type,
    semiring_char_0: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

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

thf(func_def_20,type,
    comm_semiring_1: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

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

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

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

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

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

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

thf(func_def_27,type,
    ordere779506340up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_28,type,
    ordere236663937imp_le: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_29,type,
    ordere223160158up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_30,type,
    strict2144017051up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

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

thf(func_def_32,type,
    coindu493225792length: 
      !>[X0: $tType] : ( nat > coindu1593790203_llist(X0) > extended_enat ) ).

thf(func_def_33,type,
    coindu1542816657of_aux: 
      !>[X0: $tType] : ( list(X0) > coindu1593790203_llist(X0) > list(X0) ) ).

thf(func_def_34,type,
    coindu1121789889_LCons: 
      !>[X0: $tType] : ( X0 > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).

thf(func_def_35,type,
    coindu1598213697e_LNil: 
      !>[X0: $tType] : coindu1593790203_llist(X0) ).

thf(func_def_36,type,
    coindu1079202755ist_of: 
      !>[X0: $tType] : ( list(X0) > coindu1593790203_llist(X0) ) ).

thf(func_def_37,type,
    coindu567634248member: 
      !>[X0: $tType] : ( X0 > coindu1593790203_llist(X0) > $o ) ).

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

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

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

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

thf(func_def_42,type,
    count_list: 
      !>[X0: $tType] : ( list(X0) > X0 > nat ) ).

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

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

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

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

thf(func_def_47,type,
    nth: 
      !>[X0: $tType] : ( list(X0) > nat > X0 ) ).

thf(func_def_48,type,
    ord_lexordp_eq: 
      !>[X0: $tType] : ( list(X0) > list(X0) > $o ) ).

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

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

thf(func_def_51,type,
    upt: nat > nat > list(nat) ).

thf(func_def_52,type,
    suc: nat > nat ).

thf(func_def_53,type,
    nat_triangle: nat > nat ).

thf(func_def_54,type,
    bitM: num > num ).

thf(func_def_55,type,
    inc: num > num ).

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

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

thf(func_def_58,type,
    neg_numeral_sub: 
      !>[X0: $tType] : ( num > num > X0 ) ).

thf(func_def_59,type,
    bit0: num > num ).

thf(func_def_60,type,
    one2: num ).

thf(func_def_61,type,
    numeral_numeral: 
      !>[X0: $tType] : ( num > X0 ) ).

thf(func_def_62,type,
    ring_1_iszero: 
      !>[X0: $tType] : ( X0 > $o ) ).

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

thf(func_def_64,type,
    type2: 
      !>[X0: $tType] : itself(X0) ).

thf(func_def_65,type,
    prefixes: 
      !>[X0: $tType] : ( list(X0) > list(list(X0)) ) ).

thf(func_def_66,type,
    ma: nat ).

thf(func_def_67,type,
    na: nat ).

thf(func_def_71,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_72,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_73,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

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

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

thf(func_def_76,type,
    vNOT: $o > $o ).

thf(func_def_77,type,
    vOR: $o > $o > $o ).

thf(func_def_78,type,
    vAND: $o > $o > $o ).

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

thf(func_def_80,type,
    sP0: 
      !>[X0: $tType] : ( list(X0) > X0 > X0 > list(X0) > $o ) ).

thf(func_def_81,type,
    sP1: 
      !>[X0: $tType] : ( list(X0) > list(X0) > $o ) ).

thf(func_def_82,type,
    sP2: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > $o ) ).

thf(func_def_83,type,
    sP3: nat > ( nat > $o ) > $o ).

thf(func_def_84,type,
    sP4: ( nat > nat > $o ) > $o ).

thf(func_def_85,type,
    sK5: list(nat) > nat ).

thf(func_def_86,type,
    sK6: list(nat) > list(nat) ).

thf(func_def_87,type,
    sK7: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_88,type,
    sK8: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_89,type,
    sK9: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_90,type,
    sK10: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_91,type,
    sK11: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_92,type,
    sK12: 
      !>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).

thf(func_def_93,type,
    sK13: 
      !>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).

thf(func_def_94,type,
    sK14: 
      !>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).

thf(func_def_95,type,
    sK15: 
      !>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).

thf(func_def_96,type,
    sK16: 
      !>[X0: $tType] : ( list(X0) > X0 > X0 > list(X0) > list(X0) ) ).

thf(func_def_97,type,
    sK17: 
      !>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).

thf(func_def_98,type,
    sK18: 
      !>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).

thf(func_def_99,type,
    sK19: 
      !>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).

thf(func_def_100,type,
    sK20: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

thf(func_def_101,type,
    sK21: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_102,type,
    sK22: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_103,type,
    sK23: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_104,type,
    sK24: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_105,type,
    sK25: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_106,type,
    sK26: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_107,type,
    sK27: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_108,type,
    sK28: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_109,type,
    sK29: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_110,type,
    sK30: 
      !>[X0: $tType] : ( coindu1593790203_llist(X0) > X0 ) ).

thf(func_def_111,type,
    sK31: 
      !>[X0: $tType] : ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).

thf(func_def_112,type,
    sK32: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

thf(func_def_113,type,
    sK33: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

thf(func_def_114,type,
    sK34: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

thf(func_def_115,type,
    sK35: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

thf(func_def_116,type,
    sK36: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

thf(func_def_117,type,
    sK37: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

thf(func_def_118,type,
    sK38: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

thf(func_def_119,type,
    sK39: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

thf(func_def_120,type,
    sK40: 
      !>[X0: $tType] : ( list(list(X0)) > X0 ) ).

thf(func_def_121,type,
    sK41: 
      !>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).

thf(func_def_122,type,
    sK42: 
      !>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).

thf(func_def_123,type,
    sK43: 
      !>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).

thf(func_def_124,type,
    sK44: ( nat > $o ) > nat ).

thf(func_def_125,type,
    sK45: ( extended_enat > $o ) > extended_enat ).

thf(func_def_126,type,
    sK46: ( nat > $o ) > nat ).

thf(func_def_127,type,
    sK47: ( num > $o ) > num ).

thf(func_def_128,type,
    sK48: ( list(nat) > $o ) > nat ).

thf(func_def_129,type,
    sK49: ( list(nat) > $o ) > list(nat) ).

thf(func_def_130,type,
    sK50: nat > nat > nat ).

thf(func_def_131,type,
    sK51: nat > nat > nat ).

thf(func_def_132,type,
    sK52: nat > nat > nat ).

thf(func_def_133,type,
    sK53: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_134,type,
    sK54: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).

thf(func_def_135,type,
    sK55: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_136,type,
    sK56: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_137,type,
    sK57: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_138,type,
    sK58: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).

thf(func_def_139,type,
    sK59: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_140,type,
    sK60: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_141,type,
    sK61: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).

thf(func_def_142,type,
    sK62: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).

thf(func_def_143,type,
    sK63: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).

thf(func_def_144,type,
    sK64: nat > ( nat > $o ) > nat ).

thf(func_def_145,type,
    sK65: ( nat > $o ) > nat > nat ).

thf(func_def_146,type,
    sK66: ( nat > nat > $o ) > nat ).

thf(func_def_147,type,
    sK67: ( nat > nat > $o ) > nat ).

thf(func_def_148,type,
    sK68: ( nat > nat > $o ) > nat ).

thf(func_def_149,type,
    sK69: ( nat > nat > $o ) > nat ).

thf(func_def_150,type,
    sK70: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_151,type,
    sK71: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_152,type,
    sK72: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_153,type,
    sK73: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_154,type,
    sK74: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_155,type,
    sK75: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_156,type,
    sK76: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_157,type,
    sK77: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_158,type,
    sK78: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_159,type,
    sK79: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_160,type,
    sK80: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_161,type,
    sK81: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_162,type,
    sK82: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_163,type,
    sK83: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_164,type,
    sK84: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).

thf(func_def_165,type,
    sK85: 
      !>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).

thf(func_def_166,type,
    sK86: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X0 ) ).

thf(func_def_167,type,
    sK87: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X0) ) ).

thf(func_def_168,type,
    sK88: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X1 ) ).

thf(func_def_169,type,
    sK89: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X1) ) ).

thf(func_def_170,type,
    sK90: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X1 ) ).

thf(func_def_171,type,
    sK91: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X1) ) ).

thf(func_def_172,type,
    sK92: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X0 ) ).

thf(func_def_173,type,
    sK93: 
      !>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X0) ) ).

thf(func_def_174,type,
    sK94: 
      !>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > X0 > X1 ) ).

thf(func_def_175,type,
    sK95: 
      !>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > X0 ) ).

thf(func_def_176,type,
    sK96: 
      !>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > list(X0) ) ).

thf(func_def_177,type,
    sK97: 
      !>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > list(X1) ) ).

thf(func_def_178,type,
    sK98: 
      !>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > X0 > X1 ) ).

thf(func_def_179,type,
    sK99: 
      !>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > list(X1) ) ).

thf(func_def_180,type,
    sK100: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat > X0 > X0 ) ).

thf(func_def_181,type,
    sK101: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).

thf(func_def_182,type,
    sK102: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).

thf(func_def_183,type,
    sK103: 
      !>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > X0 ) ).

thf(func_def_185,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_186,type,
    vIMP: $o > $o > $o ).

thf(func_def_187,type,
    sK105: 
      !>[X0: $tType] : ( coindu1593790203_llist(X0) > list(X0) > X0 > list(X0) ) ).

thf(func_def_188,type,
    sK106: nat > nat > nat ).

thf(func_def_189,type,
    sK107: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

thf(func_def_190,type,
    sK108: 
      !>[X0: $tType] : ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).

thf(f27859,plain,
    $false,
    inference(subsumption_resolution,[],[f27849,f1417]) ).

thf(f1417,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) ),
    inference(cnf_transformation,[],[f641]) ).

thf(f641,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) ),
    inference(fool_elimination,[],[f640]) ).

thf(f640,plain,
    ! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))),
    inference(rectify,[],[f92]) ).

thf(f92,axiom,
    ! [X24: nat,X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X24),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__add__Suc2) ).

thf(f27849,plain,
    $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma))),
    inference(trivial_inequality_removal,[],[f27841]) ).

thf(f27841,plain,
    ( ( vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))) )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma))) ) ),
    inference(superposition,[],[f1825,f1400]) ).

thf(f1400,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(cnf_transformation,[],[f1006]) ).

thf(f1006,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(ennf_transformation,[],[f611]) ).

thf(f611,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
     => ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) ) ),
    inference(fool_elimination,[],[f610]) ).

thf(f610,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)
     => ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) ) ),
    inference(rectify,[],[f30]) ).

thf(f30,axiom,
    ! [X24: nat,X25: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X24),X25)
     => ( vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X24),X25) = vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X24),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X24)),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_upt__conv__Cons) ).

thf(f1825,plain,
    vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma))))),
    inference(backward_demodulation,[],[f1824,f1359]) ).

thf(f1359,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ),
    inference(cnf_transformation,[],[f808]) ).

thf(f808,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X3: nat,X4: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,suc,X4)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_add__Suc__right) ).

thf(f1824,plain,
    vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))),
    inference(backward_demodulation,[],[f1181,f1358]) ).

thf(f1358,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ),
    inference(cnf_transformation,[],[f807]) ).

thf(f807,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X3: nat,X4: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X3)),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__Suc) ).

thf(f1181,plain,
    vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
    inference(cnf_transformation,[],[f775]) ).

thf(f775,plain,
    vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
    inference(flattening,[],[f292]) ).

thf(f292,negated_conjecture,
    vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
    inference(negated_conjecture,[],[f291]) ).

thf(f291,conjecture,
    vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) = vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : DAT137^1 : TPTP v8.2.0. Released v7.0.0.
% 0.09/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30  % Computer : n026.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Sun May 19 23:31:52 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.09/0.30  % (19079)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33  % (19082)WARNING: value z3 for option sas not known
% 0.15/0.33  % (19085)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)
% 0.15/0.33  % (19083)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33  % (19084)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)
% 0.15/0.33  % (19082)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)
% 0.15/0.33  % (19080)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33  % (19081)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33  % (19086)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)
% 0.15/0.36  % (19086)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.36  % Exception at run slice level
% 0.15/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  % (19087)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.38  % (19088)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)
% 0.15/0.39  % (19089)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)
% 0.15/0.41  % (19087)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
% 0.15/0.42  % (19088)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.43  % (19090)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)
% 11.68/1.97  % (19089)First to succeed.
% 11.68/1.98  % (19089)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19079"
% 11.68/1.98  % (19089)Refutation found. Thanks to Tanya!
% 11.68/1.98  % SZS status Theorem for theBenchmark
% 11.68/1.98  % SZS output start Proof for theBenchmark
% See solution above
% 11.68/1.98  % (19089)------------------------------
% 11.68/1.98  % (19089)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.68/1.98  % (19089)Termination reason: Refutation
% 11.68/1.98  
% 11.68/1.98  % (19089)Memory used [KB]: 9258
% 11.68/1.98  % (19089)Time elapsed: 1.591 s
% 11.68/1.98  % (19089)Instructions burned: 3475 (million)
% 11.68/1.98  % (19079)Success in time 1.665 s
%------------------------------------------------------------------------------