TSTP Solution File: DAT177^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT177^1 : 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 : n032.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 19:51:42 EDT 2024

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  125
% Syntax   : Number of formulae    :  142 (  20 unt; 120 typ;   0 def)
%            Number of atoms       :  122 (  18 equ;   0 cnn)
%            Maximal formula atoms :    2 (   5 avg)
%            Number of connectives :    8 (   6   ~;   2   |;   0   &;   0   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  216 ( 215   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  122 ( 119 usr;   6 con; 0-6 aty)
%            Number of variables   :  120 (   0   ^   8   !;   0   ?; 120   :)
%                                         ( 112  !>;   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,
    coinductive_llist: $tType > $tType ).

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

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

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

thf(func_def_1,type,
    set: $tType > $tType ).

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

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

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

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

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

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

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

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

thf(func_def_10,type,
    topolo890362671_space: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_11,type,
    topolo47006728_space: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_12,type,
    bounde1561333602nf_top: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_13,type,
    bounde1808546759up_bot: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_14,type,
    coindu328551480prefix: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > $o ) ).

thf(func_def_15,type,
    coinductive_gen_lset: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > set(X0) ) ).

thf(func_def_16,type,
    coinductive_lSup: 
      !>[X0: $tType] : ( set(coinductive_llist(X0)) > coinductive_llist(X0) ) ).

thf(func_def_17,type,
    coinductive_lappend: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

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

thf(func_def_19,type,
    coinductive_llast: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_20,type,
    coinductive_LCons: 
      !>[X0: $tType] : ( X0 > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_21,type,
    coinductive_LNil: 
      !>[X0: $tType] : coinductive_llist(X0) ).

thf(func_def_22,type,
    coindu1478340336prefix: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > $o ) ).

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

thf(func_def_24,type,
    lList2435255213lllsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_25,type,
    lList2236698231inlsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_26,type,
    lList21916056377ts_rec: 
      !>[X0: $tType,X1: $tType] : ( X0 > ( X1 > coinductive_llist(X1) > X0 > X0 ) > coinductive_llist(X1) > X0 ) ).

thf(func_def_27,type,
    lList22096119349pslsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_28,type,
    lList21612149805nflsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_29,type,
    lList21148268032oslsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

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

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

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

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

thf(func_def_34,type,
    type2: 
      !>[X0: $tType] : itself(X0) ).

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

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

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

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

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

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

thf(func_def_41,type,
    the_elem: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_42,type,
    topolo406746546ounded: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

thf(func_def_43,type,
    member: 
      !>[X0: $tType] : ( X0 > set(X0) > $o ) ).

thf(func_def_44,type,
    a2: set(a) ).

thf(func_def_45,type,
    l: coinductive_llist(a) ).

thf(func_def_46,type,
    r: coinductive_llist(a) ).

thf(func_def_47,type,
    sa: coinductive_llist(a) ).

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

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

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

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

thf(func_def_55,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

thf(func_def_57,type,
    vIMP: $o > $o > $o ).

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

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

thf(func_def_60,type,
    vOR: $o > $o > $o ).

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

thf(func_def_62,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_63,type,
    sP0: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > $o ) ).

thf(func_def_64,type,
    sP1: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > $o ) ).

thf(func_def_65,type,
    sK2: 
      !>[X0: $tType] : X0 ).

thf(func_def_66,type,
    sK3: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_67,type,
    sK4: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_68,type,
    sK5: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_69,type,
    sK6: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_70,type,
    sK7: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_71,type,
    sK8: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_72,type,
    sK9: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_73,type,
    sK10: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_74,type,
    sK11: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_75,type,
    sK12: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_76,type,
    sK13: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_77,type,
    sK14: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_78,type,
    sK15: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_79,type,
    sK16: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_80,type,
    sK17: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_81,type,
    sK18: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_82,type,
    sK19: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_83,type,
    sK20: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_84,type,
    sK21: 
      !>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).

thf(func_def_85,type,
    sK22: 
      !>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).

thf(func_def_86,type,
    sK23: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_87,type,
    sK24: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_88,type,
    sK25: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_89,type,
    sK26: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_90,type,
    sK27: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_91,type,
    sK28: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_92,type,
    sK29: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_93,type,
    sK30: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_94,type,
    sK31: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_95,type,
    sK32: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_96,type,
    sK33: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_97,type,
    sK34: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_98,type,
    sK35: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_99,type,
    sK36: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > coinductive_llist(X0) ) ).

thf(func_def_100,type,
    sK37: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).

thf(func_def_101,type,
    sK38: 
      !>[X0: $tType] : ( X0 > set(X0) > X0 > set(X0) > set(X0) ) ).

thf(func_def_102,type,
    sK39: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 > set(X0) > X0 ) ).

thf(func_def_103,type,
    sK40: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_104,type,
    sK41: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_105,type,
    sK42: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_106,type,
    sK43: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_107,type,
    sK44: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_108,type,
    sK45: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_109,type,
    sK46: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_110,type,
    sK47: 
      !>[X0: $tType] : ( coinductive_llist(X0) > set(X0) > X0 ) ).

thf(func_def_111,type,
    sK48: 
      !>[X0: $tType] : ( coinductive_llist(X0) > set(X0) > X0 ) ).

thf(func_def_112,type,
    sK49: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_113,type,
    sK50: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_114,type,
    sK51: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_115,type,
    sK52: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_116,type,
    sK53: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_117,type,
    sK54: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(f1870,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1869]) ).

thf(f1869,plain,
    $true = $false,
    inference(forward_demodulation,[],[f1868,f1838]) ).

thf(f1838,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) = $false,
    inference(trivial_inequality_removal,[],[f1837]) ).

thf(f1837,plain,
    ( ( $true != $true )
    | ( vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) = $false ) ),
    inference(superposition,[],[f962,f281]) ).

thf(f281,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f962,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) != $true,
    inference(cnf_transformation,[],[f668]) ).

thf(f668,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) != $true,
    inference(flattening,[],[f283]) ).

thf(f283,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) != $true,
    inference(fool_elimination,[],[f282]) ).

thf(f282,plain,
    ~ vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)),
    inference(rectify,[],[f279]) ).

thf(f279,negated_conjecture,
    ~ vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)),
    inference(negated_conjecture,[],[f278]) ).

thf(f278,conjecture,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f1868,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),sa),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) = $true,
    inference(backward_demodulation,[],[f1281,f1865]) ).

thf(f1865,plain,
    ! [X0: coinductive_llist(a)] : ( vAPP(coinductive_llist(a),coinductive_llist(a),vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),coinductive_llist(a)),coinductive_lappend(a),l),X0) = X0 ),
    inference(superposition,[],[f1009,f963]) ).

thf(f963,plain,
    l = coinductive_LNil(a),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,axiom,
    l = coinductive_LNil(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_LNil__fin_Ohyps) ).

thf(f1009,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_lappend(X0),coinductive_LNil(X0)),X1) = X1 ),
    inference(cnf_transformation,[],[f671]) ).

thf(f671,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_lappend(X0),coinductive_LNil(X0)),X1) = X1 ),
    inference(rectify,[],[f43]) ).

thf(f43,axiom,
    ! [X0: $tType,X23: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_lappend(X0),coinductive_LNil(X0)),X23) = X23 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lappend__code_I1_J) ).

thf(f1281,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),vAPP(coinductive_llist(a),coinductive_llist(a),vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),coinductive_llist(a)),coinductive_lappend(a),l),sa)),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) = $true,
    inference(cnf_transformation,[],[f667]) ).

thf(f667,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),vAPP(coinductive_llist(a),coinductive_llist(a),vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),coinductive_llist(a)),coinductive_lappend(a),l),sa)),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)) = $true,
    inference(fool_elimination,[],[f666]) ).

thf(f666,plain,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),vAPP(coinductive_llist(a),coinductive_llist(a),vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),coinductive_llist(a)),coinductive_lappend(a),l),sa)),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    vAPP(set(coinductive_llist(a)),$o,vAPP(coinductive_llist(a),sTfun(set(coinductive_llist(a)),$o),member(coinductive_llist(a)),vAPP(coinductive_llist(a),coinductive_llist(a),vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),coinductive_llist(a)),coinductive_lappend(a),l),sa)),vAPP(set(a),set(coinductive_llist(a)),lList21612149805nflsts(a),a2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_LNil__fin_Oprems) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : DAT177^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n032.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 23:34:52 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (9187)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (9190)WARNING: value z3 for option sas not known
% 0.13/0.38  % (9190)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)
% 0.13/0.38  % (9188)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38  % (9192)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)
% 0.13/0.38  % (9194)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)
% 0.13/0.38  % (9191)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38  % (9193)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)
% 0.13/0.39  % (9189)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.41  % (9194)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.41  % Exception at run slice level
% 0.13/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.42  % Exception at run slice level
% 0.13/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.42  % (9195)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.43  % Exception at run slice level
% 0.20/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44  % (9196)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)
% 0.20/0.44  % (9195)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.44  % Exception at run slice level
% 0.20/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.45  % (9197)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)
% 0.20/0.46  % (9198)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)
% 0.20/0.47  % (9196)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.48  % (9193)First to succeed.
% 0.20/0.49  % (9193)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9187"
% 0.20/0.49  % (9193)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (9193)------------------------------
% 0.20/0.49  % (9193)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.49  % (9193)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (9193)Memory used [KB]: 2295
% 0.20/0.49  % (9193)Time elapsed: 0.106 s
% 0.20/0.49  % (9193)Instructions burned: 227 (million)
% 0.20/0.49  % (9187)Success in time 0.13 s
%------------------------------------------------------------------------------