TSTP Solution File: ITP051^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP051^2 : 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 : n023.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 22:48:58 EDT 2024

% Result   : ContradictoryAxioms 2.42s 0.72s
% Output   : Refutation 2.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :  131
% Syntax   : Number of formulae    :  175 (  22 unt; 121 typ;   0 def)
%            Number of atoms       :  555 (  88 equ;   0 cnn)
%            Maximal formula atoms :    4 (  10 avg)
%            Number of connectives :   74 (  25   ~;  31   |;   5   &;   0   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  271 ( 268   >;   3   *;   0   +;   0  <<)
%            Number of symbols     :  122 ( 119 usr;   8 con; 0-6 aty)
%            Number of variables   :  138 (   0   ^  56   !;   2   ?; 138   :)
%                                         (  80  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

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

thf(type_def_9,type,
    list: $tType > $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_13,type,
    canoni770627133id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_14,type,
    edmond2129202899alysis: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > $o ) ).

thf(func_def_15,type,
    edmond115586663easure: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > nat ) ).

thf(func_def_16,type,
    edmond1803015688pEdges: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > set(product_prod(nat,nat)) ) ).

thf(func_def_17,type,
    edmond259086305sis_uE: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(product_prod(nat,nat)) ) ).

thf(func_def_18,type,
    finite_card: 
      !>[X0: $tType] : ( set(X0) > nat ) ).

thf(func_def_19,type,
    finite_finite2: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

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

thf(func_def_21,type,
    e: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(product_prod(nat,nat)) ) ).

thf(func_def_22,type,
    v: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(nat) ) ).

thf(func_def_23,type,
    adjacent_nodes: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > set(nat) ) ).

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

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

thf(func_def_26,type,
    incoming: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(nat) > set(product_prod(nat,nat)) ) ).

thf(func_def_27,type,
    isPath: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > list(product_prod(nat,nat)) > nat > $o ) ).

thf(func_def_28,type,
    isShortestPath: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > list(product_prod(nat,nat)) > nat > $o ) ).

thf(func_def_29,type,
    isSimplePath: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > list(product_prod(nat,nat)) > nat > $o ) ).

thf(func_def_30,type,
    min_dist: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > nat ) ).

thf(func_def_31,type,
    outgoing: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(nat) > set(product_prod(nat,nat)) ) ).

thf(func_def_32,type,
    reachableNodes: 
      !>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > set(nat) ) ).

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

thf(func_def_34,type,
    set2: 
      !>[X0: $tType] : ( list(X0) > set(X0) ) ).

thf(func_def_35,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

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

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

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

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

thf(func_def_40,type,
    c: product_prod(nat,nat) > a ).

thf(func_def_41,type,
    c2: product_prod(nat,nat) > b ).

thf(func_def_42,type,
    edges: set(product_prod(nat,nat)) ).

thf(func_def_43,type,
    p: list(product_prod(nat,nat)) ).

thf(func_def_44,type,
    p2: list(product_prod(nat,nat)) ).

thf(func_def_45,type,
    s: nat ).

thf(func_def_46,type,
    t: nat ).

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

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

thf(func_def_52,type,
    vNOT: $o > $o ).

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

thf(func_def_54,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

thf(func_def_56,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

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

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

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

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

thf(func_def_61,type,
    sP0: 
      !>[X0: $tType] : ( set(X0) > nat > $o ) ).

thf(func_def_62,type,
    sP1: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).

thf(func_def_63,type,
    sK2: list(product_prod(nat,nat)) ).

thf(func_def_64,type,
    sK3: 
      !>[X0: $tType] : ( X0 > set(X0) > X0 ) ).

thf(func_def_65,type,
    sK4: 
      !>[X0: $tType] : ( X0 > set(X0) > X0 ) ).

thf(func_def_66,type,
    sK5: 
      !>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > list(product_prod(nat,nat)) ) ).

thf(func_def_67,type,
    sK6: 
      !>[X0: $tType] : ( ( nat > $o ) > nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).

thf(func_def_68,type,
    sK7: 
      !>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).

thf(func_def_69,type,
    sK8: 
      !>[X0: $tType] : ( nat > nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).

thf(func_def_70,type,
    sK9: 
      !>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > list(product_prod(nat,nat)) ) ).

thf(func_def_71,type,
    sK10: 
      !>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).

thf(func_def_72,type,
    sK11: ( nat > $o ) > nat ).

thf(func_def_73,type,
    sK12: ( nat > $o ) > nat ).

thf(func_def_74,type,
    sK13: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_75,type,
    sK14: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_76,type,
    sK15: nat > ( nat > $o ) > nat ).

thf(func_def_77,type,
    sK16: ( nat > $o ) > nat ).

thf(func_def_78,type,
    sK17: 
      !>[X0: $tType] : ( set(list(X0)) > nat ) ).

thf(func_def_79,type,
    sK18: nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_80,type,
    sK19: nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_81,type,
    sK20: 
      !>[X0: $tType] : ( nat > list(X0) ) ).

thf(func_def_82,type,
    sK21: 
      !>[X0: $tType] : ( nat > set(X0) > set(X0) ) ).

thf(func_def_83,type,
    sK22: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_84,type,
    sK23: 
      !>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).

thf(func_def_85,type,
    sK24: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_86,type,
    sK25: 
      !>[X0: $tType] : ( set(X0) > nat > set(X0) ) ).

thf(func_def_87,type,
    sK26: ( nat > nat ) > nat ).

thf(func_def_88,type,
    sK27: ( nat > nat ) > nat ).

thf(func_def_89,type,
    sK28: ( nat > $o ) > nat ).

thf(func_def_90,type,
    sK29: nat > ( nat > $o ) > nat ).

thf(func_def_91,type,
    sK30: 
      !>[X0: $tType] : ( ( set(X0) > $o ) > set(X0) ) ).

thf(func_def_92,type,
    sK31: ( nat > $o ) > nat > nat > nat ).

thf(func_def_93,type,
    sK32: nat > nat > nat ).

thf(func_def_94,type,
    sK33: ( nat > $o ) > nat > nat > nat ).

thf(func_def_95,type,
    sK34: nat > nat > nat ).

thf(func_def_96,type,
    sK35: nat > nat > nat > nat ).

thf(func_def_97,type,
    sK36: nat > nat > nat > nat ).

thf(func_def_98,type,
    sK37: nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_99,type,
    sK38: nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_100,type,
    sK39: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_101,type,
    sK40: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_102,type,
    sK41: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_103,type,
    sK42: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_104,type,
    sK43: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X1) > X1 > X0 ) ).

thf(func_def_105,type,
    sK44: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X1) > X1 ) ).

thf(func_def_106,type,
    sK45: nat > nat > nat ).

thf(func_def_107,type,
    sK46: nat > nat > nat ).

thf(func_def_109,type,
    sK48: list(product_prod(nat,nat)) > nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_110,type,
    sK49: list(product_prod(nat,nat)) > nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_111,type,
    sK50: nat > nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_112,type,
    sK51: nat > nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_113,type,
    sK52: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_114,type,
    sK53: nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_115,type,
    sK54: nat > nat > nat ).

thf(func_def_116,type,
    sK55: nat > nat > list(product_prod(nat,nat)) ).

thf(func_def_117,type,
    sK56: nat > nat > nat ).

thf(f8806,plain,
    $false,
    inference(trivial_inequality_removal,[],[f8805]) ).

thf(f8805,plain,
    $true = $false,
    inference(backward_demodulation,[],[f1730,f8804]) ).

thf(f8804,plain,
    $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),
    inference(trivial_inequality_removal,[],[f8789]) ).

thf(f8789,plain,
    ( ( $true = $false )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)) ) ),
    inference(superposition,[],[f1726,f4405]) ).

thf(f4405,plain,
    ! [X0: nat,X1: nat] :
      ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f4385]) ).

thf(f4385,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != $true )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(superposition,[],[f2740,f2377]) ).

thf(f2377,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f2376]) ).

thf(f2376,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(superposition,[],[f1311,f277]) ).

thf(f277,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f1311,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(cnf_transformation,[],[f943]) ).

thf(f943,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( ( X0 != X1 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ) ),
    inference(ennf_transformation,[],[f567]) ).

thf(f567,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(fool_elimination,[],[f566]) ).

thf(f566,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ),
    inference(rectify,[],[f92]) ).

thf(f92,axiom,
    ! [X42: nat,X30: nat] :
      ( ( ( X30 = X42 )
        | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X42),X30) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X42),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__or__eq__imp__le) ).

thf(f2740,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(subsumption_resolution,[],[f2738,f1592]) ).

thf(f1592,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) ) ),
    inference(binary_proxy_clausification,[],[f1591]) ).

thf(f1591,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ) ),
    inference(equality_proxy_clausification,[],[f1590]) ).

thf(f1590,plain,
    ! [X0: nat,X1: nat] :
      ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ) ),
    inference(not_proxy_clausification,[],[f1585]) ).

thf(f1585,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ) ),
    inference(binary_proxy_clausification,[],[f1298]) ).

thf(f1298,plain,
    ! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ),
    inference(cnf_transformation,[],[f541]) ).

thf(f541,plain,
    ! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ),
    inference(fool_elimination,[],[f540]) ).

thf(f540,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 != X1 )
        = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) )
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ),
    inference(rectify,[],[f104]) ).

thf(f104,axiom,
    ! [X42: nat,X30: nat] :
      ( ( ( X30 != X42 )
        = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X30),X42) )
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X42),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nat__neq__iff) ).

thf(f2738,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( X0 = X1 )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f2718]) ).

thf(f2718,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( X0 = X1 )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(superposition,[],[f1335,f2377]) ).

thf(f1335,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f962]) ).

thf(f962,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(flattening,[],[f961]) ).

thf(f961,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(ennf_transformation,[],[f597]) ).

thf(f597,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f596]) ).

thf(f596,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f82]) ).

thf(f82,axiom,
    ! [X42: nat,X30: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X42),X30)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X30),X42)
       => ( X30 = X42 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_le__antisym) ).

thf(f1726,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),
    inference(forward_demodulation,[],[f1458,f1685]) ).

thf(f1685,plain,
    vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2),
    inference(backward_demodulation,[],[f1155,f1167]) ).

thf(f1167,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2),
    inference(cnf_transformation,[],[f1060]) ).

thf(f1060,plain,
    ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2) )
    & ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),sK2),t) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f837,f1059]) ).

thf(f1059,plain,
    ( ? [X0: list(product_prod(nat,nat))] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) )
        & ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t) ) )
   => ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2) )
      & ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),sK2),t) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f837,plain,
    ? [X0: list(product_prod(nat,nat))] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) )
      & ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t) ) ),
    inference(ennf_transformation,[],[f301]) ).

thf(f301,plain,
    ~ ! [X0: list(product_prod(nat,nat))] :
        ( ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t) )
       => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) != vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) ) ),
    inference(fool_elimination,[],[f300]) ).

thf(f300,plain,
    ~ ! [X0: list(product_prod(nat,nat))] :
        ( vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t)
       => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) != vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) ) ),
    inference(rectify,[],[f22]) ).

thf(f22,axiom,
    ~ ! [X4: list(product_prod(nat,nat))] :
        ( vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X4),t)
       => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) != vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_H_O_A_092_060lbrakk_062g_H_OisPath_As_Ap_H_At_059_Alength_Ap_H_A_061_Ag_H_Omin__dist_As_At_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(f1155,plain,
    vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t),
    inference(cnf_transformation,[],[f3]) ).

thf(f3,axiom,
    vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_LENP_H) ).

thf(f1458,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)) = $true,
    inference(cnf_transformation,[],[f773]) ).

thf(f773,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)) = $true,
    inference(fool_elimination,[],[f772]) ).

thf(f772,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),
    inference(rectify,[],[f11]) ).

thf(f11,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062) ).

thf(f1730,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),
    inference(forward_demodulation,[],[f1729,f1167]) ).

thf(f1729,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),
    inference(forward_demodulation,[],[f1468,f1156]) ).

thf(f1156,plain,
    vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t),
    inference(cnf_transformation,[],[f2]) ).

thf(f2,axiom,
    vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_LENP) ).

thf(f1468,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)) = $true,
    inference(cnf_transformation,[],[f793]) ).

thf(f793,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)) = $true,
    inference(fool_elimination,[],[f792]) ).

thf(f792,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_SHORTER) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : ITP051^2 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 18:25:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (6444)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (6447)WARNING: value z3 for option sas not known
% 0.14/0.39  % (6448)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (6445)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  % (6446)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (6449)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)
% 0.14/0.39  % (6447)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)
% 0.14/0.39  % (6450)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)
% 0.14/0.39  % (6451)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)
% 0.20/0.42  % (6451)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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
% 0.20/0.43  % Exception at run slice level
% 0.20/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43  % 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  % (6452)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.44  % (6453)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  % (6454)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)
% 0.20/0.47  % (6452)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.47  % (6453)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.48  % Exception at run slice level
% 0.20/0.48  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.49  % (6455)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)
% 2.42/0.72  % (6454)First to succeed.
% 2.42/0.72  % (6454)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6444"
% 2.42/0.72  % (6454)Refutation found. Thanks to Tanya!
% 2.42/0.72  % SZS status ContradictoryAxioms for theBenchmark
% 2.42/0.72  % SZS output start Proof for theBenchmark
% See solution above
% 2.42/0.72  % (6454)------------------------------
% 2.42/0.72  % (6454)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.42/0.72  % (6454)Termination reason: Refutation
% 2.42/0.72  
% 2.42/0.72  % (6454)Memory used [KB]: 3354
% 2.42/0.72  % (6454)Time elapsed: 0.280 s
% 2.42/0.72  % (6454)Instructions burned: 866 (million)
% 2.42/0.72  % (6444)Success in time 0.347 s
%------------------------------------------------------------------------------