TSTP Solution File: ITP048^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP048^1 : 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 : n013.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 22:48:43 EDT 2024

% Result   : Theorem 33.69s 5.23s
% Output   : Refutation 33.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :  152
% Syntax   : Number of formulae    :  230 (  45 unt; 135 typ;   0 def)
%            Number of atoms       :  861 ( 120 equ;   0 cnn)
%            Maximal formula atoms :    3 (   9 avg)
%            Number of connectives :  118 (  49   ~;  34   |;   3   &;   0   @)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  337 ( 336   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  127 ( 124 usr;  14 con; 0-6 aty)
%            Number of variables   :  171 (   0   ^ 152   !;   5   ?; 171   :)
%                                         (  14  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

thf(type_def_10,type,
    list_P559422087at_nat: $tType ).

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

thf(func_def_0,type,
    list_P559422087at_nat: $tType ).

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

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

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

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

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

thf(func_def_6,type,
    connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).

thf(func_def_7,type,
    connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).

thf(func_def_8,type,
    dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat > $o ).

thf(func_def_9,type,
    dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).

thf(func_def_10,type,
    isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).

thf(func_def_11,type,
    isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).

thf(func_def_12,type,
    isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).

thf(func_def_13,type,
    isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).

thf(func_def_14,type,
    isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).

thf(func_def_15,type,
    isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).

thf(func_def_16,type,
    min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).

thf(func_def_17,type,
    min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).

thf(func_def_18,type,
    reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).

thf(func_def_19,type,
    reacha1693770334pacity: ( product_prod_nat_nat > capacity ) > nat > set_nat ).

thf(func_def_20,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_21,type,
    size_s1990949619at_nat: list_P559422087at_nat > nat ).

thf(func_def_22,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_23,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_24,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_25,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_26,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_27,type,
    c: product_prod_nat_nat > capacity ).

thf(func_def_28,type,
    c2: product_prod_nat_nat > a ).

thf(func_def_29,type,
    p: list_P559422087at_nat ).

thf(func_def_30,type,
    p1: list_P559422087at_nat ).

thf(func_def_31,type,
    p1a: list_P559422087at_nat ).

thf(func_def_32,type,
    p2: list_P559422087at_nat ).

thf(func_def_33,type,
    p2_a: list_P559422087at_nat ).

thf(func_def_34,type,
    p3: list_P559422087at_nat ).

thf(func_def_35,type,
    s: nat ).

thf(func_def_36,type,
    t: nat ).

thf(func_def_37,type,
    u: nat ).

thf(func_def_38,type,
    ua: nat ).

thf(func_def_39,type,
    v: nat ).

thf(func_def_40,type,
    va: nat ).

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

thf(func_def_45,type,
    vAND: $o > $o > $o ).

thf(func_def_46,type,
    vIMP: $o > $o > $o ).

thf(func_def_47,type,
    vNOT: $o > $o ).

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

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

thf(func_def_50,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_51,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

thf(func_def_53,type,
    vOR: $o > $o > $o ).

thf(func_def_54,type,
    sP0: nat > nat > nat > $o ).

thf(func_def_55,type,
    sP1: nat > nat > nat > $o ).

thf(func_def_56,type,
    sP2: nat > nat > nat > $o ).

thf(func_def_57,type,
    sP3: nat > nat > nat > $o ).

thf(func_def_58,type,
    sK4: nat > nat ).

thf(func_def_59,type,
    sK5: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_60,type,
    sK6: ( nat > $o ) > nat ).

thf(func_def_61,type,
    sK7: ( nat > $o ) > nat ).

thf(func_def_62,type,
    sK8: ( nat > $o ) > nat ).

thf(func_def_63,type,
    sK9: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_64,type,
    sK10: nat > nat > nat ).

thf(func_def_65,type,
    sK11: nat > nat > nat ).

thf(func_def_66,type,
    sK12: nat > nat > list_P559422087at_nat ).

thf(func_def_67,type,
    sK13: nat > nat > list_P559422087at_nat ).

thf(func_def_68,type,
    sK14: ( nat > nat > $o ) > nat ).

thf(func_def_69,type,
    sK15: ( nat > nat > $o ) > nat ).

thf(func_def_70,type,
    sK16: ( nat > nat > $o ) > nat ).

thf(func_def_71,type,
    sK17: ( nat > nat > $o ) > nat ).

thf(func_def_72,type,
    sK18: ( nat > nat > $o ) > nat ).

thf(func_def_73,type,
    sK19: ( nat > nat ) > nat ).

thf(func_def_74,type,
    sK20: ( nat > nat ) > nat ).

thf(func_def_75,type,
    sK21: ( nat > nat ) > nat ).

thf(func_def_76,type,
    sK22: ( nat > nat ) > nat ).

thf(func_def_77,type,
    sK23: ( nat > nat > $o ) > nat ).

thf(func_def_78,type,
    sK24: ( nat > nat > $o ) > nat ).

thf(func_def_79,type,
    sK25: ( nat > nat > $o ) > nat ).

thf(func_def_80,type,
    sK26: ( nat > nat > $o ) > nat ).

thf(func_def_81,type,
    sK27: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_82,type,
    sK28: ( nat > $o ) > nat ).

thf(func_def_83,type,
    sK29: nat > ( nat > $o ) > nat ).

thf(func_def_84,type,
    sK30: ( nat > $o ) > nat > nat > nat ).

thf(func_def_85,type,
    sK31: nat > nat > nat ).

thf(func_def_86,type,
    sK32: ( nat > $o ) > nat > nat > nat ).

thf(func_def_87,type,
    sK33: nat > nat > nat ).

thf(func_def_88,type,
    sK34: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).

thf(func_def_89,type,
    sK35: nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).

thf(func_def_90,type,
    sK36: nat > nat > list_P559422087at_nat ).

thf(func_def_91,type,
    sK37: nat > nat > list_P559422087at_nat ).

thf(func_def_92,type,
    sK38: nat > nat > nat > nat ).

thf(func_def_93,type,
    sK39: nat > nat > nat > nat ).

thf(func_def_94,type,
    sK40: ( nat > nat ) > nat ).

thf(func_def_95,type,
    sK41: ( nat > nat ) > nat ).

thf(func_def_96,type,
    sK42: ( nat > nat ) > nat ).

thf(func_def_97,type,
    sK43: ( nat > nat ) > nat ).

thf(func_def_98,type,
    sK44: ( nat > nat ) > nat ).

thf(func_def_99,type,
    sK45: ( nat > nat ) > nat ).

thf(func_def_100,type,
    sK46: ( nat > nat ) > nat ).

thf(func_def_101,type,
    sK47: ( nat > nat ) > nat ).

thf(func_def_102,type,
    sK48: ( nat > nat ) > nat ).

thf(func_def_103,type,
    sK49: ( nat > nat ) > nat ).

thf(func_def_104,type,
    sK50: ( nat > nat ) > nat ).

thf(func_def_105,type,
    sK51: ( nat > nat ) > nat ).

thf(func_def_106,type,
    sK52: ( nat > nat ) > nat ).

thf(func_def_107,type,
    sK53: ( nat > nat ) > nat ).

thf(func_def_108,type,
    sK54: ( nat > nat ) > nat ).

thf(func_def_109,type,
    sK55: ( nat > nat ) > nat ).

thf(func_def_110,type,
    sK56: nat > nat > nat ).

thf(func_def_111,type,
    sK57: nat > nat > nat ).

thf(func_def_112,type,
    sK58: ( nat > $o ) > nat > nat > ( product_prod_nat_nat > a ) > nat ).

thf(func_def_113,type,
    sK59: nat > nat > ( product_prod_nat_nat > a ) > nat ).

thf(func_def_114,type,
    sK60: ( nat > $o ) > nat > nat > ( product_prod_nat_nat > capacity ) > nat ).

thf(func_def_115,type,
    sK61: nat > nat > ( product_prod_nat_nat > capacity ) > nat ).

thf(func_def_116,type,
    sK62: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).

thf(func_def_117,type,
    sK63: nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).

thf(func_def_118,type,
    sK64: nat > nat > nat > ( product_prod_nat_nat > a ) > nat ).

thf(func_def_119,type,
    sK65: nat > nat > nat > ( product_prod_nat_nat > capacity ) > nat ).

thf(func_def_120,type,
    sK66: nat > nat > ( product_prod_nat_nat > a ) > nat ).

thf(func_def_121,type,
    sK67: nat > nat > ( product_prod_nat_nat > capacity ) > nat ).

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

thf(func_def_123,type,
    sK68: nat > nat > nat > list_P559422087at_nat ).

thf(func_def_124,type,
    sK69: nat > nat > nat > list_P559422087at_nat ).

thf(func_def_125,type,
    sK70: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).

thf(func_def_126,type,
    sK71: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).

thf(func_def_127,type,
    sK72: nat > nat > nat ).

thf(func_def_128,type,
    sK73: nat > nat > list_P559422087at_nat ).

thf(func_def_129,type,
    sK74: nat > nat > nat ).

thf(func_def_130,type,
    sK75: nat > nat > list_P559422087at_nat ).

thf(f75261,plain,
    $false,
    inference(trivial_inequality_removal,[],[f75260]) ).

thf(f75260,plain,
    $true = $false,
    inference(forward_demodulation,[],[f75259,f64142]) ).

thf(f64142,plain,
    $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a))),
    inference(forward_demodulation,[],[f64118,f57965]) ).

thf(f57965,plain,
    ! [X2: nat,X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0) ),
    inference(forward_demodulation,[],[f57857,f57508]) ).

thf(f57508,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X1),X1)) = X0 ),
    inference(superposition,[],[f13643,f56836]) ).

thf(f56836,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X0),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X1),X1) ),
    inference(unit_resulting_resolution,[],[f56639,f56639,f1271]) ).

thf(f1271,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
      | ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f844]) ).

thf(f844,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,[],[f843]) ).

thf(f843,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,[],[f449]) ).

thf(f449,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,[],[f448]) ).

thf(f448,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,[],[f215]) ).

thf(f215,axiom,
    ! [X46: nat,X47: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X46),X47)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X47),X46)
       => ( X46 = X47 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_antisym) ).

thf(f56639,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X0),X0)),X1) ),
    inference(subsumption_resolution,[],[f56597,f1285]) ).

thf(f1285,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f477]) ).

thf(f477,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ),
    inference(fool_elimination,[],[f476]) ).

thf(f476,plain,
    ! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),
    inference(rectify,[],[f71]) ).

thf(f71,axiom,
    ! [X2: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__add1) ).

thf(f56597,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X0),X0)),X1) ) ),
    inference(superposition,[],[f1398,f13643]) ).

thf(f1398,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,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),X2)) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) = $true ) ),
    inference(cnf_transformation,[],[f941]) ).

thf(f941,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,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),X2)) != $true ) ),
    inference(ennf_transformation,[],[f617]) ).

thf(f617,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,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),X2)) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) = $true ) ),
    inference(fool_elimination,[],[f616]) ).

thf(f616,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,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),X2))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ),
    inference(rectify,[],[f44]) ).

thf(f44,axiom,
    ! [X3: nat,X4: nat,X5: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X4)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X5))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__le__imp__le__left) ).

thf(f13643,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X0),X0)) = X0 ),
    inference(forward_demodulation,[],[f13524,f2480]) ).

thf(f2480,plain,
    ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0)) = X0 ),
    inference(subsumption_resolution,[],[f2476,f2415]) ).

thf(f2415,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0))) ),
    inference(unit_resulting_resolution,[],[f1213,f1277]) ).

thf(f1277,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,X1)) )
      | ( $true != vAPP(nat,$o,X1,X0) ) ),
    inference(cnf_transformation,[],[f853]) ).

thf(f853,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( $true != vAPP(nat,$o,X1,X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,X1)) ) ),
    inference(ennf_transformation,[],[f780]) ).

thf(f780,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,X1)) )
     => ( $true != vAPP(nat,$o,X1,X0) ) ),
    inference(flattening,[],[f461]) ).

thf(f461,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,X1)) )
     => ( $true != vAPP(nat,$o,X1,X0) ) ),
    inference(fool_elimination,[],[f460]) ).

thf(f460,plain,
    ! [X0: nat,X1: nat > $o] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,X1))
     => ~ vAPP(nat,$o,X1,X0) ),
    inference(rectify,[],[f180]) ).

thf(f180,axiom,
    ! [X0: nat,X27: nat > $o] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,X27))
     => ~ vAPP(nat,$o,X27,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_not__less__Least) ).

thf(f1213,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
    inference(cnf_transformation,[],[f349]) ).

thf(f349,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
    inference(fool_elimination,[],[f348]) ).

thf(f348,plain,
    ! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0),
    inference(rectify,[],[f203]) ).

thf(f203,axiom,
    ! [X46: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X46),X46),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_order__refl) ).

thf(f2476,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0))) )
      | ( vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0)) = X0 ) ),
    inference(trivial_inequality_removal,[],[f2453]) ).

thf(f2453,plain,
    ! [X0: nat] :
      ( ( $true != $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0))) )
      | ( vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0)) = X0 ) ),
    inference(superposition,[],[f1233,f1704]) ).

thf(f1704,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0))) ),
    inference(unit_resulting_resolution,[],[f1213,f1207]) ).

thf(f1207,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true != vAPP(nat,$o,X0,X1) )
      | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)) ) ),
    inference(cnf_transformation,[],[f801]) ).

thf(f801,plain,
    ! [X0: nat > $o] :
      ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)) )
      | ! [X1: nat] : ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(ennf_transformation,[],[f337]) ).

thf(f337,plain,
    ! [X0: nat > $o] :
      ( ? [X1: nat] : ( $true = vAPP(nat,$o,X0,X1) )
     => ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)) ) ),
    inference(fool_elimination,[],[f336]) ).

thf(f336,plain,
    ! [X0: nat > $o] :
      ( ? [X1: nat] : vAPP(nat,$o,X0,X1)
     => vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)) ),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    ! [X27: nat > $o] :
      ( ? [X66: nat] : vAPP(nat,$o,X27,X66)
     => vAPP(nat,$o,X27,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_LeastI__ex) ).

thf(f1233,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_nat,X0),X1) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f807]) ).

thf(f807,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) )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f806]) ).

thf(f806,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) )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f387]) ).

thf(f387,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
    inference(fool_elimination,[],[f386]) ).

thf(f386,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
    inference(rectify,[],[f269]) ).

thf(f269,axiom,
    ! [X4: nat,X5: nat] :
      ( ( X4 != X5 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_order_Onot__eq__order__implies__strict) ).

thf(f13524,plain,
    ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X0),vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0)))) = X0 ),
    inference(unit_resulting_resolution,[],[f2225,f1275]) ).

thf(f1275,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X1),X0)) = X1 ) ),
    inference(cnf_transformation,[],[f1068]) ).

thf(f1068,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X1),X0)) = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f851,f1067]) ).

thf(f1067,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X1),X0)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f851,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
    inference(ennf_transformation,[],[f457]) ).

thf(f457,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
     => ~ ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) ),
    inference(fool_elimination,[],[f456]) ).

thf(f456,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ~ ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) ),
    inference(rectify,[],[f50]) ).

thf(f50,axiom,
    ! [X4: nat,X5: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
     => ~ ! [X36: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X4),X36) != X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__eqE) ).

thf(f2225,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0))),X0) ),
    inference(unit_resulting_resolution,[],[f1213,f1252]) ).

thf(f1252,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true != vAPP(nat,$o,X0,X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)),X1) ) ),
    inference(cnf_transformation,[],[f823]) ).

thf(f823,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)),X1) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(ennf_transformation,[],[f411]) ).

thf(f411,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)),X1) ) ),
    inference(fool_elimination,[],[f410]) ).

thf(f410,plain,
    ! [X0: nat > $o,X1: nat] :
      ( vAPP(nat,$o,X0,X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X0)),X1) ),
    inference(rectify,[],[f181]) ).

thf(f181,axiom,
    ! [X27: nat > $o,X0: nat] :
      ( vAPP(nat,$o,X27,X0)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,ord_Least_nat,X27)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Least__le) ).

thf(f57857,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK10,X1),X1))) ),
    inference(superposition,[],[f1290,f57508]) ).

thf(f1290,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f787]) ).

thf(f787,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ),
    inference(rectify,[],[f75]) ).

thf(f75,axiom,
    ! [X5: nat,X4: nat,X3: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X4),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X5),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add_Oleft__commute) ).

thf(f64118,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))) = $false,
    inference(unit_resulting_resolution,[],[f1161,f277]) ).

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

thf(f1161,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))) != $true,
    inference(cnf_transformation,[],[f758]) ).

thf(f758,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))) != $true,
    inference(flattening,[],[f279]) ).

thf(f279,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))) != $true,
    inference(fool_elimination,[],[f278]) ).

thf(f278,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))),
    inference(rectify,[],[f275]) ).

thf(f275,negated_conjecture,
    ~ 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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))),
    inference(negated_conjecture,[],[f274]) ).

thf(f274,conjecture,
    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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f75259,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a))),
    inference(forward_demodulation,[],[f75258,f1176]) ).

thf(f1176,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t)),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),t) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062) ).

thf(f75258,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a))),
    inference(forward_demodulation,[],[f74894,f57965]) ).

thf(f74894,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a))),
    inference(unit_resulting_resolution,[],[f1490,f1491,f1411]) ).

thf(f1411,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f960]) ).

thf(f960,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
    inference(flattening,[],[f959]) ).

thf(f959,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
    inference(ennf_transformation,[],[f633]) ).

thf(f633,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ) ),
    inference(fool_elimination,[],[f632]) ).

thf(f632,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
    inference(rectify,[],[f93]) ).

thf(f93,axiom,
    ! [X25: nat,X26: nat,X0: nat,X37: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X37)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X25),X26) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X25),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X26),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__mono__thms__linordered__field_I3_J) ).

thf(f1491,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)) = $true,
    inference(cnf_transformation,[],[f757]) ).

thf(f757,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)) = $true,
    inference(fool_elimination,[],[f756]) ).

thf(f756,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod_nat_nat,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),ua),t)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p2_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062) ).

thf(f1490,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)) = $true,
    inference(cnf_transformation,[],[f755]) ).

thf(f755,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)) = $true,
    inference(fool_elimination,[],[f754]) ).

thf(f754,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),
    inference(rectify,[],[f2]) ).

thf(f2,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,capacity),sTfun(nat,sTfun(nat,nat)),min_dist_capacity,c),s),ua)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,p1a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15  % Problem    : ITP048^1 : TPTP v8.2.0. Released v7.5.0.
% 0.09/0.17  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.39  % Computer : n013.cluster.edu
% 0.16/0.39  % Model    : x86_64 x86_64
% 0.16/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39  % Memory   : 8042.1875MB
% 0.16/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39  % CPULimit   : 300
% 0.16/0.39  % WCLimit    : 300
% 0.16/0.39  % DateTime   : Sat May 18 16:09:38 EDT 2024
% 0.16/0.39  % CPUTime    : 
% 0.16/0.40  % (22706)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.43  % (22707)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.24/0.43  % (22713)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)
% 0.24/0.43  % (22711)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)
% 0.24/0.43  % (22712)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)
% 0.24/0.43  % (22709)WARNING: value z3 for option sas not known
% 0.24/0.43  % (22708)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.24/0.44  % (22709)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)
% 0.24/0.46  % (22710)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.24/0.47  % (22713)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.47  % Exception at run slice level
% 0.24/0.47  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.49  % Exception at run slice level
% 0.24/0.49  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.49  % (22714)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.24/0.50  % Exception at run slice level
% 0.24/0.50  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.51  % (22716)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)
% 0.24/0.51  % (22715)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)
% 0.24/0.52  % (22714)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.52  % Exception at run slice level
% 0.24/0.52  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.53  % (22717)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)
% 0.24/0.56  % (22715)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 33.34/5.22  % (22715)First to succeed.
% 33.69/5.23  % (22715)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22706"
% 33.69/5.23  % (22715)Refutation found. Thanks to Tanya!
% 33.69/5.23  % SZS status Theorem for theBenchmark
% 33.69/5.23  % SZS output start Proof for theBenchmark
% See solution above
% 33.69/5.24  % (22715)------------------------------
% 33.69/5.24  % (22715)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 33.69/5.24  % (22715)Termination reason: Refutation
% 33.69/5.24  
% 33.69/5.24  % (22715)Memory used [KB]: 17079
% 33.69/5.24  % (22715)Time elapsed: 4.730 s
% 33.69/5.24  % (22715)Instructions burned: 9957 (million)
% 33.69/5.24  % (22706)Success in time 4.808 s
%------------------------------------------------------------------------------