Vampire-SAT---5.0.1.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : LCL820_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 12:00:44 PM UTC 2026

% Result   : Theorem 3.98s 1.10s
% Output   : Refutation 3.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   10 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   13 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :    7 (   4   ~;   1   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :   26 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   68 (  68 usr;  22 con; 0-5 aty)
%            Number of variables   :    8 (   8   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    bool: $tType ).

tff(type_def_6,type,
    dB: $tType ).

tff(type_def_7,type,
    list: $tType > $tType ).

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

tff(type_def_9,type,
    type: $tType ).

tff(type_def_10,type,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).

tff(func_def_1,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).

tff(func_def_2,type,
    combi: 
      !>[X0: $tType] : fun(X0,X0) ).

tff(func_def_3,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).

tff(func_def_4,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_5,type,
    it: fun(dB,bool) ).

tff(func_def_6,type,
    abs: dB > dB ).

tff(func_def_7,type,
    app: fun(dB,fun(dB,dB)) ).

tff(func_def_8,type,
    var: nat > dB ).

tff(func_def_9,type,
    dB_case: 
      !>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).

tff(func_def_10,type,
    dB_size: dB > nat ).

tff(func_def_11,type,
    lift: fun(dB,fun(nat,dB)) ).

tff(func_def_12,type,
    liftn: ( nat * dB * nat ) > dB ).

tff(func_def_13,type,
    subst: fun(dB,fun(dB,fun(nat,dB))) ).

tff(func_def_14,type,
    substn: ( dB * dB * nat ) > dB ).

tff(func_def_15,type,
    foldl: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).

tff(func_def_16,type,
    foldr: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).

tff(func_def_17,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_18,type,
    map: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).

tff(func_def_19,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

tff(func_def_20,type,
    shift: 
      !>[X0: $tType] : fun(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).

tff(func_def_21,type,
    atom: nat > type ).

tff(func_def_22,type,
    fun1: fun(type,fun(type,type)) ).

tff(func_def_23,type,
    type_case: 
      !>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).

tff(func_def_24,type,
    type_size: type > nat ).

tff(func_def_25,type,
    typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).

tff(func_def_26,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_27,type,
    fAll: 
      !>[X0: $tType] : fun(fun(X0,bool),bool) ).

tff(func_def_28,type,
    fFalse: bool ).

tff(func_def_29,type,
    fTrue: bool ).

tff(func_def_30,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_31,type,
    fimplies: fun(bool,fun(bool,bool)) ).

tff(func_def_32,type,
    t1: type ).

tff(func_def_33,type,
    t_a: type ).

tff(func_def_34,type,
    t: type ).

tff(func_def_35,type,
    e: fun(nat,type) ).

tff(func_def_36,type,
    ea: fun(nat,type) ).

tff(func_def_37,type,
    i: nat ).

tff(func_def_38,type,
    ia: nat ).

tff(func_def_39,type,
    n: nat ).

tff(func_def_40,type,
    rs: list(dB) ).

tff(func_def_41,type,
    t2: dB ).

tff(func_def_42,type,
    u: dB ).

tff(func_def_43,type,
    ua: dB ).

tff(func_def_44,type,
    sK0: ( type * dB * dB * fun(nat,type) ) > type ).

tff(func_def_45,type,
    sK1: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).

tff(func_def_46,type,
    sK2: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).

tff(func_def_47,type,
    sK3: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).

tff(func_def_48,type,
    sK4: type > nat ).

tff(func_def_49,type,
    sK5: type > type ).

tff(func_def_50,type,
    sK6: type > type ).

tff(func_def_51,type,
    sK7: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).

tff(func_def_52,type,
    sK8: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).

tff(func_def_53,type,
    sK9: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).

tff(func_def_54,type,
    sK10: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).

tff(func_def_55,type,
    sK11: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_56,type,
    sK12: ( type * dB * fun(nat,type) ) > type ).

tff(func_def_57,type,
    sK13: ( type * dB * fun(nat,type) ) > type ).

tff(func_def_58,type,
    sK14: ( dB * fun(nat,type) ) > type ).

tff(func_def_59,type,
    sK15: ( dB * fun(nat,type) ) > type ).

tff(func_def_60,type,
    sK16: dB > dB ).

tff(func_def_61,type,
    sK17: dB > dB ).

tff(func_def_62,type,
    sK18: dB > list(dB) ).

tff(func_def_63,type,
    sK19: dB > dB ).

tff(func_def_64,type,
    sK20: dB > list(dB) ).

tff(func_def_65,type,
    sK21: dB > nat ).

tff(pred_def_1,type,
    zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    beta: ( dB * dB ) > $o ).

tff(pred_def_3,type,
    listsp: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_4,type,
    typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).

tff(pred_def_5,type,
    pp: bool > $o ).

tff(f6,axiom,
    listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),it)),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,typ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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Var_Ohyps) ).

tff(f10,axiom,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
    <=> ( listsp(X0,X2,X3)
        & listsp(X0,X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_listsp__conj__eq) ).

tff(f114,conjecture,
    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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f115,negated_conjecture,
    ~ 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type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(n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    inference(negated_conjecture,[status(cth)],[f114]) ).

tff(f117,plain,
    ~ 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    inference(flattening,[],[f115]) ).

tff(f168,plain,
    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    inference(cnf_transformation,[],[f6]) ).

tff(f172,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
      ( ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
      | listsp(X0,X1,X3) ),
    inference(cnf_transformation,[],[f10]) ).

tff(f318,plain,
    ~ 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    inference(cnf_transformation,[],[f117]) ).

tff(f2043,plain,
    listsp(dB,aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(n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    inference(resolution,[],[f168,f172]) ).

tff(f2044,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f2043,f318]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LCL820_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42  % Computer : n002.cluster.edu
% 0.14/0.42  % Model    : x86_64 x86_64
% 0.14/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42  % Memory   : 8046.5625MB
% 0.14/0.42  % OS       : Linux 6.8.0-71-generic
% 0.14/0.42  % CPULimit : 300
% 0.14/0.42  % WCLimit  : 300
% 0.14/0.42  % DateTime : Sun Sep 27 16:59:08 UTC 2026
% 0.14/0.42  % CPUTime  : 
% 0.14/0.42  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.45  Running first-order model finding
% 0.14/0.45  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.98/1.10  % (3736729)Will run a generic schedule for satisfiability detection.
% 3.98/1.10  % (3736734)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4207607908_2999 on theBenchmark for (2999ds/0Mi)
% 3.98/1.10  % (3736735)% WARNING: option uhcvi not known.
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736735)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=528983842:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.98/1.10  % (3736736)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=954712977:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.98/1.10  % (3736737)dis+10_1_sil=32000:sp=arity:random_seed=2411685627:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.98/1.10  % (3736738)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1861169060:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.98/1.10  % (3736739)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3511566622:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.98/1.10  % (3736740)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2971938266:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.98/1.10  % (3736742)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=804628551:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736750)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=970682146:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.98/1.10  % (3736737)Instruction limit reached! 
% 3.98/1.10  % (3736737)------------------------------
% 3.98/1.10  % (3736737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736737)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736737)Termination reason: Instruction limit
% 3.98/1.10  % (3736737)Termination phase: Saturation
% 3.98/1.10  % (3736737)Time elapsed: 0.063 s
% 3.98/1.10  % (3736737)Peak memory usage: 13 MB
% 3.98/1.10  % (3736737)Instructions burned: 104 (million)
% 3.98/1.10  % (3736738)Instruction limit reached! 
% 3.98/1.10  % (3736738)------------------------------
% 3.98/1.10  % (3736738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736738)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736738)Termination reason: Instruction limit
% 3.98/1.10  % (3736738)Termination phase: Saturation
% 3.98/1.10  % (3736738)Time elapsed: 0.065 s
% 3.98/1.10  % (3736738)Peak memory usage: 13 MB
% 3.98/1.10  % (3736738)Instructions burned: 117 (million)
% 3.98/1.10  % (3736739)Instruction limit reached! 
% 3.98/1.10  % (3736739)------------------------------
% 3.98/1.10  % (3736739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736739)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736739)Termination reason: Instruction limit
% 3.98/1.10  % (3736739)Termination phase: Saturation
% 3.98/1.10  % (3736739)Time elapsed: 0.069 s
% 3.98/1.10  % (3736739)Peak memory usage: 12 MB
% 3.98/1.10  % (3736739)Instructions burned: 132 (million)
% 3.98/1.10  % (3736752)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2901396816:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.98/1.10  % (3736753)ott-21_1_sil=16000:fs=off:random_seed=818687505:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.98/1.10  % (3736740)Instruction limit reached! 
% 3.98/1.10  % (3736740)------------------------------
% 3.98/1.10  % (3736740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736740)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736754)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=756720838:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.98/1.10  % (3736740)Termination reason: Instruction limit
% 3.98/1.10  % (3736740)Termination phase: Saturation
% 3.98/1.10  % (3736740)Time elapsed: 0.088 s
% 3.98/1.10  % (3736740)Peak memory usage: 13 MB
% 3.98/1.10  % (3736740)Instructions burned: 159 (million)
% 3.98/1.10  % (3736758)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3872863535:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.98/1.10  % (3736750)Instruction limit reached! 
% 3.98/1.10  % (3736750)------------------------------
% 3.98/1.10  % (3736750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736750)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736750)Termination reason: Instruction limit
% 3.98/1.10  % (3736750)Termination phase: Saturation
% 3.98/1.10  % (3736750)Time elapsed: 0.070 s
% 3.98/1.10  % (3736750)Peak memory usage: 14 MB
% 3.98/1.10  % (3736750)Instructions burned: 131 (million)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736760)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1614565964:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.98/1.10  % (3736761)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2094916941:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736764)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1354345154:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 3.98/1.10  % (3736753)Instruction limit reached! 
% 3.98/1.10  % (3736753)------------------------------
% 3.98/1.10  % (3736753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736753)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736753)Termination reason: Instruction limit
% 3.98/1.10  % (3736753)Termination phase: Saturation
% 3.98/1.10  % (3736753)Time elapsed: 0.099 s
% 3.98/1.10  % (3736753)Peak memory usage: 13 MB
% 3.98/1.10  % (3736753)Instructions burned: 181 (million)
% 3.98/1.10  % (3736766)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2724380556:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.98/1.10  % (3736754)Instruction limit reached! 
% 3.98/1.10  % (3736754)------------------------------
% 3.98/1.10  % (3736754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736754)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736754)Termination reason: Instruction limit
% 3.98/1.10  % (3736754)Termination phase: Saturation
% 3.98/1.10  % (3736754)Time elapsed: 0.303 s
% 3.98/1.10  % (3736754)Peak memory usage: 14 MB
% 3.98/1.10  % (3736754)Instructions burned: 478 (million)
% 3.98/1.10  % (3736768)fmb+10_1_sil=64000:random_seed=3824450990:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.98/1.10  % (3736768)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736770)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=724166781:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.98/1.10  % (3736752)Instruction limit reached! 
% 3.98/1.10  % (3736752)------------------------------
% 3.98/1.10  % (3736752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736752)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736752)Termination reason: Instruction limit
% 3.98/1.10  % (3736752)Termination phase: Saturation
% 3.98/1.10  % (3736752)Time elapsed: 0.358 s
% 3.98/1.10  % (3736752)Peak memory usage: 17 MB
% 3.98/1.10  % (3736752)Instructions burned: 684 (million)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736772)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1628003654:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.98/1.10  % (3736773)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3377829972:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736776)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3733912300:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 3.98/1.10  % (3736776)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.98/1.10  % (3736764)Instruction limit reached! 
% 3.98/1.10  % (3736764)------------------------------
% 3.98/1.10  % (3736764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.10  % (3736764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.10  % (3736764)CaDiCaL version: 2.1.3
% 3.98/1.10  % (3736764)Termination reason: Instruction limit
% 3.98/1.10  % (3736764)Termination phase: Saturation
% 3.98/1.10  % (3736764)Time elapsed: 0.342 s
% 3.98/1.10  % (3736764)Peak memory usage: 18 MB
% 3.98/1.10  % (3736764)Instructions burned: 694 (million)
% 3.98/1.10  % (3736778)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3419311395:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736780)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1540644617:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.98/1.10  % Exception at run slice level
% 3.98/1.10  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.98/1.10  % (3736782)ott-2_1_sil=16000:newcnf=on:random_seed=4138653482:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 3.98/1.10  % (3736773) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3736729-3736773"...
% 3.98/1.10  % (3736773)...printing done.
% 3.98/1.10  % (3736773)Refutation found. Thanks to Tanya!
% 3.98/1.10  % SZS status Theorem for theBenchmark
% 3.98/1.10  % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.11  % (3736773)------------------------------
% 3.98/1.11  % (3736773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/1.11  % (3736773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.11  % (3736773)CaDiCaL version: 2.1.3
% 3.98/1.11  % (3736773)Termination reason: Refutation
% 3.98/1.11  % (3736773)Time elapsed: 0.120 s
% 3.98/1.11  % (3736773)Peak memory usage: 14 MB
% 3.98/1.11  % (3736773)Instructions burned: 214 (million)
% 3.98/1.11  % (3736729)Success in time 0.64 s
% 3.98/1.11  % Vampire exiting
%------------------------------------------------------------------------------