TSTP Solution File: LCL805_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL805_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 : Tue Apr 30 13:49:43 EDT 2024

% Result   : Theorem 0.06s 0.29s
% Output   : Refutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  132
% Syntax   : Number of formulae    :  207 (  80 unt;  84 typ;   0 def)
%            Number of atoms       :  218 (  53 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :  159 (  64   ~;  40   |;  27   &)
%                                         (  26 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  112 (  59   >;  53   *;   0   +;   0  <<)
%            Number of predicates  :   38 (  36 usr;  24 prp; 0-6 aty)
%            Number of functors    :   68 (  68 usr;  16 con; 0-5 aty)
%            Number of variables   :  196 ( 136   !;  15   ?; 196   :)
%                                         (  45  !>;   0  ?*;   0  @-;   0  @+)

% 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,
    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(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).

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

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

tff(func_def_4,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).

tff(func_def_5,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_6,type,
    it: fun(dB,bool) ).

tff(func_def_7,type,
    beta: fun(dB,fun(dB,bool)) ).

tff(func_def_8,type,
    abs: dB > dB ).

tff(func_def_9,type,
    app: fun(dB,fun(dB,dB)) ).

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

tff(func_def_11,type,
    dB_case: 
      !>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).

tff(func_def_12,type,
    dB_size: dB > nat ).

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

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

tff(func_def_15,type,
    subst: fun(dB,fun(dB,fun(nat,dB))) ).

tff(func_def_16,type,
    substn: ( dB * dB * nat ) > dB ).

tff(func_def_17,type,
    foldl: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).

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

tff(func_def_19,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_20,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_21,type,
    list_rec: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).

tff(func_def_22,type,
    list_size: 
      !>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).

tff(func_def_23,type,
    map: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).

tff(func_def_24,type,
    monoid_add_listsum: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_25,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

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

tff(func_def_27,type,
    fFalse: bool ).

tff(func_def_28,type,
    fTrue: bool ).

tff(func_def_29,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_30,type,
    a: dB ).

tff(func_def_31,type,
    as: list(dB) ).

tff(func_def_32,type,
    i: nat ).

tff(func_def_33,type,
    n: nat ).

tff(func_def_34,type,
    rs: list(dB) ).

tff(func_def_35,type,
    t: dB ).

tff(func_def_36,type,
    u: dB ).

tff(func_def_37,type,
    ua: dB ).

tff(func_def_38,type,
    sK5: dB > dB ).

tff(func_def_39,type,
    sK6: dB > dB ).

tff(func_def_40,type,
    sK7: dB > dB ).

tff(func_def_41,type,
    sK8: dB > nat ).

tff(func_def_42,type,
    sK9: dB > dB ).

tff(func_def_43,type,
    sK10: dB > list(dB) ).

tff(func_def_44,type,
    sK11: dB > nat ).

tff(func_def_45,type,
    sK12: dB > dB ).

tff(func_def_46,type,
    sK13: dB > dB ).

tff(func_def_47,type,
    sK14: dB > list(dB) ).

tff(func_def_48,type,
    sK15: dB > list(dB) ).

tff(func_def_49,type,
    sK16: dB > dB ).

tff(func_def_50,type,
    sK17: dB > dB ).

tff(func_def_51,type,
    sK18: dB > nat ).

tff(func_def_52,type,
    sK19: ( dB * dB ) > dB ).

tff(func_def_53,type,
    sK20: ( dB * list(dB) * dB ) > dB ).

tff(func_def_54,type,
    sK21: ( dB * list(dB) * dB ) > dB ).

tff(func_def_55,type,
    sK22: ( dB * list(dB) * dB ) > list(dB) ).

tff(func_def_56,type,
    sK23: ( dB * list(dB) * dB ) > list(dB) ).

tff(func_def_57,type,
    sK24: ( dB * list(dB) * dB ) > dB ).

tff(func_def_58,type,
    sK25: ( dB * list(dB) * nat ) > list(dB) ).

tff(func_def_59,type,
    sK26: ( dB * dB * dB ) > dB ).

tff(func_def_60,type,
    sK27: ( dB * dB * dB ) > dB ).

tff(func_def_61,type,
    sK28: ( dB * dB * dB ) > dB ).

tff(func_def_62,type,
    sK29: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_63,type,
    sK30: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).

tff(func_def_64,type,
    sK31: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).

tff(func_def_65,type,
    sK32: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).

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

tff(pred_def_2,type,
    monoid_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    equal_equal: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_4,type,
    step1: 
      !>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $o ) ).

tff(pred_def_5,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_6,type,
    listsp: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_7,type,
    null: 
      !>[X0: $tType] : ( list(X0) > $o ) ).

tff(pred_def_8,type,
    pp: bool > $o ).

tff(pred_def_9,type,
    sP0: dB > $o ).

tff(pred_def_10,type,
    sP1: dB > $o ).

tff(pred_def_11,type,
    sP2: ( dB * list(dB) * dB ) > $o ).

tff(pred_def_12,type,
    sP3: ( dB * dB * dB ) > $o ).

tff(pred_def_13,type,
    sP4: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0 ) > $o ) ).

tff(f642,plain,
    $false,
    inference(avatar_sat_refutation,[],[f538,f543,f548,f553,f557,f561,f565,f569,f573,f578,f583,f588,f592,f596,f600,f604,f609,f613,f617,f621,f625,f632,f639,f641]) ).

tff(f641,plain,
    ( ~ spl33_8
    | spl33_23 ),
    inference(avatar_contradiction_clause,[],[f640]) ).

tff(f640,plain,
    ( $false
    | ~ spl33_8
    | spl33_23 ),
    inference(resolution,[],[f638,f568]) ).

tff(f568,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0))
    | ~ spl33_8 ),
    inference(avatar_component_clause,[],[f567]) ).

tff(f567,plain,
    ( spl33_8
  <=> ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_8])]) ).

tff(f638,plain,
    ( ~ listsp(dB,it,nil(dB))
    | spl33_23 ),
    inference(avatar_component_clause,[],[f636]) ).

tff(f636,plain,
    ( spl33_23
  <=> listsp(dB,it,nil(dB)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_23])]) ).

tff(f639,plain,
    ( ~ spl33_23
    | spl33_22 ),
    inference(avatar_split_clause,[],[f634,f629,f636]) ).

tff(f629,plain,
    ( spl33_22
  <=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_22])]) ).

tff(f634,plain,
    ( ~ listsp(dB,it,nil(dB))
    | spl33_22 ),
    inference(forward_demodulation,[],[f633,f402]) ).

tff(f402,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
    inference(cnf_transformation,[],[f158]) ).

tff(f158,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X1: $tType,X0: $tType,X9: fun(X1,X0)] : ( nil(X0) = map(X1,X0,X9,nil(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_map_Osimps_I1_J) ).

tff(f633,plain,
    ( ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),nil(dB)))
    | spl33_22 ),
    inference(forward_demodulation,[],[f631,f402]) ).

tff(f631,plain,
    ( ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB))))
    | spl33_22 ),
    inference(avatar_component_clause,[],[f629]) ).

tff(f632,plain,
    ~ spl33_22,
    inference(avatar_split_clause,[],[f327,f629]) ).

tff(f327,plain,
    ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,plain,
    ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
    inference(flattening,[],[f113]) ).

tff(f113,negated_conjecture,
    ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
    inference(negated_conjecture,[],[f112]) ).

tff(f112,conjecture,
    listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f625,plain,
    spl33_21,
    inference(avatar_split_clause,[],[f398,f623]) ).

tff(f623,plain,
    ( spl33_21
  <=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_21])]) ).

tff(f398,plain,
    ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
    inference(cnf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X0: $tType,X77: list(X0),X78: X0] : ( cons(X0,X78,X77) != X77 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_not__Cons__self2) ).

tff(f621,plain,
    spl33_20,
    inference(avatar_split_clause,[],[f367,f619]) ).

tff(f619,plain,
    ( spl33_20
  <=> ! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_20])]) ).

tff(f367,plain,
    ! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
    inference(cnf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
    inference(rectify,[],[f45]) ).

tff(f45,axiom,
    ! [X13: nat,X5: dB] : ( liftn(zero_zero(nat),X5,X13) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_liftn__0) ).

tff(f617,plain,
    spl33_19,
    inference(avatar_split_clause,[],[f342,f615]) ).

tff(f615,plain,
    ( spl33_19
  <=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_19])]) ).

tff(f342,plain,
    ! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,plain,
    ! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X27: nat] : pp(aa(dB,bool,it,var(X27))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Var__IT) ).

tff(f613,plain,
    spl33_18,
    inference(avatar_split_clause,[],[f341,f611]) ).

tff(f611,plain,
    ( spl33_18
  <=> ! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_18])]) ).

tff(f341,plain,
    ! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,plain,
    ! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
    inference(rectify,[],[f28]) ).

tff(f28,axiom,
    ! [X26: nat] : ( zero_zero(nat) = size_size(dB,var(X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osize_I4_J) ).

tff(f609,plain,
    spl33_17,
    inference(avatar_split_clause,[],[f336,f606]) ).

tff(f606,plain,
    ( spl33_17
  <=> ( rs = cons(dB,a,as) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_17])]) ).

tff(f336,plain,
    rs = cons(dB,a,as),
    inference(cnf_transformation,[],[f99]) ).

tff(f99,axiom,
    rs = cons(dB,a,as),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Cons) ).

tff(f604,plain,
    spl33_16,
    inference(avatar_split_clause,[],[f397,f602]) ).

tff(f602,plain,
    ( spl33_16
  <=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,nil(X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_16])]) ).

tff(f397,plain,
    ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,nil(X0),X1),
    inference(cnf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,fun(X0,bool))] : ~ step1(X0,X2,nil(X0),X1),
    inference(rectify,[],[f85]) ).

tff(f85,axiom,
    ! [X0: $tType,X8: list(X0),X43: fun(X0,fun(X0,bool))] : ~ step1(X0,X43,nil(X0),X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_not__Nil__step1) ).

tff(f600,plain,
    spl33_15,
    inference(avatar_split_clause,[],[f396,f598]) ).

tff(f598,plain,
    ( spl33_15
  <=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,X1,nil(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_15])]) ).

tff(f396,plain,
    ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,X1,nil(X0)),
    inference(cnf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,fun(X0,bool))] : ~ step1(X0,X2,X1,nil(X0)),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X0: $tType,X8: list(X0),X43: fun(X0,fun(X0,bool))] : ~ step1(X0,X43,X8,nil(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not__step1__Nil) ).

tff(f596,plain,
    spl33_14,
    inference(avatar_split_clause,[],[f395,f594]) ).

tff(f594,plain,
    ( spl33_14
  <=> ! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_14])]) ).

tff(f395,plain,
    ! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1)),
    inference(cnf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: $tType,X1: list(X0),X2: X0] : ~ null(X0,cons(X0,X2,X1)),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X0: $tType,X77: list(X0),X78: X0] : ~ null(X0,cons(X0,X78,X77)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_null__rec_I1_J) ).

tff(f592,plain,
    spl33_13,
    inference(avatar_split_clause,[],[f340,f590]) ).

tff(f590,plain,
    ( spl33_13
  <=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_13])]) ).

tff(f340,plain,
    ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,plain,
    ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X26: nat] : ( zero_zero(nat) = dB_size(var(X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_dB_Osize_I1_J) ).

tff(f588,plain,
    spl33_12,
    inference(avatar_split_clause,[],[f335,f585]) ).

tff(f585,plain,
    ( spl33_12
  <=> pp(aa(dB,bool,it,u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_12])]) ).

tff(f335,plain,
    pp(aa(dB,bool,it,u)),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    pp(aa(dB,bool,it,u)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).

tff(f583,plain,
    spl33_11,
    inference(avatar_split_clause,[],[f334,f580]) ).

tff(f580,plain,
    ( spl33_11
  <=> pp(aa(dB,bool,it,ua)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_11])]) ).

tff(f334,plain,
    pp(aa(dB,bool,it,ua)),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    pp(aa(dB,bool,it,ua)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).

tff(f578,plain,
    spl33_10,
    inference(avatar_split_clause,[],[f333,f575]) ).

tff(f575,plain,
    ( spl33_10
  <=> pp(aa(dB,bool,it,t)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_10])]) ).

tff(f333,plain,
    pp(aa(dB,bool,it,t)),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    pp(aa(dB,bool,it,t)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).

tff(f573,plain,
    spl33_9,
    inference(avatar_split_clause,[],[f508,f571]) ).

tff(f571,plain,
    ( spl33_9
  <=> ! [X0: $tType,X2: list(X0)] : equal_equal(list(X0),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_9])]) ).

tff(f508,plain,
    ! [X0: $tType,X2: list(X0)] : equal_equal(list(X0),X2,X2),
    inference(equality_resolution,[],[f434]) ).

tff(f434,plain,
    ! [X0: $tType,X2: list(X0),X1: list(X0)] :
      ( equal_equal(list(X0),X2,X1)
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f299,plain,
    ! [X0: $tType,X1: list(X0),X2: list(X0)] :
      ( ( equal_equal(list(X0),X2,X1)
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ~ equal_equal(list(X0),X2,X1) ) ),
    inference(nnf_transformation,[],[f177]) ).

tff(f177,plain,
    ! [X0: $tType,X1: list(X0),X2: list(X0)] :
      ( equal_equal(list(X0),X2,X1)
    <=> ( X1 = X2 ) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X0: $tType,X52: list(X0),X14: list(X0)] :
      ( equal_equal(list(X0),X14,X52)
    <=> ( X14 = X52 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_equal__list__def) ).

tff(f569,plain,
    spl33_8,
    inference(avatar_split_clause,[],[f366,f567]) ).

tff(f366,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
    inference(cnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X0: $tType,X7: fun(X0,bool)] : listsp(X0,X7,nil(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_listsp_ONil) ).

tff(f565,plain,
    spl33_7,
    inference(avatar_split_clause,[],[f364,f563]) ).

tff(f563,plain,
    ( spl33_7
  <=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_7])]) ).

tff(f364,plain,
    ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
    inference(cnf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X49: dB,X26: nat] : ( var(X26) != abs(X49) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_dB_Osimps_I6_J) ).

tff(f561,plain,
    spl33_6,
    inference(avatar_split_clause,[],[f355,f559]) ).

tff(f559,plain,
    ( spl33_6
  <=> ! [X0: dB] :
        ( sP1(X0)
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_6])]) ).

tff(f355,plain,
    ! [X0: dB] :
      ( sP1(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f263]) ).

tff(f263,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X1: dB] :
              ( ~ pp(aa(dB,bool,it,X1))
              | ( abs(X1) != X0 ) )
          & ! [X2: list(dB),X3: nat] :
              ( ~ listsp(dB,it,X2)
              | ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
      & ( sP0(X0)
        | ( pp(aa(dB,bool,it,sK9(X0)))
          & ( abs(sK9(X0)) = X0 ) )
        | ( listsp(dB,it,sK10(X0))
          & ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f260,f262,f261]) ).

tff(f261,plain,
    ! [X0: dB] :
      ( ? [X4: dB] :
          ( pp(aa(dB,bool,it,X4))
          & ( abs(X4) = X0 ) )
     => ( pp(aa(dB,bool,it,sK9(X0)))
        & ( abs(sK9(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f262,plain,
    ! [X0: dB] :
      ( ? [X5: list(dB),X6: nat] :
          ( listsp(dB,it,X5)
          & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
     => ( listsp(dB,it,sK10(X0))
        & ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f260,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X1: dB] :
              ( ~ pp(aa(dB,bool,it,X1))
              | ( abs(X1) != X0 ) )
          & ! [X2: list(dB),X3: nat] :
              ( ~ listsp(dB,it,X2)
              | ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
      & ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(rectify,[],[f259]) ).

tff(f259,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X4: dB] :
              ( ~ pp(aa(dB,bool,it,X4))
              | ( abs(X4) != X0 ) )
          & ! [X5: list(dB),X6: nat] :
              ( ~ listsp(dB,it,X5)
              | ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
      & ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(flattening,[],[f258]) ).

tff(f258,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X4: dB] :
              ( ~ pp(aa(dB,bool,it,X4))
              | ( abs(X4) != X0 ) )
          & ! [X5: list(dB),X6: nat] :
              ( ~ listsp(dB,it,X5)
              | ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
      & ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: dB] :
      ( sP1(X0)
    <=> ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f557,plain,
    spl33_5,
    inference(avatar_split_clause,[],[f339,f555]) ).

tff(f555,plain,
    ( spl33_5
  <=> ! [X0: $tType] : null(X0,nil(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_5])]) ).

tff(f339,plain,
    ! [X0: $tType] : null(X0,nil(X0)),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,plain,
    ! [X0: $tType] : null(X0,nil(X0)),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X1: $tType] : null(X1,nil(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_null__rec_I2_J) ).

tff(f553,plain,
    spl33_4,
    inference(avatar_split_clause,[],[f331,f550]) ).

tff(f550,plain,
    ( spl33_4
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_4])]) ).

tff(f331,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f548,plain,
    spl33_3,
    inference(avatar_split_clause,[],[f330,f545]) ).

tff(f545,plain,
    ( spl33_3
  <=> monoid_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_3])]) ).

tff(f330,plain,
    monoid_add(nat),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    monoid_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).

tff(f543,plain,
    spl33_2,
    inference(avatar_split_clause,[],[f329,f540]) ).

tff(f540,plain,
    ( spl33_2
  <=> zero(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_2])]) ).

tff(f329,plain,
    zero(nat),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    zero(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

tff(f538,plain,
    ~ spl33_1,
    inference(avatar_split_clause,[],[f328,f535]) ).

tff(f535,plain,
    ( spl33_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl33_1])]) ).

tff(f328,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem    : LCL805_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.07  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.06/0.26  % Computer : n017.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit   : 300
% 0.06/0.26  % WCLimit    : 300
% 0.06/0.26  % DateTime   : Mon Apr 29 22:06:18 EDT 2024
% 0.06/0.26  % CPUTime    : 
% 0.06/0.26  % (29536)Running in auto input_syntax mode. Trying TPTP
% 0.06/0.27  % (29544)WARNING: value z3 for option sas not known
% 0.06/0.28  % (29543)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.06/0.28  % (29542)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.06/0.28  % (29546)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.06/0.28  % (29544)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)
% 0.06/0.28  % (29547)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)
% 0.06/0.28  % (29548)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)
% 0.06/0.28  % (29549)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)
% 0.06/0.28  % (29549)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.06/0.28  % Exception at run slice level
% 0.06/0.28  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.28  % Exception at run slice level
% 0.06/0.28  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.28  % Exception at run slice level
% 0.06/0.28  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.28  % (29547)First to succeed.
% 0.06/0.29  % (29548)Also succeeded, but the first one will report.
% 0.06/0.29  % (29547)Refutation found. Thanks to Tanya!
% 0.06/0.29  % SZS status Theorem for theBenchmark
% 0.06/0.29  % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.29  % (29547)------------------------------
% 0.06/0.29  % (29547)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.06/0.29  % (29547)Termination reason: Refutation
% 0.06/0.29  
% 0.06/0.29  % (29547)Memory used [KB]: 1189
% 0.06/0.29  % (29547)Time elapsed: 0.010 s
% 0.06/0.29  % (29547)Instructions burned: 28 (million)
% 0.06/0.29  % (29547)------------------------------
% 0.06/0.29  % (29547)------------------------------
% 0.06/0.29  % (29536)Success in time 0.022 s
%------------------------------------------------------------------------------