TSTP Solution File: DAT100_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT100_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.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 11:04:06 EDT 2024

% Result   : Theorem 63.90s 9.49s
% Output   : Refutation 63.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  211 (  19 unt;   8 typ;   0 def)
%            Number of atoms       :  556 ( 152 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  575 ( 222   ~; 283   |;  35   &)
%                                         (  34 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number arithmetic     :  926 (  97 atm;  13 fun; 753 num;  63 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   36 (  32 usr;  32 prp; 0-2 aty)
%            Number of functors    :   14 (   6 usr;   7 con; 0-2 aty)
%            Number of variables   :  109 (  95   !;  14   ?; 109   :)

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

tff(func_def_0,type,
    nil: list ).

tff(func_def_1,type,
    cons: ( $int * list ) > list ).

tff(func_def_2,type,
    head: list > $int ).

tff(func_def_3,type,
    tail: list > list ).

tff(func_def_11,type,
    sK0: ( $int * list ) > $int ).

tff(func_def_12,type,
    sK1: ( $int * list ) > list ).

tff(pred_def_1,type,
    inRange: ( $int * list ) > $o ).

tff(f226716,plain,
    $false,
    inference(avatar_sat_refutation,[],[f46,f5215,f7479,f20514,f20520,f20526,f20535,f41690,f41703,f41716,f46509,f48227,f48231,f48234,f48249,f48255,f48265,f48278,f48284,f48298,f48320,f48332,f48333,f48334,f48335,f48341,f48356,f48374,f48378,f49059,f49065,f49093,f49098,f49110,f49112,f49115,f226712,f226715]) ).

tff(f226715,plain,
    ( ~ spl2_13
    | spl2_29 ),
    inference(avatar_contradiction_clause,[],[f226714]) ).

tff(f226714,plain,
    ( $false
    | ~ spl2_13
    | spl2_29 ),
    inference(subsumption_resolution,[],[f226713,f49063]) ).

tff(f49063,plain,
    ( ( 5 != sK0(4,cons(5,cons(2,nil))) )
    | spl2_29 ),
    inference(avatar_component_clause,[],[f49062]) ).

tff(f49062,plain,
    ( spl2_29
  <=> ( 5 = sK0(4,cons(5,cons(2,nil))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).

tff(f226713,plain,
    ( ( 5 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_13 ),
    inference(forward_demodulation,[],[f226704,f32]) ).

tff(f32,plain,
    ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).

tff(f226704,plain,
    ( ( sK0(4,cons(5,cons(2,nil))) = head(cons(5,cons(2,nil))) )
    | ~ spl2_13 ),
    inference(superposition,[],[f32,f46508]) ).

tff(f46508,plain,
    ( ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),sK1(4,cons(5,cons(2,nil)))) )
    | ~ spl2_13 ),
    inference(avatar_component_clause,[],[f46506]) ).

tff(f46506,plain,
    ( spl2_13
  <=> ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),sK1(4,cons(5,cons(2,nil)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).

tff(f226712,plain,
    ( spl2_31
    | ~ spl2_13 ),
    inference(avatar_split_clause,[],[f226707,f46506,f226709]) ).

tff(f226709,plain,
    ( spl2_31
  <=> ( cons(2,nil) = sK1(4,cons(5,cons(2,nil))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).

tff(f226707,plain,
    ( ( cons(2,nil) = sK1(4,cons(5,cons(2,nil))) )
    | ~ spl2_13 ),
    inference(forward_demodulation,[],[f226703,f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).

tff(f226703,plain,
    ( ( sK1(4,cons(5,cons(2,nil))) = tail(cons(5,cons(2,nil))) )
    | ~ spl2_13 ),
    inference(superposition,[],[f33,f46508]) ).

tff(f49115,plain,
    ( spl2_30
    | ~ spl2_28 ),
    inference(avatar_split_clause,[],[f49114,f49056,f49095]) ).

tff(f49095,plain,
    ( spl2_30
  <=> ( cons(5,cons(2,nil)) = cons(5,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).

tff(f49056,plain,
    ( spl2_28
  <=> ( nil = tail(cons(5,cons(2,nil))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).

tff(f49114,plain,
    ( ( cons(5,cons(2,nil)) = cons(5,nil) )
    | ~ spl2_28 ),
    inference(forward_demodulation,[],[f49113,f32]) ).

tff(f49113,plain,
    ( ( cons(5,cons(2,nil)) = cons(head(cons(5,cons(2,nil))),nil) )
    | ~ spl2_28 ),
    inference(subsumption_resolution,[],[f49108,f31]) ).

tff(f31,plain,
    ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).

tff(f49108,plain,
    ( ( cons(5,cons(2,nil)) = cons(head(cons(5,cons(2,nil))),nil) )
    | ( nil = cons(5,cons(2,nil)) )
    | ~ spl2_28 ),
    inference(superposition,[],[f30,f49058]) ).

tff(f49058,plain,
    ( ( nil = tail(cons(5,cons(2,nil))) )
    | ~ spl2_28 ),
    inference(avatar_component_clause,[],[f49056]) ).

tff(f30,plain,
    ! [X0: list] :
      ( ( cons(head(X0),tail(X0)) = X0 )
      | ( nil = X0 ) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0: list] :
      ( ( cons(head(X0),tail(X0)) = X0 )
      | ( nil = X0 ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X1: list] :
      ( ( cons(head(X1),tail(X1)) = X1 )
      | ( nil = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).

tff(f49112,plain,
    ~ spl2_28,
    inference(avatar_contradiction_clause,[],[f49111]) ).

tff(f49111,plain,
    ( $false
    | ~ spl2_28 ),
    inference(subsumption_resolution,[],[f49107,f31]) ).

tff(f49107,plain,
    ( ( nil = cons(2,nil) )
    | ~ spl2_28 ),
    inference(superposition,[],[f33,f49058]) ).

tff(f49110,plain,
    ~ spl2_28,
    inference(avatar_contradiction_clause,[],[f49109]) ).

tff(f49109,plain,
    ( $false
    | ~ spl2_28 ),
    inference(subsumption_resolution,[],[f49106,f31]) ).

tff(f49106,plain,
    ( ( nil = cons(2,nil) )
    | ~ spl2_28 ),
    inference(superposition,[],[f49058,f33]) ).

tff(f49098,plain,
    ( spl2_30
    | ~ spl2_21
    | ~ spl2_29 ),
    inference(avatar_split_clause,[],[f49074,f49062,f48281,f49095]) ).

tff(f48281,plain,
    ( spl2_21
  <=> ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).

tff(f49074,plain,
    ( ( cons(5,cons(2,nil)) = cons(5,nil) )
    | ~ spl2_21
    | ~ spl2_29 ),
    inference(backward_demodulation,[],[f48283,f49064]) ).

tff(f49064,plain,
    ( ( 5 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_29 ),
    inference(avatar_component_clause,[],[f49062]) ).

tff(f48283,plain,
    ( ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),nil) )
    | ~ spl2_21 ),
    inference(avatar_component_clause,[],[f48281]) ).

tff(f49093,plain,
    ( ~ spl2_9
    | ~ spl2_29 ),
    inference(avatar_contradiction_clause,[],[f49092]) ).

tff(f49092,plain,
    ( $false
    | ~ spl2_9
    | ~ spl2_29 ),
    inference(evaluation,[],[f49066]) ).

tff(f49066,plain,
    ( $less(5,4)
    | ~ spl2_9
    | ~ spl2_29 ),
    inference(backward_demodulation,[],[f41689,f49064]) ).

tff(f41689,plain,
    ( $less(sK0(4,cons(5,cons(2,nil))),4)
    | ~ spl2_9 ),
    inference(avatar_component_clause,[],[f41687]) ).

tff(f41687,plain,
    ( spl2_9
  <=> $less(sK0(4,cons(5,cons(2,nil))),4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

tff(f49065,plain,
    ( spl2_29
    | ~ spl2_21 ),
    inference(avatar_split_clause,[],[f49060,f48281,f49062]) ).

tff(f49060,plain,
    ( ( 5 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_21 ),
    inference(forward_demodulation,[],[f49051,f32]) ).

tff(f49051,plain,
    ( ( sK0(4,cons(5,cons(2,nil))) = head(cons(5,cons(2,nil))) )
    | ~ spl2_21 ),
    inference(superposition,[],[f32,f48283]) ).

tff(f49059,plain,
    ( spl2_28
    | ~ spl2_21 ),
    inference(avatar_split_clause,[],[f49050,f48281,f49056]) ).

tff(f49050,plain,
    ( ( nil = tail(cons(5,cons(2,nil))) )
    | ~ spl2_21 ),
    inference(superposition,[],[f33,f48283]) ).

tff(f48378,plain,
    ( ~ spl2_26
    | ~ spl2_15
    | spl2_20 ),
    inference(avatar_split_clause,[],[f48377,f48275,f48242,f48338]) ).

tff(f48338,plain,
    ( spl2_26
  <=> ( cons(5,cons(2,nil)) = cons(0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).

tff(f48242,plain,
    ( spl2_15
  <=> ( nil = sK1(4,cons(5,cons(2,nil))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).

tff(f48275,plain,
    ( spl2_20
  <=> ( cons(5,cons(2,nil)) = cons(0,sK1(4,cons(5,cons(2,nil)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).

tff(f48377,plain,
    ( ( cons(5,cons(2,nil)) != cons(0,nil) )
    | ~ spl2_15
    | spl2_20 ),
    inference(forward_demodulation,[],[f48276,f48244]) ).

tff(f48244,plain,
    ( ( nil = sK1(4,cons(5,cons(2,nil))) )
    | ~ spl2_15 ),
    inference(avatar_component_clause,[],[f48242]) ).

tff(f48276,plain,
    ( ( cons(5,cons(2,nil)) != cons(0,sK1(4,cons(5,cons(2,nil)))) )
    | spl2_20 ),
    inference(avatar_component_clause,[],[f48275]) ).

tff(f48374,plain,
    ( spl2_27
    | ~ spl2_21
    | ~ spl2_24 ),
    inference(avatar_split_clause,[],[f48365,f48325,f48281,f48371]) ).

tff(f48371,plain,
    ( spl2_27
  <=> ( cons(5,cons(2,nil)) = cons(1,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).

tff(f48325,plain,
    ( spl2_24
  <=> ( 1 = sK0(4,cons(5,cons(2,nil))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).

tff(f48365,plain,
    ( ( cons(5,cons(2,nil)) = cons(1,nil) )
    | ~ spl2_21
    | ~ spl2_24 ),
    inference(backward_demodulation,[],[f48283,f48327]) ).

tff(f48327,plain,
    ( ( 1 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_24 ),
    inference(avatar_component_clause,[],[f48325]) ).

tff(f48356,plain,
    ( spl2_26
    | ~ spl2_18
    | ~ spl2_21 ),
    inference(avatar_split_clause,[],[f48350,f48281,f48258,f48338]) ).

tff(f48258,plain,
    ( spl2_18
  <=> ( 0 = sK0(4,cons(5,cons(2,nil))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).

tff(f48350,plain,
    ( ( cons(5,cons(2,nil)) = cons(0,nil) )
    | ~ spl2_18
    | ~ spl2_21 ),
    inference(backward_demodulation,[],[f48283,f48260]) ).

tff(f48260,plain,
    ( ( 0 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_18 ),
    inference(avatar_component_clause,[],[f48258]) ).

tff(f48341,plain,
    ( spl2_26
    | ~ spl2_15
    | ~ spl2_20 ),
    inference(avatar_split_clause,[],[f48336,f48275,f48242,f48338]) ).

tff(f48336,plain,
    ( ( cons(5,cons(2,nil)) = cons(0,nil) )
    | ~ spl2_15
    | ~ spl2_20 ),
    inference(forward_demodulation,[],[f48277,f48244]) ).

tff(f48277,plain,
    ( ( cons(5,cons(2,nil)) = cons(0,sK1(4,cons(5,cons(2,nil)))) )
    | ~ spl2_20 ),
    inference(avatar_component_clause,[],[f48275]) ).

tff(f48335,plain,
    ( spl2_18
    | spl2_19
    | spl2_10 ),
    inference(avatar_split_clause,[],[f48292,f41697,f48262,f48258]) ).

tff(f48262,plain,
    ( spl2_19
  <=> $less(0,sK0(4,cons(5,cons(2,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).

tff(f41697,plain,
    ( spl2_10
  <=> $less(sK0(4,cons(5,cons(2,nil))),0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

tff(f48292,plain,
    ( $less(0,sK0(4,cons(5,cons(2,nil))))
    | ( 0 = sK0(4,cons(5,cons(2,nil))) )
    | spl2_10 ),
    inference(resolution,[],[f41698,f16]) ).

tff(f16,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f41698,plain,
    ( ~ $less(sK0(4,cons(5,cons(2,nil))),0)
    | spl2_10 ),
    inference(avatar_component_clause,[],[f41697]) ).

tff(f48334,plain,
    ( spl2_18
    | spl2_19
    | spl2_10 ),
    inference(avatar_split_clause,[],[f48293,f41697,f48262,f48258]) ).

tff(f48293,plain,
    ( $less(0,sK0(4,cons(5,cons(2,nil))))
    | ( 0 = sK0(4,cons(5,cons(2,nil))) )
    | spl2_10 ),
    inference(resolution,[],[f41698,f16]) ).

tff(f48333,plain,
    ( spl2_24
    | spl2_25
    | spl2_23 ),
    inference(avatar_split_clause,[],[f48323,f48317,f48329,f48325]) ).

tff(f48329,plain,
    ( spl2_25
  <=> $less(1,sK0(4,cons(5,cons(2,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).

tff(f48317,plain,
    ( spl2_23
  <=> $less(sK0(4,cons(5,cons(2,nil))),1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).

tff(f48323,plain,
    ( $less(1,sK0(4,cons(5,cons(2,nil))))
    | ( 1 = sK0(4,cons(5,cons(2,nil))) )
    | spl2_23 ),
    inference(resolution,[],[f48319,f16]) ).

tff(f48319,plain,
    ( ~ $less(sK0(4,cons(5,cons(2,nil))),1)
    | spl2_23 ),
    inference(avatar_component_clause,[],[f48317]) ).

tff(f48332,plain,
    ( spl2_24
    | spl2_25
    | spl2_23 ),
    inference(avatar_split_clause,[],[f48322,f48317,f48329,f48325]) ).

tff(f48322,plain,
    ( $less(1,sK0(4,cons(5,cons(2,nil))))
    | ( 1 = sK0(4,cons(5,cons(2,nil))) )
    | spl2_23 ),
    inference(resolution,[],[f48319,f16]) ).

tff(f48320,plain,
    ( ~ spl2_23
    | ~ spl2_19 ),
    inference(avatar_split_clause,[],[f48307,f48262,f48317]) ).

tff(f48307,plain,
    ( ~ $less(sK0(4,cons(5,cons(2,nil))),1)
    | ~ spl2_19 ),
    inference(resolution,[],[f48264,f104]) ).

tff(f104,plain,
    ! [X0: $int] :
      ( ~ $less(0,X0)
      | ~ $less(X0,1) ),
    inference(superposition,[],[f77,f11]) ).

tff(f11,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f77,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(1,X0))
      | ~ $less(X0,X1) ),
    inference(superposition,[],[f20,f9]) ).

tff(f9,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(X0,1))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_161,[]) ).

tff(f48264,plain,
    ( $less(0,sK0(4,cons(5,cons(2,nil))))
    | ~ spl2_19 ),
    inference(avatar_component_clause,[],[f48262]) ).

tff(f48298,plain,
    ( spl2_22
    | spl2_10 ),
    inference(avatar_split_clause,[],[f48291,f41697,f48295]) ).

tff(f48295,plain,
    ( spl2_22
  <=> $less(-1,sK0(4,cons(5,cons(2,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).

tff(f48291,plain,
    ( $less(-1,sK0(4,cons(5,cons(2,nil))))
    | spl2_10 ),
    inference(resolution,[],[f41698,f63]) ).

tff(f63,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | $less(-1,X0) ),
    inference(evaluation,[],[f62]) ).

tff(f62,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | $less($uminus(1),X0) ),
    inference(superposition,[],[f18,f47]) ).

tff(f47,plain,
    ! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
    inference(superposition,[],[f13,f19]) ).

tff(f19,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f13,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_147,[]) ).

tff(f48284,plain,
    ( spl2_21
    | ~ spl2_13
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f48279,f48242,f46506,f48281]) ).

tff(f48279,plain,
    ( ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),nil) )
    | ~ spl2_13
    | ~ spl2_15 ),
    inference(forward_demodulation,[],[f46508,f48244]) ).

tff(f48278,plain,
    ( spl2_20
    | ~ spl2_13
    | ~ spl2_18 ),
    inference(avatar_split_clause,[],[f48272,f48258,f46506,f48275]) ).

tff(f48272,plain,
    ( ( cons(5,cons(2,nil)) = cons(0,sK1(4,cons(5,cons(2,nil)))) )
    | ~ spl2_13
    | ~ spl2_18 ),
    inference(backward_demodulation,[],[f46508,f48260]) ).

tff(f48265,plain,
    ( spl2_18
    | spl2_19
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f48256,f41713,f48262,f48258]) ).

tff(f41713,plain,
    ( spl2_12
  <=> inRange(4,cons(5,cons(2,nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).

tff(f48256,plain,
    ( $less(0,sK0(4,cons(5,cons(2,nil))))
    | ( 0 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_12 ),
    inference(subsumption_resolution,[],[f48237,f31]) ).

tff(f48237,plain,
    ( ( nil = cons(5,cons(2,nil)) )
    | $less(0,sK0(4,cons(5,cons(2,nil))))
    | ( 0 = sK0(4,cons(5,cons(2,nil))) )
    | ~ spl2_12 ),
    inference(resolution,[],[f41714,f4454]) ).

tff(f4454,plain,
    ! [X0: list,X1: $int] :
      ( ~ inRange(X1,X0)
      | ( nil = X0 )
      | $less(0,sK0(X1,X0))
      | ( 0 = sK0(X1,X0) ) ),
    inference(resolution,[],[f35,f16]) ).

tff(f35,plain,
    ! [X0: $int,X1: list] :
      ( ~ $less(sK0(X0,X1),0)
      | ( nil = X1 )
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ( inRange(X0,sK1(X0,X1))
          & $less(sK0(X0,X1),X0)
          & ~ $less(sK0(X0,X1),0)
          & ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f27]) ).

tff(f27,plain,
    ! [X0: $int,X1: list] :
      ( ? [X4: $int,X5: list] :
          ( inRange(X0,X5)
          & $less(X4,X0)
          & ~ $less(X4,0)
          & ( cons(X4,X5) = X1 ) )
     => ( inRange(X0,sK1(X0,X1))
        & $less(sK0(X0,X1),X0)
        & ~ $less(sK0(X0,X1),0)
        & ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X4: $int,X5: list] :
            ( inRange(X0,X5)
            & $less(X4,X0)
            & ~ $less(X4,0)
            & ( cons(X4,X5) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(rectify,[],[f25]) ).

tff(f25,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(flattening,[],[f24]) ).

tff(f24,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(nnf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
    <=> ( ? [X0: $int,X3: list] :
            ( inRange(X2,X3)
            & $less(X0,X2)
            & ~ $less(X0,0)
            & ( cons(X0,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(theory_normalization,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
    <=> ( ? [X0: $int,X3: list] :
            ( inRange(X2,X3)
            & $less(X0,X2)
            & $lesseq(0,X0)
            & ( cons(X0,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).

tff(f41714,plain,
    ( inRange(4,cons(5,cons(2,nil)))
    | ~ spl2_12 ),
    inference(avatar_component_clause,[],[f41713]) ).

tff(f48255,plain,
    ( spl2_17
    | spl2_15
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f48250,f41713,f48242,f48252]) ).

tff(f48252,plain,
    ( spl2_17
  <=> $less(sK0(4,sK1(4,cons(5,cons(2,nil)))),4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).

tff(f48250,plain,
    ( ( nil = sK1(4,cons(5,cons(2,nil))) )
    | $less(sK0(4,sK1(4,cons(5,cons(2,nil)))),4)
    | ~ spl2_12 ),
    inference(subsumption_resolution,[],[f48236,f31]) ).

tff(f48236,plain,
    ( ( nil = cons(5,cons(2,nil)) )
    | ( nil = sK1(4,cons(5,cons(2,nil))) )
    | $less(sK0(4,sK1(4,cons(5,cons(2,nil)))),4)
    | ~ spl2_12 ),
    inference(resolution,[],[f41714,f5961]) ).

tff(f5961,plain,
    ! [X0: list,X1: $int] :
      ( ~ inRange(X1,X0)
      | ( nil = X0 )
      | ( nil = sK1(X1,X0) )
      | $less(sK0(X1,sK1(X1,X0)),X1) ),
    inference(resolution,[],[f37,f36]) ).

tff(f36,plain,
    ! [X0: $int,X1: list] :
      ( ~ inRange(X0,X1)
      | ( nil = X1 )
      | $less(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f37,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,sK1(X0,X1))
      | ( nil = X1 )
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f48249,plain,
    ( spl2_15
    | spl2_16
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f48240,f41713,f48246,f48242]) ).

tff(f48246,plain,
    ( spl2_16
  <=> ( sK1(4,cons(5,cons(2,nil))) = cons(sK0(4,sK1(4,cons(5,cons(2,nil)))),sK1(4,sK1(4,cons(5,cons(2,nil))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).

tff(f48240,plain,
    ( ( sK1(4,cons(5,cons(2,nil))) = cons(sK0(4,sK1(4,cons(5,cons(2,nil)))),sK1(4,sK1(4,cons(5,cons(2,nil))))) )
    | ( nil = sK1(4,cons(5,cons(2,nil))) )
    | ~ spl2_12 ),
    inference(subsumption_resolution,[],[f48235,f31]) ).

tff(f48235,plain,
    ( ( sK1(4,cons(5,cons(2,nil))) = cons(sK0(4,sK1(4,cons(5,cons(2,nil)))),sK1(4,sK1(4,cons(5,cons(2,nil))))) )
    | ( nil = cons(5,cons(2,nil)) )
    | ( nil = sK1(4,cons(5,cons(2,nil))) )
    | ~ spl2_12 ),
    inference(resolution,[],[f41714,f7470]) ).

tff(f7470,plain,
    ! [X0: $int,X1: list] :
      ( ~ inRange(X0,X1)
      | ( sK1(X0,X1) = cons(sK0(X0,sK1(X0,X1)),sK1(X0,sK1(X0,X1))) )
      | ( nil = X1 )
      | ( nil = sK1(X0,X1) ) ),
    inference(resolution,[],[f34,f37]) ).

tff(f34,plain,
    ! [X0: $int,X1: list] :
      ( ~ inRange(X0,X1)
      | ( nil = X1 )
      | ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 ) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f48234,plain,
    ( spl2_12
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(avatar_split_clause,[],[f48233,f20517,f43,f41713]) ).

tff(f43,plain,
    ( spl2_1
  <=> inRange(4,cons(1,cons(5,cons(2,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

tff(f20517,plain,
    ( spl2_6
  <=> ( cons(5,cons(2,nil)) = sK1(4,cons(1,cons(5,cons(2,nil)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

tff(f48233,plain,
    ( inRange(4,cons(5,cons(2,nil)))
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(subsumption_resolution,[],[f48232,f45]) ).

tff(f45,plain,
    ( inRange(4,cons(1,cons(5,cons(2,nil))))
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f43]) ).

tff(f48232,plain,
    ( inRange(4,cons(5,cons(2,nil)))
    | ~ inRange(4,cons(1,cons(5,cons(2,nil))))
    | ~ spl2_6 ),
    inference(subsumption_resolution,[],[f48223,f31]) ).

tff(f48223,plain,
    ( inRange(4,cons(5,cons(2,nil)))
    | ( nil = cons(1,cons(5,cons(2,nil))) )
    | ~ inRange(4,cons(1,cons(5,cons(2,nil))))
    | ~ spl2_6 ),
    inference(superposition,[],[f37,f20519]) ).

tff(f20519,plain,
    ( ( cons(5,cons(2,nil)) = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_6 ),
    inference(avatar_component_clause,[],[f20517]) ).

tff(f48231,plain,
    ( spl2_10
    | spl2_14
    | ~ spl2_9 ),
    inference(avatar_split_clause,[],[f45393,f41687,f48229,f41697]) ).

tff(f48229,plain,
    ( spl2_14
  <=> ! [X0: list] :
        ( ~ inRange(4,X0)
        | ( cons(sK0(4,cons(5,cons(2,nil))),X0) = cons(sK0(4,cons(sK0(4,cons(5,cons(2,nil))),X0)),sK1(4,cons(sK0(4,cons(5,cons(2,nil))),X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).

tff(f45393,plain,
    ( ! [X0: list] :
        ( ~ inRange(4,X0)
        | ( cons(sK0(4,cons(5,cons(2,nil))),X0) = cons(sK0(4,cons(sK0(4,cons(5,cons(2,nil))),X0)),sK1(4,cons(sK0(4,cons(5,cons(2,nil))),X0))) )
        | $less(sK0(4,cons(5,cons(2,nil))),0) )
    | ~ spl2_9 ),
    inference(resolution,[],[f7473,f41689]) ).

tff(f7473,plain,
    ! [X2: $int,X0: $int,X1: list] :
      ( ~ $less(X0,X2)
      | ~ inRange(X2,X1)
      | ( cons(X0,X1) = cons(sK0(X2,cons(X0,X1)),sK1(X2,cons(X0,X1))) )
      | $less(X0,0) ),
    inference(subsumption_resolution,[],[f7471,f31]) ).

tff(f7471,plain,
    ! [X2: $int,X0: $int,X1: list] :
      ( ( cons(X0,X1) = nil )
      | ( cons(X0,X1) = cons(sK0(X2,cons(X0,X1)),sK1(X2,cons(X0,X1))) )
      | ~ inRange(X2,X1)
      | ~ $less(X0,X2)
      | $less(X0,0) ),
    inference(resolution,[],[f34,f40]) ).

tff(f40,plain,
    ! [X2: $int,X3: list,X0: $int] :
      ( inRange(X0,cons(X2,X3))
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0) ),
    inference(equality_resolution,[],[f39]) ).

tff(f39,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( inRange(X0,X1)
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0)
      | ( cons(X2,X3) != X1 ) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f48227,plain,
    ( ~ spl2_1
    | ~ spl2_6
    | spl2_12 ),
    inference(avatar_contradiction_clause,[],[f48226]) ).

tff(f48226,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_6
    | spl2_12 ),
    inference(subsumption_resolution,[],[f48225,f45]) ).

tff(f48225,plain,
    ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
    | ~ spl2_6
    | spl2_12 ),
    inference(subsumption_resolution,[],[f48224,f31]) ).

tff(f48224,plain,
    ( ( nil = cons(1,cons(5,cons(2,nil))) )
    | ~ inRange(4,cons(1,cons(5,cons(2,nil))))
    | ~ spl2_6
    | spl2_12 ),
    inference(subsumption_resolution,[],[f48223,f41715]) ).

tff(f41715,plain,
    ( ~ inRange(4,cons(5,cons(2,nil)))
    | spl2_12 ),
    inference(avatar_component_clause,[],[f41713]) ).

tff(f46509,plain,
    ( spl2_13
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(avatar_split_clause,[],[f46504,f20517,f43,f46506]) ).

tff(f46504,plain,
    ( ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),sK1(4,cons(5,cons(2,nil)))) )
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(subsumption_resolution,[],[f46503,f31]) ).

tff(f46503,plain,
    ( ( nil = cons(5,cons(2,nil)) )
    | ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),sK1(4,cons(5,cons(2,nil)))) )
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(forward_demodulation,[],[f46502,f20519]) ).

tff(f46502,plain,
    ( ( cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),sK1(4,cons(5,cons(2,nil)))) )
    | ( nil = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(forward_demodulation,[],[f46501,f20519]) ).

tff(f46501,plain,
    ( ( sK1(4,cons(1,cons(5,cons(2,nil)))) = cons(sK0(4,sK1(4,cons(1,cons(5,cons(2,nil))))),sK1(4,sK1(4,cons(1,cons(5,cons(2,nil)))))) )
    | ( nil = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f46499,f31]) ).

tff(f46499,plain,
    ( ( sK1(4,cons(1,cons(5,cons(2,nil)))) = cons(sK0(4,sK1(4,cons(1,cons(5,cons(2,nil))))),sK1(4,sK1(4,cons(1,cons(5,cons(2,nil)))))) )
    | ( nil = cons(1,cons(5,cons(2,nil))) )
    | ( nil = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_1 ),
    inference(resolution,[],[f7470,f45]) ).

tff(f41716,plain,
    ( ~ spl2_12
    | ~ spl2_10 ),
    inference(avatar_split_clause,[],[f41711,f41697,f41713]) ).

tff(f41711,plain,
    ( ~ inRange(4,cons(5,cons(2,nil)))
    | ~ spl2_10 ),
    inference(subsumption_resolution,[],[f41704,f31]) ).

tff(f41704,plain,
    ( ( nil = cons(5,cons(2,nil)) )
    | ~ inRange(4,cons(5,cons(2,nil)))
    | ~ spl2_10 ),
    inference(resolution,[],[f41699,f35]) ).

tff(f41699,plain,
    ( $less(sK0(4,cons(5,cons(2,nil))),0)
    | ~ spl2_10 ),
    inference(avatar_component_clause,[],[f41697]) ).

tff(f41703,plain,
    ( spl2_10
    | spl2_11
    | ~ spl2_9 ),
    inference(avatar_split_clause,[],[f41691,f41687,f41701,f41697]) ).

tff(f41701,plain,
    ( spl2_11
  <=> ! [X0: list] :
        ( ~ inRange(4,X0)
        | $less(sK0(4,cons(sK0(4,cons(5,cons(2,nil))),X0)),4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).

tff(f41691,plain,
    ( ! [X0: list] :
        ( ~ inRange(4,X0)
        | $less(sK0(4,cons(5,cons(2,nil))),0)
        | $less(sK0(4,cons(sK0(4,cons(5,cons(2,nil))),X0)),4) )
    | ~ spl2_9 ),
    inference(resolution,[],[f41689,f6716]) ).

tff(f6716,plain,
    ! [X2: $int,X0: $int,X1: list] :
      ( ~ $less(X2,X0)
      | ~ inRange(X0,X1)
      | $less(X2,0)
      | $less(sK0(X0,cons(X2,X1)),X0) ),
    inference(subsumption_resolution,[],[f6714,f31]) ).

tff(f6714,plain,
    ! [X2: $int,X0: $int,X1: list] :
      ( ~ inRange(X0,X1)
      | ~ $less(X2,X0)
      | $less(X2,0)
      | ( nil = cons(X2,X1) )
      | $less(sK0(X0,cons(X2,X1)),X0) ),
    inference(resolution,[],[f40,f36]) ).

tff(f41690,plain,
    ( spl2_9
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(avatar_split_clause,[],[f41685,f20517,f43,f41687]) ).

tff(f41685,plain,
    ( $less(sK0(4,cons(5,cons(2,nil))),4)
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(forward_demodulation,[],[f41684,f20519]) ).

tff(f41684,plain,
    ( $less(sK0(4,sK1(4,cons(1,cons(5,cons(2,nil))))),4)
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(subsumption_resolution,[],[f41683,f31]) ).

tff(f41683,plain,
    ( ( nil = cons(5,cons(2,nil)) )
    | $less(sK0(4,sK1(4,cons(1,cons(5,cons(2,nil))))),4)
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(forward_demodulation,[],[f41682,f20519]) ).

tff(f41682,plain,
    ( ( nil = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | $less(sK0(4,sK1(4,cons(1,cons(5,cons(2,nil))))),4)
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f41680,f31]) ).

tff(f41680,plain,
    ( ( nil = cons(1,cons(5,cons(2,nil))) )
    | ( nil = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | $less(sK0(4,sK1(4,cons(1,cons(5,cons(2,nil))))),4)
    | ~ spl2_1 ),
    inference(resolution,[],[f5961,f45]) ).

tff(f20535,plain,
    ( spl2_8
    | ~ spl2_3
    | ~ spl2_7 ),
    inference(avatar_split_clause,[],[f20528,f20523,f7476,f20532]) ).

tff(f20532,plain,
    ( spl2_8
  <=> ( cons(1,cons(5,cons(2,nil))) = cons(1,sK1(4,cons(1,cons(5,cons(2,nil))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

tff(f7476,plain,
    ( spl2_3
  <=> ( cons(1,cons(5,cons(2,nil))) = cons(sK0(4,cons(1,cons(5,cons(2,nil)))),sK1(4,cons(1,cons(5,cons(2,nil))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f20523,plain,
    ( spl2_7
  <=> ( 1 = sK0(4,cons(1,cons(5,cons(2,nil)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

tff(f20528,plain,
    ( ( cons(1,cons(5,cons(2,nil))) = cons(1,sK1(4,cons(1,cons(5,cons(2,nil))))) )
    | ~ spl2_3
    | ~ spl2_7 ),
    inference(backward_demodulation,[],[f7478,f20525]) ).

tff(f20525,plain,
    ( ( 1 = sK0(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f20523]) ).

tff(f7478,plain,
    ( ( cons(1,cons(5,cons(2,nil))) = cons(sK0(4,cons(1,cons(5,cons(2,nil)))),sK1(4,cons(1,cons(5,cons(2,nil))))) )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f7476]) ).

tff(f20526,plain,
    ( spl2_7
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f20521,f7476,f20523]) ).

tff(f20521,plain,
    ( ( 1 = sK0(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_3 ),
    inference(forward_demodulation,[],[f20505,f32]) ).

tff(f20505,plain,
    ( ( sK0(4,cons(1,cons(5,cons(2,nil)))) = head(cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_3 ),
    inference(superposition,[],[f32,f7478]) ).

tff(f20520,plain,
    ( spl2_6
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f20515,f7476,f20517]) ).

tff(f20515,plain,
    ( ( cons(5,cons(2,nil)) = sK1(4,cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_3 ),
    inference(forward_demodulation,[],[f20504,f33]) ).

tff(f20504,plain,
    ( ( sK1(4,cons(1,cons(5,cons(2,nil)))) = tail(cons(1,cons(5,cons(2,nil)))) )
    | ~ spl2_3 ),
    inference(superposition,[],[f33,f7478]) ).

tff(f20514,plain,
    ( spl2_4
    | spl2_5
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f20503,f7476,f20512,f20508]) ).

tff(f20508,plain,
    ( spl2_4
  <=> $less(sK0(4,cons(1,cons(5,cons(2,nil)))),0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

tff(f20512,plain,
    ( spl2_5
  <=> ! [X0: $int] :
        ( inRange(X0,cons(1,cons(5,cons(2,nil))))
        | ~ $less(sK0(4,cons(1,cons(5,cons(2,nil)))),X0)
        | ~ inRange(X0,sK1(4,cons(1,cons(5,cons(2,nil))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

tff(f20503,plain,
    ( ! [X0: $int] :
        ( inRange(X0,cons(1,cons(5,cons(2,nil))))
        | ~ inRange(X0,sK1(4,cons(1,cons(5,cons(2,nil)))))
        | ~ $less(sK0(4,cons(1,cons(5,cons(2,nil)))),X0)
        | $less(sK0(4,cons(1,cons(5,cons(2,nil)))),0) )
    | ~ spl2_3 ),
    inference(superposition,[],[f40,f7478]) ).

tff(f7479,plain,
    ( spl2_3
    | ~ spl2_1 ),
    inference(avatar_split_clause,[],[f7474,f43,f7476]) ).

tff(f7474,plain,
    ( ( cons(1,cons(5,cons(2,nil))) = cons(sK0(4,cons(1,cons(5,cons(2,nil)))),sK1(4,cons(1,cons(5,cons(2,nil))))) )
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f7472,f31]) ).

tff(f7472,plain,
    ( ( nil = cons(1,cons(5,cons(2,nil))) )
    | ( cons(1,cons(5,cons(2,nil))) = cons(sK0(4,cons(1,cons(5,cons(2,nil)))),sK1(4,cons(1,cons(5,cons(2,nil))))) )
    | ~ spl2_1 ),
    inference(resolution,[],[f34,f45]) ).

tff(f5215,plain,
    ( spl2_2
    | ~ spl2_1 ),
    inference(avatar_split_clause,[],[f5210,f43,f5212]) ).

tff(f5212,plain,
    ( spl2_2
  <=> $less(sK0(4,cons(1,cons(5,cons(2,nil)))),4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f5210,plain,
    ( $less(sK0(4,cons(1,cons(5,cons(2,nil)))),4)
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f5209,f31]) ).

tff(f5209,plain,
    ( ( nil = cons(1,cons(5,cons(2,nil))) )
    | $less(sK0(4,cons(1,cons(5,cons(2,nil)))),4)
    | ~ spl2_1 ),
    inference(resolution,[],[f36,f45]) ).

tff(f46,plain,
    spl2_1,
    inference(avatar_split_clause,[],[f29,f43]) ).

tff(f29,plain,
    inRange(4,cons(1,cons(5,cons(2,nil)))),
    inference(cnf_transformation,[],[f21]) ).

tff(f21,plain,
    inRange(4,cons(1,cons(5,cons(2,nil)))),
    inference(flattening,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ~ inRange(4,cons(1,cons(5,cons(2,nil)))),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ~ inRange(4,cons(1,cons(5,cons(2,nil)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : DAT100_1 : TPTP v8.1.2. Released v6.1.0.
% 0.03/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Apr 29 22:10:14 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (32655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (32658)WARNING: value z3 for option sas not known
% 0.22/0.38  % (32657)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38  % (32656)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38  % (32659)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38  % (32660)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)
% 0.22/0.38  % (32661)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)
% 0.22/0.38  % (32662)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)
% 0.22/0.38  % (32658)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)
% 0.22/0.38  % (32657)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38  % (32656)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38  % (32657)Terminated due to inappropriate strategy.
% 0.22/0.38  % (32657)------------------------------
% 0.22/0.38  % (32657)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38  % (32657)Termination reason: Inappropriate
% 0.22/0.38  
% 0.22/0.38  % (32659)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38  % (32656)Terminated due to inappropriate strategy.
% 0.22/0.38  % (32656)------------------------------
% 0.22/0.38  % (32656)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38  % (32657)Memory used [KB]: 730
% 0.22/0.38  % (32656)Termination reason: Inappropriate
% 0.22/0.38  
% 0.22/0.38  % (32657)Time elapsed: 0.002 s
% 0.22/0.38  % (32656)Memory used [KB]: 729
% 0.22/0.38  % (32657)Instructions burned: 2 (million)
% 0.22/0.38  % (32656)Time elapsed: 0.003 s
% 0.22/0.38  % (32657)------------------------------
% 0.22/0.38  % (32657)------------------------------
% 0.22/0.38  % (32656)Instructions burned: 2 (million)
% 0.22/0.38  % (32656)------------------------------
% 0.22/0.38  % (32656)------------------------------
% 0.22/0.38  % (32659)Terminated due to inappropriate strategy.
% 0.22/0.38  % (32659)------------------------------
% 0.22/0.38  % (32659)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38  % (32659)Termination reason: Inappropriate
% 0.22/0.38  
% 0.22/0.38  % (32659)Memory used [KB]: 729
% 0.22/0.38  % (32659)Time elapsed: 0.002 s
% 0.22/0.38  % (32659)Instructions burned: 2 (million)
% 0.22/0.38  % (32659)------------------------------
% 0.22/0.38  % (32659)------------------------------
% 0.22/0.40  % (32663)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40  % (32664)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)
% 0.22/0.40  % (32665)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)
% 0.22/0.40  % (32663)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.40  % (32663)Terminated due to inappropriate strategy.
% 0.22/0.40  % (32663)------------------------------
% 0.22/0.40  % (32663)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40  % (32663)Termination reason: Inappropriate
% 0.22/0.40  
% 0.22/0.40  % (32663)Memory used [KB]: 729
% 0.22/0.40  % (32663)Time elapsed: 0.003 s
% 0.22/0.40  % (32663)Instructions burned: 2 (million)
% 0.22/0.40  % (32663)------------------------------
% 0.22/0.40  % (32663)------------------------------
% 0.22/0.42  % (32666)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)
% 63.90/9.48  % (32666)First to succeed.
% 63.90/9.49  % (32666)Refutation found. Thanks to Tanya!
% 63.90/9.49  % SZS status Theorem for theBenchmark
% 63.90/9.49  % SZS output start Proof for theBenchmark
% See solution above
% 63.90/9.49  % (32666)------------------------------
% 63.90/9.49  % (32666)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 63.90/9.49  % (32666)Termination reason: Refutation
% 63.90/9.49  
% 63.90/9.49  % (32666)Memory used [KB]: 63653
% 63.90/9.49  % (32666)Time elapsed: 9.065 s
% 63.90/9.49  % (32666)Instructions burned: 27613 (million)
% 63.90/9.49  % (32666)------------------------------
% 63.90/9.49  % (32666)------------------------------
% 63.90/9.49  % (32655)Success in time 9.065 s
%------------------------------------------------------------------------------