TSTP Solution File: DAT086_1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : DAT086_1 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 05:51:51 EDT 2024

% Result   : Theorem 0.22s 0.54s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  121 (  25 unt;  16 typ;   0 def)
%            Number of atoms       :  280 (  47 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  258 (  83   ~; 146   |;  13   &)
%                                         (  12 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  372 ( 118 atm;  29 fun; 122 num; 103 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   25 (  14   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  11 usr;  10 prp; 0-2 aty)
%            Number of functors    :   21 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :  170 ( 164   !;   6   ?; 170   :)

% 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_5,type,
    length: list > $int ).

tff(func_def_8,type,
    count: ( $int * list ) > $int ).

tff(func_def_9,type,
    append: ( list * list ) > list ).

tff(func_def_13,type,
    sK0: ( $int * list ) > $int ).

tff(func_def_14,type,
    sK1: ( $int * list ) > list ).

tff(func_def_15,type,
    sK2: ( $int * list ) > $int ).

tff(func_def_16,type,
    sK3: ( $int * list ) > list ).

tff(func_def_17,type,
    sK4: ( $int * list ) > $int ).

tff(func_def_18,type,
    sK5: ( $int * list ) > list ).

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

tff(pred_def_2,type,
    inRange: ( $int * list ) > $o ).

tff(f1692,plain,
    $false,
    inference(avatar_smt_refutation,[],[f78,f260,f490,f769,f1599,f1633,f1682,f1691]) ).

tff(f1691,plain,
    ~ spl6_9,
    inference(avatar_contradiction_clause,[],[f1687]) ).

tff(f1687,plain,
    ( $false
    | ~ spl6_9 ),
    inference(resolution,[],[f1632,f25]) ).

tff(f25,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_150,[]) ).

tff(f1632,plain,
    ( ! [X0: $int] : $less(X0,3)
    | ~ spl6_9 ),
    inference(avatar_component_clause,[],[f1631]) ).

tff(f1631,plain,
    ( spl6_9
  <=> ! [X0: $int] : $less(X0,3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).

tff(f1682,plain,
    ( ~ spl6_1
    | ~ spl6_8 ),
    inference(avatar_contradiction_clause,[],[f1681]) ).

tff(f1681,plain,
    ( $false
    | ~ spl6_1
    | ~ spl6_8 ),
    inference(evaluation,[],[f1678]) ).

tff(f1678,plain,
    ( $less($sum(4,0),4)
    | ~ spl6_1
    | ~ spl6_8 ),
    inference(superposition,[],[f1664,f77]) ).

tff(f77,plain,
    ( ( 0 = length(nil) )
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f76]) ).

tff(f76,plain,
    ( spl6_1
  <=> ( 0 = length(nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

tff(f1664,plain,
    ( ! [X1: list] : $less($sum(4,length(X1)),4)
    | ~ spl6_8 ),
    inference(evaluation,[],[f1663]) ).

tff(f1663,plain,
    ( ! [X1: list] : $less($sum(3,$sum(1,length(X1))),4)
    | ~ spl6_8 ),
    inference(superposition,[],[f1659,f65]) ).

tff(f65,plain,
    ! [X0: list,X1: $int] : ( length(cons(X1,X0)) = $sum(1,length(X0)) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0: list,X1: $int] : ( length(cons(X1,X0)) = $sum(1,length(X0)) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X4: list,X3: $int] : ( length(cons(X3,X4)) = $sum(1,length(X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

tff(f1659,plain,
    ( ! [X1: list] : $less($sum(3,length(X1)),4)
    | ~ spl6_8 ),
    inference(evaluation,[],[f1658]) ).

tff(f1658,plain,
    ( ! [X1: list] : $less($sum(2,$sum(1,length(X1))),4)
    | ~ spl6_8 ),
    inference(superposition,[],[f1654,f65]) ).

tff(f1654,plain,
    ( ! [X1: list] : $less($sum(2,length(X1)),4)
    | ~ spl6_8 ),
    inference(evaluation,[],[f1652]) ).

tff(f1652,plain,
    ( ! [X1: list] : $less($sum(1,$sum(1,length(X1))),4)
    | ~ spl6_8 ),
    inference(superposition,[],[f1637,f65]) ).

tff(f1637,plain,
    ( ! [X1: list] : $less($sum(1,length(X1)),4)
    | ~ spl6_8 ),
    inference(superposition,[],[f1629,f65]) ).

tff(f1629,plain,
    ( ! [X1: list] : $less(length(X1),4)
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f1628]) ).

tff(f1628,plain,
    ( spl6_8
  <=> ! [X1: list] : $less(length(X1),4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

tff(f1633,plain,
    ( spl6_8
    | spl6_9 ),
    inference(avatar_split_clause,[],[f1572,f1631,f1628]) ).

tff(f1572,plain,
    ! [X0: $int,X1: list] :
      ( $less(X0,3)
      | $less(length(X1),4) ),
    inference(forward_demodulation,[],[f1571,f51]) ).

tff(f51,plain,
    ! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
    inference(rectify,[],[f1]) ).

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

tff(f1571,plain,
    ! [X0: $int,X1: list] :
      ( $less(head(cons(X0,X1)),3)
      | $less(length(X1),4) ),
    inference(subsumption_resolution,[],[f1554,f64]) ).

tff(f64,plain,
    ! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X1: $int,X0: list] : ( nil != cons(X1,X0) ),
    inference(rectify,[],[f4]) ).

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

tff(f1554,plain,
    ! [X0: $int,X1: list] :
      ( ( cons(X0,X1) = nil )
      | $less(length(X1),4)
      | $less(head(cons(X0,X1)),3) ),
    inference(resolution,[],[f1484,f231]) ).

tff(f231,plain,
    ! [X2: $int,X0: list,X1: $int] :
      ( inRange(X1,cons(X2,X0))
      | $less(length(X0),4)
      | $less(X1,3) ),
    inference(resolution,[],[f147,f99]) ).

tff(f99,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f94,f20]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_143,[]) ).

tff(f94,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(resolution,[],[f29,f25]) ).

tff(f29,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_155,[]) ).

tff(f147,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: list] :
      ( ~ $less(X2,$sum(1,length(X1)))
      | $less(X2,4)
      | $less(X3,3)
      | inRange(X3,cons(X0,X1)) ),
    inference(superposition,[],[f136,f65]) ).

tff(f136,plain,
    ! [X2: $int,X0: $int,X1: list] :
      ( ~ $less(X0,length(X1))
      | $less(X2,3)
      | inRange(X2,X1)
      | $less(X0,4) ),
    inference(resolution,[],[f26,f68]) ).

tff(f68,plain,
    ! [X0: $int,X1: list] :
      ( $less(length(X1),4)
      | inRange(X0,X1)
      | $less(X0,3) ),
    inference(cnf_transformation,[],[f47]) ).

tff(f47,plain,
    ! [X1: list,X0: $int] :
      ( inRange(X0,X1)
      | $less(length(X1),4)
      | $less(X0,3) ),
    inference(flattening,[],[f46]) ).

tff(f46,plain,
    ! [X1: list,X0: $int] :
      ( inRange(X0,X1)
      | $less(X0,3)
      | $less(length(X1),4) ),
    inference(ennf_transformation,[],[f39]) ).

tff(f39,plain,
    ! [X1: list,X0: $int] :
      ( ( ~ $less(X0,3)
        & ~ $less(length(X1),4) )
     => inRange(X0,X1) ),
    inference(rectify,[],[f19]) ).

tff(f19,plain,
    ! [X5: $int,X1: list] :
      ( ( ~ $less(length(X1),4)
        & ~ $less(X5,3) )
     => inRange(X5,X1) ),
    inference(theory_normalization,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ~ ! [X5: $int,X1: list] :
          ( ( $greatereq(length(X1),4)
            & $greatereq(X5,3) )
         => inRange(X5,X1) ),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ~ ! [X5: $int,X1: list] :
        ( ( $greatereq(length(X1),4)
          & $greatereq(X5,3) )
       => inRange(X5,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

tff(f26,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_151,[]) ).

tff(f1484,plain,
    ! [X0: list] :
      ( ~ inRange(head(X0),X0)
      | ( nil = X0 ) ),
    inference(resolution,[],[f1456,f25]) ).

tff(f1456,plain,
    ! [X0: $int,X1: list] :
      ( $less(head(X1),X0)
      | ( nil = X1 )
      | ~ inRange(X0,X1) ),
    inference(backward_subsumption_demodulation,[],[f53,f288]) ).

tff(f288,plain,
    ! [X0: $int,X1: list] :
      ( ( head(X1) = sK0(X0,X1) )
      | ~ inRange(X0,X1)
      | ( nil = X1 ) ),
    inference(superposition,[],[f51,f55]) ).

tff(f55,plain,
    ! [X0: $int,X1: list] :
      ( ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 )
      | ~ inRange(X0,X1)
      | ( nil = X1 ) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X1: list,X0: $int] :
      ( ( ? [X3: $int,X2: list] :
            ( inRange(X0,X2)
            & ( cons(X3,X2) = X1 )
            & ~ $less(X3,0)
            & $less(X3,X0) )
        | ( nil = X1 ) )
    <=> inRange(X0,X1) ),
    inference(rectify,[],[f17]) ).

tff(f17,plain,
    ! [X5: $int,X1: list] :
      ( inRange(X5,X1)
    <=> ( ( nil = X1 )
        | ? [X4: list,X0: $int] :
            ( inRange(X5,X4)
            & ~ $less(X0,0)
            & ( cons(X0,X4) = X1 )
            & $less(X0,X5) ) ) ),
    inference(theory_normalization,[],[f6]) ).

tff(f6,axiom,
    ! [X5: $int,X1: list] :
      ( inRange(X5,X1)
    <=> ( ( nil = X1 )
        | ? [X4: list,X0: $int] :
            ( inRange(X5,X4)
            & $lesseq(0,X0)
            & ( cons(X0,X4) = X1 )
            & $less(X0,X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

tff(f53,plain,
    ! [X0: $int,X1: list] :
      ( $less(sK0(X0,X1),X0)
      | ( nil = X1 )
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f1599,plain,
    ~ spl6_2,
    inference(avatar_contradiction_clause,[],[f1593]) ).

tff(f1593,plain,
    ( $false
    | ~ spl6_2 ),
    inference(resolution,[],[f1568,f25]) ).

tff(f1568,plain,
    ( ! [X0: $int] : $less(X0,3)
    | ~ spl6_2 ),
    inference(forward_demodulation,[],[f1567,f51]) ).

tff(f1567,plain,
    ( ! [X0: $int] : $less(head(cons(X0,nil)),3)
    | ~ spl6_2 ),
    inference(subsumption_resolution,[],[f1563,f64]) ).

tff(f1563,plain,
    ( ! [X0: $int] :
        ( ( nil = cons(X0,nil) )
        | $less(head(cons(X0,nil)),3) )
    | ~ spl6_2 ),
    inference(resolution,[],[f1484,f256]) ).

tff(f256,plain,
    ( ! [X2: $int,X1: $int] :
        ( inRange(X1,cons(X2,nil))
        | $less(X1,3) )
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f255]) ).

tff(f255,plain,
    ( spl6_2
  <=> ! [X2: $int,X1: $int] :
        ( $less(X1,3)
        | inRange(X1,cons(X2,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

tff(f769,plain,
    ( spl6_6
    | spl6_7
    | ~ spl6_1
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(avatar_split_clause,[],[f694,f485,f255,f76,f767,f764]) ).

tff(f764,plain,
    ( spl6_6
  <=> ! [X1: $int] :
        ( $less(X1,3)
        | ~ $less(X1,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

tff(f767,plain,
    ( spl6_7
  <=> ! [X0: $int] : inRange(0,cons(X0,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

tff(f485,plain,
    ( spl6_4
  <=> ! [X2: list,X1: $int] :
        ( inRange(X1,X2)
        | $less(length(tail(X2)),0)
        | $less(X1,3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

tff(f694,plain,
    ( ! [X0: $int,X1: $int] :
        ( inRange(0,cons(X0,nil))
        | $less(X1,3)
        | ~ $less(X1,0) )
    | ~ spl6_1
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(superposition,[],[f692,f77]) ).

tff(f692,plain,
    ( ! [X2: $int,X0: $int,X1: list] :
        ( inRange(length(X1),cons(X0,X1))
        | ~ $less(X2,length(X1))
        | $less(X2,3) )
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(superposition,[],[f618,f61]) ).

tff(f61,plain,
    ! [X0: list,X1: $int] : ( tail(cons(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: list,X1: $int] : ( tail(cons(X1,X0)) = X0 ),
    inference(rectify,[],[f2]) ).

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

tff(f618,plain,
    ( ! [X0: list,X1: $int] :
        ( ~ $less(X1,length(tail(X0)))
        | $less(X1,3)
        | inRange(length(tail(X0)),X0) )
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(resolution,[],[f616,f26]) ).

tff(f616,plain,
    ( ! [X0: list] :
        ( $less(length(tail(X0)),3)
        | inRange(length(tail(X0)),X0) )
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(factoring,[],[f610]) ).

tff(f610,plain,
    ( ! [X0: $int,X1: list] :
        ( $less(length(tail(X1)),3)
        | $less(X0,3)
        | inRange(X0,X1) )
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(subsumption_resolution,[],[f606,f64]) ).

tff(f606,plain,
    ( ! [X2: $int,X0: $int,X1: list] :
        ( ( nil = cons(X2,nil) )
        | $less(length(tail(X1)),3)
        | inRange(X0,X1)
        | $less(X0,3) )
    | ~ spl6_2
    | ~ spl6_4 ),
    inference(resolution,[],[f598,f256]) ).

tff(f598,plain,
    ( ! [X2: list,X0: $int,X1: list] :
        ( ~ inRange(length(tail(X1)),X2)
        | $less(X0,3)
        | inRange(X0,X1)
        | ( nil = X2 ) )
    | ~ spl6_4 ),
    inference(subsumption_resolution,[],[f595,f54]) ).

tff(f54,plain,
    ! [X0: $int,X1: list] :
      ( ~ $less(sK0(X0,X1),0)
      | ( nil = X1 )
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f595,plain,
    ( ! [X2: list,X0: $int,X1: list] :
        ( inRange(X0,X1)
        | $less(sK0(length(tail(X1)),X2),0)
        | ~ inRange(length(tail(X1)),X2)
        | $less(X0,3)
        | ( nil = X2 ) )
    | ~ spl6_4 ),
    inference(resolution,[],[f514,f53]) ).

tff(f514,plain,
    ( ! [X2: $int,X0: $int,X1: list] :
        ( ~ $less(X2,length(tail(X1)))
        | inRange(X0,X1)
        | $less(X2,0)
        | $less(X0,3) )
    | ~ spl6_4 ),
    inference(resolution,[],[f486,f26]) ).

tff(f486,plain,
    ( ! [X2: list,X1: $int] :
        ( $less(length(tail(X2)),0)
        | inRange(X1,X2)
        | $less(X1,3) )
    | ~ spl6_4 ),
    inference(avatar_component_clause,[],[f485]) ).

tff(f490,plain,
    ( spl6_4
    | spl6_5 ),
    inference(avatar_split_clause,[],[f411,f488,f485]) ).

tff(f488,plain,
    ( spl6_5
  <=> ! [X0: $int] :
        ( $less(X0,4)
        | $less(-1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

tff(f411,plain,
    ! [X2: list,X0: $int,X1: $int] :
      ( inRange(X1,X2)
      | $less(X1,3)
      | $less(X0,4)
      | $less(-1,X0)
      | $less(length(tail(X2)),0) ),
    inference(resolution,[],[f273,f98]) ).

tff(f98,plain,
    ! [X0: $int] :
      ( $less(-1,X0)
      | $less(X0,0) ),
    inference(evaluation,[],[f97]) ).

tff(f97,plain,
    ! [X0: $int] :
      ( $less($uminus(1),X0)
      | $less(X0,0) ),
    inference(superposition,[],[f29,f80]) ).

tff(f80,plain,
    ! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
    inference(superposition,[],[f24,f30]) ).

tff(f30,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_156,[]) ).

tff(f24,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_148,[]) ).

tff(f273,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: list] :
      ( ~ $less(X3,length(tail(X1)))
      | $less(X2,4)
      | $less(X0,3)
      | inRange(X0,X1)
      | $less(X3,X2) ),
    inference(resolution,[],[f271,f26]) ).

tff(f271,plain,
    ! [X2: $int,X0: list,X1: $int] :
      ( $less(length(tail(X0)),X2)
      | $less(X1,3)
      | inRange(X1,X0)
      | $less(X2,4) ),
    inference(subsumption_resolution,[],[f270,f58]) ).

tff(f58,plain,
    ! [X0: $int,X1: list] :
      ( ( nil != X1 )
      | inRange(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f270,plain,
    ! [X2: $int,X0: list,X1: $int] :
      ( $less(X1,3)
      | inRange(X1,X0)
      | $less(length(tail(X0)),X2)
      | $less(X2,4)
      | ( nil = X0 ) ),
    inference(superposition,[],[f232,f66]) ).

tff(f66,plain,
    ! [X0: list] :
      ( ( cons(head(X0),tail(X0)) = X0 )
      | ( nil = X0 ) ),
    inference(cnf_transformation,[],[f41]) ).

tff(f41,plain,
    ! [X0: list] :
      ( ( nil = X0 )
      | ( cons(head(X0),tail(X0)) = X0 ) ),
    inference(rectify,[],[f3]) ).

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

tff(f232,plain,
    ! [X2: $int,X3: list,X0: $int,X1: $int] :
      ( inRange(X1,cons(X2,X3))
      | $less(length(X3),X0)
      | $less(X0,4)
      | $less(X1,3) ),
    inference(resolution,[],[f147,f95]) ).

tff(f95,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(1,X0))
      | $less(X0,X1) ),
    inference(superposition,[],[f29,f20]) ).

tff(f260,plain,
    ( spl6_2
    | spl6_3
    | ~ spl6_1 ),
    inference(avatar_split_clause,[],[f241,f76,f258,f255]) ).

tff(f258,plain,
    ( spl6_3
  <=> ! [X0: $int] :
        ( $less(X0,4)
        | ~ $less(X0,1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

tff(f241,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X0,4)
        | $less(X1,3)
        | inRange(X1,cons(X2,nil))
        | ~ $less(X0,1) )
    | ~ spl6_1 ),
    inference(evaluation,[],[f238]) ).

tff(f238,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( inRange(X1,cons(X2,nil))
        | $less(X1,3)
        | $less(X0,4)
        | ~ $less(X0,$sum(1,0)) )
    | ~ spl6_1 ),
    inference(superposition,[],[f147,f77]) ).

tff(f78,plain,
    spl6_1,
    inference(avatar_split_clause,[],[f49,f76]) ).

tff(f49,plain,
    0 = length(nil),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    0 = length(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT086_1 : TPTP v8.2.0. Released v6.1.0.
% 0.11/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Jun 22 06:37:39 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.36  This is a TF0_THM_EQU_ARI problem
% 0.12/0.36  Running first-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.42  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (5658)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59848Mi)
% 0.22/0.42  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (5659)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/34Mi)
% 0.22/0.42  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (5660)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/8Mi)
% 0.22/0.42  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (5661)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.22/0.42  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (5664)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/32Mi)
% 0.22/0.42  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (5662)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.22/0.43  % (5661)Instruction limit reached!
% 0.22/0.43  % (5661)------------------------------
% 0.22/0.43  % (5661)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (5661)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (5661)Termination reason: Time limit
% 0.22/0.43  % (5661)Termination phase: Saturation
% 0.22/0.43  
% 0.22/0.43  % (5661)Memory used [KB]: 823
% 0.22/0.43  % (5661)Time elapsed: 0.004 s
% 0.22/0.43  % (5661)Instructions burned: 3 (million)
% 0.22/0.43  % (5664)Refutation not found, incomplete strategy% (5664)------------------------------
% 0.22/0.43  % (5664)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (5664)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (5664)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43  
% 0.22/0.43  % (5664)Memory used [KB]: 838
% 0.22/0.43  % (5664)Time elapsed: 0.005 s
% 0.22/0.43  % (5664)Instructions burned: 4 (million)
% 0.22/0.43  % (5664)------------------------------
% 0.22/0.43  % (5664)------------------------------
% 0.22/0.43  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (5663)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/15Mi)
% 0.22/0.43  % (5660)Instruction limit reached!
% 0.22/0.43  % (5660)------------------------------
% 0.22/0.43  % (5660)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (5660)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (5660)Termination reason: Time limit
% 0.22/0.43  % (5660)Termination phase: Saturation
% 0.22/0.43  
% 0.22/0.43  % (5660)Memory used [KB]: 893
% 0.22/0.43  % (5660)Time elapsed: 0.009 s
% 0.22/0.43  % (5660)Instructions burned: 8 (million)
% 0.22/0.44  % (5663)Instruction limit reached!
% 0.22/0.44  % (5663)------------------------------
% 0.22/0.44  % (5663)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.44  % (5663)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.44  % (5663)Termination reason: Time limit
% 0.22/0.44  % (5663)Termination phase: Saturation
% 0.22/0.44  
% 0.22/0.44  % (5663)Memory used [KB]: 904
% 0.22/0.44  % (5663)Time elapsed: 0.013 s
% 0.22/0.44  % (5663)Instructions burned: 15 (million)
% 0.22/0.45  % (5659)Instruction limit reached!
% 0.22/0.45  % (5659)------------------------------
% 0.22/0.45  % (5659)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.45  % (5659)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.45  % (5659)Termination reason: Time limit
% 0.22/0.45  % (5659)Termination phase: Saturation
% 0.22/0.45  
% 0.22/0.45  % (5659)Memory used [KB]: 1149
% 0.22/0.45  % (5659)Time elapsed: 0.026 s
% 0.22/0.45  % (5659)Instructions burned: 35 (million)
% 0.22/0.45  % (5662)Instruction limit reached!
% 0.22/0.45  % (5662)------------------------------
% 0.22/0.45  % (5662)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.45  % (5662)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.45  % (5662)Termination reason: Time limit
% 0.22/0.45  % (5662)Termination phase: Saturation
% 0.22/0.45  
% 0.22/0.45  % (5662)Memory used [KB]: 1260
% 0.22/0.45  % (5662)Time elapsed: 0.027 s
% 0.22/0.45  % (5662)Instructions burned: 38 (million)
% 0.22/0.49  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.49  % (5692)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.22/0.49  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.49  % (5689)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.22/0.49  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.49  % (5694)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.49  % (5694)Instruction limit reached!
% 0.22/0.49  % (5694)------------------------------
% 0.22/0.49  % (5694)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.49  % (5694)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.49  % (5694)Termination reason: Time limit
% 0.22/0.49  % (5694)Termination phase: Preprocessing 3
% 0.22/0.49  
% 0.22/0.49  % (5694)Memory used [KB]: 748
% 0.22/0.49  % (5694)Time elapsed: 0.003 s
% 0.22/0.49  % (5694)Instructions burned: 2 (million)
% 0.22/0.50  % (5692)Instruction limit reached!
% 0.22/0.50  % (5692)------------------------------
% 0.22/0.50  % (5692)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.50  % (5692)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.50  % (5692)Termination reason: Time limit
% 0.22/0.50  % (5692)Termination phase: Saturation
% 0.22/0.50  
% 0.22/0.50  % (5692)Memory used [KB]: 1057
% 0.22/0.50  % (5692)Time elapsed: 0.013 s
% 0.22/0.50  % (5692)Instructions burned: 27 (million)
% 0.22/0.50  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.50  % (5696)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.22/0.50  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.50  % (5697)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.50  % (5689)Instruction limit reached!
% 0.22/0.50  % (5689)------------------------------
% 0.22/0.50  % (5689)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.50  % (5689)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.50  % (5689)Termination reason: Time limit
% 0.22/0.50  % (5689)Termination phase: Saturation
% 0.22/0.50  
% 0.22/0.50  % (5689)Memory used [KB]: 1114
% 0.22/0.50  % (5689)Time elapsed: 0.020 s
% 0.22/0.50  % (5689)Instructions burned: 36 (million)
% 0.22/0.50  % (5697)Instruction limit reached!
% 0.22/0.50  % (5697)------------------------------
% 0.22/0.50  % (5697)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.50  % (5697)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.50  % (5697)Termination reason: Time limit
% 0.22/0.50  % (5697)Termination phase: Saturation
% 0.22/0.50  
% 0.22/0.50  % (5697)Memory used [KB]: 925
% 0.22/0.50  % (5697)Time elapsed: 0.003 s
% 0.22/0.50  % (5697)Instructions burned: 4 (million)
% 0.22/0.51  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51  % (5698)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.51  % (5698)Instruction limit reached!
% 0.22/0.51  % (5698)------------------------------
% 0.22/0.51  % (5698)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.51  % (5698)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.51  % (5698)Termination reason: Time limit
% 0.22/0.51  % (5698)Termination phase: Preprocessing 2
% 0.22/0.51  
% 0.22/0.51  % (5698)Memory used [KB]: 744
% 0.22/0.51  % (5698)Time elapsed: 0.002 s
% 0.22/0.51  % (5698)Instructions burned: 2 (million)
% 0.22/0.52  % (5696)Instruction limit reached!
% 0.22/0.52  % (5696)------------------------------
% 0.22/0.52  % (5696)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.52  % (5696)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.52  % (5696)Termination reason: Time limit
% 0.22/0.52  % (5696)Termination phase: Saturation
% 0.22/0.52  
% 0.22/0.52  % (5696)Memory used [KB]: 1219
% 0.22/0.52  % (5696)Time elapsed: 0.018 s
% 0.22/0.52  % (5696)Instructions burned: 35 (million)
% 0.22/0.53  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.53  % (5707)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/21Mi)
% 0.22/0.53  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.53  % (5708)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/50Mi)
% 0.22/0.53  % (5658)First to succeed.
% 0.22/0.54  % (5658)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5655"
% 0.22/0.54  % (5655)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.54  % (5658)Refutation found. Thanks to Tanya!
% 0.22/0.54  % SZS status Theorem for theBenchmark
% 0.22/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54  % (5658)------------------------------
% 0.22/0.54  % (5658)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.54  % (5658)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.54  % (5658)Termination reason: Refutation
% 0.22/0.54  
% 0.22/0.54  % (5658)Memory used [KB]: 1545
% 0.22/0.54  % (5658)Time elapsed: 0.117 s
% 0.22/0.54  % (5658)Instructions burned: 233 (million)
% 0.22/0.54  % (5658)------------------------------
% 0.22/0.54  % (5658)------------------------------
% 0.22/0.54  % (5655)Success in time 0.168 s
%------------------------------------------------------------------------------