TSTP Solution File: DAT093_1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT093_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 : n002.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 11:04:03 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   51
% Syntax   : Number of formulae    :  105 (  39 unt;  18 typ;   0 def)
%            Number of atoms       :  247 ( 103 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  244 (  84   ~;  75   |;  61   &)
%                                         (  21 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  183 (  30 atm;  32 fun;  41 num;  80 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   29 (  16   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   23 (  19 usr;  16 prp; 0-2 aty)
%            Number of functors    :   17 (  13 usr;   3 con; 0-2 aty)
%            Number of variables   :  168 ( 132   !;  36   ?; 168   :)

% 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_11,type,
    sK2: ( $int * list ) > $int ).

tff(func_def_12,type,
    sK3: ( $int * list ) > list ).

tff(func_def_13,type,
    sK4: ( $int * list ) > $int ).

tff(func_def_14,type,
    sK5: ( $int * list ) > list ).

tff(func_def_15,type,
    sK6: ( $int * list ) > $int ).

tff(func_def_16,type,
    sK7: ( $int * list ) > list ).

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

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

tff(pred_def_6,type,
    sP0: ( $int * list ) > $o ).

tff(pred_def_7,type,
    sP1: ( $int * list ) > $o ).

tff(f169,plain,
    $false,
    inference(avatar_sat_refutation,[],[f101,f105,f109,f114,f125,f129,f133,f137,f141,f145,f149,f153,f157,f161,f165,f168]) ).

tff(f168,plain,
    ( ~ spl8_4
    | ~ spl8_9 ),
    inference(avatar_contradiction_clause,[],[f167]) ).

tff(f167,plain,
    ( $false
    | ~ spl8_4
    | ~ spl8_9 ),
    inference(evaluation,[],[f166]) ).

tff(f166,plain,
    ( ( 0 = $sum(1,0) )
    | ~ spl8_4
    | ~ spl8_9 ),
    inference(superposition,[],[f140,f113]) ).

tff(f113,plain,
    ( ( 0 = length(nil) )
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f111]) ).

tff(f111,plain,
    ( spl8_4
  <=> ( 0 = length(nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

tff(f140,plain,
    ( ! [X0: list] : ( length(X0) = $sum(1,length(X0)) )
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f139]) ).

tff(f139,plain,
    ( spl8_9
  <=> ! [X0: list] : ( length(X0) = $sum(1,length(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

tff(f165,plain,
    spl8_15,
    inference(avatar_split_clause,[],[f76,f163]) ).

tff(f163,plain,
    ( spl8_15
  <=> ! [X0: $int,X1: list] :
        ( sP0(X0,X1)
        | ~ inRange(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).

tff(f76,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | ~ inRange(X0,X1) ) ),
    inference(nnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f35,f43]) ).

tff(f43,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f35,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,[],[f17]) ).

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

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

tff(f161,plain,
    spl8_14,
    inference(avatar_split_clause,[],[f68,f159]) ).

tff(f159,plain,
    ( spl8_14
  <=> ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).

tff(f68,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(f157,plain,
    spl8_13,
    inference(avatar_split_clause,[],[f67,f155]) ).

tff(f155,plain,
    ( spl8_13
  <=> ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).

tff(f67,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(f153,plain,
    spl8_12,
    inference(avatar_split_clause,[],[f23,f151]) ).

tff(f151,plain,
    ( spl8_12
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

tff(f23,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f149,plain,
    spl8_11,
    inference(avatar_split_clause,[],[f95,f147]) ).

tff(f147,plain,
    ( spl8_11
  <=> ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).

tff(f95,plain,
    ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
    inference(equality_resolution,[],[f94]) ).

tff(f94,plain,
    ! [X1: list,X4: $int,X5: list] :
      ( sP1(X4,X1)
      | ( cons(X4,X5) != X1 ) ),
    inference(equality_resolution,[],[f84]) ).

tff(f84,plain,
    ! [X0: $int,X1: list,X4: $int,X5: list] :
      ( sP1(X0,X1)
      | ( X0 != X4 )
      | ( cons(X4,X5) != X1 ) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f59,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ( in(X0,sK5(X0,X1))
          & ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
        | ( ( sK6(X0,X1) = X0 )
          & ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f56,f58,f57]) ).

tff(f57,plain,
    ! [X0: $int,X1: list] :
      ( ? [X6: $int,X7: list] :
          ( in(X0,X7)
          & ( cons(X6,X7) = X1 ) )
     => ( in(X0,sK5(X0,X1))
        & ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f58,plain,
    ! [X0: $int,X1: list] :
      ( ? [X8: $int,X9: list] :
          ( ( X0 = X8 )
          & ( cons(X8,X9) = X1 ) )
     => ( ( sK6(X0,X1) = X0 )
        & ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f56,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X6: $int,X7: list] :
            ( in(X0,X7)
            & ( cons(X6,X7) = X1 ) )
        | ? [X8: $int,X9: list] :
            ( ( X0 = X8 )
            & ( cons(X8,X9) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f55]) ).

tff(f55,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(flattening,[],[f54]) ).

tff(f54,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: list] :
      ( sP1(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f145,plain,
    spl8_10,
    inference(avatar_split_clause,[],[f66,f143]) ).

tff(f143,plain,
    ( spl8_10
  <=> ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

tff(f66,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(f141,plain,
    ( spl8_9
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(avatar_split_clause,[],[f121,f111,f99,f139]) ).

tff(f99,plain,
    ( spl8_1
  <=> ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

tff(f121,plain,
    ( ! [X0: list] : ( length(X0) = $sum(1,length(X0)) )
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(forward_demodulation,[],[f120,f64]) ).

tff(f64,plain,
    ! [X0: list] : ( append(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: list] : ( append(nil,X0) = X0 ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X1: list] : ( append(nil,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).

tff(f120,plain,
    ( ! [X0: list] : ( length(append(nil,X0)) = $sum(1,length(X0)) )
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(forward_demodulation,[],[f117,f19]) ).

tff(f19,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f117,plain,
    ( ! [X0: list] : ( length(append(nil,X0)) = $sum(length(X0),1) )
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(evaluation,[],[f116]) ).

tff(f116,plain,
    ( ! [X0: list] : ( length(append(nil,X0)) = $sum($sum(0,length(X0)),1) )
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(superposition,[],[f100,f113]) ).

tff(f100,plain,
    ( ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) )
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f99]) ).

tff(f137,plain,
    spl8_8,
    inference(avatar_split_clause,[],[f64,f135]) ).

tff(f135,plain,
    ( spl8_8
  <=> ! [X0: list] : ( append(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

tff(f133,plain,
    spl8_7,
    inference(avatar_split_clause,[],[f63,f131]) ).

tff(f131,plain,
    ( spl8_7
  <=> ! [X0: $int] : ( 0 = count(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

tff(f63,plain,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    inference(cnf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).

tff(f129,plain,
    spl8_6,
    inference(avatar_split_clause,[],[f29,f127]) ).

tff(f127,plain,
    ( spl8_6
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

tff(f29,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f125,plain,
    spl8_5,
    inference(avatar_split_clause,[],[f21,f123]) ).

tff(f123,plain,
    ( spl8_5
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

tff(f21,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f114,plain,
    spl8_4,
    inference(avatar_split_clause,[],[f62,f111]) ).

tff(f62,plain,
    0 = length(nil),
    inference(cnf_transformation,[],[f7]) ).

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

tff(f109,plain,
    spl8_3,
    inference(avatar_split_clause,[],[f92,f107]) ).

tff(f107,plain,
    ( spl8_3
  <=> ! [X0: $int] : sP0(X0,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

tff(f92,plain,
    ! [X0: $int] : sP0(X0,nil),
    inference(equality_resolution,[],[f74]) ).

tff(f74,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ( nil != X1 ) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f51,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ( inRange(X0,sK3(X0,X1))
          & $less(sK2(X0,X1),X0)
          & ~ $less(sK2(X0,X1),0)
          & ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f49,f50]) ).

tff(f50,plain,
    ! [X0: $int,X1: list] :
      ( ? [X4: $int,X5: list] :
          ( inRange(X0,X5)
          & $less(X4,X0)
          & ~ $less(X4,0)
          & ( cons(X4,X5) = X1 ) )
     => ( inRange(X0,sK3(X0,X1))
        & $less(sK2(X0,X1),X0)
        & ~ $less(sK2(X0,X1),0)
        & ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f49,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(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 )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f48]) ).

tff(f48,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(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 )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f47]) ).

tff(f47,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(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 )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f43]) ).

tff(f105,plain,
    spl8_2,
    inference(avatar_split_clause,[],[f24,f103]) ).

tff(f103,plain,
    ( spl8_2
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

tff(f24,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f101,plain,
    spl8_1,
    inference(avatar_split_clause,[],[f61,f99]) ).

tff(f61,plain,
    ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
    inference(flattening,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ~ ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ~ ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : DAT093_1 : TPTP v8.1.2. Released v6.1.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Apr 29 22:27:09 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (11732)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (11735)WARNING: value z3 for option sas not known
% 0.13/0.36  % (11735)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)
% 0.13/0.37  % (11733)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (11734)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (11736)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (11737)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)
% 0.13/0.37  % (11738)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)
% 0.13/0.37  % (11739)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)
% 0.13/0.37  % (11733)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (11733)Terminated due to inappropriate strategy.
% 0.13/0.37  % (11733)------------------------------
% 0.13/0.37  % (11733)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (11733)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (11733)Memory used [KB]: 802
% 0.13/0.37  % (11733)Time elapsed: 0.003 s
% 0.13/0.37  % (11733)Instructions burned: 3 (million)
% 0.13/0.37  % (11733)------------------------------
% 0.13/0.37  % (11733)------------------------------
% 0.13/0.37  % (11734)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (11734)Terminated due to inappropriate strategy.
% 0.13/0.37  % (11734)------------------------------
% 0.13/0.37  % (11734)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (11734)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (11734)Memory used [KB]: 803
% 0.13/0.37  % (11734)Time elapsed: 0.003 s
% 0.13/0.37  % (11734)Instructions burned: 3 (million)
% 0.13/0.37  % (11734)------------------------------
% 0.13/0.37  % (11734)------------------------------
% 0.13/0.37  % (11736)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (11736)Terminated due to inappropriate strategy.
% 0.13/0.37  % (11736)------------------------------
% 0.13/0.37  % (11736)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (11736)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (11736)Memory used [KB]: 802
% 0.13/0.37  % (11736)Time elapsed: 0.003 s
% 0.13/0.37  % (11736)Instructions burned: 3 (million)
% 0.13/0.37  % (11736)------------------------------
% 0.13/0.37  % (11736)------------------------------
% 0.13/0.37  % (11737)First to succeed.
% 0.13/0.37  % (11738)Also succeeded, but the first one will report.
% 0.13/0.37  % (11737)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (11737)------------------------------
% 0.13/0.38  % (11737)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (11737)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (11737)Memory used [KB]: 859
% 0.13/0.38  % (11737)Time elapsed: 0.007 s
% 0.13/0.38  % (11737)Instructions burned: 9 (million)
% 0.13/0.38  % (11737)------------------------------
% 0.13/0.38  % (11737)------------------------------
% 0.13/0.38  % (11732)Success in time 0.022 s
%------------------------------------------------------------------------------