TSTP Solution File: ANA111^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA111^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n025.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 May 20 18:40:31 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   44 (  15 unt;  21 typ;   0 def)
%            Number of atoms       :  126 (  36 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :  640 (  12   ~;   4   |;   5   &; 615   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   57 (  57   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   5 con; 0-5 aty)
%            Number of variables   :   63 (   0   ^  49   !;   6   ?;  63   :)
%                                         (   8  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    'type/nums/num': $tType ).

thf(type_def_6,type,
    'type/realax/real': $tType ).

thf(func_def_0,type,
    'type/realax/real': $tType ).

thf(func_def_1,type,
    'type/nums/num': $tType ).

thf(func_def_2,type,
    'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).

thf(func_def_3,type,
    'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).

thf(func_def_4,type,
    'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).

thf(func_def_5,type,
    'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).

thf(func_def_6,type,
    'const/nums/_0': 'type/nums/num' ).

thf(func_def_7,type,
    'const/iterate/sum': 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).

thf(func_def_8,type,
    'const/iterate/neutral': 
      !>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).

thf(func_def_9,type,
    'const/iterate/monoidal': 
      !>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).

thf(func_def_10,type,
    'const/iterate/iterate': 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).

thf(func_def_11,type,
    'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).

thf(func_def_12,type,
    'const/class/COND': 
      !>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).

thf(func_def_13,type,
    'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).

thf(func_def_15,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_19,type,
    sK0: 'type/nums/num' > 'type/realax/real' ).

thf(func_def_20,type,
    sK1: 'type/nums/num' ).

thf(func_def_21,type,
    sK2: 'type/nums/num' ).

thf(func_def_23,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(f31,plain,
    $false,
    inference(trivial_inequality_removal,[],[f30]) ).

thf(f30,plain,
    ( ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ sK0 )
   != ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ sK0 ) ),
    inference(superposition,[],[f23,f28]) ).

thf(f28,plain,
    ! [X2: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num'] :
      ( ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) ) @ X2 )
      = ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) @ ( X2 @ ( 'const/nums/SUC' @ X1 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) ) ),
    inference(trivial_inequality_removal,[],[f27]) ).

thf(f27,plain,
    ! [X2: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num'] :
      ( ( $true != $true )
      | ( ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) ) @ X2 )
        = ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) @ ( X2 @ ( 'const/nums/SUC' @ X1 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) ) ) ),
    inference(superposition,[],[f20,f19]) ).

thf(f19,plain,
    ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
    = $true ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
    = $true ),
    inference(fool_elimination,[],[f10]) ).

thf(f10,plain,
    'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).

thf(f20,plain,
    ! [X0: $tType,X2: X0 > X0 > X0,X1: 'type/nums/num' > X0,X4: 'type/nums/num',X5: 'type/nums/num'] :
      ( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
       != $true )
      | ( ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X4 @ ( 'const/nums/SUC' @ X5 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X4 @ X5 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X5 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X4 @ X5 ) @ X1 ) )
        = ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X4 @ ( 'const/nums/SUC' @ X5 ) ) @ X1 ) ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
      ( ( ! [X3: 'type/nums/num'] :
            ( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 )
            = ( 'const/class/COND' @ X0
              @ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
                = X3 )
              @ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
              @ ( 'const/iterate/neutral' @ X0 @ X2 ) ) )
        & ! [X4: 'type/nums/num',X5: 'type/nums/num'] :
            ( ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X4 @ ( 'const/nums/SUC' @ X5 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X4 @ X5 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X5 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X4 @ X5 ) @ X1 ) )
            = ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X4 @ ( 'const/nums/SUC' @ X5 ) ) @ X1 ) ) )
      | ( ( 'const/iterate/monoidal' @ X0 @ X2 )
       != $true ) ),
    inference(rectify,[],[f12]) ).

thf(f12,plain,
    ! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
      ( ( ! [X5: 'type/nums/num'] :
            ( ( 'const/class/COND' @ X0
              @ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
                = X5 )
              @ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
              @ ( 'const/iterate/neutral' @ X0 @ X2 ) )
            = ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) )
        & ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
            ( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X1 )
            = ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) ) ) )
      | ( ( 'const/iterate/monoidal' @ X0 @ X2 )
       != $true ) ),
    inference(ennf_transformation,[],[f9]) ).

thf(f9,plain,
    ! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
      ( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
        = $true )
     => ( ! [X5: 'type/nums/num'] :
            ( ( 'const/class/COND' @ X0
              @ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
                = X5 )
              @ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
              @ ( 'const/iterate/neutral' @ X0 @ X2 ) )
            = ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) )
        & ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
            ( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X1 )
            = ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) ) ) ) ),
    inference(fool_elimination,[],[f8]) ).

thf(f8,plain,
    ! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
      ( ( 'const/iterate/monoidal' @ X0 @ X2 )
     => ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
            ( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X1 )
            = ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) ) )
        & ! [X5: 'type/nums/num'] :
            ( ( 'const/class/COND' @ X0
              @ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
                = X5 )
              @ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
              @ ( 'const/iterate/neutral' @ X0 @ X2 ) )
            = ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
      ( ( 'const/iterate/monoidal' @ X0 @ X2 )
     => ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
            ( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X1 )
            = ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) ) )
        & ! [X3: 'type/nums/num'] :
            ( ( 'const/class/COND' @ X0
              @ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
                = X3 )
              @ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
              @ ( 'const/iterate/neutral' @ X0 @ X2 ) )
            = ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_NUMSEG_') ).

thf(f23,plain,
    ( ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ sK0 )
   != ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) @ ( sK0 @ ( 'const/nums/SUC' @ sK2 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ),
    inference(definition_unfolding,[],[f22,f18,f18,f18]) ).

thf(f18,plain,
    ! [X0: $tType] :
      ( 'const/iterate/sum'
      @ ( X0
        = ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType] :
      ( 'const/iterate/sum'
      @ ( X0
        = ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_') ).

thf(f22,plain,
    ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ sK0 )
   != ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) @ ( sK0 @ ( 'const/nums/SUC' @ sK2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ),
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ sK0 )
   != ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) @ ( sK0 @ ( 'const/nums/SUC' @ sK2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15]) ).

thf(f15,plain,
    ( ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
        ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ X0 )
       != ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) @ ( X0 @ ( 'const/nums/SUC' @ X2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) )
   => ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ sK0 )
     != ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sK1 @ ( 'const/nums/SUC' @ sK2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) @ ( sK0 @ ( 'const/nums/SUC' @ sK2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
      ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ X0 )
     != ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) @ ( X0 @ ( 'const/nums/SUC' @ X2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,negated_conjecture,
    ~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
        ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ X0 )
        = ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) @ ( X0 @ ( 'const/nums/SUC' @ X2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) ),
    inference(negated_conjecture,[],[f5]) ).

thf(f5,conjecture,
    ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
      ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ X0 )
      = ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X1 @ ( 'const/nums/SUC' @ X2 ) ) @ ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) @ ( X0 @ ( 'const/nums/SUC' @ X2 ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CLAUSES_NUMSEG_1') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : ANA111^1 : TPTP v8.2.0. Released v7.0.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 07:40:53 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a TH1_THM_EQU_NAR problem
% 0.11/0.32  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.34  % (31646)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.11/0.34  % (31647)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.11/0.34  % (31649)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34  % (31648)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34  % (31650)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.11/0.34  % (31651)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.34  % (31652)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.11/0.34  % (31648)Instruction limit reached!
% 0.11/0.34  % (31648)------------------------------
% 0.11/0.34  % (31648)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (31648)Termination reason: Unknown
% 0.11/0.34  % (31648)Termination phase: Property scanning
% 0.11/0.34  % (31649)Instruction limit reached!
% 0.11/0.34  % (31649)------------------------------
% 0.11/0.34  % (31649)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (31649)Termination reason: Unknown
% 0.11/0.34  % (31649)Termination phase: Property scanning
% 0.11/0.34  
% 0.11/0.34  % (31649)Memory used [KB]: 1023
% 0.11/0.34  % (31649)Time elapsed: 0.003 s
% 0.11/0.34  % (31649)Instructions burned: 3 (million)
% 0.11/0.34  % (31649)------------------------------
% 0.11/0.34  % (31649)------------------------------
% 0.11/0.34  
% 0.11/0.34  % (31648)Memory used [KB]: 895
% 0.11/0.34  % (31648)Time elapsed: 0.003 s
% 0.11/0.34  % (31648)Instructions burned: 3 (million)
% 0.11/0.34  % (31648)------------------------------
% 0.11/0.34  % (31648)------------------------------
% 0.11/0.34  % (31652)Instruction limit reached!
% 0.11/0.34  % (31652)------------------------------
% 0.11/0.34  % (31652)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (31652)Termination reason: Unknown
% 0.11/0.34  % (31652)Termination phase: Function definition elimination
% 0.11/0.34  
% 0.11/0.34  % (31652)Memory used [KB]: 895
% 0.11/0.34  % (31652)Time elapsed: 0.003 s
% 0.11/0.34  % (31652)Instructions burned: 3 (million)
% 0.11/0.34  % (31652)------------------------------
% 0.11/0.34  % (31652)------------------------------
% 0.11/0.34  % (31650)Refutation not found, incomplete strategy
% 0.11/0.34  % (31650)------------------------------
% 0.11/0.34  % (31650)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (31650)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.34  
% 0.11/0.34  
% 0.11/0.34  % (31650)Memory used [KB]: 5500
% 0.11/0.34  % (31650)Time elapsed: 0.003 s
% 0.11/0.34  % (31650)Instructions burned: 3 (million)
% 0.11/0.34  % (31650)------------------------------
% 0.11/0.34  % (31650)------------------------------
% 0.11/0.34  % (31646)Instruction limit reached!
% 0.11/0.34  % (31646)------------------------------
% 0.11/0.34  % (31646)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (31646)Termination reason: Unknown
% 0.11/0.34  % (31645)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34  % (31646)Termination phase: Saturation
% 0.11/0.34  
% 0.11/0.34  % (31646)Memory used [KB]: 5500
% 0.11/0.34  % (31646)Time elapsed: 0.004 s
% 0.11/0.34  % (31646)Instructions burned: 4 (million)
% 0.11/0.34  % (31646)------------------------------
% 0.11/0.34  % (31646)------------------------------
% 0.11/0.35  % (31647)First to succeed.
% 0.11/0.35  % (31647)Refutation found. Thanks to Tanya!
% 0.11/0.35  % SZS status Theorem for theBenchmark
% 0.11/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35  % (31647)------------------------------
% 0.11/0.35  % (31647)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (31647)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (31647)Memory used [KB]: 5628
% 0.11/0.35  % (31647)Time elapsed: 0.008 s
% 0.11/0.35  % (31647)Instructions burned: 7 (million)
% 0.11/0.35  % (31647)------------------------------
% 0.11/0.35  % (31647)------------------------------
% 0.11/0.35  % (31644)Success in time 0.019 s
% 0.11/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------