TSTP Solution File: SEV478^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV478^1 : 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 : n010.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 May 21 04:13:56 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   48 (  10 unt;  20 typ;   0 def)
%            Number of atoms       :  179 (  61 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :  841 (  29   ~;  11   |;  13   &; 773   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   69 (  69   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   4 con; 0-5 aty)
%            Number of variables   :  131 (  23   ^  80   !;  12   ?; 131   :)
%                                         (  16  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_6,type,
    'type/nums/num': $tType ).

thf(type_def_7,type,
    sK0: $tType ).

thf(func_def_0,type,
    'type/nums/num': $tType ).

thf(func_def_1,type,
    'const/sets/ITSET': 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > ( X0 > $o ) > X1 > X1 ) ).

thf(func_def_2,type,
    'const/sets/INSERT': 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).

thf(func_def_3,type,
    'const/sets/IN': 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).

thf(func_def_4,type,
    'const/sets/FINITE': 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_5,type,
    'const/sets/EMPTY': 
      !>[X0: $tType] : ( X0 > $o ) ).

thf(func_def_6,type,
    'const/sets/CARD': 
      !>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).

thf(func_def_7,type,
    'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).

thf(func_def_8,type,
    'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).

thf(func_def_9,type,
    'const/nums/_0': 'type/nums/num' ).

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

thf(func_def_12,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_17,type,
    sK1: sK0 ).

thf(func_def_18,type,
    sK2: sK0 > $o ).

thf(func_def_19,type,
    sK3: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X0 ) ).

thf(func_def_20,type,
    sK4: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X0 ) ).

thf(func_def_21,type,
    sK5: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X1 ) ).

thf(func_def_23,type,
    ph7: 
      !>[X0: $tType] : X0 ).

thf(f41,plain,
    $false,
    inference(trivial_inequality_removal,[],[f40]) ).

thf(f40,plain,
    ( ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
   != ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ) ),
    inference(superposition,[],[f17,f39]) ).

thf(f39,plain,
    ! [X0: sK0] :
      ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) )
      = ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 ) ) ),
    inference(forward_demodulation,[],[f38,f24]) ).

thf(f24,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( 'const/sets/CARD' @ X0 @ X1 )
      = ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
        @ ^ [Y0: X0] : 'const/nums/SUC'
        @ X1
        @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
    inference(beta_eta_normalization,[],[f23]) ).

thf(f23,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( 'const/sets/CARD' @ X0 @ X1 )
      = ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
        @ ^ [Y0: X0,Y1: 'type/nums/num'] : ( 'const/nums/SUC' @ Y1 )
        @ X1
        @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( 'const/sets/CARD' @ X0 @ X1 )
      = ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
        @ ^ [Y0: X0,Y1: 'type/nums/num'] : ( 'const/nums/SUC' @ Y1 )
        @ X1
        @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
    inference(fool_elimination,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( 'const/sets/CARD' @ X0 @ X1 )
      = ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
        @ ^ [X2: X0,X3: 'type/nums/num'] : ( 'const/nums/SUC' @ X3 )
        @ X1
        @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/CARD_') ).

thf(f38,plain,
    ! [X0: sK0] :
      ( ( 'const/sets/ITSET' @ sK0 @ 'type/nums/num'
        @ ^ [Y0: sK0] : 'const/nums/SUC'
        @ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 )
        @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
      = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ),
    inference(trivial_inequality_removal,[],[f37]) ).

thf(f37,plain,
    ! [X0: sK0] :
      ( ( ( 'const/nums/SUC'
          @ ( 'const/nums/SUC'
            @ ( sK5 @ sK0 @ 'type/nums/num'
              @ ^ [Y0: sK0] : 'const/nums/SUC' ) ) )
       != ( 'const/nums/SUC'
          @ ( 'const/nums/SUC'
            @ ( sK5 @ sK0 @ 'type/nums/num'
              @ ^ [Y0: sK0] : 'const/nums/SUC' ) ) ) )
      | ( ( 'const/sets/ITSET' @ sK0 @ 'type/nums/num'
          @ ^ [Y0: sK0] : 'const/nums/SUC'
          @ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 )
          @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
        = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f36]) ).

thf(f36,plain,
    ! [X0: sK0] :
      ( ( ( ^ [Y0: sK0] : 'const/nums/SUC'
          @ ( sK4 @ sK0 @ 'type/nums/num'
            @ ^ [Y0: sK0] : 'const/nums/SUC' )
          @ ( ^ [Y0: sK0] : 'const/nums/SUC'
            @ ( sK3 @ sK0 @ 'type/nums/num'
              @ ^ [Y0: sK0] : 'const/nums/SUC' )
            @ ( sK5 @ sK0 @ 'type/nums/num'
              @ ^ [Y0: sK0] : 'const/nums/SUC' ) ) )
       != ( ^ [Y0: sK0] : 'const/nums/SUC'
          @ ( sK3 @ sK0 @ 'type/nums/num'
            @ ^ [Y0: sK0] : 'const/nums/SUC' )
          @ ( ^ [Y0: sK0] : 'const/nums/SUC'
            @ ( sK4 @ sK0 @ 'type/nums/num'
              @ ^ [Y0: sK0] : 'const/nums/SUC' )
            @ ( sK5 @ sK0 @ 'type/nums/num'
              @ ^ [Y0: sK0] : 'const/nums/SUC' ) ) ) )
      | ( ( 'const/sets/ITSET' @ sK0 @ 'type/nums/num'
          @ ^ [Y0: sK0] : 'const/nums/SUC'
          @ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 )
          @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
        = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 )
          @ ( ^ [Y0: sK0] : 'const/nums/SUC'
            @ X0
            @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ) ),
    inference(superposition,[],[f33,f24]) ).

thf(f33,plain,
    ! [X0: $tType,X2: sK0 > X0 > X0,X3: X0,X1: sK0] :
      ( ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X2 @ sK2 @ X3 ) @ ( X2 @ X1 @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X2 @ sK2 @ X3 ) ) )
        = ( 'const/sets/ITSET' @ sK0 @ X0 @ X2 @ ( 'const/sets/INSERT' @ sK0 @ X1 @ sK2 ) @ X3 ) )
      | ( ( X2 @ ( sK3 @ sK0 @ X0 @ X2 ) @ ( X2 @ ( sK4 @ sK0 @ X0 @ X2 ) @ ( sK5 @ sK0 @ X0 @ X2 ) ) )
       != ( X2 @ ( sK4 @ sK0 @ X0 @ X2 ) @ ( X2 @ ( sK3 @ sK0 @ X0 @ X2 ) @ ( sK5 @ sK0 @ X0 @ X2 ) ) ) ) ),
    inference(trivial_inequality_removal,[],[f32]) ).

thf(f32,plain,
    ! [X0: $tType,X2: sK0 > X0 > X0,X3: X0,X1: sK0] :
      ( ( $true != $true )
      | ( ( X2 @ ( sK3 @ sK0 @ X0 @ X2 ) @ ( X2 @ ( sK4 @ sK0 @ X0 @ X2 ) @ ( sK5 @ sK0 @ X0 @ X2 ) ) )
       != ( X2 @ ( sK4 @ sK0 @ X0 @ X2 ) @ ( X2 @ ( sK3 @ sK0 @ X0 @ X2 ) @ ( sK5 @ sK0 @ X0 @ X2 ) ) ) )
      | ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X2 @ sK2 @ X3 ) @ ( X2 @ X1 @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X2 @ sK2 @ X3 ) ) )
        = ( 'const/sets/ITSET' @ sK0 @ X0 @ X2 @ ( 'const/sets/INSERT' @ sK0 @ X1 @ sK2 ) @ X3 ) ) ),
    inference(superposition,[],[f20,f18]) ).

thf(f18,plain,
    ( $true
    = ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ( $true
      = ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
    & ( ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
     != ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13]) ).

thf(f13,plain,
    ( ? [X0: $tType,X1: X0,X2: X0 > $o] :
        ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
          = $true )
        & ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
         != ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) )
   => ( ( $true
        = ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
      & ( ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
       != ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ? [X0: $tType,X1: X0,X2: X0 > $o] :
      ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
        = $true )
      & ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
       != ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
        ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
          = $true )
       => ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
          = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
    inference(fool_elimination,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
        ( ( 'const/sets/FINITE' @ X0 @ X2 )
       => ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
          = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
    inference(rectify,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
        ( ( 'const/sets/FINITE' @ X0 @ X2 )
       => ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
          = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ! [X0: $tType,X1: X0,X2: X0 > $o] :
      ( ( 'const/sets/FINITE' @ X0 @ X2 )
     => ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
        = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/CARD_CLAUSES_1') ).

thf(f20,plain,
    ! [X1: $tType,X0: $tType,X2: X0 > X1 > X1,X3: X1,X8: X0 > $o,X7: X0] :
      ( ( $true
       != ( 'const/sets/FINITE' @ X0 @ X8 ) )
      | ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
        = ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) )
      | ( ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) )
       != ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) ) ) ),
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    ! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
      ( ( ( ( sK4 @ X0 @ X1 @ X2 )
         != ( sK3 @ X0 @ X1 @ X2 ) )
        & ( ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) )
         != ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) ) ) )
      | ( ! [X7: X0,X8: X0 > $o] :
            ( ( $true
             != ( 'const/sets/FINITE' @ X0 @ X8 ) )
            | ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
              = ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) )
        & ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
          = X3 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f12,f15]) ).

thf(f15,plain,
    ! [X1: $tType,X0: $tType,X2: X0 > X1 > X1] :
      ( ? [X4: X0,X5: X0,X6: X1] :
          ( ( X4 != X5 )
          & ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
           != ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) ) )
     => ( ( ( sK4 @ X0 @ X1 @ X2 )
         != ( sK3 @ X0 @ X1 @ X2 ) )
        & ( ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) )
         != ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
      ( ? [X4: X0,X5: X0,X6: X1] :
          ( ( X4 != X5 )
          & ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
           != ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) ) )
      | ( ! [X7: X0,X8: X0 > $o] :
            ( ( $true
             != ( 'const/sets/FINITE' @ X0 @ X8 ) )
            | ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
              = ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) )
        & ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
          = X3 ) ) ),
    inference(ennf_transformation,[],[f10]) ).

thf(f10,plain,
    ! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
      ( ! [X4: X0,X5: X0,X6: X1] :
          ( ( X4 != X5 )
         => ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
            = ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) ) )
     => ( ! [X7: X0,X8: X0 > $o] :
            ( ( $true
              = ( 'const/sets/FINITE' @ X0 @ X8 ) )
           => ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
              = ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) )
        & ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
          = X3 ) ) ),
    inference(fool_elimination,[],[f9]) ).

thf(f9,plain,
    ! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
      ( ! [X4: X0,X5: X0,X6: X1] :
          ( ( X4 != X5 )
         => ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
            = ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) ) )
     => ( ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
          = X3 )
        & ! [X7: X0,X8: X0 > $o] :
            ( ( 'const/sets/FINITE' @ X0 @ X8 )
           => ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
              = ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: $tType,X4: $tType,X1: X0 > X4 > X4,X2: X4] :
      ( ! [X3: X0,X5: X0,X6: X4] :
          ( ( X3 != X5 )
         => ( ( X1 @ X3 @ ( X1 @ X5 @ X6 ) )
            = ( X1 @ X5 @ ( X1 @ X3 @ X6 ) ) ) )
     => ( ( ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ 'const/sets/EMPTY' @ X0 @ X2 )
          = X2 )
        & ! [X3: X0,X5: X0 > $o] :
            ( ( 'const/sets/FINITE' @ X0 @ X5 )
           => ( ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X5 ) @ X2 )
              = ( 'const/class/COND' @ X4 @ ( 'const/sets/IN' @ X0 @ X3 @ X5 ) @ ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2 ) @ ( X1 @ X3 @ ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_RECURSION_') ).

thf(f17,plain,
    ( ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
   != ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ),
    inference(cnf_transformation,[],[f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEV478^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.14  % 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
% 0.13/0.35  % Computer : n010.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   : Sun May 19 19:14:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TH1_THM_EQU_NAR problem
% 0.13/0.35  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
% 0.13/0.37  % (12503)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)
% 0.13/0.37  % (12502)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37  % (12496)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37  % (12498)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)
% 0.13/0.37  % (12497)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)
% 0.13/0.37  % (12500)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)
% 0.13/0.37  % (12499)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37  % (12503)Instruction limit reached!
% 0.13/0.37  % (12503)------------------------------
% 0.13/0.37  % (12503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (12503)Termination reason: Unknown
% 0.13/0.37  % (12503)Termination phase: Property scanning
% 0.13/0.37  
% 0.13/0.37  % (12503)Memory used [KB]: 1023
% 0.13/0.37  % (12503)Time elapsed: 0.003 s
% 0.13/0.37  % (12503)Instructions burned: 3 (million)
% 0.13/0.37  % (12503)------------------------------
% 0.13/0.37  % (12503)------------------------------
% 0.13/0.37  % (12501)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)
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.13/0.37  % (12499)Instruction limit reached!
% 0.13/0.37  % (12499)------------------------------
% 0.13/0.37  % (12499)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (12499)Termination reason: Unknown
% 0.13/0.37  % (12499)Termination phase: Preprocessing 3
% 0.13/0.37  
% 0.13/0.37  % (12499)Memory used [KB]: 895
% 0.13/0.37  % (12499)Time elapsed: 0.003 s
% 0.13/0.37  % (12499)Instructions burned: 2 (million)
% 0.13/0.37  % (12499)------------------------------
% 0.13/0.37  % (12499)------------------------------
% 0.13/0.37  % (12497)Instruction limit reached!
% 0.13/0.37  % (12497)------------------------------
% 0.13/0.37  % (12497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (12497)Termination reason: Unknown
% 0.13/0.37  % (12497)Termination phase: Saturation
% 0.13/0.37  
% 0.13/0.37  % (12497)Memory used [KB]: 1023
% 0.13/0.37  % (12497)Time elapsed: 0.004 s
% 0.13/0.37  % (12497)Instructions burned: 4 (million)
% 0.13/0.37  % (12497)------------------------------
% 0.13/0.37  % (12497)------------------------------
% 0.13/0.37  % (12501)Refutation not found, incomplete strategy
% 0.13/0.37  % (12501)------------------------------
% 0.13/0.37  % (12501)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (12501)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.37  
% 0.13/0.37  
% 0.13/0.37  % (12501)Memory used [KB]: 5500
% 0.13/0.37  % (12501)Time elapsed: 0.004 s
% 0.13/0.37  % (12501)Instructions burned: 3 (million)
% 0.13/0.37  % (12501)------------------------------
% 0.13/0.37  % (12501)------------------------------
% 0.13/0.38  % (12502)Instruction limit reached!
% 0.13/0.38  % (12502)------------------------------
% 0.13/0.38  % (12502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38  % (12502)Termination reason: Unknown
% 0.13/0.38  % (12502)Termination phase: Saturation
% 0.13/0.38  
% 0.13/0.38  % (12502)Memory used [KB]: 5756
% 0.13/0.38  % (12502)Time elapsed: 0.011 s
% 0.13/0.38  % (12502)Instructions burned: 18 (million)
% 0.13/0.38  % (12502)------------------------------
% 0.13/0.38  % (12502)------------------------------
% 0.13/0.38  % (12498)First to succeed.
% 0.13/0.38  % (12498)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (12498)------------------------------
% 0.13/0.38  % (12498)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38  % (12498)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (12498)Memory used [KB]: 5756
% 0.13/0.38  % (12498)Time elapsed: 0.015 s
% 0.13/0.38  % (12498)Instructions burned: 17 (million)
% 0.13/0.38  % (12498)------------------------------
% 0.13/0.38  % (12498)------------------------------
% 0.13/0.38  % (12495)Success in time 0.036 s
% 0.13/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------