TSTP Solution File: SEV218^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEV218^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n029.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 04:15:27 EDT 2024

% Result   : Theorem 0.12s 0.38s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  108 (   4 unt;  20 typ;   0 def)
%            Number of atoms       : 1059 ( 195 equ;   0 cnn)
%            Maximal formula atoms :   11 (  12 avg)
%            Number of connectives :  292 (  81   ~; 118   |;  62   &;   0   @)
%                                         (  10 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   41 (  40   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  26 usr;  16 con; 0-6 aty)
%            Number of variables   :  156 (   0   ^  97   !;  53   ?; 156   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    a: $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_0,type,
    a: $tType ).

thf(func_def_1,type,
    cQ: a > a > $o ).

thf(func_def_5,type,
    sP0: $o ).

thf(func_def_6,type,
    sK1: a ).

thf(func_def_7,type,
    sK2: a ).

thf(func_def_8,type,
    sK3: a ).

thf(func_def_9,type,
    sK4: a ).

thf(func_def_10,type,
    sK5: a ).

thf(func_def_11,type,
    sK6: a ).

thf(func_def_12,type,
    sK7: a > a > $o ).

thf(func_def_13,type,
    sK8: a > a ).

thf(func_def_15,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_16,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_17,type,
    vAND: $o > $o > $o ).

thf(func_def_18,type,
    vOR: $o > $o > $o ).

thf(func_def_19,type,
    vIMP: $o > $o > $o ).

thf(func_def_20,type,
    vNOT: $o > $o ).

thf(func_def_21,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f609,plain,
    $false,
    inference(avatar_sat_refutation,[],[f39,f44,f49,f58,f63,f131,f371,f608]) ).

thf(f608,plain,
    ( spl9_2
    | ~ spl9_3
    | ~ spl9_4 ),
    inference(avatar_contradiction_clause,[],[f607]) ).

thf(f607,plain,
    ( $false
    | spl9_2
    | ~ spl9_3
    | ~ spl9_4 ),
    inference(trivial_inequality_removal,[],[f596]) ).

thf(f596,plain,
    ( ( $true = $false )
    | spl9_2
    | ~ spl9_3
    | ~ spl9_4 ),
    inference(backward_demodulation,[],[f48,f563]) ).

thf(f563,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
    | spl9_2
    | ~ spl9_3 ),
    inference(trivial_inequality_removal,[],[f562]) ).

thf(f562,plain,
    ( ( $true = $false )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
    | spl9_2
    | ~ spl9_3 ),
    inference(superposition,[],[f125,f540]) ).

thf(f540,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK2) )
    | spl9_2
    | ~ spl9_3 ),
    inference(trivial_inequality_removal,[],[f539]) ).

thf(f539,plain,
    ( ( $true = $false )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK2) )
    | spl9_2
    | ~ spl9_3 ),
    inference(superposition,[],[f492,f389]) ).

thf(f389,plain,
    ( ! [X0: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK3) )
        | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK2) ) )
    | ~ spl9_3 ),
    inference(trivial_inequality_removal,[],[f388]) ).

thf(f388,plain,
    ( ! [X0: a] :
        ( ( $true = $false )
        | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK3) )
        | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK2) ) )
    | ~ spl9_3 ),
    inference(superposition,[],[f123,f43]) ).

thf(f43,plain,
    ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
    | ~ spl9_3 ),
    inference(avatar_component_clause,[],[f41]) ).

thf(f41,plain,
    ( spl9_3
  <=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).

thf(f123,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $false )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f122]) ).

thf(f122,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( $true != $true )
      | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $false )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(superposition,[],[f30,f4]) ).

thf(f4,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f30,plain,
    ! [X6: a,X4: a,X5: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

thf(f25,plain,
    ! [X6: a,X4: a,X5: a] :
      ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f20,plain,
    ( ( ( $true = sP0 )
      | ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) ) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) )
    & ! [X4: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X4) )
        & ! [X5: a] :
            ( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) ) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),vAPP(a,a,sK8,X4)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f15,f19,f18,f17,f16]) ).

thf(f16,plain,
    ( ? [X0: a,X1: a] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
   => ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
      & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f17,plain,
    ( ? [X2: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X2) )
   => ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
    introduced(choice_axiom,[]) ).

thf(f18,plain,
    ( ? [X3: a > a > $o] :
      ! [X4: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X4) )
        & ! [X5: a] :
            ( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X5) ) )
        & ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X7) ) )
   => ! [X4: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X4) )
        & ! [X5: a] :
            ( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) ) )
        & ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X7) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f19,plain,
    ! [X4: a] :
      ( ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X7) )
     => ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),vAPP(a,a,sK8,X4)) ) ),
    introduced(choice_axiom,[]) ).

thf(f15,plain,
    ( ( ( $true = sP0 )
      | ? [X0: a,X1: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
      | ? [X2: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X2) ) )
    & ? [X3: a > a > $o] :
      ! [X4: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X4) )
        & ! [X5: a] :
            ( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X5) ) )
        & ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X7) ) ) ),
    inference(rectify,[],[f10]) ).

thf(f10,plain,
    ( ( ( $true = sP0 )
      | ? [X8: a,X9: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) ) )
      | ? [X10: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) )
    & ? [X0: a > a > $o] :
      ! [X1: a] :
        ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
        & ! [X2: a] :
            ( ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) )
            | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) != $true ) )
        & ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) ) ),
    inference(definition_folding,[],[f8,f9]) ).

thf(f9,plain,
    ( ? [X5: a,X6: a,X7: a] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
    | ( $true != sP0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f8,plain,
    ( ( ? [X5: a,X6: a,X7: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
      | ? [X8: a,X9: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) ) )
      | ? [X10: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) )
    & ? [X0: a > a > $o] :
      ! [X1: a] :
        ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
        & ! [X2: a] :
            ( ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) )
            | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) != $true ) )
        & ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ( ( ? [X5: a,X6: a,X7: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
      | ? [X8: a,X9: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) ) )
      | ? [X10: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) )
    & ? [X0: a > a > $o] :
      ! [X1: a] :
        ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
        & ! [X2: a] :
            ( ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) )
            | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) != $true ) )
        & ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ( ? [X0: a > a > $o] :
        ! [X1: a] :
          ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
          & ! [X2: a] :
              ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) = $true )
             => ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) ) )
          & ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) )
     => ( ! [X5: a,X6: a,X7: a] :
            ( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
              & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
           => ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) ) )
        & ! [X8: a,X9: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) )
           => ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) ) )
        & ! [X10: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ( ? [X0: a > a > $o] :
        ! [X1: a] :
          ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1)
          & ! [X2: a] :
              ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2)
             => ! [X3: a] :
                  ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3)
                <=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) ) )
          & ? [X4: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) )
     => ( ! [X5: a,X6: a,X7: a] :
            ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7)
              & vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) )
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
        & ! [X8: a,X9: a] :
            ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9)
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
        & ! [X10: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ? [X0: a > a > $o] :
        ! [X1: a] :
          ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1)
          & ! [X3: a] :
              ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3)
             => ! [X4: a] :
                  ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4)
                <=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X3),X4) ) )
          & ? [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) )
     => ( ! [X1: a,X4: a,X2: a] :
            ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X2)
              & vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4) )
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) )
        & ! [X1: a,X4: a] :
            ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4)
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X1) )
        & ! [X1: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X1) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ? [X0: a > a > $o] :
      ! [X1: a] :
        ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1)
        & ! [X3: a] :
            ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3)
           => ! [X4: a] :
                ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4)
              <=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X3),X4) ) )
        & ? [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) )
   => ( ! [X1: a,X4: a,X2: a] :
          ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X2)
            & vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4) )
         => vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) )
      & ! [X1: a,X4: a] :
          ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4)
         => vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X1) )
      & ! [X1: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM559A_pme) ).

thf(f492,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK3) )
    | spl9_2 ),
    inference(trivial_inequality_removal,[],[f489]) ).

thf(f489,plain,
    ( ( $true = $false )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK3) )
    | spl9_2 ),
    inference(superposition,[],[f190,f437]) ).

thf(f437,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK3),sK1) )
    | spl9_2 ),
    inference(trivial_inequality_removal,[],[f436]) ).

thf(f436,plain,
    ( ( $true = $false )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK3),sK1) )
    | spl9_2 ),
    inference(superposition,[],[f125,f386]) ).

thf(f386,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK3),sK1) )
    | spl9_2 ),
    inference(trivial_inequality_removal,[],[f380]) ).

thf(f380,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK3),sK1) )
    | spl9_2 ),
    inference(superposition,[],[f38,f190]) ).

thf(f38,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
    | spl9_2 ),
    inference(avatar_component_clause,[],[f36]) ).

thf(f36,plain,
    ( spl9_2
  <=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

thf(f190,plain,
    ! [X0: a,X1: a] :
      ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f171]) ).

thf(f171,plain,
    ! [X0: a,X1: a] :
      ( ( $true = $false )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(superposition,[],[f26,f105]) ).

thf(f105,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f104]) ).

thf(f104,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( $true != $true )
      | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(superposition,[],[f29,f4]) ).

thf(f29,plain,
    ! [X6: a,X4: a,X5: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

thf(f26,plain,
    ! [X4: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X4) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f125,plain,
    ! [X0: a,X1: a] :
      ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f119]) ).

thf(f119,plain,
    ! [X0: a,X1: a] :
      ( ( $true != $true )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(superposition,[],[f30,f26]) ).

thf(f48,plain,
    ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
    | ~ spl9_4 ),
    inference(avatar_component_clause,[],[f46]) ).

thf(f46,plain,
    ( spl9_4
  <=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).

thf(f371,plain,
    ( spl9_6
    | ~ spl9_7 ),
    inference(avatar_contradiction_clause,[],[f370]) ).

thf(f370,plain,
    ( $false
    | spl9_6
    | ~ spl9_7 ),
    inference(trivial_inequality_removal,[],[f359]) ).

thf(f359,plain,
    ( ( $true = $false )
    | spl9_6
    | ~ spl9_7 ),
    inference(backward_demodulation,[],[f62,f326]) ).

thf(f326,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
    | spl9_6 ),
    inference(trivial_inequality_removal,[],[f325]) ).

thf(f325,plain,
    ( ( $true = $false )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
    | spl9_6 ),
    inference(superposition,[],[f125,f307]) ).

thf(f307,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK4),sK5) )
    | spl9_6 ),
    inference(trivial_inequality_removal,[],[f294]) ).

thf(f294,plain,
    ( ( $true = $false )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK4),sK5) )
    | spl9_6 ),
    inference(superposition,[],[f133,f190]) ).

thf(f133,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
    | spl9_6 ),
    inference(trivial_inequality_removal,[],[f132]) ).

thf(f132,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
    | spl9_6 ),
    inference(superposition,[],[f57,f4]) ).

thf(f57,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
    | spl9_6 ),
    inference(avatar_component_clause,[],[f55]) ).

thf(f55,plain,
    ( spl9_6
  <=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

thf(f62,plain,
    ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
    | ~ spl9_7 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f60,plain,
    ( spl9_7
  <=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).

thf(f131,plain,
    spl9_5,
    inference(avatar_contradiction_clause,[],[f130]) ).

thf(f130,plain,
    ( $false
    | spl9_5 ),
    inference(trivial_inequality_removal,[],[f126]) ).

thf(f126,plain,
    ( ( $true = $false )
    | spl9_5 ),
    inference(superposition,[],[f115,f98]) ).

thf(f98,plain,
    ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) )
    | spl9_5 ),
    inference(trivial_inequality_removal,[],[f97]) ).

thf(f97,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) )
    | spl9_5 ),
    inference(superposition,[],[f53,f4]) ).

thf(f53,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) )
    | spl9_5 ),
    inference(avatar_component_clause,[],[f51]) ).

thf(f51,plain,
    ( spl9_5
  <=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

thf(f115,plain,
    ! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X0) ),
    inference(trivial_inequality_removal,[],[f111]) ).

thf(f111,plain,
    ! [X0: a] :
      ( ( $true = $false )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X0) ) ),
    inference(superposition,[],[f26,f107]) ).

thf(f107,plain,
    ! [X0: a,X1: a] :
      ( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) ),
    inference(trivial_inequality_removal,[],[f102]) ).

thf(f102,plain,
    ! [X0: a,X1: a] :
      ( ( $true != $true )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) )
      | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
    inference(superposition,[],[f29,f26]) ).

thf(f63,plain,
    ( ~ spl9_5
    | spl9_7
    | spl9_1 ),
    inference(avatar_split_clause,[],[f27,f32,f60,f51]) ).

thf(f32,plain,
    ( spl9_1
  <=> ( $true = sP0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

thf(f27,plain,
    ( ( $true = sP0 )
    | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
    | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f58,plain,
    ( ~ spl9_5
    | ~ spl9_6
    | spl9_1 ),
    inference(avatar_split_clause,[],[f28,f32,f55,f51]) ).

thf(f28,plain,
    ( ( $true = sP0 )
    | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
    | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f49,plain,
    ( ~ spl9_1
    | spl9_4 ),
    inference(avatar_split_clause,[],[f21,f46,f32]) ).

thf(f21,plain,
    ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
      & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
      & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) ) )
    | ( $true != sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f12,f13]) ).

thf(f13,plain,
    ( ? [X0: a,X1: a,X2: a] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X2) )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
   => ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
      & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
      & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X0: a,X1: a,X2: a] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X2) )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
    | ( $true != sP0 ) ),
    inference(rectify,[],[f11]) ).

thf(f11,plain,
    ( ? [X5: a,X6: a,X7: a] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
    | ( $true != sP0 ) ),
    inference(nnf_transformation,[],[f9]) ).

thf(f44,plain,
    ( ~ spl9_1
    | spl9_3 ),
    inference(avatar_split_clause,[],[f22,f41,f32]) ).

thf(f22,plain,
    ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f39,plain,
    ( ~ spl9_1
    | ~ spl9_2 ),
    inference(avatar_split_clause,[],[f23,f36,f32]) ).

thf(f23,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEV218^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 18:51:07 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  % (26856)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35  % (26862)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35  % (26860)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.35  % (26863)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35  % (26858)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35  % (26860)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.35  % Exception at run slice level
% 0.12/0.35  % Exception at run slice level
% 0.12/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.35  % (26857)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36  % Exception at run slice level
% 0.12/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36  % Exception at run slice level
% 0.12/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36  % (26859)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.12/0.36  % (26859)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37  % (26861)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.37  % (26864)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.37  % (26866)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.37  % Exception at run slice level
% 0.12/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37  WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.12/0.37  % (26866)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37  % Exception at run slice level
% 0.12/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37  % (26865)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.12/0.37  WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.12/0.37  % (26862)First to succeed.
% 0.12/0.37  % (26867)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.37  % (26865)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37  % (26862)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26856"
% 0.12/0.38  % (26862)Refutation found. Thanks to Tanya!
% 0.12/0.38  % SZS status Theorem for theBenchmark
% 0.12/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38  % (26862)------------------------------
% 0.12/0.38  % (26862)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.38  % (26862)Termination reason: Refutation
% 0.12/0.38  
% 0.12/0.38  % (26862)Memory used [KB]: 916
% 0.12/0.38  % (26862)Time elapsed: 0.022 s
% 0.12/0.38  % (26862)Instructions burned: 44 (million)
% 0.12/0.38  % (26856)Success in time 0.035 s
%------------------------------------------------------------------------------