TSTP Solution File: DAT056^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% 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 : Mon May 20 19:51:17 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   86 (  19 unt;  24 typ;   0 def)
%            Number of atoms       :  882 (  93 equ;   0 cnn)
%            Maximal formula atoms :    4 (  14 avg)
%            Number of connectives :  127 (  55   ~;  48   |;   6   &;   0   @)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   22 (  21   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  29 usr;  20 con; 0-6 aty)
%            Number of variables   :  162 (   0   ^ 124   !;  32   ?; 162   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

thf(func_def_1,type,
    a: $tType ).

thf(func_def_2,type,
    ap: lst > lst > lst ).

thf(func_def_3,type,
    cns: a > lst > lst ).

thf(func_def_4,type,
    nl: lst ).

thf(func_def_5,type,
    xs: lst ).

thf(func_def_9,type,
    sK0: lst ).

thf(func_def_10,type,
    sK1: lst ).

thf(func_def_11,type,
    sK2: a ).

thf(func_def_12,type,
    sK3: lst ).

thf(func_def_13,type,
    sK4: lst ).

thf(func_def_14,type,
    sK5: lst ).

thf(func_def_15,type,
    sK6: lst ).

thf(func_def_16,type,
    sK7: lst ).

thf(func_def_18,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_19,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

thf(func_def_21,type,
    vOR: $o > $o > $o ).

thf(func_def_22,type,
    vIMP: $o > $o > $o ).

thf(func_def_23,type,
    vNOT: $o > $o ).

thf(func_def_24,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f111,plain,
    $false,
    inference(avatar_sat_refutation,[],[f37,f41,f74,f78,f82,f89,f95,f107,f110]) ).

thf(f110,plain,
    ( ~ spl8_6
    | spl8_8 ),
    inference(avatar_contradiction_clause,[],[f109]) ).

thf(f109,plain,
    ( $false
    | ~ spl8_6
    | spl8_8 ),
    inference(trivial_inequality_removal,[],[f108]) ).

thf(f108,plain,
    ( ( vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5))) != vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5))) )
    | ~ spl8_6
    | spl8_8 ),
    inference(forward_demodulation,[],[f106,f85]) ).

thf(f85,plain,
    ( ! [X8: lst,X7: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) )
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f84]) ).

thf(f84,plain,
    ( spl8_6
  <=> ! [X8: lst,X7: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

thf(f106,plain,
    ( ( vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),sK4)),sK5)) != vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5))) )
    | spl8_8 ),
    inference(avatar_component_clause,[],[f104]) ).

thf(f104,plain,
    ( spl8_8
  <=> ( vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),sK4)),sK5)) = vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

thf(f107,plain,
    ( spl8_7
    | ~ spl8_8
    | ~ spl8_5 ),
    inference(avatar_split_clause,[],[f102,f80,f104,f87]) ).

thf(f87,plain,
    ( spl8_7
  <=> ! [X2: lst,X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

thf(f80,plain,
    ( spl8_5
  <=> ! [X2: a,X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),X1)),X0) = vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

thf(f102,plain,
    ( ! [X2: lst,X0: lst,X1: lst] :
        ( ( vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),sK4)),sK5)) != vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5))) )
        | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) ) )
    | ~ spl8_5 ),
    inference(forward_demodulation,[],[f101,f81]) ).

thf(f81,plain,
    ( ! [X2: a,X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),X1)),X0) = vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X0)) )
    | ~ spl8_5 ),
    inference(avatar_component_clause,[],[f80]) ).

thf(f101,plain,
    ( ! [X2: lst,X0: lst,X1: lst] :
        ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),sK4)),sK5)) )
        | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) ) )
    | ~ spl8_5 ),
    inference(forward_demodulation,[],[f100,f81]) ).

thf(f100,plain,
    ( ! [X2: lst,X0: lst,X1: lst] :
        ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),sK4))),sK5) )
        | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) ) )
    | ~ spl8_5 ),
    inference(forward_demodulation,[],[f29,f81]) ).

thf(f29,plain,
    ! [X2: lst,X0: lst,X1: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),sK4)),sK5) ) ),
    inference(trivial_inequality_removal,[],[f28]) ).

thf(f28,plain,
    ! [X2: lst,X0: lst,X1: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),sK4)),sK5) ) ),
    inference(forward_demodulation,[],[f27,f23]) ).

thf(f23,plain,
    ! [X0: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X0) = X0 ),
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ! [X0: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X0) = X0 ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X7: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X7) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2p_Osimps_I1_J) ).

thf(f27,plain,
    ! [X2: lst,X0: lst,X1: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7)) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),sK4)),sK5) ) ),
    inference(forward_demodulation,[],[f25,f23]) ).

thf(f25,plain,
    ! [X2: lst,X0: lst,X1: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),sK4)),sK5) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),sK6)),sK7) ) ),
    inference(cnf_transformation,[],[f21]) ).

thf(f21,plain,
    ! [X0: lst] :
      ( ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),sK4)),sK5) )
        & ! [X7: lst,X8: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) ) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),sK6)),sK7) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7])],[f17,f20,f19,f18]) ).

thf(f18,plain,
    ( ? [X3: a,X4: lst] :
        ( ? [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),X5)),X6) )
        & ! [X7: lst,X8: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),X7)),X8) ) )
   => ( ? [X6: lst,X5: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),X5)),X6) )
      & ! [X8: lst,X7: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f19,plain,
    ( ? [X6: lst,X5: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),X5)),X6) )
   => ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK4),sK5)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,sK2),sK3)),sK4)),sK5) ) ),
    introduced(choice_axiom,[]) ).

thf(f20,plain,
    ( ? [X9: lst,X10: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X9),X10)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X9)),X10) )
   => ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),sK6)),sK7) ) ),
    introduced(choice_axiom,[]) ).

thf(f17,plain,
    ! [X0: lst] :
      ( ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ? [X3: a,X4: lst] :
          ( ? [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),X5)),X6) )
          & ! [X7: lst,X8: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),X7)),X8) ) )
      | ? [X9: lst,X10: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X9),X10)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X9)),X10) ) ),
    inference(rectify,[],[f14]) ).

thf(f14,plain,
    ! [X0: lst] :
      ( ! [X9: lst,X10: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X9),X10)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X9)),X10) )
      | ? [X3: a,X4: lst] :
          ( ? [X7: lst,X8: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),X7)),X8) )
          & ! [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),X5)),X6) ) )
      | ? [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X1)),X2) ) ),
    inference(flattening,[],[f13]) ).

thf(f13,plain,
    ! [X0: lst] :
      ( ! [X9: lst,X10: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X9),X10)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X9)),X10) )
      | ? [X3: a,X4: lst] :
          ( ? [X7: lst,X8: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),X7)),X8) )
          & ! [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),X5)),X6) ) )
      | ? [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X1)),X2) ) ),
    inference(ennf_transformation,[],[f10]) ).

thf(f10,plain,
    ! [X0: lst] :
      ( ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X1)),X2) )
     => ( ! [X3: a,X4: lst] :
            ( ! [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),X5)),X6) )
           => ! [X7: lst,X8: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),X7)),X8) ) )
       => ! [X9: lst,X10: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X9),X10)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X9)),X10) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: lst] :
      ( ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X1)),X2) )
     => ( ! [X3: a,X4: lst] :
            ( ! [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X4),X5)),X6) )
           => ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X3),X4)),X1)),X2) ) )
       => ! [X5: lst,X6: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X5),X6)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X5)),X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).

thf(f95,plain,
    ( spl8_3
    | ~ spl8_7 ),
    inference(avatar_contradiction_clause,[],[f94]) ).

thf(f94,plain,
    ( $false
    | spl8_3
    | ~ spl8_7 ),
    inference(trivial_inequality_removal,[],[f93]) ).

thf(f93,plain,
    ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) )
    | spl8_3
    | ~ spl8_7 ),
    inference(superposition,[],[f73,f88]) ).

thf(f88,plain,
    ( ! [X2: lst,X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f87]) ).

thf(f73,plain,
    ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),sK0)),sK1) )
    | spl8_3 ),
    inference(avatar_component_clause,[],[f71]) ).

thf(f71,plain,
    ( spl8_3
  <=> ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),sK0)),sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

thf(f89,plain,
    ( spl8_6
    | spl8_7 ),
    inference(avatar_split_clause,[],[f32,f87,f84]) ).

thf(f32,plain,
    ! [X2: lst,X0: lst,X1: lst,X8: lst,X7: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) ) ),
    inference(trivial_inequality_removal,[],[f31]) ).

thf(f31,plain,
    ! [X2: lst,X0: lst,X1: lst,X8: lst,X7: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) ) ),
    inference(forward_demodulation,[],[f30,f23]) ).

thf(f30,plain,
    ! [X2: lst,X0: lst,X1: lst,X8: lst,X7: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7)) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) ) ),
    inference(forward_demodulation,[],[f24,f23]) ).

thf(f24,plain,
    ! [X2: lst,X0: lst,X1: lst,X8: lst,X7: lst] :
      ( ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)),X2) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X7),X8)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK3),X7)),X8) )
      | ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK6),sK7)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),sK6)),sK7) ) ),
    inference(cnf_transformation,[],[f21]) ).

thf(f82,plain,
    spl8_5,
    inference(avatar_split_clause,[],[f26,f80]) ).

thf(f26,plain,
    ! [X2: a,X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),X1)),X0) = vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X0)) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X0: lst,X1: lst,X2: a] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),X1)),X0) = vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X2),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X0)) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X7: lst,X8: lst,X9: a] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X9),X8)),X7) = vAPP(lst,lst,vAPP(a,sTfun(lst,lst),cns,X9),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X8),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1p_Osimps_I2_J) ).

thf(f78,plain,
    spl8_4,
    inference(avatar_split_clause,[],[f23,f76]) ).

thf(f76,plain,
    ( spl8_4
  <=> ! [X0: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,nl),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

thf(f74,plain,
    ~ spl8_3,
    inference(avatar_split_clause,[],[f22,f71]) ).

thf(f22,plain,
    vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),sK0)),sK1),
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),sK0)),sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f15]) ).

thf(f15,plain,
    ( ? [X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),X0)),X1) )
   => ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,sK0),sK1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),sK0)),sK1) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ? [X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)) != vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),X0)),X1) ),
    inference(ennf_transformation,[],[f8]) ).

thf(f8,plain,
    ~ ! [X0: lst,X1: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X0),X1)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),X0)),X1) ),
    inference(rectify,[],[f5]) ).

thf(f5,negated_conjecture,
    ~ ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),X1)),X2) ),
    inference(negated_conjecture,[],[f4]) ).

thf(f4,conjecture,
    ! [X1: lst,X2: lst] : ( vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,X1),X2)) = vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,vAPP(lst,lst,vAPP(lst,sTfun(lst,lst),ap,xs),X1)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f41,plain,
    spl8_2,
    inference(avatar_split_clause,[],[f7,f39]) ).

thf(f39,plain,
    ( spl8_2
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

thf(f7,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f37,plain,
    ~ spl8_1,
    inference(avatar_split_clause,[],[f6,f34]) ).

thf(f34,plain,
    ( spl8_1
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

thf(f6,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n029.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun May 19 23:39:53 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (28618)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (28621)WARNING: value z3 for option sas not known
% 0.15/0.37  % (28620)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (28619)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (28623)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)
% 0.15/0.37  % (28624)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)
% 0.15/0.37  % Exception at run slice level% Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  
% 0.15/0.37  % (28621)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)
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % (28622)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (28623)First to succeed.
% 0.15/0.37  % (28624)Also succeeded, but the first one will report.
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  % (28621)Also succeeded, but the first one will report.
% 0.15/0.38  % (28623)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28618"
% 0.15/0.38  % (28625)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)
% 0.15/0.38  % (28623)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (28623)------------------------------
% 0.15/0.38  % (28623)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (28623)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (28623)Memory used [KB]: 815
% 0.15/0.38  % (28623)Time elapsed: 0.009 s
% 0.15/0.38  % (28623)Instructions burned: 14 (million)
% 0.15/0.38  % (28618)Success in time 0.012 s
%------------------------------------------------------------------------------