TSTP Solution File: SEU997^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU997^5 : 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 : n024.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 04:07:10 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   78 (  50 unt;  18 typ;   0 def)
%            Number of atoms       : 1179 ( 252 equ;   0 cnn)
%            Maximal formula atoms :   42 (  19 avg)
%            Number of connectives :  204 (  11   ~;   0   |; 184   &;   0   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   51 (  50   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   6 con; 0-6 aty)
%            Number of variables   :  354 (   0   ^ 305   !;  43   ?; 354   :)
%                                         (   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_4,type,
    sK0: a > a > a ).

thf(func_def_5,type,
    sK1: a > a > a ).

thf(func_def_6,type,
    sK2: a ).

thf(func_def_7,type,
    sK3: a ).

thf(func_def_8,type,
    sK4: a ).

thf(func_def_9,type,
    sK5: a ).

thf(func_def_10,type,
    sK6: a ).

thf(func_def_11,type,
    sK7: a > a ).

thf(func_def_13,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_14,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_15,type,
    vAND: $o > $o > $o ).

thf(func_def_16,type,
    vOR: $o > $o > $o ).

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

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

thf(func_def_19,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f2951,plain,
    $false,
    inference(subsumption_resolution,[],[f2950,f33]) ).

thf(f33,plain,
    sK5 != sK6,
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ( sK5 != sK6 )
    & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6) )
    & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6) )
    & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5) )
    & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5) )
    & ! [X7: a] :
        ( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),vAPP(a,a,sK7,X7)) )
        & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),vAPP(a,a,sK7,X7)) ) )
    & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X9) = X9 )
    & ! [X10: a] : ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X10) )
    & ! [X11: a] : ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X11) )
    & ! [X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X12) = X12 )
    & ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),X15)) )
    & ! [X16: a,X17: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),X17)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),X18)) )
    & ! [X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X19),X20)),X20) = X20 )
    & ! [X21: a,X22: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X21),X22)),X22) = X22 )
    & ! [X23: a,X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X23),X24) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X23) )
    & ! [X25: a,X26: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X26),X25) )
    & ! [X27: a,X28: a,X29: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X27),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X28),X29)) )
    & ! [X30: a,X31: a,X32: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X30),X31)),X32) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X30),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X31),X32)) )
    & ! [X33: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X33),X33) = X33 )
    & ! [X34: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X34),X34) = X34 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
        ( ? [X4: a,X5: a,X6: a] :
            ( ( X5 != X6 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X6) = X3 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X6) = X2 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
        & ! [X7: a] :
          ? [X8: a] :
            ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X8) = X3 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X8) = X2 ) )
        & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X9) = X9 )
        & ! [X10: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X10) = X3 )
        & ! [X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X11) = X2 )
        & ! [X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X12) = X12 )
        & ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X15)) )
        & ! [X16: a,X17: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X17)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X18)) )
        & ! [X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X19),X20)),X20) = X20 )
        & ! [X21: a,X22: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X22)),X22) = X22 )
        & ! [X23: a,X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X24) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X23) )
        & ! [X25: a,X26: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X25),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X26),X25) )
        & ! [X27: a,X28: a,X29: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X27),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X28),X29)) )
        & ! [X30: a,X31: a,X32: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X30),X31)),X32) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X30),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X31),X32)) )
        & ! [X33: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X33),X33) = X33 )
        & ! [X34: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X34),X34) = X34 ) )
   => ( ? [X6: a,X5: a,X4: a] :
          ( ( X5 != X6 )
          & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X4),X6) )
          & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X4),X6) )
          & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X4),X5) )
          & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X4),X5) ) )
      & ! [X7: a] :
        ? [X8: a] :
          ( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X8) )
          & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X8) ) )
      & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X9) = X9 )
      & ! [X10: a] : ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X10) )
      & ! [X11: a] : ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X11) )
      & ! [X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X12) = X12 )
      & ! [X15: a,X14: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),X15)) )
      & ! [X18: a,X17: a,X16: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),X17)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),X18)) )
      & ! [X20: a,X19: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X19),X20)),X20) = X20 )
      & ! [X22: a,X21: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X21),X22)),X22) = X22 )
      & ! [X24: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X23),X24) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X23) )
      & ! [X26: a,X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X26),X25) )
      & ! [X29: a,X28: a,X27: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X27),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X28),X29)) )
      & ! [X32: a,X31: a,X30: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X30),X31)),X32) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X30),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X31),X32)) )
      & ! [X33: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X33),X33) = X33 )
      & ! [X34: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X34),X34) = X34 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X6: a,X5: a,X4: a] :
        ( ( X5 != X6 )
        & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X4),X6) )
        & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X4),X6) )
        & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X4),X5) )
        & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X4),X5) ) )
   => ( ( sK5 != sK6 )
      & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6) )
      & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6) )
      & ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5) )
      & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X7: a] :
      ( ? [X8: a] :
          ( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X8) )
          & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X8) ) )
     => ( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),vAPP(a,a,sK7,X7)) )
        & ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),vAPP(a,a,sK7,X7)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
      ( ? [X4: a,X5: a,X6: a] :
          ( ( X5 != X6 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X6) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X6) = X2 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
      & ! [X7: a] :
        ? [X8: a] :
          ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X8) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X8) = X2 ) )
      & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X9) = X9 )
      & ! [X10: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X10) = X3 )
      & ! [X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X11) = X2 )
      & ! [X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X12) = X12 )
      & ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X15)) )
      & ! [X16: a,X17: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X17)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X18)) )
      & ! [X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X19),X20)),X20) = X20 )
      & ! [X21: a,X22: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X22)),X22) = X22 )
      & ! [X23: a,X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X24) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X23) )
      & ! [X25: a,X26: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X25),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X26),X25) )
      & ! [X27: a,X28: a,X29: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X27),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X28),X29)) )
      & ! [X30: a,X31: a,X32: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X30),X31)),X32) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X30),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X31),X32)) )
      & ! [X33: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X33),X33) = X33 )
      & ! [X34: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X34),X34) = X34 ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ? [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
      ( ? [X32: a,X33: a,X34: a] :
          ( ( X33 != X34 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X32),X34) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X32),X34) = X2 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X32),X33) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X32),X33) = X2 ) )
      & ! [X4: a] :
        ? [X5: a] :
          ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
      & ! [X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X6) = X6 )
      & ! [X7: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X7) = X3 )
      & ! [X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X8) = X2 )
      & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X9) = X9 )
      & ! [X10: a,X11: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X11),X12)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X11)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X12)) )
      & ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),X15)) )
      & ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X16),X17)),X17) = X17 )
      & ! [X18: a,X19: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19)),X19) = X19 )
      & ! [X20: a,X21: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X21) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X20) )
      & ! [X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X23),X22) )
      & ! [X24: a,X25: a,X26: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X25)),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X25),X26)) )
      & ! [X27: a,X28: a,X29: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X27),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X28),X29)) )
      & ! [X30: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X30),X30) = X30 )
      & ! [X31: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X31),X31) = X31 ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ? [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
      ( ? [X32: a,X33: a,X34: a] :
          ( ( X33 != X34 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X32),X34) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X32),X34) = X2 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X32),X33) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X32),X33) = X2 ) )
      & ! [X4: a] :
        ? [X5: a] :
          ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
          & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
      & ! [X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X6) = X6 )
      & ! [X7: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X7) = X3 )
      & ! [X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X8) = X2 )
      & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X9) = X9 )
      & ! [X10: a,X11: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X11),X12)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X11)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X12)) )
      & ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),X15)) )
      & ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X16),X17)),X17) = X17 )
      & ! [X18: a,X19: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19)),X19) = X19 )
      & ! [X20: a,X21: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X21) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X20) )
      & ! [X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X23),X22) )
      & ! [X24: a,X25: a,X26: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X25)),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X25),X26)) )
      & ! [X27: a,X28: a,X29: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X27),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X28),X29)) )
      & ! [X30: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X30),X30) = X30 )
      & ! [X31: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X31),X31) = X31 ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
        ( ( ! [X4: a] :
            ? [X5: a] :
              ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
          & ! [X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X6) = X6 )
          & ! [X7: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X7) = X3 )
          & ! [X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X8) = X2 )
          & ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X9) = X9 )
          & ! [X10: a,X11: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X11),X12)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X11)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X12)) )
          & ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X13),X15)) )
          & ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X16),X17)),X17) = X17 )
          & ! [X18: a,X19: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19)),X19) = X19 )
          & ! [X20: a,X21: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X21) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X20) )
          & ! [X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X23),X22) )
          & ! [X24: a,X25: a,X26: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X25)),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X25),X26)) )
          & ! [X27: a,X28: a,X29: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X27),X28)),X29) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X27),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X28),X29)) )
          & ! [X30: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X30),X30) = X30 )
          & ! [X31: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X31),X31) = X31 ) )
       => ! [X32: a,X33: a,X34: a] :
            ( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X32),X34) = X3 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X32),X34) = X2 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X32),X33) = X3 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X32),X33) = X2 ) )
           => ( X33 = X34 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
        ( ( ! [X4: a] :
            ? [X5: a] :
              ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
          & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4) = X4 )
          & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X4) = X3 )
          & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X4) = X2 )
          & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X4) = X4 )
          & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X6)) )
          & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X6)) )
          & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5)),X5) = X5 )
          & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X5) = X5 )
          & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X4) )
          & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X4) )
          & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6)) )
          & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5)),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6)) )
          & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X4) = X4 )
          & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X4) = X4 ) )
       => ! [X4: a,X5: a,X6: a] :
            ( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X6) = X3 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X6) = X2 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
              & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
           => ( X5 = X6 ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > a > a,X1: a > a > a,X2: a,X3: a] :
      ( ( ! [X4: a] :
          ? [X5: a] :
            ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
        & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4) = X4 )
        & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X4) = X3 )
        & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X4) = X2 )
        & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X4) = X4 )
        & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5)),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X6)) )
        & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X6)) )
        & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5)),X5) = X5 )
        & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X5) = X5 )
        & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X4) )
        & ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X4) )
        & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6)) )
        & ! [X4: a,X5: a,X6: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5)),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6)) )
        & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X4) = X4 )
        & ! [X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X4) = X4 ) )
     => ! [X4: a,X5: a,X6: a] :
          ( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X6) = X3 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X6) = X2 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5) = X3 )
            & ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X4),X5) = X2 ) )
         => ( X5 = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCD_LATTICE_THM_pme) ).

thf(f2950,plain,
    sK5 = sK6,
    inference(forward_demodulation,[],[f2915,f2914]) ).

thf(f2914,plain,
    sK5 = vAPP(a,a,sK7,sK4),
    inference(superposition,[],[f2869,f1533]) ).

thf(f1533,plain,
    sK4 = vAPP(a,a,sK7,sK5),
    inference(forward_demodulation,[],[f1532,f41]) ).

thf(f41,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3) = X0 ),
    inference(superposition,[],[f17,f26]) ).

thf(f26,plain,
    ! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X9) = X9 ),
    inference(cnf_transformation,[],[f12]) ).

thf(f17,plain,
    ! [X26: a,X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X26) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X26),X25) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f1532,plain,
    vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) = vAPP(a,a,sK7,sK5),
    inference(forward_demodulation,[],[f1512,f1264]) ).

thf(f1264,plain,
    vAPP(a,a,sK7,sK5) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,sK7,sK5)),
    inference(superposition,[],[f19,f1249]) ).

thf(f1249,plain,
    sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,sK7,sK5)),
    inference(forward_demodulation,[],[f1228,f62]) ).

thf(f62,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),sK2) = X0 ),
    inference(superposition,[],[f18,f23]) ).

thf(f23,plain,
    ! [X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X12) = X12 ),
    inference(cnf_transformation,[],[f12]) ).

thf(f18,plain,
    ! [X24: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X23),X24) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X23) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f1228,plain,
    vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,sK7,sK5)),
    inference(superposition,[],[f450,f27]) ).

thf(f27,plain,
    ! [X7: a] : ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),vAPP(a,a,sK7,X7)) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f450,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) ),
    inference(forward_demodulation,[],[f400,f26]) ).

thf(f400,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) ),
    inference(superposition,[],[f21,f30]) ).

thf(f30,plain,
    sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5),
    inference(cnf_transformation,[],[f12]) ).

thf(f21,plain,
    ! [X18: a,X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),X17)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X16),X18)) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f19,plain,
    ! [X21: a,X22: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X21),X22)),X22) = X22 ),
    inference(cnf_transformation,[],[f12]) ).

thf(f1512,plain,
    vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,sK7,sK5)),
    inference(superposition,[],[f651,f28]) ).

thf(f28,plain,
    ! [X7: a] : ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),vAPP(a,a,sK7,X7)) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f651,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) ),
    inference(forward_demodulation,[],[f585,f23]) ).

thf(f585,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) ),
    inference(superposition,[],[f22,f29]) ).

thf(f29,plain,
    sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5),
    inference(cnf_transformation,[],[f12]) ).

thf(f22,plain,
    ! [X14: a,X15: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),X14)),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X13),X15)) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f2869,plain,
    ! [X0: a] : ( vAPP(a,a,sK7,vAPP(a,a,sK7,X0)) = X0 ),
    inference(forward_demodulation,[],[f2868,f41]) ).

thf(f2868,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3) = vAPP(a,a,sK7,vAPP(a,a,sK7,X0)) ),
    inference(forward_demodulation,[],[f2824,f2608]) ).

thf(f2608,plain,
    ! [X0: a] : ( vAPP(a,a,sK7,vAPP(a,a,sK7,X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,sK7,vAPP(a,a,sK7,X0))) ),
    inference(superposition,[],[f19,f2564]) ).

thf(f2564,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,sK7,vAPP(a,a,sK7,X0))) = X0 ),
    inference(forward_demodulation,[],[f2514,f62]) ).

thf(f2514,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),sK2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,sK7,vAPP(a,a,sK7,X0))) ),
    inference(superposition,[],[f440,f27]) ).

thf(f440,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,sK7,X0)),X1)) ),
    inference(forward_demodulation,[],[f392,f26]) ).

thf(f392,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,sK7,X0)),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) ),
    inference(superposition,[],[f21,f28]) ).

thf(f2824,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,sK7,vAPP(a,a,sK7,X0))) ),
    inference(superposition,[],[f636,f28]) ).

thf(f636,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,sK7,X0)),X1)) ),
    inference(forward_demodulation,[],[f574,f23]) ).

thf(f574,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,sK7,X0)),X1)) ),
    inference(superposition,[],[f22,f27]) ).

thf(f2915,plain,
    sK6 = vAPP(a,a,sK7,sK4),
    inference(superposition,[],[f2869,f1672]) ).

thf(f1672,plain,
    sK4 = vAPP(a,a,sK7,sK6),
    inference(forward_demodulation,[],[f1671,f41]) ).

thf(f1671,plain,
    vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) = vAPP(a,a,sK7,sK6),
    inference(forward_demodulation,[],[f1650,f1340]) ).

thf(f1340,plain,
    vAPP(a,a,sK7,sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,sK7,sK6)),
    inference(superposition,[],[f19,f1324]) ).

thf(f1324,plain,
    sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,sK7,sK6)),
    inference(forward_demodulation,[],[f1302,f62]) ).

thf(f1302,plain,
    vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,sK7,sK6)),
    inference(superposition,[],[f451,f27]) ).

thf(f451,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) ),
    inference(forward_demodulation,[],[f401,f26]) ).

thf(f401,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) ),
    inference(superposition,[],[f21,f32]) ).

thf(f32,plain,
    sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6),
    inference(cnf_transformation,[],[f12]) ).

thf(f1650,plain,
    vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,sK7,sK6)),
    inference(superposition,[],[f652,f28]) ).

thf(f652,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) ),
    inference(forward_demodulation,[],[f586,f23]) ).

thf(f586,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) ),
    inference(superposition,[],[f22,f31]) ).

thf(f31,plain,
    sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU997^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 18:13:07 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (23147)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (23150)WARNING: value z3 for option sas not known
% 0.13/0.36  % (23151)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (23148)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (23149)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (23152)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36  % (23153)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36  % (23150)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36  % (23154)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.36  % Exception at run slice level% Exception at run slice level
% 0.13/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.36  % (23154)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.36  % Exception at run slice level
% 0.13/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.36  
% 0.13/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38  % (23155)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.38  % (23156)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.13/0.38  % (23157)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.13/0.38  % (23155)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.38  % (23156)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.38  % Exception at run slice level
% 0.13/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.40  % (23158)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.21/0.50  % (23157)First to succeed.
% 0.21/0.51  % (23157)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23147"
% 0.21/0.51  % (23157)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Theorem for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51  % (23157)------------------------------
% 0.21/0.51  % (23157)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.51  % (23157)Termination reason: Refutation
% 0.21/0.51  
% 0.21/0.51  % (23157)Memory used [KB]: 2132
% 0.21/0.51  % (23157)Time elapsed: 0.127 s
% 0.21/0.51  % (23157)Instructions burned: 316 (million)
% 0.21/0.51  % (23147)Success in time 0.149 s
%------------------------------------------------------------------------------