TSTP Solution File: SEU850^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU850^5 : 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 : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 04:06:52 EDT 2024

% Result   : Theorem 0.14s 0.31s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   62 (   5 unt;  18 typ;   0 def)
%            Number of atoms       :  640 ( 144 equ;   0 cnn)
%            Maximal formula atoms :   12 (  14 avg)
%            Number of connectives :  168 (  49   ~;  51   |;  48   &;   0   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   89 (  88   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   3 con; 0-6 aty)
%            Number of variables   :   88 (   0   ^  52   !;  30   ?;  88   :)
%                                         (   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,
    sP0: ( a > $o ) > ( a > $o ) > $o ).

thf(func_def_5,type,
    sP1: ( a > $o ) > ( a > $o ) > $o ).

thf(func_def_6,type,
    sK2: ( a > $o ) > ( a > $o ) > a ).

thf(func_def_7,type,
    sK3: ( a > $o ) > ( a > $o ) > a ).

thf(func_def_8,type,
    sK4: a > $o ).

thf(func_def_9,type,
    sK5: a > $o ).

thf(func_def_10,type,
    sK6: a > $o ).

thf(func_def_11,type,
    sK7: a ).

thf(func_def_12,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_13,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_14,type,
    vAND: $o > $o > $o ).

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

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

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

thf(func_def_18,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f92,plain,
    $false,
    inference(unit_resulting_resolution,[],[f84,f85,f26]) ).

thf(f26,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X1),X0) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f19,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
        & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,X1),X0)) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f17,f18]) ).

thf(f18,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ? [X2: a] :
          ( ( $true != vAPP(a,$o,X0,X2) )
          & ( $true = vAPP(a,$o,X1,X2) ) )
     => ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
        & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f17,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ? [X2: a] :
          ( ( $true != vAPP(a,$o,X0,X2) )
          & ( $true = vAPP(a,$o,X1,X2) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X1),X0) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,plain,
    ! [X1: a > $o,X0: a > $o] :
      ( ? [X5: a] :
          ( ( $true != vAPP(a,$o,X1,X5) )
          & ( $true = vAPP(a,$o,X0,X5) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
    inference(nnf_transformation,[],[f9]) ).

thf(f9,plain,
    ! [X1: a > $o,X0: a > $o] :
      ( ? [X5: a] :
          ( ( $true != vAPP(a,$o,X1,X5) )
          & ( $true = vAPP(a,$o,X0,X5) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f85,plain,
    $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,sK4),sK4)),
    inference(unit_resulting_resolution,[],[f84,f25]) ).

thf(f25,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X1),X0) )
      | ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK3,X1),X0)) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f84,plain,
    $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4),
    inference(subsumption_resolution,[],[f82,f39]) ).

thf(f39,plain,
    ( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) ) ),
    inference(subsumption_resolution,[],[f38,f33]) ).

thf(f33,plain,
    ( ( $true != vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) ) ),
    inference(forward_demodulation,[],[f32,f27]) ).

thf(f27,plain,
    sK4 = sK5,
    inference(cnf_transformation,[],[f22]) ).

thf(f22,plain,
    ( ( ( ( $true != vAPP(a,$o,sK4,sK7) )
        & ( $true = vAPP(a,$o,sK6,sK7) ) )
      | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK6) )
      | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) )
    & ( sK5 = sK6 )
    & ( sK4 = sK5 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f11,f21,f20]) ).

thf(f20,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ? [X3: a] :
              ( ( vAPP(a,$o,X0,X3) != $true )
              & ( vAPP(a,$o,X2,X3) = $true ) )
          | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X2) )
          | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) )
        & ( X1 = X2 )
        & ( X0 = X1 ) )
   => ( ( ? [X3: a] :
            ( ( $true != vAPP(a,$o,sK4,X3) )
            & ( $true = vAPP(a,$o,sK6,X3) ) )
        | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK6) )
        | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) )
      & ( sK5 = sK6 )
      & ( sK4 = sK5 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f21,plain,
    ( ? [X3: a] :
        ( ( $true != vAPP(a,$o,sK4,X3) )
        & ( $true = vAPP(a,$o,sK6,X3) ) )
   => ( ( $true != vAPP(a,$o,sK4,sK7) )
      & ( $true = vAPP(a,$o,sK6,sK7) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ? [X3: a] :
            ( ( vAPP(a,$o,X0,X3) != $true )
            & ( vAPP(a,$o,X2,X3) = $true ) )
        | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X2) )
        | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) )
      & ( X1 = X2 )
      & ( X0 = X1 ) ),
    inference(definition_folding,[],[f8,f10,f9]) ).

thf(f10,plain,
    ! [X2: a > $o,X1: a > $o] :
      ( ? [X4: a] :
          ( ( $true != vAPP(a,$o,X2,X4) )
          & ( $true = vAPP(a,$o,X1,X4) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

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

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

thf(f6,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ( X1 = X2 )
          & ( X0 = X1 ) )
       => ( ! [X3: a] :
              ( ( vAPP(a,$o,X2,X3) = $true )
             => ( vAPP(a,$o,X0,X3) = $true ) )
          & ! [X4: a] :
              ( ( $true = vAPP(a,$o,X1,X4) )
             => ( $true = vAPP(a,$o,X2,X4) ) )
          & ! [X5: a] :
              ( ( $true = vAPP(a,$o,X0,X5) )
             => ( $true = vAPP(a,$o,X1,X5) ) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ( X1 = X2 )
          & ( X0 = X1 ) )
       => ( ! [X3: a] :
              ( vAPP(a,$o,X2,X3)
             => vAPP(a,$o,X0,X3) )
          & ! [X4: a] :
              ( vAPP(a,$o,X1,X4)
             => vAPP(a,$o,X2,X4) )
          & ! [X5: a] :
              ( vAPP(a,$o,X0,X5)
             => vAPP(a,$o,X1,X5) ) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ( X1 = X2 )
        & ( X0 = X1 ) )
     => ( ! [X3: a] :
            ( vAPP(a,$o,X2,X3)
           => vAPP(a,$o,X0,X3) )
        & ! [X3: a] :
            ( vAPP(a,$o,X1,X3)
           => vAPP(a,$o,X2,X3) )
        & ! [X3: a] :
            ( vAPP(a,$o,X0,X3)
           => vAPP(a,$o,X1,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM9_pme) ).

thf(f32,plain,
    ( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true != vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(forward_demodulation,[],[f31,f27]) ).

thf(f31,plain,
    ( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK5) )
    | ( $true != vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(forward_demodulation,[],[f30,f28]) ).

thf(f28,plain,
    sK5 = sK6,
    inference(cnf_transformation,[],[f22]) ).

thf(f30,plain,
    ( ( $true != vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK6) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(cnf_transformation,[],[f22]) ).

thf(f38,plain,
    ( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true = vAPP(a,$o,sK4,sK7) ) ),
    inference(forward_demodulation,[],[f37,f27]) ).

thf(f37,plain,
    ( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true = vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(forward_demodulation,[],[f36,f27]) ).

thf(f36,plain,
    ( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK5) )
    | ( $true = vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(forward_demodulation,[],[f35,f28]) ).

thf(f35,plain,
    ( ( $true = vAPP(a,$o,sK4,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK6) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(forward_demodulation,[],[f34,f27]) ).

thf(f34,plain,
    ( ( $true = vAPP(a,$o,sK5,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK6) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(forward_demodulation,[],[f29,f28]) ).

thf(f29,plain,
    ( ( $true = vAPP(a,$o,sK6,sK7) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK5),sK6) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK5) ) ),
    inference(cnf_transformation,[],[f22]) ).

thf(f82,plain,
    ( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) ) ),
    inference(trivial_inequality_removal,[],[f79]) ).

thf(f79,plain,
    ( ( $true != $true )
    | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,sK4),sK4) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) ) ),
    inference(superposition,[],[f24,f75]) ).

thf(f75,plain,
    ( ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,sK4),sK4)) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) ) ),
    inference(trivial_inequality_removal,[],[f72]) ).

thf(f72,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,sK4),sK4)) )
    | ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP0,sK4),sK4) ) ),
    inference(superposition,[],[f23,f39]) ).

thf(f23,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) )
      | ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,X1),X0)) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,X1),X0)) )
        & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,X1),X0)) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f13,f14]) ).

thf(f14,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ? [X2: a] :
          ( ( $true != vAPP(a,$o,X0,X2) )
          & ( $true = vAPP(a,$o,X1,X2) ) )
     => ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,X1),X0)) )
        & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ? [X2: a] :
          ( ( $true != vAPP(a,$o,X0,X2) )
          & ( $true = vAPP(a,$o,X1,X2) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
    inference(rectify,[],[f12]) ).

thf(f12,plain,
    ! [X2: a > $o,X1: a > $o] :
      ( ? [X4: a] :
          ( ( $true != vAPP(a,$o,X2,X4) )
          & ( $true = vAPP(a,$o,X1,X4) ) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X2) ) ),
    inference(nnf_transformation,[],[f10]) ).

thf(f24,plain,
    ! [X0: a > $o,X1: a > $o] :
      ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK2,X1),X0)) )
      | ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem    : SEU850^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29  % Computer : n025.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Sun May 19 17:00:38 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.09/0.29  % (10772)Running in auto input_syntax mode. Trying TPTP
% 0.09/0.30  % (10775)WARNING: value z3 for option sas not known
% 0.09/0.30  % (10775)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)
% 0.09/0.31  % (10773)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.09/0.31  % (10777)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)
% 0.09/0.31  % (10778)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)
% 0.09/0.31  % (10774)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.09/0.31  % (10779)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)
% 0.09/0.31  % Exception at run slice level
% 0.09/0.31  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.31  % Exception at run slice level
% 0.09/0.31  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% (10779)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.09/0.31  
% 0.09/0.31  % (10776)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.09/0.31  % Exception at run slice level
% 0.09/0.31  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.31  % (10779)First to succeed.
% 0.09/0.31  % (10777)Also succeeded, but the first one will report.
% 0.09/0.31  % (10775)Also succeeded, but the first one will report.
% 0.14/0.31  % (10779)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10772"
% 0.14/0.31  % (10779)Refutation found. Thanks to Tanya!
% 0.14/0.31  % SZS status Theorem for theBenchmark
% 0.14/0.31  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.31  % (10779)------------------------------
% 0.14/0.31  % (10779)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.31  % (10779)Termination reason: Refutation
% 0.14/0.31  
% 0.14/0.31  % (10779)Memory used [KB]: 782
% 0.14/0.31  % (10779)Time elapsed: 0.006 s
% 0.14/0.31  % (10779)Instructions burned: 10 (million)
% 0.14/0.31  % (10772)Success in time 0.008 s
%------------------------------------------------------------------------------