TSTP Solution File: NUM691^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 : Sun May  5 08:41:53 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  116 (   4 unt;  16 typ;   0 def)
%            Number of atoms       :  817 ( 139 equ;   0 cnn)
%            Maximal formula atoms :    4 (   8 avg)
%            Number of connectives :  299 ( 154   ~;  99   |;   5   &;   0   @)
%                                         (   4 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   22 (  21   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;  10 con; 0-6 aty)
%            Number of variables   :   73 (   0   ^  67   !;   0   ?;  73   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

thf(func_def_1,type,
    x: nat ).

thf(func_def_2,type,
    y: nat ).

thf(func_def_3,type,
    z: nat ).

thf(func_def_4,type,
    u: nat ).

thf(func_def_5,type,
    more: nat > nat > $o ).

thf(func_def_7,type,
    pl: nat > nat > nat ).

thf(func_def_11,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_12,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_13,type,
    vAND: $o > $o > $o ).

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

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

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

thf(func_def_17,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f169,plain,
    $false,
    inference(avatar_sat_refutation,[],[f84,f99,f114,f116,f118,f123,f144,f146,f148,f162,f165,f168]) ).

thf(f168,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f167]) ).

thf(f167,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f166,f79]) ).

thf(f79,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f77]) ).

thf(f77,plain,
    ( spl0_1
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f166,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f157,f94]) ).

thf(f94,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f92]) ).

thf(f92,plain,
    ( spl0_3
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f157,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f156]) ).

thf(f156,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
    inference(superposition,[],[f36,f41]) ).

thf(f41,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(cnf_transformation,[],[f33]) ).

thf(f33,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
      | ( ( X0 != X1 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ) ),
    inference(flattening,[],[f32]) ).

thf(f32,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
      | ( ( X0 != X1 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f26]) ).

thf(f26,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
       => ( X0 = X1 ) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
    inference(flattening,[],[f19]) ).

thf(f19,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
       => ( X0 = X1 ) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
    inference(fool_elimination,[],[f18]) ).

thf(f18,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
       => ( X0 = X1 ) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: nat,X2: nat,X3: nat,X4: nat] :
      ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
       => ( X1 = X2 ) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X3),X4)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22a) ).

thf(f36,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true,
    inference(cnf_transformation,[],[f28]) ).

thf(f28,plain,
    ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) )
    & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true ) ),
    inference(ennf_transformation,[],[f22]) ).

thf(f22,plain,
    ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true )
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
    inference(flattening,[],[f11]) ).

thf(f11,plain,
    ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true )
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
    inference(fool_elimination,[],[f10]) ).

thf(f10,plain,
    ~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u))
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,negated_conjecture,
    ~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u))
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
    inference(negated_conjecture,[],[f6]) ).

thf(f6,conjecture,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u))
   => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23) ).

thf(f165,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f164]) ).

thf(f164,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f163,f79]) ).

thf(f163,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f158,f94]) ).

thf(f158,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f155]) ).

thf(f155,plain,
    ( ( $true = $false )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
    inference(superposition,[],[f150,f41]) ).

thf(f150,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) = $false,
    inference(trivial_inequality_removal,[],[f149]) ).

thf(f149,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) = $false ) ),
    inference(superposition,[],[f36,f9]) ).

thf(f9,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f162,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f161]) ).

thf(f161,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f160,f79]) ).

thf(f160,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f159,f94]) ).

thf(f159,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f154]) ).

thf(f154,plain,
    ( ( $true = $false )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
    inference(superposition,[],[f41,f150]) ).

thf(f148,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f147]) ).

thf(f147,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f140,f79]) ).

thf(f140,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f139]) ).

thf(f139,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_4 ),
    inference(superposition,[],[f124,f47]) ).

thf(f47,plain,
    ! [X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(equality_resolution,[],[f44]) ).

thf(f44,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( X2 != X3 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(cnf_transformation,[],[f35]) ).

thf(f35,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( ( X2 != X3 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(flattening,[],[f34]) ).

thf(f34,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( ( X2 != X3 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(ennf_transformation,[],[f27]) ).

thf(f27,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
     => ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
         => ( X2 = X3 ) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
    inference(flattening,[],[f21]) ).

thf(f21,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
     => ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
         => ( X2 = X3 ) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
    inference(fool_elimination,[],[f20]) ).

thf(f20,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
     => ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3)
         => ( X2 = X3 ) )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X1: nat,X2: nat,X3: nat,X4: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
     => ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X3),X4)
         => ( X3 = X4 ) )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).

thf(f124,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) )
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f36,f98]) ).

thf(f98,plain,
    ( ( z = u )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f96]) ).

thf(f96,plain,
    ( spl0_4
  <=> ( z = u ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f146,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f145]) ).

thf(f145,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f141,f79]) ).

thf(f141,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f138]) ).

thf(f138,plain,
    ( ( $true = $false )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_4 ),
    inference(superposition,[],[f133,f47]) ).

thf(f133,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) )
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f132]) ).

thf(f132,plain,
    ( ( $true != $true )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) )
    | ~ spl0_4 ),
    inference(superposition,[],[f124,f9]) ).

thf(f144,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f143]) ).

thf(f143,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f142,f79]) ).

thf(f142,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f137]) ).

thf(f137,plain,
    ( ( $true = $false )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
    | ~ spl0_4 ),
    inference(superposition,[],[f47,f133]) ).

thf(f123,plain,
    ( ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f122]) ).

thf(f122,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f121]) ).

thf(f121,plain,
    ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(superposition,[],[f100,f98]) ).

thf(f100,plain,
    ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u) )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f37,f83]) ).

thf(f83,plain,
    ( ( x = y )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f81]) ).

thf(f81,plain,
    ( spl0_2
  <=> ( x = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f37,plain,
    vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u),
    inference(cnf_transformation,[],[f28]) ).

thf(f118,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f117]) ).

thf(f117,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f110,f94]) ).

thf(f110,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f109]) ).

thf(f109,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f101,f46]) ).

thf(f46,plain,
    ! [X2: nat,X3: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) ) ),
    inference(equality_resolution,[],[f42]) ).

thf(f42,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f33]) ).

thf(f101,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)) )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f36,f83]) ).

thf(f116,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f115]) ).

thf(f115,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f111,f94]) ).

thf(f111,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f108]) ).

thf(f108,plain,
    ( ( $true = $false )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f103,f46]) ).

thf(f103,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)) )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f102]) ).

thf(f102,plain,
    ( ( $true != $true )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)) )
    | ~ spl0_2 ),
    inference(superposition,[],[f101,f9]) ).

thf(f114,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f113]) ).

thf(f113,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f112,f94]) ).

thf(f112,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f107]) ).

thf(f107,plain,
    ( ( $true = $false )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f46,f103]) ).

thf(f99,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f39,f96,f92]) ).

thf(f39,plain,
    ( ( z = u )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ( ( z = u )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true ) ),
    inference(ennf_transformation,[],[f24]) ).

thf(f24,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
   => ( z = u ) ),
    inference(flattening,[],[f15]) ).

thf(f15,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
   => ( z = u ) ),
    inference(fool_elimination,[],[f14]) ).

thf(f14,plain,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u)
   => ( z = u ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u)
   => ( z = u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).

thf(f84,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f38,f81,f77]) ).

thf(f38,plain,
    ( ( x = y )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
    inference(cnf_transformation,[],[f29]) ).

thf(f29,plain,
    ( ( x = y )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
    inference(ennf_transformation,[],[f23]) ).

thf(f23,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
   => ( x = y ) ),
    inference(flattening,[],[f13]) ).

thf(f13,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
   => ( x = y ) ),
    inference(fool_elimination,[],[f12]) ).

thf(f12,plain,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
   => ( x = y ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 14:33:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (7714)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (7717)WARNING: value z3 for option sas not known
% 0.21/0.37  % (7716)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37  % (7717)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)
% 0.21/0.37  % (7718)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37  % (7715)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37  % (7719)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)
% 0.21/0.37  % (7720)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)
% 0.21/0.37  % (7721)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)
% 0.21/0.37  % (7721)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37  % Exception at run slice level% Exception at run slice level
% 0.21/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37  
% 0.21/0.37  % Exception at run slice level
% 0.21/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38  % (7717)First to succeed.
% 0.21/0.38  % (7717)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7714"
% 0.21/0.38  % (7717)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (7717)------------------------------
% 0.21/0.38  % (7717)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (7717)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (7717)Memory used [KB]: 794
% 0.21/0.38  % (7717)Time elapsed: 0.011 s
% 0.21/0.38  % (7717)Instructions burned: 15 (million)
% 0.21/0.38  % (7714)Success in time 0.013 s
%------------------------------------------------------------------------------