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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : LCL961^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:15:29 AM UTC 2026

% Result   : Theorem 0.18s 0.27s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   60 (  43 unt;   0 typ;   0 def)
%            Number of atoms       :  381 (  72 equ;   0 cnn)
%            Maximal formula atoms :   14 (   6 avg)
%            Number of connectives :  528 (  21   ~;  22   |;   3   &; 385   @)
%                                         (   0 <=>;  63  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  28 usr;   8 con; 0-4 aty)
%                                         (  34  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  122 (  95   ^;  27   !;   0   ?; 122   :)

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

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

thf(func_def_0,type,
    mrel: mworld > mworld > $o ).

thf(func_def_1,type,
    mactual: mworld ).

thf(func_def_2,type,
    mlocal: ( mworld > $o ) > $o ).

thf(func_def_4,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(func_def_5,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_6,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_7,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_8,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_9,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(func_def_10,type,
    mdia: ( mworld > $o ) > mworld > $o ).

thf(func_def_11,type,
    p: mworld > $o ).

thf(func_def_12,type,
    q: mworld > $o ).

thf(func_def_13,type,
    db0: 
      !>[X0: $tType] : X0 ).

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

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

thf(func_def_16,type,
    db1: 
      !>[X0: $tType] : X0 ).

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

thf(func_def_18,type,
    db2: 
      !>[X0: $tType] : X0 ).

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

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

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

thf(func_def_22,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_23,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_26,type,
    sK0: mworld ).

thf(func_def_27,type,
    sK1: mworld ).

thf(func_def_28,type,
    sK2: mworld ).

thf(func_def_29,type,
    sK3: mworld ).

thf(f1,axiom,
    ( mlocal
    = ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).

thf(f4,axiom,
    ( mor
    = ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
          | ( X0 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).

thf(f5,axiom,
    ( mimplies
    = ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
         => ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).

thf(f7,axiom,
    ( mbox
    = ( ^ [X0: mworld > $o,X1: mworld] :
        ! [X2: mworld] :
          ( ( mrel @ X1 @ X2 )
         => ( X0 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).

thf(f10,axiom,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( mrel @ X0 @ X1 )
        & ( mrel @ X0 @ X2 ) )
     => ( mrel @ X2 @ X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).

thf(f11,conjecture,
    mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel16) ).

thf(f12,negated_conjecture,
    ~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

thf(f13,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(fool_elimination,[],[f1]) ).

thf(f18,plain,
    ( mor
    = ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
          | ( X0 @ X2 ) ) ) ),
    inference(rectify,[],[f4]) ).

thf(f19,plain,
    ( mor
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
          | ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f18]) ).

thf(f20,plain,
    ( mimplies
    = ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
         => ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f5]) ).

thf(f21,plain,
    ( mimplies
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
         => ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f20]) ).

thf(f24,plain,
    ( mbox
    = ( ^ [X0: mworld > $o,X1: mworld] :
        ! [X2: mworld] :
          ( ( mrel @ X1 @ X2 )
         => ( X0 @ X2 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f25,plain,
    ( mbox
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ( !! @ mworld
          @ ^ [Y2: mworld] :
              ( ( mrel @ Y1 @ Y2 )
             => ( Y0 @ Y2 ) ) ) ) ),
    inference(fool_elimination,[],[f24]) ).

thf(f30,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( mrel @ X0 @ X1 )
        & ( mrel @ X0 @ X2 ) )
     => ( mrel @ X2 @ X1 ) ),
    inference(rectify,[],[f10]) ).

thf(f31,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( ( mrel @ X0 @ X1 )
          = $true )
        & ( ( mrel @ X0 @ X2 )
          = $true ) )
     => ( ( mrel @ X2 @ X1 )
        = $true ) ),
    inference(fool_elimination,[],[f30]) ).

thf(f32,plain,
    ~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
    inference(rectify,[],[f12]) ).

thf(f33,plain,
    ( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
   != $true ),
    inference(fool_elimination,[],[f32]) ).

thf(f34,plain,
    ( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
   != $true ),
    inference(flattening,[],[f33]) ).

thf(f35,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( mrel @ X2 @ X1 )
        = $true )
      | ( ( mrel @ X0 @ X1 )
       != $true )
      | ( ( mrel @ X0 @ X2 )
       != $true ) ),
    inference(ennf_transformation,[],[f31]) ).

thf(f36,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( mrel @ X2 @ X1 )
        = $true )
      | ( ( mrel @ X0 @ X1 )
       != $true )
      | ( ( mrel @ X0 @ X2 )
       != $true ) ),
    inference(flattening,[],[f35]) ).

thf(f37,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f40,plain,
    ( mor
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
          | ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f41,plain,
    ( mimplies
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
         => ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f21]) ).

thf(f43,plain,
    ( mbox
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ( !! @ mworld
          @ ^ [Y2: mworld] :
              ( ( mrel @ Y1 @ Y2 )
             => ( Y0 @ Y2 ) ) ) ) ),
    inference(cnf_transformation,[],[f25]) ).

thf(f46,plain,
    ! [X2: mworld,X0: mworld,X1: mworld] :
      ( ( ( mrel @ X0 @ X2 )
       != $true )
      | ( ( mrel @ X0 @ X1 )
       != $true )
      | ( ( mrel @ X2 @ X1 )
        = $true ) ),
    inference(cnf_transformation,[],[f36]) ).

thf(f47,plain,
    ( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
   != $true ),
    inference(cnf_transformation,[],[f34]) ).

thf(f50,plain,
    ( $true
   != ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
      @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
            ( ( Y0 @ Y2 )
            | ( Y1 @ Y2 ) )
        @ ( ^ [Y0: mworld > $o,Y1: mworld] :
              ( !! @ mworld
              @ ^ [Y2: mworld] :
                  ( ( mrel @ Y1 @ Y2 )
                 => ( Y0 @ Y2 ) ) )
          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                ( ( Y0 @ Y2 )
               => ( Y1 @ Y2 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ p )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ q ) ) )
        @ ( ^ [Y0: mworld > $o,Y1: mworld] :
              ( !! @ mworld
              @ ^ [Y2: mworld] :
                  ( ( mrel @ Y1 @ Y2 )
                 => ( Y0 @ Y2 ) ) )
          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                ( ( Y0 @ Y2 )
               => ( Y1 @ Y2 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ q )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ p ) ) ) ) ) ),
    inference(definition_unfolding,[],[f47,f37,f40,f43,f41,f43,f43,f43,f41,f43,f43]) ).

thf(f51,plain,
    ( $true
   != ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) )
             => ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ Y0 @ Y1 )
                   => ( q @ Y1 ) ) ) ) ) )
      | ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ Y0 @ Y1 )
                   => ( q @ Y1 ) ) )
             => ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f50]) ).

thf(f52,plain,
    ( $false
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( q @ Y1 ) ) )
           => ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) ) ) ) ) ),
    inference(or_proxy_clausification,[],[f51]) ).

thf(f53,plain,
    ( $false
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) )
           => ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( q @ Y1 ) ) ) ) ) ) ),
    inference(or_proxy_clausification,[],[f51]) ).

thf(f54,plain,
    ( $false
    = ( ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) )
           => ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( q @ Y1 ) ) ) ) )
      @ sK0 ) ),
    inference(sigma_proxy_clausification,[],[f53]) ).

thf(f55,plain,
    ( $false
    = ( ( mrel @ mactual @ sK0 )
     => ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK0 @ Y0 )
             => ( p @ Y0 ) ) )
       => ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK0 @ Y0 )
             => ( q @ Y0 ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f54]) ).

thf(f56,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK0 @ Y0 )
           => ( p @ Y0 ) ) )
     => ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK0 @ Y0 )
           => ( q @ Y0 ) ) ) ) ),
    inference(imp_proxy_clausification,[],[f55]) ).

thf(f57,plain,
    ( $true
    = ( mrel @ mactual @ sK0 ) ),
    inference(imp_proxy_clausification,[],[f55]) ).

thf(f59,plain,
    ( $true
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ sK0 @ Y0 )
         => ( p @ Y0 ) ) ) ),
    inference(imp_proxy_clausification,[],[f56]) ).

thf(f60,plain,
    ! [X1: mworld] :
      ( $true
      = ( ^ [Y0: mworld] :
            ( ( mrel @ sK0 @ Y0 )
           => ( p @ Y0 ) )
        @ X1 ) ),
    inference(pi_proxy_clausification,[],[f59]) ).

thf(f61,plain,
    ! [X1: mworld] :
      ( $true
      = ( ( mrel @ sK0 @ X1 )
       => ( p @ X1 ) ) ),
    inference(beta-eta_normalization,[],[f60]) ).

thf(f62,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK0 @ X1 ) )
      | ( $true
        = ( p @ X1 ) ) ),
    inference(imp_proxy_clausification,[],[f61]) ).

thf(f67,plain,
    ( $false
    = ( ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( q @ Y1 ) ) )
           => ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) ) ) )
      @ sK2 ) ),
    inference(sigma_proxy_clausification,[],[f52]) ).

thf(f68,plain,
    ( $false
    = ( ( mrel @ mactual @ sK2 )
     => ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( q @ Y0 ) ) )
       => ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( p @ Y0 ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f67]) ).

thf(f69,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( q @ Y0 ) ) )
     => ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( p @ Y0 ) ) ) ) ),
    inference(imp_proxy_clausification,[],[f68]) ).

thf(f70,plain,
    ( $true
    = ( mrel @ mactual @ sK2 ) ),
    inference(imp_proxy_clausification,[],[f68]) ).

thf(f71,plain,
    ( $false
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( p @ Y0 ) ) ) ),
    inference(imp_proxy_clausification,[],[f69]) ).

thf(f76,plain,
    ( $false
    = ( ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( p @ Y0 ) )
      @ sK3 ) ),
    inference(sigma_proxy_clausification,[],[f71]) ).

thf(f77,plain,
    ( $false
    = ( ( mrel @ sK2 @ sK3 )
     => ( p @ sK3 ) ) ),
    inference(beta-eta_normalization,[],[f76]) ).

thf(f78,plain,
    ( $false
    = ( p @ sK3 ) ),
    inference(imp_proxy_clausification,[],[f77]) ).

thf(f79,plain,
    ( $true
    = ( mrel @ sK2 @ sK3 ) ),
    inference(imp_proxy_clausification,[],[f77]) ).

thf(f210,plain,
    ! [X0: mworld] :
      ( ( $true != $true )
      | ( $true
       != ( mrel @ mactual @ X0 ) )
      | ( $true
        = ( mrel @ sK2 @ X0 ) ) ),
    inference(constrained_superposition,[],[f46,f70]) ).

thf(f217,plain,
    ! [X0: mworld] :
      ( ( $true
       != ( mrel @ mactual @ X0 ) )
      | ( $true
        = ( mrel @ sK2 @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f210]) ).

thf(f247,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK0 ) ) ),
    inference(constrained_superposition,[],[f217,f57]) ).

thf(f250,plain,
    ( $true
    = ( mrel @ sK2 @ sK0 ) ),
    inference(trivial_inequality_removal,[],[f247]) ).

thf(f273,plain,
    ! [X0: mworld] :
      ( ( $true != $true )
      | ( $true
       != ( mrel @ sK2 @ X0 ) )
      | ( $true
        = ( mrel @ sK0 @ X0 ) ) ),
    inference(constrained_superposition,[],[f46,f250]) ).

thf(f276,plain,
    ! [X0: mworld] :
      ( ( $true
       != ( mrel @ sK2 @ X0 ) )
      | ( $true
        = ( mrel @ sK0 @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f273]) ).

thf(f473,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK0 @ sK3 ) ) ),
    inference(constrained_superposition,[],[f276,f79]) ).

thf(f474,plain,
    ( $true
    = ( mrel @ sK0 @ sK3 ) ),
    inference(trivial_inequality_removal,[],[f473]) ).

thf(f483,plain,
    ( ( $true = $false )
    | ( $true
      = ( p @ sK3 ) ) ),
    inference(constrained_superposition,[],[f62,f474]) ).

thf(f484,plain,
    ( $true
    = ( p @ sK3 ) ),
    inference(trivial_inequality_removal,[],[f483]) ).

thf(f488,plain,
    $true = $false,
    inference(forward_demodulation,[],[f484,f78]) ).

thf(f489,plain,
    $false,
    inference(trivial_inequality_removal,[],[f488]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL961^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18  % Computer : n009.cluster.edu
% 0.10/0.18  % Model    : x86_64 x86_64
% 0.10/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18  % Memory   : 8046.5625MB
% 0.10/0.18  % OS       : Linux 6.8.0-71-generic
% 0.10/0.18  % CPULimit : 300
% 0.10/0.18  % WCLimit  : 300
% 0.10/0.18  % DateTime : Tue Sep 29 10:58:00 UTC 2026
% 0.10/0.18  % CPUTime  : 
% 0.10/0.18  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21  Running first-order model finding
% 0.10/0.21  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.27  % (3855188)Will run a generic schedule for satisfiability detection.
% 0.18/0.27  % (3855194)% WARNING: option uhcvi not known.
% 0.18/0.27  % (3855197)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3458245870:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27  % (3855197)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27  % (3855194)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3153614931:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27  % (3855195)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=687686144:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27  % (3855196)dis+10_1_sil=32000:sp=arity:random_seed=3419345130:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27  % (3855194)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27  % (3855194)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27  % (3855193)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2687442849_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27  % Exception at run slice level
% 0.18/0.27  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27  % (3855198)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1606702893:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27  % (3855195) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3855188-3855195"...
% 0.18/0.27  % (3855199)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2746792061:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27  % (3855195)...printing done.
% 0.18/0.27  % (3855195)Refutation found. Thanks to Tanya!
% 0.18/0.27  % SZS status Theorem for theBenchmark
% 0.18/0.27  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.28  % (3855195)------------------------------
% 0.18/0.28  % (3855195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28  % (3855195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28  % (3855195)CaDiCaL version: 2.1.3
% 0.18/0.28  % (3855195)Termination reason: Refutation
% 0.18/0.28  % (3855195)Time elapsed: 0.017 s
% 0.18/0.28  % (3855195)Peak memory usage: 12 MB
% 0.18/0.28  % (3855195)Instructions burned: 26 (million)
% 0.18/0.28  % (3855188)Success in time 0.06 s
% 0.18/0.28  % Vampire exiting
%------------------------------------------------------------------------------