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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SYO223^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n019.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 08:49:33 AM UTC 2026

% Result   : Theorem 0.22s 0.29s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   67 (   8 unt;   0 typ;   2 def)
%            Number of atoms       :  595 ( 141 equ;   0 cnn)
%            Maximal formula atoms :    6 (   8 avg)
%            Number of connectives :  520 (  87   ~; 129   |;  30   &; 257   @)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  15 usr;   9 con; 0-4 aty)
%                                         (   0  !!;   7  ??;   0 @@+;   0 @@-)
%            Number of variables   :  109 (   2 sgn  85   !;   7   ?; 109   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_1,type,
    cLIKE: $i > $i > $o ).

thf(func_def_2,type,
    cUNIQUE: $i > $o ).

thf(func_def_8,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_9,type,
    vAND: $o > $o > $o ).

thf(func_def_10,type,
    db0: 
      !>[X0: $tType] : X0 ).

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

thf(func_def_12,type,
    vNOT: $o > $o ).

thf(func_def_15,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f1,conjecture,
    ( ( ( cUNIQUE @ cS )
      & ! [X0: $i] :
          ( ( cUNIQUE @ X0 )
         => ! [X1: $i] : ( X0 = X1 ) ) )
   => ? [X2: $i > $o] :
        ( ( ( X2 @ cJ )
          = ( ? [X0: $i] :
                ( ( cLIKE @ cJ @ X0 )
                & ( cUNIQUE @ X0 ) ) ) )
        & ( ( X2 @ cP )
          = ( cLIKE @ cP @ cS ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cLING2) ).

thf(f2,negated_conjecture,
    ~ ( ( ( cUNIQUE @ cS )
        & ! [X0: $i] :
            ( ( cUNIQUE @ X0 )
           => ! [X1: $i] : ( X0 = X1 ) ) )
     => ? [X2: $i > $o] :
          ( ( ( X2 @ cJ )
            = ( ? [X0: $i] :
                  ( ( cLIKE @ cJ @ X0 )
                  & ( cUNIQUE @ X0 ) ) ) )
          & ( ( X2 @ cP )
            = ( cLIKE @ cP @ cS ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

thf(f3,plain,
    ~ ( ( ( cUNIQUE @ cS )
        & ! [X0: $i] :
            ( ( cUNIQUE @ X0 )
           => ! [X1: $i] : ( X0 = X1 ) ) )
     => ? [X2: $i > $o] :
          ( ( ( X2 @ cJ )
            = ( ? [X3: $i] :
                  ( ( cLIKE @ cJ @ X3 )
                  & ( cUNIQUE @ X3 ) ) ) )
          & ( ( X2 @ cP )
            = ( cLIKE @ cP @ cS ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f4,plain,
    ~ ( ( ( ( cUNIQUE @ cS )
          = $true )
        & ! [X0: $i] :
            ( ( ( cUNIQUE @ X0 )
              = $true )
           => ! [X1: $i] : ( X0 = X1 ) ) )
     => ? [X2: $i > $o] :
          ( ( ( X2 @ cJ )
            = ( ?? @ $i
              @ ^ [Y0: $i] :
                  ( ( cUNIQUE @ Y0 )
                  & ( cLIKE @ cJ @ Y0 ) ) ) )
          & ( ( X2 @ cP )
            = ( cLIKE @ cP @ cS ) ) ) ),
    inference(fool_elimination,[],[f3]) ).

thf(f5,plain,
    ( ! [X2: $i > $o] :
        ( ( ( X2 @ cJ )
         != ( ?? @ $i
            @ ^ [Y0: $i] :
                ( ( cUNIQUE @ Y0 )
                & ( cLIKE @ cJ @ Y0 ) ) ) )
        | ( ( X2 @ cP )
         != ( cLIKE @ cP @ cS ) ) )
    & ( ( cUNIQUE @ cS )
      = $true )
    & ! [X0: $i] :
        ( ! [X1: $i] : ( X0 = X1 )
        | ( ( cUNIQUE @ X0 )
         != $true ) ) ),
    inference(ennf_transformation,[],[f4]) ).

thf(f6,plain,
    ( ! [X2: $i > $o] :
        ( ( ( X2 @ cJ )
         != ( ?? @ $i
            @ ^ [Y0: $i] :
                ( ( cUNIQUE @ Y0 )
                & ( cLIKE @ cJ @ Y0 ) ) ) )
        | ( ( X2 @ cP )
         != ( cLIKE @ cP @ cS ) ) )
    & ( ( cUNIQUE @ cS )
      = $true )
    & ! [X0: $i] :
        ( ! [X1: $i] : ( X0 = X1 )
        | ( ( cUNIQUE @ X0 )
         != $true ) ) ),
    inference(flattening,[],[f5]) ).

thf(f7,plain,
    ( ! [X0: $i > $o] :
        ( ( ( ?? @ $i
            @ ^ [Y0: $i] :
                ( ( cUNIQUE @ Y0 )
                & ( cLIKE @ cJ @ Y0 ) ) )
         != ( X0 @ cJ ) )
        | ( ( cLIKE @ cP @ cS )
         != ( X0 @ cP ) ) )
    & ( ( cUNIQUE @ cS )
      = $true )
    & ! [X1: $i] :
        ( ! [X2: $i] : ( X1 = X2 )
        | ( $true
         != ( cUNIQUE @ X1 ) ) ) ),
    inference(rectify,[],[f6]) ).

thf(f8,plain,
    ! [X2: $i,X1: $i] :
      ( ( $true
       != ( cUNIQUE @ X1 ) )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f7]) ).

thf(f9,plain,
    ( ( cUNIQUE @ cS )
    = $true ),
    inference(cnf_transformation,[],[f7]) ).

thf(f10,plain,
    ! [X0: $i > $o] :
      ( ( ( ?? @ $i
          @ ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) ) )
       != ( X0 @ cJ ) )
      | ( ( cLIKE @ cP @ cS )
       != ( X0 @ cP ) ) ),
    inference(cnf_transformation,[],[f7]) ).

thf(f13,plain,
    ! [X0: $i > $o] :
      ( ( $true
        = ( ?? @ $i
          @ ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) ) ) )
      | ( ( cLIKE @ cP @ cS )
       != ( X0 @ cP ) )
      | ( $true
        = ( X0 @ cJ ) ) ),
    inference(xor_proxy_clausification,[],[f10]) ).

thf(f14,plain,
    ! [X0: $i > $o] :
      ( ( ( ?? @ $i
          @ ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) ) )
        = $false )
      | ( ( cLIKE @ cP @ cS )
       != ( X0 @ cP ) )
      | ( ( X0 @ cJ )
        = $false ) ),
    inference(xor_proxy_clausification,[],[f10]) ).

thf(f15,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( $false
        = ( ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) )
          @ X1 ) )
      | ( ( cLIKE @ cP @ cS )
       != ( X0 @ cP ) )
      | ( ( X0 @ cJ )
        = $false ) ),
    inference(pi_proxy_clausification,[],[f14]) ).

thf(f17,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( $false
        = ( ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) )
          @ X1 ) )
      | ( ( cLIKE @ cP @ cS )
        = $false )
      | ( ( X0 @ cJ )
        = $false )
      | ( ( X0 @ cP )
        = $false ) ),
    inference(xor_proxy_clausification,[],[f15]) ).

thf(f18,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( $false
        = ( ( cUNIQUE @ X1 )
          & ( cLIKE @ cJ @ X1 ) ) )
      | ( ( cLIKE @ cP @ cS )
        = $false )
      | ( ( X0 @ cJ )
        = $false )
      | ( ( X0 @ cP )
        = $false ) ),
    inference(beta-eta_normalization,[],[f17]) ).

thf(f19,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( $false
        = ( cLIKE @ cJ @ X1 ) )
      | ( ( cLIKE @ cP @ cS )
        = $false )
      | ( ( X0 @ cJ )
        = $false )
      | ( ( X0 @ cP )
        = $false )
      | ( ( cUNIQUE @ X1 )
        = $false ) ),
    inference(and_proxy_clausification,[],[f18]) ).

thf(f22,plain,
    ! [X0: $i > $o] :
      ( ( $true
        = ( ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) )
          @ sK0 ) )
      | ( ( cLIKE @ cP @ cS )
       != ( X0 @ cP ) )
      | ( $true
        = ( X0 @ cJ ) ) ),
    inference(sigma_proxy_clausification,[],[f13]) ).

thf(f23,plain,
    ! [X0: $i > $o] :
      ( ( $true
        = ( ^ [Y0: $i] :
              ( ( cUNIQUE @ Y0 )
              & ( cLIKE @ cJ @ Y0 ) )
          @ sK0 ) )
      | ( ( cLIKE @ cP @ cS )
        = $true )
      | ( $true
        = ( X0 @ cJ ) )
      | ( $true
        = ( X0 @ cP ) ) ),
    inference(xor_proxy_clausification,[],[f22]) ).

thf(f28,plain,
    ! [X0: $i > $o] :
      ( ( $true
        = ( ( cUNIQUE @ sK0 )
          & ( cLIKE @ cJ @ sK0 ) ) )
      | ( ( cLIKE @ cP @ cS )
        = $true )
      | ( $true
        = ( X0 @ cJ ) )
      | ( $true
        = ( X0 @ cP ) ) ),
    inference(beta-eta_normalization,[],[f23]) ).

thf(f29,plain,
    ! [X0: $i > $o] :
      ( ( $true
        = ( cLIKE @ cJ @ sK0 ) )
      | ( ( cLIKE @ cP @ cS )
        = $true )
      | ( $true
        = ( X0 @ cJ ) )
      | ( $true
        = ( X0 @ cP ) ) ),
    inference(and_proxy_clausification,[],[f28]) ).

thf(f32,definition,
    ( spl1_1
  <=> ! [X2: $i,X1: $i] : ( X1 = X2 ) ),
    introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).

thf(f33,plain,
    ( ! [X2: $i,X1: $i] : ( X1 = X2 )
    | ~ spl1_1 ),
    inference(avatar_component_clause,[],[f32]) ).

thf(f37,plain,
    ! [X0: $i] :
      ( ( $true != $true )
      | ( cS = X0 ) ),
    inference(constrained_superposition,[],[f8,f9]) ).

thf(f38,plain,
    ! [X0: $i] : ( cS = X0 ),
    inference(trivial_inequality_removal,[],[f37]) ).

thf(f60,definition,
    ( spl1_7
  <=> ( $true
      = ( cLIKE @ cJ @ sK0 ) ) ),
    introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).

thf(f61,plain,
    ( ( $true
     != ( cLIKE @ cJ @ sK0 ) )
    | spl1_7 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f62,plain,
    ( ( $true
      = ( cLIKE @ cJ @ sK0 ) )
    | ~ spl1_7 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f1227,plain,
    ( ! [X0: $i > $o] :
        ( ( ( cLIKE @ cP @ cS )
          = $true )
        | ( $true
          = ( X0 @ cJ ) )
        | ( $true
          = ( X0 @ cP ) ) )
    | spl1_7 ),
    inference(forward_subsumption_resolution,[],[f29,f61]) ).

thf(f1228,plain,
    ! [X0: $i,X1: $i] : ( X0 = X1 ),
    inference(constrained_superposition,[],[f38,f38]) ).

thf(f1232,plain,
    ( ( $true
     != ( cLIKE @ cJ @ cS ) )
    | spl1_7 ),
    inference(constrained_superposition,[],[f61,f38]) ).

thf(f1250,plain,
    spl1_1,
    inference(avatar_split_clause,[],[f1228,f32]) ).

thf(f1261,plain,
    ( ! [X0: $i] :
        ( ( cUNIQUE @ X0 )
        = $true )
    | ~ spl1_1 ),
    inference(constrained_superposition,[],[f9,f33]) ).

thf(f1265,plain,
    ( ! [X0: $i] :
        ( $true
       != ( cLIKE @ X0 @ sK0 ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(constrained_superposition,[],[f61,f33]) ).

thf(f1271,plain,
    ( ! [X0: $i] :
        ( $true
       != ( cLIKE @ X0 @ cS ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(forward_demodulation,[],[f1265,f38]) ).

thf(f1290,plain,
    ( ! [X0: $i > $o] :
        ( ( $true
          = ( X0 @ cJ ) )
        | ( $true
          = ( X0 @ cP ) ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(forward_subsumption_resolution,[],[f1227,f1271]) ).

thf(f1291,plain,
    ( ! [X0: $i > $o] :
        ( ( $true
          = ( X0 @ cS ) )
        | ( $true
          = ( X0 @ cJ ) ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(forward_demodulation,[],[f1290,f38]) ).

thf(f1307,plain,
    ( ! [X0: $i > $i] :
        ( ( $true != $true )
        | ( $true
          = ( ^ [Y0: $i] :
                ( cLIKE @ ( X0 @ Y0 )
                @ ( ^ [Y1: $i] : cS
                  @ Y0 ) )
            @ cJ ) )
        | ( cJ
         != ( X0 @ cS ) ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(constrained_superposition,[],[f1232,f1291]) ).

thf(f1345,plain,
    ( ! [X0: $i > $i] :
        ( ( $true
          = ( ^ [Y0: $i] :
                ( cLIKE @ ( X0 @ Y0 )
                @ ( ^ [Y1: $i] : cS
                  @ Y0 ) )
            @ cJ ) )
        | ( cJ
         != ( X0 @ cS ) ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(trivial_inequality_removal,[],[f1307]) ).

thf(f1346,plain,
    ( ! [X0: $i > $i] :
        ( ( $true
          = ( cLIKE @ ( X0 @ cJ ) @ cS ) )
        | ( cJ
         != ( X0 @ cS ) ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(beta-eta_normalization,[],[f1345]) ).

thf(f1390,plain,
    ( ! [X0: $i > $i] :
        ( cJ
       != ( X0 @ cS ) )
    | ~ spl1_1
    | spl1_7 ),
    inference(forward_subsumption_resolution,[],[f1346,f1271]) ).

thf(f1406,plain,
    ( $false
    | ~ spl1_1
    | spl1_7 ),
    inference(forward_subsumption_resolution,[],[f1390,f33]) ).

thf(f1407,plain,
    ( ~ spl1_1
    | spl1_7 ),
    inference(avatar_contradiction_clause,[],[f1406]) ).

thf(f1416,plain,
    ( ( $true
      = ( cLIKE @ cJ @ cS ) )
    | ~ spl1_7 ),
    inference(forward_demodulation,[],[f62,f38]) ).

thf(f1471,plain,
    ( ! [X0: $i] :
        ( ( cLIKE @ cJ @ X0 )
        = $true )
    | ~ spl1_7 ),
    inference(constrained_superposition,[],[f1416,f38]) ).

thf(f1474,plain,
    ( ! [X0: $i] :
        ( $true
        = ( cLIKE @ X0 @ cS ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(constrained_superposition,[],[f1416,f33]) ).

thf(f1476,plain,
    ( ! [X0: $i,X1: $i] :
        ( $true
        = ( cLIKE @ X0 @ X1 ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(constrained_superposition,[],[f1471,f33]) ).

thf(f1507,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( $true = $false )
        | ( ( cLIKE @ cP @ cS )
          = $false )
        | ( ( X0 @ cJ )
          = $false )
        | ( ( X0 @ cP )
          = $false )
        | ( ( cUNIQUE @ X1 )
          = $false ) )
    | ~ spl1_7 ),
    inference(forward_demodulation,[],[f19,f1471]) ).

thf(f1508,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( ( cLIKE @ cP @ cS )
          = $false )
        | ( ( X0 @ cJ )
          = $false )
        | ( ( X0 @ cP )
          = $false )
        | ( ( cUNIQUE @ X1 )
          = $false ) )
    | ~ spl1_7 ),
    inference(trivial_inequality_removal,[],[f1507]) ).

thf(f1509,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( $true = $false )
        | ( ( X0 @ cJ )
          = $false )
        | ( ( X0 @ cP )
          = $false )
        | ( ( cUNIQUE @ X1 )
          = $false ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(forward_demodulation,[],[f1508,f1474]) ).

thf(f1510,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( ( X0 @ cJ )
          = $false )
        | ( ( X0 @ cP )
          = $false )
        | ( ( cUNIQUE @ X1 )
          = $false ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(trivial_inequality_removal,[],[f1509]) ).

thf(f1511,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( $false
          = ( X0 @ cS ) )
        | ( ( X0 @ cJ )
          = $false )
        | ( ( cUNIQUE @ X1 )
          = $false ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(forward_demodulation,[],[f1510,f38]) ).

thf(f1512,plain,
    ( ! [X0: $i > $o] :
        ( ( $true = $false )
        | ( $false
          = ( X0 @ cS ) )
        | ( ( X0 @ cJ )
          = $false ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(forward_demodulation,[],[f1511,f1261]) ).

thf(f1513,plain,
    ( ! [X0: $i > $o] :
        ( ( $false
          = ( X0 @ cS ) )
        | ( ( X0 @ cJ )
          = $false ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(trivial_inequality_removal,[],[f1512]) ).

thf(f1534,plain,
    ( ! [X2: $i,X3: $i,X0: $i > $i,X1: $i > $i] :
        ( ( $true = $false )
        | ( $false
          = ( ^ [Y0: $i] : ( cLIKE @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) )
            @ cJ ) )
        | ( ( X0 @ cS )
         != X2 )
        | ( ( X1 @ cS )
         != X3 ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(constrained_superposition,[],[f1513,f1476]) ).

thf(f1594,plain,
    ( ! [X2: $i,X3: $i,X0: $i > $i,X1: $i > $i] :
        ( ( $false
          = ( ^ [Y0: $i] : ( cLIKE @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) )
            @ cJ ) )
        | ( ( X0 @ cS )
         != X2 )
        | ( ( X1 @ cS )
         != X3 ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(trivial_inequality_removal,[],[f1534]) ).

thf(f1595,plain,
    ( ! [X2: $i,X3: $i,X0: $i > $i,X1: $i > $i] :
        ( ( $false
          = ( cLIKE @ ( X0 @ cJ ) @ ( X1 @ cJ ) ) )
        | ( ( X0 @ cS )
         != X2 )
        | ( ( X1 @ cS )
         != X3 ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(beta-eta_normalization,[],[f1594]) ).

thf(f1646,plain,
    ( ! [X3: $i,X0: $i > $i,X1: $i > $i] :
        ( ( $false
          = ( cLIKE @ ( X0 @ cJ ) @ ( X1 @ cJ ) ) )
        | ( ( X1 @ cS )
         != X3 ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(forward_subsumption_resolution,[],[f1595,f33]) ).

thf(f1695,plain,
    ( ! [X0: $i > $i,X1: $i > $i] :
        ( $false
        = ( cLIKE @ ( X0 @ cJ ) @ ( X1 @ cJ ) ) )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(forward_subsumption_resolution,[],[f1646,f33]) ).

thf(f1730,plain,
    ( ( $true = $false )
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(forward_demodulation,[],[f1695,f1476]) ).

thf(f1731,plain,
    ( $false
    | ~ spl1_1
    | ~ spl1_7 ),
    inference(trivial_inequality_removal,[],[f1730]) ).

thf(f1732,plain,
    ( ~ spl1_1
    | ~ spl1_7 ),
    inference(avatar_contradiction_clause,[],[f1731]) ).

cnf(s231,plain,
    spl1_1,
    inference(sat_conversion,[],[f1250]) ).

cnf(s277,plain,
    ( ~ spl1_1
    | spl1_7 ),
    inference(sat_conversion,[],[f1407]) ).

cnf(s363,plain,
    ( ~ spl1_1
    | ~ spl1_7 ),
    inference(sat_conversion,[],[f1732]) ).

cnf(s365,plain,
    ~ spl1_7,
    inference(rat,[],[s363,s231]) ).

cnf(s367,plain,
    $false,
    inference(rat,[],[s277,s365,s231]) ).

thf(f1736,plain,
    $false,
    inference(avatar_sat_refutation,[],[s367]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : SYO223^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21  % Computer : n019.cluster.edu
% 0.11/0.21  % Model    : x86_64 x86_64
% 0.11/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21  % Memory   : 8046.5625MB
% 0.11/0.21  % OS       : Linux 6.8.0-71-generic
% 0.11/0.22  % CPULimit : 300
% 0.11/0.22  % WCLimit  : 300
% 0.11/0.22  % DateTime : Tue Sep 29 16:40:18 UTC 2026
% 0.11/0.22  % CPUTime  : 
% 0.11/0.22  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.25  Running first-order model finding
% 0.11/0.25  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
% 0.22/0.29  % (1027497)Will run a generic schedule for satisfiability detection.
% 0.22/0.29  % (1027504)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3839488232:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.22/0.29  % (1027503)% WARNING: option uhcvi not known.
% 0.22/0.29  % (1027502)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2492292676_3000 on theBenchmark for (3000ds/0Mi)
% 0.22/0.29  % (1027503)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1327684938:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.22/0.29  % (1027505)dis+10_1_sil=32000:sp=arity:random_seed=942394871:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.29  % (1027506)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=772349152:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.22/0.29  % Exception at run slice level
% 0.22/0.29  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.29  % (1027507)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1050021572:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.22/0.29  % (1027503)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29  % (1027503)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.29  % (1027508)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3262531473:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.22/0.29  % (1027506)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29  % (1027504) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1027497-1027504"...
% 0.22/0.29  % (1027504)...printing done.
% 0.22/0.29  % (1027504)Refutation found. Thanks to Tanya!
% 0.22/0.29  % SZS status Theorem for theBenchmark
% 0.22/0.29  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29  % (1027504)------------------------------
% 0.22/0.29  % (1027504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29  % (1027504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29  % (1027504)CaDiCaL version: 2.1.3
% 0.22/0.29  % (1027504)Termination reason: Refutation
% 0.22/0.29  % (1027504)Time elapsed: 0.020 s
% 0.22/0.29  % (1027504)Peak memory usage: 13 MB
% 0.22/0.29  % (1027504)Instructions burned: 67 (million)
% 0.22/0.29  % (1027497)Success in time 0.034 s
% 0.22/0.29  % Vampire exiting
%------------------------------------------------------------------------------