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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SYO385^5 : 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 : n005.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 08:49:50 AM UTC 2026

% Result   : Theorem 0.11s 0.27s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   59 (  23 unt;   0 typ;   3 def)
%            Number of atoms       :  645 ( 129 equ;   0 cnn)
%            Maximal formula atoms :   41 (  10 avg)
%            Number of connectives :  804 ( 124   ~; 100   |;  65   &; 512   @)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   9 con; 0-3 aty)
%            Number of variables   :  154 (   0 sgn 154   !;   0   ?; 154   :)

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

thf(func_def_0,type,
    cQ_3: $i > $i > $i > $o ).

thf(func_def_1,type,
    f: $i > $i ).

thf(func_def_2,type,
    cP_2: $i > $i > $o ).

thf(func_def_3,type,
    cQ_2: $i > $i > $i > $o ).

thf(func_def_8,type,
    cP_1: $i > $i > $o ).

thf(func_def_9,type,
    cQ_1: $i > $i > $i > $o ).

thf(f1,conjecture,
    ~ ( ! [X0: $i,X1: $i,X2: $i] :
          ~ ( cQ_3 @ X0 @ X1 @ X2 )
      & ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
          ( ( cQ_3 @ X3 @ X4 @ X5 )
          | ~ ( cP_2 @ ( f @ X2 ) @ X5 )
          | ~ ( cP_2 @ ( f @ X1 ) @ X4 )
          | ~ ( cP_2 @ ( f @ X0 ) @ X3 )
          | ~ ( cQ_2 @ X0 @ X1 @ X2 ) )
      & ! [X0: $i,X1: $i] :
          ( ( cP_2 @ ( f @ X0 ) @ X1 )
          | ~ ( cP_2 @ X0 @ X1 ) )
      & ! [X0: $i] : ( cP_2 @ d @ X0 )
      & ( cP_2 @ c @ c )
      & ( cP_2 @ b @ b )
      & ( cP_2 @ a @ a )
      & ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
          ( ( cQ_2 @ X3 @ X4 @ X5 )
          | ~ ( cP_1 @ ( f @ X2 ) @ X5 )
          | ~ ( cP_1 @ ( f @ X1 ) @ X4 )
          | ~ ( cP_1 @ ( f @ X0 ) @ X3 )
          | ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
      & ! [X0: $i,X1: $i] :
          ( ( cP_1 @ ( f @ X0 ) @ X1 )
          | ~ ( cP_1 @ X0 @ X1 ) )
      & ! [X0: $i] : ( cP_1 @ d @ X0 )
      & ( cP_1 @ c @ c )
      & ( cP_1 @ b @ b )
      & ( cP_1 @ a @ a )
      & ( cQ_1 @ a @ b @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_2) ).

thf(f2,negated_conjecture,
    ~ ~ ( ! [X0: $i,X1: $i,X2: $i] :
            ~ ( cQ_3 @ X0 @ X1 @ X2 )
        & ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
            ( ( cQ_3 @ X3 @ X4 @ X5 )
            | ~ ( cP_2 @ ( f @ X2 ) @ X5 )
            | ~ ( cP_2 @ ( f @ X1 ) @ X4 )
            | ~ ( cP_2 @ ( f @ X0 ) @ X3 )
            | ~ ( cQ_2 @ X0 @ X1 @ X2 ) )
        & ! [X0: $i,X1: $i] :
            ( ( cP_2 @ ( f @ X0 ) @ X1 )
            | ~ ( cP_2 @ X0 @ X1 ) )
        & ! [X0: $i] : ( cP_2 @ d @ X0 )
        & ( cP_2 @ c @ c )
        & ( cP_2 @ b @ b )
        & ( cP_2 @ a @ a )
        & ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
            ( ( cQ_2 @ X3 @ X4 @ X5 )
            | ~ ( cP_1 @ ( f @ X2 ) @ X5 )
            | ~ ( cP_1 @ ( f @ X1 ) @ X4 )
            | ~ ( cP_1 @ ( f @ X0 ) @ X3 )
            | ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
        & ! [X0: $i,X1: $i] :
            ( ( cP_1 @ ( f @ X0 ) @ X1 )
            | ~ ( cP_1 @ X0 @ X1 ) )
        & ! [X0: $i] : ( cP_1 @ d @ X0 )
        & ( cP_1 @ c @ c )
        & ( cP_1 @ b @ b )
        & ( cP_1 @ a @ a )
        & ( cQ_1 @ a @ b @ c ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

thf(f3,plain,
    ~ ~ ( ! [X0: $i,X1: $i,X2: $i] :
            ~ ( cQ_3 @ X0 @ X1 @ X2 )
        & ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
            ( ( cQ_3 @ X6 @ X7 @ X8 )
            | ~ ( cP_2 @ ( f @ X5 ) @ X8 )
            | ~ ( cP_2 @ ( f @ X4 ) @ X7 )
            | ~ ( cP_2 @ ( f @ X3 ) @ X6 )
            | ~ ( cQ_2 @ X3 @ X4 @ X5 ) )
        & ! [X9: $i,X10: $i] :
            ( ( cP_2 @ ( f @ X9 ) @ X10 )
            | ~ ( cP_2 @ X9 @ X10 ) )
        & ! [X11: $i] : ( cP_2 @ d @ X11 )
        & ( cP_2 @ c @ c )
        & ( cP_2 @ b @ b )
        & ( cP_2 @ a @ a )
        & ! [X12: $i,X13: $i,X14: $i,X15: $i,X16: $i,X17: $i] :
            ( ( cQ_2 @ X15 @ X16 @ X17 )
            | ~ ( cP_1 @ ( f @ X14 ) @ X17 )
            | ~ ( cP_1 @ ( f @ X13 ) @ X16 )
            | ~ ( cP_1 @ ( f @ X12 ) @ X15 )
            | ~ ( cQ_1 @ X12 @ X13 @ X14 ) )
        & ! [X18: $i,X19: $i] :
            ( ( cP_1 @ ( f @ X18 ) @ X19 )
            | ~ ( cP_1 @ X18 @ X19 ) )
        & ! [X20: $i] : ( cP_1 @ d @ X20 )
        & ( cP_1 @ c @ c )
        & ( cP_1 @ b @ b )
        & ( cP_1 @ a @ a )
        & ( cQ_1 @ a @ b @ c ) ),
    inference(rectify,[],[f2]) ).

thf(f4,plain,
    ~ ~ ( ! [X0: $i,X1: $i,X2: $i] :
            ( ( cQ_3 @ X0 @ X1 @ X2 )
           != $true )
        & ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
            ( ( ( cQ_3 @ X6 @ X7 @ X8 )
              = $true )
            | ( ( cP_2 @ ( f @ X5 ) @ X8 )
             != $true )
            | ( ( cP_2 @ ( f @ X4 ) @ X7 )
             != $true )
            | ( ( cP_2 @ ( f @ X3 ) @ X6 )
             != $true )
            | ( ( cQ_2 @ X3 @ X4 @ X5 )
             != $true ) )
        & ! [X9: $i,X10: $i] :
            ( ( ( cP_2 @ ( f @ X9 ) @ X10 )
              = $true )
            | ( ( cP_2 @ X9 @ X10 )
             != $true ) )
        & ! [X11: $i] :
            ( ( cP_2 @ d @ X11 )
            = $true )
        & ( ( cP_2 @ c @ c )
          = $true )
        & ( ( cP_2 @ b @ b )
          = $true )
        & ( ( cP_2 @ a @ a )
          = $true )
        & ! [X12: $i,X13: $i,X14: $i,X15: $i,X16: $i,X17: $i] :
            ( ( ( cQ_2 @ X15 @ X16 @ X17 )
              = $true )
            | ( ( cP_1 @ ( f @ X14 ) @ X17 )
             != $true )
            | ( ( cP_1 @ ( f @ X13 ) @ X16 )
             != $true )
            | ( ( cP_1 @ ( f @ X12 ) @ X15 )
             != $true )
            | ( ( cQ_1 @ X12 @ X13 @ X14 )
             != $true ) )
        & ! [X18: $i,X19: $i] :
            ( ( ( cP_1 @ ( f @ X18 ) @ X19 )
              = $true )
            | ( ( cP_1 @ X18 @ X19 )
             != $true ) )
        & ! [X20: $i] :
            ( ( cP_1 @ d @ X20 )
            = $true )
        & ( ( cP_1 @ c @ c )
          = $true )
        & ( ( cP_1 @ b @ b )
          = $true )
        & ( ( cP_1 @ a @ a )
          = $true )
        & ( ( cQ_1 @ a @ b @ c )
          = $true ) ),
    inference(fool_elimination,[],[f3]) ).

thf(f5,plain,
    ( ! [X0: $i,X1: $i,X2: $i] :
        ( ( cQ_3 @ X0 @ X1 @ X2 )
       != $true )
    & ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
        ( ( ( cQ_3 @ X6 @ X7 @ X8 )
          = $true )
        | ( ( cP_2 @ ( f @ X5 ) @ X8 )
         != $true )
        | ( ( cP_2 @ ( f @ X4 ) @ X7 )
         != $true )
        | ( ( cP_2 @ ( f @ X3 ) @ X6 )
         != $true )
        | ( ( cQ_2 @ X3 @ X4 @ X5 )
         != $true ) )
    & ! [X9: $i,X10: $i] :
        ( ( ( cP_2 @ ( f @ X9 ) @ X10 )
          = $true )
        | ( ( cP_2 @ X9 @ X10 )
         != $true ) )
    & ! [X11: $i] :
        ( ( cP_2 @ d @ X11 )
        = $true )
    & ( ( cP_2 @ c @ c )
      = $true )
    & ( ( cP_2 @ b @ b )
      = $true )
    & ( ( cP_2 @ a @ a )
      = $true )
    & ! [X12: $i,X13: $i,X14: $i,X15: $i,X16: $i,X17: $i] :
        ( ( ( cQ_2 @ X15 @ X16 @ X17 )
          = $true )
        | ( ( cP_1 @ ( f @ X14 ) @ X17 )
         != $true )
        | ( ( cP_1 @ ( f @ X13 ) @ X16 )
         != $true )
        | ( ( cP_1 @ ( f @ X12 ) @ X15 )
         != $true )
        | ( ( cQ_1 @ X12 @ X13 @ X14 )
         != $true ) )
    & ! [X18: $i,X19: $i] :
        ( ( ( cP_1 @ ( f @ X18 ) @ X19 )
          = $true )
        | ( ( cP_1 @ X18 @ X19 )
         != $true ) )
    & ! [X20: $i] :
        ( ( cP_1 @ d @ X20 )
        = $true )
    & ( ( cP_1 @ c @ c )
      = $true )
    & ( ( cP_1 @ b @ b )
      = $true )
    & ( ( cP_1 @ a @ a )
      = $true )
    & ( ( cQ_1 @ a @ b @ c )
      = $true ) ),
    inference(flattening,[],[f4]) ).

thf(f6,plain,
    ( ( cQ_1 @ a @ b @ c )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f7,plain,
    ( ( cP_1 @ a @ a )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f8,plain,
    ( ( cP_1 @ b @ b )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f9,plain,
    ( ( cP_1 @ c @ c )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f11,plain,
    ! [X18: $i,X19: $i] :
      ( ( ( cP_1 @ X18 @ X19 )
       != $true )
      | ( ( cP_1 @ ( f @ X18 ) @ X19 )
        = $true ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f12,plain,
    ! [X16: $i,X14: $i,X17: $i,X15: $i,X12: $i,X13: $i] :
      ( ( ( cQ_1 @ X12 @ X13 @ X14 )
       != $true )
      | ( ( cP_1 @ ( f @ X14 ) @ X17 )
       != $true )
      | ( ( cP_1 @ ( f @ X13 ) @ X16 )
       != $true )
      | ( ( cP_1 @ ( f @ X12 ) @ X15 )
       != $true )
      | ( ( cQ_2 @ X15 @ X16 @ X17 )
        = $true ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f13,plain,
    ( ( cP_2 @ a @ a )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f14,plain,
    ( ( cP_2 @ b @ b )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f15,plain,
    ( ( cP_2 @ c @ c )
    = $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f17,plain,
    ! [X10: $i,X9: $i] :
      ( ( ( cP_2 @ X9 @ X10 )
       != $true )
      | ( ( cP_2 @ ( f @ X9 ) @ X10 )
        = $true ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f18,plain,
    ! [X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
      ( ( ( cQ_3 @ X6 @ X7 @ X8 )
        = $true )
      | ( ( cP_2 @ ( f @ X5 ) @ X8 )
       != $true )
      | ( ( cP_2 @ ( f @ X4 ) @ X7 )
       != $true )
      | ( ( cP_2 @ ( f @ X3 ) @ X6 )
       != $true )
      | ( ( cQ_2 @ X3 @ X4 @ X5 )
       != $true ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f19,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( cQ_3 @ X0 @ X1 @ X2 )
     != $true ),
    inference(cnf_transformation,[],[f5]) ).

thf(f23,plain,
    ( ( $true != $true )
    | ( $true
      = ( cP_1 @ ( f @ c ) @ c ) ) ),
    inference(constrained_superposition,[],[f11,f9]) ).

thf(f24,plain,
    ( ( $true != $true )
    | ( $true
      = ( cP_1 @ ( f @ b ) @ b ) ) ),
    inference(constrained_superposition,[],[f11,f8]) ).

thf(f25,plain,
    ( ( $true != $true )
    | ( $true
      = ( cP_1 @ ( f @ a ) @ a ) ) ),
    inference(constrained_superposition,[],[f11,f7]) ).

thf(f26,plain,
    ( $true
    = ( cP_1 @ ( f @ a ) @ a ) ),
    inference(trivial_inequality_removal,[],[f25]) ).

thf(f27,plain,
    ( $true
    = ( cP_1 @ ( f @ b ) @ b ) ),
    inference(trivial_inequality_removal,[],[f24]) ).

thf(f28,plain,
    ( $true
    = ( cP_1 @ ( f @ c ) @ c ) ),
    inference(trivial_inequality_removal,[],[f23]) ).

thf(f31,plain,
    ( ( $true != $true )
    | ( $true
      = ( cP_2 @ ( f @ c ) @ c ) ) ),
    inference(constrained_superposition,[],[f17,f15]) ).

thf(f32,plain,
    ( ( $true != $true )
    | ( $true
      = ( cP_2 @ ( f @ b ) @ b ) ) ),
    inference(constrained_superposition,[],[f17,f14]) ).

thf(f33,plain,
    ( ( $true != $true )
    | ( $true
      = ( cP_2 @ ( f @ a ) @ a ) ) ),
    inference(constrained_superposition,[],[f17,f13]) ).

thf(f34,plain,
    ( $true
    = ( cP_2 @ ( f @ a ) @ a ) ),
    inference(trivial_inequality_removal,[],[f33]) ).

thf(f35,plain,
    ( $true
    = ( cP_2 @ ( f @ b ) @ b ) ),
    inference(trivial_inequality_removal,[],[f32]) ).

thf(f36,plain,
    ( $true
    = ( cP_2 @ ( f @ c ) @ c ) ),
    inference(trivial_inequality_removal,[],[f31]) ).

thf(f61,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( $true != $true )
      | ( $true
       != ( cP_1 @ ( f @ c ) @ X0 ) )
      | ( $true
       != ( cP_1 @ ( f @ b ) @ X1 ) )
      | ( $true
       != ( cP_1 @ ( f @ a ) @ X2 ) )
      | ( $true
        = ( cQ_2 @ X2 @ X1 @ X0 ) ) ),
    inference(constrained_superposition,[],[f12,f6]) ).

thf(f64,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( $true
       != ( cP_1 @ ( f @ a ) @ X2 ) )
      | ( $true
       != ( cP_1 @ ( f @ b ) @ X1 ) )
      | ( $true
       != ( cP_1 @ ( f @ c ) @ X0 ) )
      | ( $true
        = ( cQ_2 @ X2 @ X1 @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f61]) ).

thf(f65,plain,
    ! [X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
      ( ( ( cQ_2 @ X3 @ X4 @ X5 )
       != $true )
      | ( ( cP_2 @ ( f @ X4 ) @ X7 )
       != $true )
      | ( ( cP_2 @ ( f @ X3 ) @ X6 )
       != $true )
      | ( ( cP_2 @ ( f @ X5 ) @ X8 )
       != $true ) ),
    inference(forward_subsumption_resolution,[],[f18,f19]) ).

thf(f88,plain,
    ! [X0: $i,X1: $i] :
      ( ( $true != $true )
      | ( $true
       != ( cP_1 @ ( f @ b ) @ X0 ) )
      | ( $true
       != ( cP_1 @ ( f @ c ) @ X1 ) )
      | ( $true
        = ( cQ_2 @ a @ X0 @ X1 ) ) ),
    inference(constrained_superposition,[],[f64,f26]) ).

thf(f91,plain,
    ! [X0: $i,X1: $i] :
      ( ( $true
       != ( cP_1 @ ( f @ b ) @ X0 ) )
      | ( $true
       != ( cP_1 @ ( f @ c ) @ X1 ) )
      | ( $true
        = ( cQ_2 @ a @ X0 @ X1 ) ) ),
    inference(trivial_inequality_removal,[],[f88]) ).

thf(f160,plain,
    ! [X0: $i] :
      ( ( $true != $true )
      | ( $true
       != ( cP_1 @ ( f @ c ) @ X0 ) )
      | ( $true
        = ( cQ_2 @ a @ b @ X0 ) ) ),
    inference(constrained_superposition,[],[f91,f27]) ).

thf(f163,plain,
    ! [X0: $i] :
      ( ( $true
       != ( cP_1 @ ( f @ c ) @ X0 ) )
      | ( $true
        = ( cQ_2 @ a @ b @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f160]) ).

thf(f610,plain,
    ( ( $true != $true )
    | ( $true
      = ( cQ_2 @ a @ b @ c ) ) ),
    inference(constrained_superposition,[],[f163,f28]) ).

thf(f613,plain,
    ( $true
    = ( cQ_2 @ a @ b @ c ) ),
    inference(trivial_inequality_removal,[],[f610]) ).

thf(f647,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( $true != $true )
      | ( $true
       != ( cP_2 @ ( f @ b ) @ X0 ) )
      | ( $true
       != ( cP_2 @ ( f @ a ) @ X1 ) )
      | ( $true
       != ( cP_2 @ ( f @ c ) @ X2 ) ) ),
    inference(constrained_superposition,[],[f65,f613]) ).

thf(f648,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( $true
       != ( cP_2 @ ( f @ b ) @ X0 ) )
      | ( $true
       != ( cP_2 @ ( f @ a ) @ X1 ) )
      | ( $true
       != ( cP_2 @ ( f @ c ) @ X2 ) ) ),
    inference(trivial_inequality_removal,[],[f647]) ).

thf(f650,definition,
    ( spl0_1
  <=> ! [X2: $i] :
        ( $true
       != ( cP_2 @ ( f @ c ) @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).

thf(f651,plain,
    ( ! [X2: $i] :
        ( $true
       != ( cP_2 @ ( f @ c ) @ X2 ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f650]) ).

thf(f653,definition,
    ( spl0_2
  <=> ! [X1: $i] :
        ( $true
       != ( cP_2 @ ( f @ a ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).

thf(f654,plain,
    ( ! [X1: $i] :
        ( $true
       != ( cP_2 @ ( f @ a ) @ X1 ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f653]) ).

thf(f656,definition,
    ( spl0_3
  <=> ! [X0: $i] :
        ( $true
       != ( cP_2 @ ( f @ b ) @ X0 ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).

thf(f657,plain,
    ( ! [X0: $i] :
        ( $true
       != ( cP_2 @ ( f @ b ) @ X0 ) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f656]) ).

thf(f658,plain,
    ( spl0_1
    | spl0_2
    | spl0_3 ),
    inference(avatar_split_clause,[],[f648,f656,f653,f650]) ).

thf(f691,plain,
    ( $false
    | ~ spl0_2 ),
    inference(backward_subsumption_resolution,[],[f34,f654]) ).

thf(f696,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f691]) ).

thf(f877,plain,
    ( $false
    | ~ spl0_3 ),
    inference(backward_subsumption_resolution,[],[f35,f657]) ).

thf(f882,plain,
    ~ spl0_3,
    inference(avatar_contradiction_clause,[],[f877]) ).

thf(f945,plain,
    ( $false
    | ~ spl0_1 ),
    inference(backward_subsumption_resolution,[],[f36,f651]) ).

thf(f950,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f945]) ).

cnf(s1,plain,
    ( spl0_1
    | spl0_2
    | spl0_3 ),
    inference(sat_conversion,[],[f658]) ).

cnf(s2,plain,
    ~ spl0_2,
    inference(sat_conversion,[],[f696]) ).

cnf(s3,plain,
    ~ spl0_3,
    inference(sat_conversion,[],[f882]) ).

cnf(s4,plain,
    ~ spl0_1,
    inference(sat_conversion,[],[f950]) ).

cnf(s5,plain,
    $false,
    inference(rat,[],[s1,s3,s2,s4]) ).

thf(f951,plain,
    $false,
    inference(avatar_sat_refutation,[],[s5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SYO385^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.16  % Computer : n005.cluster.edu
% 0.11/0.16  % Model    : x86_64 x86_64
% 0.11/0.16  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16  % Memory   : 8046.5625MB
% 0.11/0.16  % OS       : Linux 6.8.0-71-generic
% 0.11/0.16  % CPULimit : 300
% 0.11/0.16  % WCLimit  : 300
% 0.11/0.16  % DateTime : Tue Sep 29 16:49:46 UTC 2026
% 0.11/0.17  % CPUTime  : 
% 0.11/0.17  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.20  Running first-order model finding
% 0.11/0.20  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
% 0.11/0.27  % (1910608)Will run a generic schedule for satisfiability detection.
% 0.11/0.27  % (1910614)% WARNING: option uhcvi not known.
% 0.11/0.27  % (1910616)dis+10_1_sil=32000:sp=arity:random_seed=2771733118:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.27  % (1910613)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2735780858_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.27  % (1910615)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=336773875:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.27  % (1910617)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1208291055:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.27  % (1910618)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4223727589:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.27  % (1910619)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2751357808:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.27  % (1910617)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.27  % Exception at run slice level
% 0.11/0.27  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.27  % (1910614)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=307100904:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.27  % (1910614)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.27  % (1910614)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.11/0.27  % (1910626)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3455730445:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.11/0.27  % Exception at run slice level
% 0.11/0.27  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.27  % (1910614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1910608-1910614"...
% 0.11/0.27  % (1910614)...printing done.
% 0.11/0.27  % (1910614)Refutation found. Thanks to Tanya!
% 0.11/0.27  % SZS status Theorem for theBenchmark
% 0.11/0.27  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.27  % (1910614)------------------------------
% 0.11/0.27  % (1910614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.27  % (1910614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.27  % (1910614)CaDiCaL version: 2.1.3
% 0.11/0.27  % (1910614)Termination reason: Refutation
% 0.11/0.27  % (1910614)Time elapsed: 0.029 s
% 0.11/0.27  % (1910614)Peak memory usage: 13 MB
% 0.11/0.27  % (1910614)Instructions burned: 96 (million)
% 0.11/0.27  % (1910608)Success in time 0.066 s
% 0.11/0.27  % Vampire exiting
%------------------------------------------------------------------------------