TSTP Solution File: SYO175^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYO175^5 : 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 09:10:29 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   87 (  15 unt;  23 typ;   0 def)
%            Number of atoms       : 1053 ( 183 equ;   0 cnn)
%            Maximal formula atoms :   16 (  16 avg)
%            Number of connectives :  280 (  85   ~;  75   |; 104   &;   0   @)
%                                         (   4 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   24 (  23   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;  14 con; 0-6 aty)
%            Number of variables   :  125 (   0   ^  86   !;  33   ?; 125   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    a: $tType ).

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

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

thf(func_def_1,type,
    a: $tType ).

thf(func_def_2,type,
    cGRAIN: p ).

thf(func_def_3,type,
    cVEG_EATS: a > p > $o ).

thf(func_def_4,type,
    cMEAT_EATS: a > a > $o ).

thf(func_def_5,type,
    cSNAIL: a ).

thf(func_def_6,type,
    cCATERPILLAR: a ).

thf(func_def_7,type,
    cBIRD: a ).

thf(func_def_8,type,
    cWOLF: a ).

thf(func_def_9,type,
    cFOX: a ).

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

thf(func_def_14,type,
    sK0: p ).

thf(func_def_15,type,
    sK1: p ).

thf(func_def_17,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_18,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

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

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

thf(func_def_22,type,
    vNOT: $o > $o ).

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

thf(f169,plain,
    $false,
    inference(avatar_sat_refutation,[],[f122,f131,f142,f149,f168]) ).

thf(f168,plain,
    ~ spl2_4,
    inference(avatar_contradiction_clause,[],[f167]) ).

thf(f167,plain,
    ( $false
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f159]) ).

thf(f159,plain,
    ( ( $true = $false )
    | ~ spl2_4 ),
    inference(superposition,[],[f130,f57]) ).

thf(f57,plain,
    vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) = $false,
    inference(trivial_inequality_removal,[],[f56]) ).

thf(f56,plain,
    ( ( $true != $true )
    | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) = $false ) ),
    inference(superposition,[],[f20,f4]) ).

thf(f4,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f20,plain,
    vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true,
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ! [X0: a,X1: a] :
        ( ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN) != $true )
        | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) != $true ) )
    & ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),sK0) )
    & ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),sK1) )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
    & ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
    & ! [X4: a] :
        ( ! [X5: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X4),X5) )
            | ! [X6: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X5),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X5),X4) ) )
        | ! [X7: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X4),X7) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12,f11]) ).

thf(f11,plain,
    ( ? [X2: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X2) )
   => ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),sK0) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X3: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X3) )
   => ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),sK1) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ! [X0: a,X1: a] :
        ( ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN) != $true )
        | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) != $true ) )
    & ? [X2: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X2) )
    & ? [X3: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X3) )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
    & ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
    & ! [X4: a] :
        ( ! [X5: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X4),X5) )
            | ! [X6: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X5),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X5),X4) ) )
        | ! [X7: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X4),X7) ) ) ),
    inference(rectify,[],[f9]) ).

thf(f9,plain,
    ( ! [X6: a,X7: a] :
        ( ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) )
    & ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
    & ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
    & ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
    & ! [X2: a] :
        ( ! [X3: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) )
            | ! [X4: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
        | ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) ),
    inference(flattening,[],[f8]) ).

thf(f8,plain,
    ( ! [X6: a,X7: a] :
        ( ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) )
    & ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
    & ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
    & ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
    & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
    & ! [X2: a] :
        ( ! [X3: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) )
            | ! [X4: p] : ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
        | ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ( ( ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
        & ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
        & ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
        & ! [X2: a] :
            ( ! [X3: a] :
                ( ( ? [X4: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
                  & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
               => ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) ) )
            | ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) )
     => ? [X6: a,X7: a] :
          ( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ~ ( ( ? [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0) )
        & ? [X1: p] : ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR) = $true )
        & ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN) != $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true )
        & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD) = $true )
        & ! [X2: a] :
            ( ! [X3: a] :
                ( ( ? [X4: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4) )
                  & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) ) )
               => ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) ) )
            | ! [X5: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) ) )
     => ? [X6: a,X7: a] :
          ( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ? [X0: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X0)
        & ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1)
        & ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR)
        & ~ vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN)
        & ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD)
        & ! [X2: a] :
            ( ! [X3: a] :
                ( ( ? [X4: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X3),X4)
                  & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X3),X2) )
               => vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X3) )
            | ! [X5: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X5) ) )
     => ? [X6: a,X7: a] :
          ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X7),cGRAIN)
          & vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X6),X7) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X1)
        & ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1)
        & ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR)
        & ~ vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN)
        & ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD)
        & ! [X0: a] :
            ( ! [X2: a] :
                ( ( ? [X3: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3)
                  & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X2),X0) )
               => vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X2) )
            | ! [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) ) )
     => ? [X0: a,X1: a] :
          ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN)
          & vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),X1)
      & ? [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cCATERPILLAR),X1)
      & ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL)
      & vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cCATERPILLAR)
      & ~ vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),cGRAIN)
      & ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX)
      & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF)
      & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX)
      & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD)
      & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cCATERPILLAR),cBIRD)
      & ! [X0: a] :
          ( ! [X2: a] :
              ( ( ? [X3: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3)
                & vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X2),X0) )
             => vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X2) )
          | ! [X1: p] : vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) ) )
   => ? [X0: a,X1: a] :
        ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN)
        & vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPUZ031_1_HO) ).

thf(f130,plain,
    ( ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f129]) ).

thf(f129,plain,
    ( spl2_4
  <=> ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f149,plain,
    ~ spl2_1,
    inference(avatar_contradiction_clause,[],[f148]) ).

thf(f148,plain,
    ( $false
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f143]) ).

thf(f143,plain,
    ( ( $true = $false )
    | ~ spl2_1 ),
    inference(backward_demodulation,[],[f94,f118]) ).

thf(f118,plain,
    ( ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f117]) ).

thf(f117,plain,
    ( spl2_1
  <=> ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f94,plain,
    ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ),
    inference(trivial_inequality_removal,[],[f93]) ).

thf(f93,plain,
    ! [X0: p] :
      ( ( $true = $false )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ) ),
    inference(forward_demodulation,[],[f92,f59]) ).

thf(f59,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $false,
    inference(trivial_inequality_removal,[],[f58]) ).

thf(f58,plain,
    ( ( $true != $true )
    | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $false ) ),
    inference(superposition,[],[f22,f4]) ).

thf(f22,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) != $true,
    inference(cnf_transformation,[],[f13]) ).

thf(f92,plain,
    ! [X0: p] :
      ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $true )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ) ),
    inference(trivial_inequality_removal,[],[f89]) ).

thf(f89,plain,
    ! [X0: p] :
      ( ( $true != $true )
      | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cBIRD),cSNAIL) = $true )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X0) ) ),
    inference(superposition,[],[f69,f16]) ).

thf(f16,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),cBIRD) = $true,
    inference(cnf_transformation,[],[f13]) ).

thf(f69,plain,
    ! [X0: a,X1: p] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),X0) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cSNAIL) )
      | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $true ) ),
    inference(trivial_inequality_removal,[],[f66]) ).

thf(f66,plain,
    ! [X0: a,X1: p] :
      ( ( $true != $true )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cSNAIL) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cSNAIL),X0) )
      | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $true ) ),
    inference(superposition,[],[f14,f24]) ).

thf(f24,plain,
    $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cSNAIL),sK0),
    inference(cnf_transformation,[],[f13]) ).

thf(f14,plain,
    ! [X6: p,X7: p,X4: a,X5: a] :
      ( ( $true != vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X5),X6) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X4),X5) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X5),X4) )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X4),X7) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f142,plain,
    ( ~ spl2_2
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f141]) ).

thf(f141,plain,
    ( $false
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f136]) ).

thf(f136,plain,
    ( ( $true = $false )
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f121,f127]) ).

thf(f127,plain,
    ( ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f126]) ).

thf(f126,plain,
    ( spl2_3
  <=> ! [X1: p] : ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f121,plain,
    ( ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f120]) ).

thf(f120,plain,
    ( spl2_2
  <=> ! [X0: p] : ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f131,plain,
    ( spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f124,f129,f126]) ).

thf(f124,plain,
    ! [X0: p,X1: p] :
      ( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
    inference(trivial_inequality_removal,[],[f123]) ).

thf(f123,plain,
    ! [X0: p,X1: p] :
      ( ( $true = $false )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
    inference(forward_demodulation,[],[f111,f55]) ).

thf(f55,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $false,
    inference(trivial_inequality_removal,[],[f54]) ).

thf(f54,plain,
    ( ( $true != $true )
    | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $false ) ),
    inference(superposition,[],[f19,f4]) ).

thf(f19,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) != $true,
    inference(cnf_transformation,[],[f13]) ).

thf(f111,plain,
    ! [X0: p,X1: p] :
      ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $true )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
    inference(trivial_inequality_removal,[],[f108]) ).

thf(f108,plain,
    ! [X0: p,X1: p] :
      ( ( $true != $true )
      | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cWOLF),cFOX) = $true )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cWOLF),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X1) ) ),
    inference(superposition,[],[f68,f18]) ).

thf(f18,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cFOX),cWOLF) = $true,
    inference(cnf_transformation,[],[f13]) ).

thf(f68,plain,
    ! [X2: a,X3: p,X0: a,X1: p] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X0),X2) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X0) )
      | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3) = $true )
      | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $false ) ),
    inference(trivial_inequality_removal,[],[f67]) ).

thf(f67,plain,
    ! [X2: a,X3: p,X0: a,X1: p] :
      ( ( $true != $true )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X2),X0) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,X0),X2) )
      | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X2),X3) = $true )
      | ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X0),X1) = $false ) ),
    inference(superposition,[],[f14,f4]) ).

thf(f122,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f115,f120,f117]) ).

thf(f115,plain,
    ! [X0: p,X1: p] :
      ( ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
    inference(subsumption_resolution,[],[f112,f97]) ).

thf(f97,plain,
    ! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cBIRD) ),
    inference(trivial_inequality_removal,[],[f96]) ).

thf(f96,plain,
    ! [X0: a] :
      ( ( $true != $true )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),cBIRD) ) ),
    inference(superposition,[],[f25,f94]) ).

thf(f25,plain,
    ! [X0: a,X1: a] :
      ( ( vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,X1),cGRAIN) != $true )
      | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f112,plain,
    ! [X0: p,X1: p] :
      ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cFOX),cBIRD) )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
    inference(trivial_inequality_removal,[],[f107]) ).

thf(f107,plain,
    ! [X0: p,X1: p] :
      ( ( $true != $true )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cMEAT_EATS,cFOX),cBIRD) )
      | ( $true = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cFOX),X0) )
      | ( $false = vAPP(p,$o,vAPP(a,sTfun(p,$o),cVEG_EATS,cBIRD),X1) ) ),
    inference(superposition,[],[f68,f17]) ).

thf(f17,plain,
    vAPP(a,$o,vAPP(a,sTfun(a,$o),cSMALLER,cBIRD),cFOX) = $true,
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO175^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 09:33:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (6906)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (6908)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (6913)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  % (6911)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (6907)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  % (6910)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % Exception at run slice level% (6912)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % (6910)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % (6909)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.37  % (6909)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % (6912)First to succeed.
% 0.13/0.38  % (6909)Also succeeded, but the first one will report.
% 0.13/0.38  % (6912)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6906"
% 0.13/0.38  % (6911)Also succeeded, but the first one will report.
% 0.13/0.38  % (6912)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (6912)------------------------------
% 0.13/0.38  % (6912)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38  % (6912)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (6912)Memory used [KB]: 856
% 0.13/0.38  % (6912)Time elapsed: 0.012 s
% 0.13/0.38  % (6912)Instructions burned: 18 (million)
% 0.13/0.38  % (6906)Success in time 0.04 s
%------------------------------------------------------------------------------