TSTP Solution File: COM137+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : COM137+1 : TPTP v8.2.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n018.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 : Mon Jun 24 04:58:31 EDT 2024

% Result   : Theorem 1.01s 0.60s
% Output   : Refutation 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  105 (  13 unt;   0 def)
%            Number of atoms       :  363 ( 116 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  384 ( 126   ~; 145   |;  84   &)
%                                         (   4 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-3 aty)
%            Number of functors    :   21 (  21 usr;   6 con; 0-3 aty)
%            Number of variables   :  300 ( 228   !;  72   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3587,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2694,f2700,f3340,f3541,f3586]) ).

fof(f3586,plain,
    ( ~ spl91_4
    | ~ spl91_13 ),
    inference(avatar_contradiction_clause,[],[f3585]) ).

fof(f3585,plain,
    ( $false
    | ~ spl91_4
    | ~ spl91_13 ),
    inference(subsumption_resolution,[],[f3584,f292]) ).

fof(f292,plain,
    ~ vtcheck(sK15,vapp(ve1app,ve2app),sK16),
    inference(cnf_transformation,[],[f219]) ).

fof(f219,plain,
    ( ~ vtcheck(sK15,vapp(ve1app,ve2app),sK16)
    & vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    & ~ visFreeVar(sK13,vapp(ve1app,ve2app)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f117,f218]) ).

fof(f218,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ vtcheck(X2,vapp(ve1app,ve2app),X3)
        & vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3)
        & ~ visFreeVar(X0,vapp(ve1app,ve2app)) )
   => ( ~ vtcheck(sK15,vapp(ve1app,ve2app),sK16)
      & vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
      & ~ visFreeVar(sK13,vapp(ve1app,ve2app)) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ? [X0,X1,X2,X3] :
      ( ~ vtcheck(X2,vapp(ve1app,ve2app),X3)
      & vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3)
      & ~ visFreeVar(X0,vapp(ve1app,ve2app)) ),
    inference(flattening,[],[f116]) ).

fof(f116,plain,
    ? [X0,X1,X2,X3] :
      ( ~ vtcheck(X2,vapp(ve1app,ve2app),X3)
      & vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3)
      & ~ visFreeVar(X0,vapp(ve1app,ve2app)) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f60,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3)
          & ~ visFreeVar(X0,vapp(ve1app,ve2app)) )
       => vtcheck(X2,vapp(ve1app,ve2app),X3) ),
    inference(rectify,[],[f59]) ).

fof(f59,negated_conjecture,
    ~ ! [X8,X9,X19,X14] :
        ( ( vtcheck(vbind(X8,X9,X19),vapp(ve1app,ve2app),X14)
          & ~ visFreeVar(X8,vapp(ve1app,ve2app)) )
       => vtcheck(X19,vapp(ve1app,ve2app),X14) ),
    inference(negated_conjecture,[],[f58]) ).

fof(f58,conjecture,
    ! [X8,X9,X19,X14] :
      ( ( vtcheck(vbind(X8,X9,X19),vapp(ve1app,ve2app),X14)
        & ~ visFreeVar(X8,vapp(ve1app,ve2app)) )
     => vtcheck(X19,vapp(ve1app,ve2app),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3584,plain,
    ( vtcheck(sK15,vapp(ve1app,ve2app),sK16)
    | ~ spl91_4
    | ~ spl91_13 ),
    inference(resolution,[],[f3463,f3545]) ).

fof(f3545,plain,
    ( vtcheck(sK15,ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ spl91_13 ),
    inference(subsumption_resolution,[],[f3542,f563]) ).

fof(f563,plain,
    ~ visFreeVar(sK13,ve2app),
    inference(resolution,[],[f489,f290]) ).

fof(f290,plain,
    ~ visFreeVar(sK13,vapp(ve1app,ve2app)),
    inference(cnf_transformation,[],[f219]) ).

fof(f489,plain,
    ! [X2,X3,X4] :
      ( visFreeVar(X3,vapp(X2,X4))
      | ~ visFreeVar(X3,X4) ),
    inference(equality_resolution,[],[f488]) ).

fof(f488,plain,
    ! [X2,X3,X0,X4] :
      ( visFreeVar(X0,vapp(X2,X4))
      | ~ visFreeVar(X3,X4)
      | X0 != X3 ),
    inference(equality_resolution,[],[f414]) ).

fof(f414,plain,
    ! [X2,X3,X0,X1,X4] :
      ( visFreeVar(X0,X1)
      | ~ visFreeVar(X3,X4)
      | vapp(X2,X4) != X1
      | X0 != X3 ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( visFreeVar(X3,X4)
          | visFreeVar(X3,X2)
          | ~ visFreeVar(X0,X1) )
        & ( visFreeVar(X0,X1)
          | ( ~ visFreeVar(X3,X4)
            & ~ visFreeVar(X3,X2) ) ) )
      | vapp(X2,X4) != X1
      | X0 != X3 ),
    inference(flattening,[],[f159]) ).

fof(f159,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( visFreeVar(X3,X4)
          | visFreeVar(X3,X2)
          | ~ visFreeVar(X0,X1) )
        & ( visFreeVar(X0,X1)
          | ( ~ visFreeVar(X3,X4)
            & ~ visFreeVar(X3,X2) ) ) )
      | vapp(X2,X4) != X1
      | X0 != X3 ),
    inference(ennf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( vapp(X2,X4) = X1
        & X0 = X3 )
     => ( ( visFreeVar(X0,X1)
         => ( visFreeVar(X3,X4)
            | visFreeVar(X3,X2) ) )
        & ( ( visFreeVar(X3,X4)
            | visFreeVar(X3,X2) )
         => visFreeVar(X0,X1) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X3,X11,X13,X12] :
      ( ( vapp(X11,X12) = X3
        & X0 = X13 )
     => ( ( visFreeVar(X0,X3)
         => ( visFreeVar(X13,X12)
            | visFreeVar(X13,X11) ) )
        & ( ( visFreeVar(X13,X12)
            | visFreeVar(X13,X11) )
         => visFreeVar(X0,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3542,plain,
    ( vtcheck(sK15,ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | visFreeVar(sK13,ve2app)
    | ~ spl91_13 ),
    inference(resolution,[],[f3536,f406]) ).

fof(f406,plain,
    ! [X2,X3,X0,X1] :
      ( ~ vtcheck(vbind(X0,X1,X2),ve2app,X3)
      | vtcheck(X2,ve2app,X3)
      | visFreeVar(X0,ve2app) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0,X1,X2,X3] :
      ( vtcheck(X2,ve2app,X3)
      | ~ vtcheck(vbind(X0,X1,X2),ve2app,X3)
      | visFreeVar(X0,ve2app) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0,X1,X2,X3] :
      ( vtcheck(X2,ve2app,X3)
      | ~ vtcheck(vbind(X0,X1,X2),ve2app,X3)
      | visFreeVar(X0,ve2app) ),
    inference(ennf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2,X3] :
      ( ( vtcheck(vbind(X0,X1,X2),ve2app,X3)
        & ~ visFreeVar(X0,ve2app) )
     => vtcheck(X2,ve2app,X3) ),
    inference(rectify,[],[f57]) ).

fof(f57,axiom,
    ! [X8,X9,X19,X14] :
      ( ( vtcheck(vbind(X8,X9,X19),ve2app,X14)
        & ~ visFreeVar(X8,ve2app) )
     => vtcheck(X19,ve2app,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3536,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ spl91_13 ),
    inference(avatar_component_clause,[],[f3534]) ).

fof(f3534,plain,
    ( spl91_13
  <=> vtcheck(vbind(sK13,sK14,sK15),ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_13])]) ).

fof(f3463,plain,
    ( ! [X0] :
        ( ~ vtcheck(sK15,X0,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
        | vtcheck(sK15,vapp(ve1app,X0),sK16) )
    | ~ spl91_4 ),
    inference(resolution,[],[f3444,f419]) ).

fof(f419,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ vtcheck(X1,X2,varrow(X0,X4))
      | ~ vtcheck(X1,X3,X0)
      | vtcheck(X1,vapp(X2,X3),X4) ),
    inference(cnf_transformation,[],[f168]) ).

fof(f168,plain,
    ! [X0,X1,X2,X3,X4] :
      ( vtcheck(X1,vapp(X2,X3),X4)
      | ~ vtcheck(X1,X3,X0)
      | ~ vtcheck(X1,X2,varrow(X0,X4)) ),
    inference(flattening,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1,X2,X3,X4] :
      ( vtcheck(X1,vapp(X2,X3),X4)
      | ~ vtcheck(X1,X3,X0)
      | ~ vtcheck(X1,X2,varrow(X0,X4)) ),
    inference(ennf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( vtcheck(X1,X3,X0)
        & vtcheck(X1,X2,varrow(X0,X4)) )
     => vtcheck(X1,vapp(X2,X3),X4) ),
    inference(rectify,[],[f53]) ).

fof(f53,axiom,
    ! [X9,X19,X11,X12,X14] :
      ( ( vtcheck(X19,X12,X9)
        & vtcheck(X19,X11,varrow(X9,X14)) )
     => vtcheck(X19,vapp(X11,X12),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3444,plain,
    ( vtcheck(sK15,ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | ~ spl91_4 ),
    inference(subsumption_resolution,[],[f3440,f566]) ).

fof(f566,plain,
    ~ visFreeVar(sK13,ve1app),
    inference(resolution,[],[f491,f290]) ).

fof(f491,plain,
    ! [X2,X3,X4] :
      ( visFreeVar(X3,vapp(X2,X4))
      | ~ visFreeVar(X3,X2) ),
    inference(equality_resolution,[],[f490]) ).

fof(f490,plain,
    ! [X2,X3,X0,X4] :
      ( visFreeVar(X0,vapp(X2,X4))
      | ~ visFreeVar(X3,X2)
      | X0 != X3 ),
    inference(equality_resolution,[],[f413]) ).

fof(f413,plain,
    ! [X2,X3,X0,X1,X4] :
      ( visFreeVar(X0,X1)
      | ~ visFreeVar(X3,X2)
      | vapp(X2,X4) != X1
      | X0 != X3 ),
    inference(cnf_transformation,[],[f160]) ).

fof(f3440,plain,
    ( vtcheck(sK15,ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | visFreeVar(sK13,ve1app)
    | ~ spl91_4 ),
    inference(resolution,[],[f3335,f405]) ).

fof(f405,plain,
    ! [X2,X3,X0,X1] :
      ( ~ vtcheck(vbind(X0,X1,X2),ve1app,X3)
      | vtcheck(X2,ve1app,X3)
      | visFreeVar(X0,ve1app) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0,X1,X2,X3] :
      ( vtcheck(X2,ve1app,X3)
      | ~ vtcheck(vbind(X0,X1,X2),ve1app,X3)
      | visFreeVar(X0,ve1app) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ! [X0,X1,X2,X3] :
      ( vtcheck(X2,ve1app,X3)
      | ~ vtcheck(vbind(X0,X1,X2),ve1app,X3)
      | visFreeVar(X0,ve1app) ),
    inference(ennf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2,X3] :
      ( ( vtcheck(vbind(X0,X1,X2),ve1app,X3)
        & ~ visFreeVar(X0,ve1app) )
     => vtcheck(X2,ve1app,X3) ),
    inference(rectify,[],[f56]) ).

fof(f56,axiom,
    ! [X8,X9,X19,X14] :
      ( ( vtcheck(vbind(X8,X9,X19),ve1app,X14)
        & ~ visFreeVar(X8,ve1app) )
     => vtcheck(X19,ve1app,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3335,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | ~ spl91_4 ),
    inference(avatar_component_clause,[],[f3333]) ).

fof(f3333,plain,
    ( spl91_4
  <=> vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_4])]) ).

fof(f3541,plain,
    ( spl91_13
    | ~ spl91_1
    | spl91_2 ),
    inference(avatar_split_clause,[],[f3540,f2691,f2687,f3534]) ).

fof(f2687,plain,
    ( spl91_1
  <=> vapp(ve1app,ve2app) = vapp(sK46(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK47(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_1])]) ).

fof(f2691,plain,
    ( spl91_2
  <=> sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl91_2])]) ).

fof(f3540,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ spl91_1
    | spl91_2 ),
    inference(subsumption_resolution,[],[f3539,f291]) ).

fof(f291,plain,
    vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16),
    inference(cnf_transformation,[],[f219]) ).

fof(f3539,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    | ~ spl91_1
    | spl91_2 ),
    inference(subsumption_resolution,[],[f3538,f339]) ).

fof(f339,plain,
    ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X3,X5] : vvar(X0) != vapp(X3,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3538,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | vapp(ve1app,ve2app) = vvar(sK49(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    | ~ spl91_1
    | spl91_2 ),
    inference(subsumption_resolution,[],[f3530,f2692]) ).

fof(f2692,plain,
    ( ~ sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app))
    | spl91_2 ),
    inference(avatar_component_clause,[],[f2691]) ).

fof(f3530,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve2app,sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app))
    | vapp(ve1app,ve2app) = vvar(sK49(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    | ~ spl91_1 ),
    inference(superposition,[],[f350,f3488]) ).

fof(f3488,plain,
    ( ve2app = sK47(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15))
    | ~ spl91_1 ),
    inference(equality_resolution,[],[f3117]) ).

fof(f3117,plain,
    ( ! [X0,X1] :
        ( vapp(ve1app,ve2app) != vapp(X0,X1)
        | sK47(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)) = X1 )
    | ~ spl91_1 ),
    inference(superposition,[],[f370,f2689]) ).

fof(f2689,plain,
    ( vapp(ve1app,ve2app) = vapp(sK46(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK47(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ spl91_1 ),
    inference(avatar_component_clause,[],[f2687]) ).

fof(f370,plain,
    ! [X2,X3,X0,X1] :
      ( vapp(X0,X1) != vapp(X2,X3)
      | X1 = X3 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0,X1,X2,X3] :
      ( ( vapp(X0,X1) = vapp(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | vapp(X0,X1) != vapp(X2,X3) ) ),
    inference(flattening,[],[f143]) ).

fof(f143,plain,
    ! [X0,X1,X2,X3] :
      ( ( vapp(X0,X1) = vapp(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | vapp(X0,X1) != vapp(X2,X3) ) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( X1 = X3
          & X0 = X2 )
       => vapp(X0,X1) = vapp(X2,X3) )
      & ( vapp(X0,X1) = vapp(X2,X3)
       => ( X1 = X3
          & X0 = X2 ) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X3,X5,X6,X7] :
      ( ( ( X5 = X7
          & X3 = X6 )
       => vapp(X3,X5) = vapp(X6,X7) )
      & ( vapp(X3,X5) = vapp(X6,X7)
       => ( X5 = X7
          & X3 = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f350,plain,
    ! [X2,X0,X1] :
      ( vtcheck(X2,sK47(X0,X1,X2),sK48(X0,X1,X2))
      | sP5(X2,X1,X0)
      | vvar(sK49(X0,X1,X2)) = X0
      | ~ vtcheck(X2,X0,X1) ),
    inference(cnf_transformation,[],[f251]) ).

fof(f251,plain,
    ! [X0,X1,X2] :
      ( ( vtcheck(X2,sK47(X0,X1,X2),sK48(X0,X1,X2))
        & vtcheck(X2,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
        & vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X0 )
      | sP5(X2,X1,X0)
      | ( vsomeType(X1) = vlookup(sK49(X0,X1,X2),X2)
        & vvar(sK49(X0,X1,X2)) = X0 )
      | ~ vtcheck(X2,X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48,sK49])],[f248,f250,f249]) ).

fof(f249,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( vtcheck(X2,X4,X5)
          & vtcheck(X2,X3,varrow(X5,X1))
          & vapp(X3,X4) = X0 )
     => ( vtcheck(X2,sK47(X0,X1,X2),sK48(X0,X1,X2))
        & vtcheck(X2,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
        & vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f250,plain,
    ! [X0,X1,X2] :
      ( ? [X6] :
          ( vsomeType(X1) = vlookup(X6,X2)
          & vvar(X6) = X0 )
     => ( vsomeType(X1) = vlookup(sK49(X0,X1,X2),X2)
        & vvar(sK49(X0,X1,X2)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f248,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( vtcheck(X2,X4,X5)
          & vtcheck(X2,X3,varrow(X5,X1))
          & vapp(X3,X4) = X0 )
      | sP5(X2,X1,X0)
      | ? [X6] :
          ( vsomeType(X1) = vlookup(X6,X2)
          & vvar(X6) = X0 )
      | ~ vtcheck(X2,X0,X1) ),
    inference(rectify,[],[f208]) ).

fof(f208,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( vtcheck(X2,X4,X5)
          & vtcheck(X2,X3,varrow(X5,X1))
          & vapp(X3,X4) = X0 )
      | sP5(X2,X1,X0)
      | ? [X10] :
          ( vsomeType(X1) = vlookup(X10,X2)
          & vvar(X10) = X0 )
      | ~ vtcheck(X2,X0,X1) ),
    inference(definition_folding,[],[f136,f207]) ).

fof(f207,plain,
    ! [X2,X1,X0] :
      ( ? [X6,X7,X8,X9] :
          ( vtcheck(vbind(X6,X8,X2),X7,X9)
          & varrow(X8,X9) = X1
          & vabs(X6,X8,X7) = X0 )
      | ~ sP5(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f136,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( vtcheck(X2,X4,X5)
          & vtcheck(X2,X3,varrow(X5,X1))
          & vapp(X3,X4) = X0 )
      | ? [X6,X7,X8,X9] :
          ( vtcheck(vbind(X6,X8,X2),X7,X9)
          & varrow(X8,X9) = X1
          & vabs(X6,X8,X7) = X0 )
      | ? [X10] :
          ( vsomeType(X1) = vlookup(X10,X2)
          & vvar(X10) = X0 )
      | ~ vtcheck(X2,X0,X1) ),
    inference(flattening,[],[f135]) ).

fof(f135,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( vtcheck(X2,X4,X5)
          & vtcheck(X2,X3,varrow(X5,X1))
          & vapp(X3,X4) = X0 )
      | ? [X6,X7,X8,X9] :
          ( vtcheck(vbind(X6,X8,X2),X7,X9)
          & varrow(X8,X9) = X1
          & vabs(X6,X8,X7) = X0 )
      | ? [X10] :
          ( vsomeType(X1) = vlookup(X10,X2)
          & vvar(X10) = X0 )
      | ~ vtcheck(X2,X0,X1) ),
    inference(ennf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( vtcheck(X2,X0,X1)
     => ( ? [X3,X4,X5] :
            ( vtcheck(X2,X4,X5)
            & vtcheck(X2,X3,varrow(X5,X1))
            & vapp(X3,X4) = X0 )
        | ? [X6,X7,X8,X9] :
            ( vtcheck(vbind(X6,X8,X2),X7,X9)
            & varrow(X8,X9) = X1
            & vabs(X6,X8,X7) = X0 )
        | ? [X10] :
            ( vsomeType(X1) = vlookup(X10,X2)
            & vvar(X10) = X0 ) ) ),
    inference(rectify,[],[f54]) ).

fof(f54,axiom,
    ! [X10,X14,X19] :
      ( vtcheck(X19,X10,X14)
     => ( ? [X11,X12,X9] :
            ( vtcheck(X19,X12,X9)
            & vtcheck(X19,X11,varrow(X9,X14))
            & vapp(X11,X12) = X10 )
        | ? [X8,X12,X32,X33] :
            ( vtcheck(vbind(X8,X32,X19),X12,X33)
            & varrow(X32,X33) = X14
            & vabs(X8,X32,X12) = X10 )
        | ? [X8] :
            ( vlookup(X8,X19) = vsomeType(X14)
            & vvar(X8) = X10 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3340,plain,
    ( spl91_4
    | ~ spl91_1
    | spl91_2 ),
    inference(avatar_split_clause,[],[f3339,f2691,f2687,f3333]) ).

fof(f3339,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | ~ spl91_1
    | spl91_2 ),
    inference(subsumption_resolution,[],[f3338,f291]) ).

fof(f3338,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    | ~ spl91_1
    | spl91_2 ),
    inference(subsumption_resolution,[],[f3337,f339]) ).

fof(f3337,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | vapp(ve1app,ve2app) = vvar(sK49(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    | ~ spl91_1
    | spl91_2 ),
    inference(subsumption_resolution,[],[f3325,f2692]) ).

fof(f3325,plain,
    ( vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(sK48(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK16))
    | sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app))
    | vapp(ve1app,ve2app) = vvar(sK49(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
    | ~ spl91_1 ),
    inference(superposition,[],[f348,f3281]) ).

fof(f3281,plain,
    ( ve1app = sK46(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15))
    | ~ spl91_1 ),
    inference(equality_resolution,[],[f3115]) ).

fof(f3115,plain,
    ( ! [X0,X1] :
        ( vapp(ve1app,ve2app) != vapp(X0,X1)
        | sK46(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)) = X0 )
    | ~ spl91_1 ),
    inference(superposition,[],[f369,f2689]) ).

fof(f369,plain,
    ! [X2,X3,X0,X1] :
      ( vapp(X0,X1) != vapp(X2,X3)
      | X0 = X2 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f348,plain,
    ! [X2,X0,X1] :
      ( vtcheck(X2,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
      | sP5(X2,X1,X0)
      | vvar(sK49(X0,X1,X2)) = X0
      | ~ vtcheck(X2,X0,X1) ),
    inference(cnf_transformation,[],[f251]) ).

fof(f2700,plain,
    ~ spl91_2,
    inference(avatar_contradiction_clause,[],[f2699]) ).

fof(f2699,plain,
    ( $false
    | ~ spl91_2 ),
    inference(subsumption_resolution,[],[f2697,f410]) ).

fof(f410,plain,
    ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2,X3,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X2,X3,X5,X6] : vabs(X0,X2,X3) != vapp(X5,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f2697,plain,
    ( vapp(ve1app,ve2app) = vabs(sK42(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app)),sK44(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app)),sK43(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app)))
    | ~ spl91_2 ),
    inference(resolution,[],[f2693,f343]) ).

fof(f343,plain,
    ! [X2,X0,X1] :
      ( ~ sP5(X0,X1,X2)
      | vabs(sK42(X0,X1,X2),sK44(X0,X1,X2),sK43(X0,X1,X2)) = X2 ),
    inference(cnf_transformation,[],[f247]) ).

fof(f247,plain,
    ! [X0,X1,X2] :
      ( ( vtcheck(vbind(sK42(X0,X1,X2),sK44(X0,X1,X2),X0),sK43(X0,X1,X2),sK45(X0,X1,X2))
        & varrow(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X1
        & vabs(sK42(X0,X1,X2),sK44(X0,X1,X2),sK43(X0,X1,X2)) = X2 )
      | ~ sP5(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44,sK45])],[f245,f246]) ).

fof(f246,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5,X6] :
          ( vtcheck(vbind(X3,X5,X0),X4,X6)
          & varrow(X5,X6) = X1
          & vabs(X3,X5,X4) = X2 )
     => ( vtcheck(vbind(sK42(X0,X1,X2),sK44(X0,X1,X2),X0),sK43(X0,X1,X2),sK45(X0,X1,X2))
        & varrow(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X1
        & vabs(sK42(X0,X1,X2),sK44(X0,X1,X2),sK43(X0,X1,X2)) = X2 ) ),
    introduced(choice_axiom,[]) ).

fof(f245,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5,X6] :
          ( vtcheck(vbind(X3,X5,X0),X4,X6)
          & varrow(X5,X6) = X1
          & vabs(X3,X5,X4) = X2 )
      | ~ sP5(X0,X1,X2) ),
    inference(rectify,[],[f244]) ).

fof(f244,plain,
    ! [X2,X1,X0] :
      ( ? [X6,X7,X8,X9] :
          ( vtcheck(vbind(X6,X8,X2),X7,X9)
          & varrow(X8,X9) = X1
          & vabs(X6,X8,X7) = X0 )
      | ~ sP5(X2,X1,X0) ),
    inference(nnf_transformation,[],[f207]) ).

fof(f2693,plain,
    ( sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app))
    | ~ spl91_2 ),
    inference(avatar_component_clause,[],[f2691]) ).

fof(f2694,plain,
    ( spl91_1
    | spl91_2 ),
    inference(avatar_split_clause,[],[f2685,f2691,f2687]) ).

fof(f2685,plain,
    ( sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app))
    | vapp(ve1app,ve2app) = vapp(sK46(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK47(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15))) ),
    inference(subsumption_resolution,[],[f2680,f339]) ).

fof(f2680,plain,
    ( sP5(vbind(sK13,sK14,sK15),sK16,vapp(ve1app,ve2app))
    | vapp(ve1app,ve2app) = vvar(sK49(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)))
    | vapp(ve1app,ve2app) = vapp(sK46(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15)),sK47(vapp(ve1app,ve2app),sK16,vbind(sK13,sK14,sK15))) ),
    inference(resolution,[],[f346,f291]) ).

fof(f346,plain,
    ! [X2,X0,X1] :
      ( ~ vtcheck(X2,X0,X1)
      | sP5(X2,X1,X0)
      | vvar(sK49(X0,X1,X2)) = X0
      | vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X0 ),
    inference(cnf_transformation,[],[f251]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14  % Problem    : COM137+1 : TPTP v8.2.0. Released v6.4.0.
% 0.05/0.14  % Command    : run_vampire %s %d THM
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Thu Jun 20 23:34:09 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.38  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.38  Running first-order theorem proving
% 0.14/0.38  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.45  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.45  % (1640)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.25/0.46  % (1640)Refutation not found, incomplete strategy% (1640)------------------------------
% 0.25/0.46  % (1640)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.25/0.46  % (1640)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.25/0.46  % (1640)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.46  
% 0.25/0.46  % (1640)Memory used [KB]: 1257
% 0.25/0.46  % (1640)Time elapsed: 0.008 s
% 0.25/0.46  % (1640)Instructions burned: 8 (million)
% 0.25/0.46  % (1640)------------------------------
% 0.25/0.46  % (1640)------------------------------
% 0.25/0.47  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.47  % (1636)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.25/0.47  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.47  % (1642)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.25/0.48  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.48  % (1639)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.25/0.48  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.48  % (1641)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.25/0.48  % (1641)Refutation not found, incomplete strategy% (1641)------------------------------
% 0.25/0.48  % (1641)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.25/0.48  % (1641)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.25/0.48  % (1641)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.48  
% 0.25/0.48  % (1641)Memory used [KB]: 1180
% 0.25/0.48  % (1641)Time elapsed: 0.004 s
% 0.25/0.48  % (1641)Instructions burned: 4 (million)
% 0.25/0.48  % (1641)------------------------------
% 0.25/0.48  % (1641)------------------------------
% 0.25/0.48  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.48  % (1638)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.25/0.50  % (1635)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.50  % (1637)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.80/0.54  % (1642)Instruction limit reached!
% 0.80/0.54  % (1642)------------------------------
% 0.80/0.54  % (1642)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.80/0.54  % (1642)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.80/0.54  % (1642)Termination reason: Time limit
% 0.80/0.54  % (1642)Termination phase: Saturation
% 0.80/0.54  
% 0.80/0.54  % (1642)Memory used [KB]: 2324
% 0.80/0.54  % (1642)Time elapsed: 0.063 s
% 0.80/0.54  % (1642)Instructions burned: 124 (million)
% 1.01/0.54  % (1635)Running in auto input_syntax mode. Trying TPTP
% 1.01/0.54  % (1643)lrs+1011_1:1_sil=16000:sos=on:erd=off:i=126:nm=2:ep=RST_0 on theBenchmark for (2999ds/126Mi)
% 1.01/0.54  % (1635)Running in auto input_syntax mode. Trying TPTP
% 1.01/0.54  % (1644)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:st=1.5:i=145:ss=axioms:sgt=4_0 on theBenchmark for (2999ds/145Mi)
% 1.01/0.55  % (1643)Refutation not found, incomplete strategy% (1643)------------------------------
% 1.01/0.55  % (1643)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.01/0.55  % (1643)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.01/0.55  % (1643)Termination reason: Refutation not found, incomplete strategy
% 1.01/0.55  
% 1.01/0.55  % (1643)Memory used [KB]: 1514
% 1.01/0.55  % (1643)Time elapsed: 0.033 s
% 1.01/0.55  % (1643)Instructions burned: 12 (million)
% 1.01/0.55  % (1643)------------------------------
% 1.01/0.55  % (1643)------------------------------
% 1.01/0.57  % (1635)Running in auto input_syntax mode. Trying TPTP
% 1.01/0.57  % (1645)ott+1002_2835555:1048576_to=lpo:sil=2000:sos=on:fs=off:nwc=10.3801:avsqc=3:updr=off:avsq=on:st=2:s2a=on:i=173:s2at=3:afp=10000:aac=none:avsqr=13357983,1048576:awrs=converge:awrsf=460:bd=off:nm=13:ins=2:fsr=off:amm=sco:afq=1.16719:ss=axioms:rawr=on:fd=off_0 on theBenchmark for (2998ds/173Mi)
% 1.01/0.58  % (1645)Refutation not found, incomplete strategy% (1645)------------------------------
% 1.01/0.58  % (1645)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.01/0.58  % (1645)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.01/0.58  % (1645)Termination reason: Refutation not found, incomplete strategy
% 1.01/0.58  
% 1.01/0.58  % (1645)Memory used [KB]: 1364
% 1.01/0.58  % (1645)Time elapsed: 0.005 s
% 1.01/0.58  % (1645)Instructions burned: 9 (million)
% 1.01/0.58  % (1645)------------------------------
% 1.01/0.58  % (1645)------------------------------
% 1.01/0.59  % (1639)First to succeed.
% 1.01/0.60  % (1639)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1635"
% 1.01/0.60  % (1635)Running in auto input_syntax mode. Trying TPTP
% 1.01/0.60  % (1639)Refutation found. Thanks to Tanya!
% 1.01/0.60  % SZS status Theorem for theBenchmark
% 1.01/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.01/0.60  % (1639)------------------------------
% 1.01/0.60  % (1639)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.01/0.60  % (1639)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.01/0.60  % (1639)Termination reason: Refutation
% 1.01/0.60  
% 1.01/0.60  % (1639)Memory used [KB]: 4582
% 1.01/0.60  % (1639)Time elapsed: 0.140 s
% 1.01/0.60  % (1639)Instructions burned: 301 (million)
% 1.01/0.60  % (1639)------------------------------
% 1.01/0.60  % (1639)------------------------------
% 1.01/0.60  % (1635)Success in time 0.204 s
%------------------------------------------------------------------------------