TSTP Solution File: COM149+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : COM149+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 : Wed May 31 12:04:09 EDT 2023

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   52 (  12 unt;   0 def)
%            Number of atoms       :  148 (  68 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  145 (  49   ~;  48   |;  37   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-4 aty)
%            Number of functors    :   21 (  21 usr;   4 con; 0-3 aty)
%            Number of variables   :  128 (;  85   !;  43   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [VVar0,VVar1,VTyp0,VExp0] : vvar(VVar0) != vabs(VVar1,VTyp0,VExp0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [VVar0,VExp0,VExp1] : vvar(VVar0) != vapp(VExp0,VExp1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [VTyp0] : vnoType != vsomeType(VTyp0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [Vx,VVar0,VCtx0,RESULT] :
      ( ( VVar0 = Vx
        & VCtx0 = vempty )
     => ( RESULT = vlookup(VVar0,VCtx0)
       => RESULT = vnoType ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,axiom,
    ! [Ve,VT,VC] :
      ( vtcheck(VC,Ve,VT)
     => ( ? [Vx] :
            ( Ve = vvar(Vx)
            & vlookup(Vx,VC) = vsomeType(VT) )
        | ? [Vx,Ve2,VT1,VT2] :
            ( Ve = vabs(Vx,VT1,Ve2)
            & VT = varrow(VT1,VT2)
            & vtcheck(vbind(Vx,VT1,VC),Ve2,VT2) )
        | ? [Ve1,Ve2,VS] :
            ( Ve = vapp(Ve1,Ve2)
            & vtcheck(VC,Ve1,varrow(VS,VT))
            & vtcheck(VC,Ve2,VS) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f57,conjecture,
    ! [VT,Vx] :
      ( ( vtcheck(vempty,vvar(Vx),VT)
        & ~ visValue(vvar(Vx)) )
     => ? [Veout] : vreduce(vvar(Vx)) = vsomeExp(Veout) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f58,negated_conjecture,
    ~ ! [VT,Vx] :
        ( ( vtcheck(vempty,vvar(Vx),VT)
          & ~ visValue(vvar(Vx)) )
       => ? [Veout] : vreduce(vvar(Vx)) = vsomeExp(Veout) ),
    inference(negated_conjecture,[status(cth)],[f57]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f75,plain,
    ! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f115,plain,
    ! [X0] : vnoType != vsomeType(X0),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f124,plain,
    ! [Vx,VVar0,VCtx0,RESULT] :
      ( VVar0 != Vx
      | VCtx0 != vempty
      | RESULT != vlookup(VVar0,VCtx0)
      | RESULT = vnoType ),
    inference(pre_NNF_transformation,[status(esa)],[f22]) ).

fof(f125,plain,
    ! [VVar0,VCtx0] :
      ( ! [Vx] : VVar0 != Vx
      | VCtx0 != vempty
      | ! [RESULT] :
          ( RESULT != vlookup(VVar0,VCtx0)
          | RESULT = vnoType ) ),
    inference(miniscoping,[status(esa)],[f124]) ).

fof(f126,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != X1
      | X2 != vempty
      | X3 != vlookup(X0,X2)
      | X3 = vnoType ),
    inference(cnf_transformation,[status(esa)],[f125]) ).

fof(f238,plain,
    ! [Ve,VT,VC] :
      ( ~ vtcheck(VC,Ve,VT)
      | ? [Vx] :
          ( Ve = vvar(Vx)
          & vlookup(Vx,VC) = vsomeType(VT) )
      | ? [Vx,Ve2,VT1,VT2] :
          ( Ve = vabs(Vx,VT1,Ve2)
          & VT = varrow(VT1,VT2)
          & vtcheck(vbind(Vx,VT1,VC),Ve2,VT2) )
      | ? [Ve1,Ve2,VS] :
          ( Ve = vapp(Ve1,Ve2)
          & vtcheck(VC,Ve1,varrow(VS,VT))
          & vtcheck(VC,Ve2,VS) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f239,plain,
    ! [Ve,VT,VC] :
      ( pd0_3(VC,VT,Ve)
     => ( ? [Vx] :
            ( Ve = vvar(Vx)
            & vlookup(Vx,VC) = vsomeType(VT) )
        | ? [Vx,Ve2,VT1,VT2] :
            ( Ve = vabs(Vx,VT1,Ve2)
            & VT = varrow(VT1,VT2)
            & vtcheck(vbind(Vx,VT1,VC),Ve2,VT2) ) ) ),
    introduced(predicate_definition,[f238]) ).

fof(f240,plain,
    ! [Ve,VT,VC] :
      ( ~ vtcheck(VC,Ve,VT)
      | pd0_3(VC,VT,Ve)
      | ? [Ve1,Ve2,VS] :
          ( Ve = vapp(Ve1,Ve2)
          & vtcheck(VC,Ve1,varrow(VS,VT))
          & vtcheck(VC,Ve2,VS) ) ),
    inference(formula_renaming,[status(thm)],[f238,f239]) ).

fof(f241,plain,
    ! [Ve,VT,VC] :
      ( ~ vtcheck(VC,Ve,VT)
      | pd0_3(VC,VT,Ve)
      | ? [Ve2,VS] :
          ( ? [Ve1] :
              ( Ve = vapp(Ve1,Ve2)
              & vtcheck(VC,Ve1,varrow(VS,VT)) )
          & vtcheck(VC,Ve2,VS) ) ),
    inference(miniscoping,[status(esa)],[f240]) ).

fof(f242,plain,
    ! [Ve,VT,VC] :
      ( ~ vtcheck(VC,Ve,VT)
      | pd0_3(VC,VT,Ve)
      | ( Ve = vapp(sk0_20(VC,VT,Ve),sk0_18(VC,VT,Ve))
        & vtcheck(VC,sk0_20(VC,VT,Ve),varrow(sk0_19(VC,VT,Ve),VT))
        & vtcheck(VC,sk0_18(VC,VT,Ve),sk0_19(VC,VT,Ve)) ) ),
    inference(skolemization,[status(esa)],[f241]) ).

fof(f243,plain,
    ! [X0,X1,X2] :
      ( ~ vtcheck(X0,X1,X2)
      | pd0_3(X0,X2,X1)
      | X1 = vapp(sk0_20(X0,X2,X1),sk0_18(X0,X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f242]) ).

fof(f252,plain,
    ? [VT,Vx] :
      ( vtcheck(vempty,vvar(Vx),VT)
      & ~ visValue(vvar(Vx))
      & ! [Veout] : vreduce(vvar(Vx)) != vsomeExp(Veout) ),
    inference(pre_NNF_transformation,[status(esa)],[f58]) ).

fof(f253,plain,
    ? [Vx] :
      ( ? [VT] : vtcheck(vempty,vvar(Vx),VT)
      & ~ visValue(vvar(Vx))
      & ! [Veout] : vreduce(vvar(Vx)) != vsomeExp(Veout) ),
    inference(miniscoping,[status(esa)],[f252]) ).

fof(f254,plain,
    ( vtcheck(vempty,vvar(sk0_21),sk0_22)
    & ~ visValue(vvar(sk0_21))
    & ! [Veout] : vreduce(vvar(sk0_21)) != vsomeExp(Veout) ),
    inference(skolemization,[status(esa)],[f253]) ).

fof(f255,plain,
    vtcheck(vempty,vvar(sk0_21),sk0_22),
    inference(cnf_transformation,[status(esa)],[f254]) ).

fof(f288,plain,
    ! [Ve,VT,VC] :
      ( ~ pd0_3(VC,VT,Ve)
      | ? [Vx] :
          ( Ve = vvar(Vx)
          & vlookup(Vx,VC) = vsomeType(VT) )
      | ? [Vx,Ve2,VT1,VT2] :
          ( Ve = vabs(Vx,VT1,Ve2)
          & VT = varrow(VT1,VT2)
          & vtcheck(vbind(Vx,VT1,VC),Ve2,VT2) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f239]) ).

fof(f289,plain,
    ! [Ve,VT,VC,Vx] :
      ( pd0_7(Vx,VC,VT,Ve)
     => ( Ve = vvar(Vx)
        & vlookup(Vx,VC) = vsomeType(VT) ) ),
    introduced(predicate_definition,[f288]) ).

fof(f290,plain,
    ! [Ve,VT,VC] :
      ( ~ pd0_3(VC,VT,Ve)
      | ? [Vx] : pd0_7(Vx,VC,VT,Ve)
      | ? [Vx,Ve2,VT1,VT2] :
          ( Ve = vabs(Vx,VT1,Ve2)
          & VT = varrow(VT1,VT2)
          & vtcheck(vbind(Vx,VT1,VC),Ve2,VT2) ) ),
    inference(formula_renaming,[status(thm)],[f288,f289]) ).

fof(f291,plain,
    ! [Ve,VT,VC] :
      ( ~ pd0_3(VC,VT,Ve)
      | pd0_7(sk0_37(VC,VT,Ve),VC,VT,Ve)
      | ( Ve = vabs(sk0_38(VC,VT,Ve),sk0_40(VC,VT,Ve),sk0_39(VC,VT,Ve))
        & VT = varrow(sk0_40(VC,VT,Ve),sk0_41(VC,VT,Ve))
        & vtcheck(vbind(sk0_38(VC,VT,Ve),sk0_40(VC,VT,Ve),VC),sk0_39(VC,VT,Ve),sk0_41(VC,VT,Ve)) ) ),
    inference(skolemization,[status(esa)],[f290]) ).

fof(f292,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_3(X0,X1,X2)
      | pd0_7(sk0_37(X0,X1,X2),X0,X1,X2)
      | X2 = vabs(sk0_38(X0,X1,X2),sk0_40(X0,X1,X2),sk0_39(X0,X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f291]) ).

fof(f319,plain,
    ! [Ve,VT,VC,Vx] :
      ( ~ pd0_7(Vx,VC,VT,Ve)
      | ( Ve = vvar(Vx)
        & vlookup(Vx,VC) = vsomeType(VT) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f289]) ).

fof(f321,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_7(X0,X1,X2,X3)
      | vlookup(X0,X1) = vsomeType(X2) ),
    inference(cnf_transformation,[status(esa)],[f319]) ).

fof(f389,plain,
    ! [X0] : vlookup(X0,vempty) = vnoType,
    inference(destructive_equality_resolution,[status(esa)],[f126]) ).

fof(f433,plain,
    ( spl0_0
  <=> pd0_3(vempty,sk0_22,vvar(sk0_21)) ),
    introduced(split_symbol_definition) ).

fof(f434,plain,
    ( pd0_3(vempty,sk0_22,vvar(sk0_21))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f433]) ).

fof(f436,plain,
    ( spl0_1
  <=> vvar(sk0_21) = vapp(sk0_20(vempty,sk0_22,vvar(sk0_21)),sk0_18(vempty,sk0_22,vvar(sk0_21))) ),
    introduced(split_symbol_definition) ).

fof(f437,plain,
    ( vvar(sk0_21) = vapp(sk0_20(vempty,sk0_22,vvar(sk0_21)),sk0_18(vempty,sk0_22,vvar(sk0_21)))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f436]) ).

fof(f439,plain,
    ( pd0_3(vempty,sk0_22,vvar(sk0_21))
    | vvar(sk0_21) = vapp(sk0_20(vempty,sk0_22,vvar(sk0_21)),sk0_18(vempty,sk0_22,vvar(sk0_21))) ),
    inference(resolution,[status(thm)],[f243,f255]) ).

fof(f440,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f439,f433,f436]) ).

fof(f441,plain,
    ( spl0_2
  <=> pd0_7(sk0_37(vempty,sk0_22,vvar(sk0_21)),vempty,sk0_22,vvar(sk0_21)) ),
    introduced(split_symbol_definition) ).

fof(f442,plain,
    ( pd0_7(sk0_37(vempty,sk0_22,vvar(sk0_21)),vempty,sk0_22,vvar(sk0_21))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f441]) ).

fof(f444,plain,
    ( spl0_3
  <=> vvar(sk0_21) = vabs(sk0_38(vempty,sk0_22,vvar(sk0_21)),sk0_40(vempty,sk0_22,vvar(sk0_21)),sk0_39(vempty,sk0_22,vvar(sk0_21))) ),
    introduced(split_symbol_definition) ).

fof(f445,plain,
    ( vvar(sk0_21) = vabs(sk0_38(vempty,sk0_22,vvar(sk0_21)),sk0_40(vempty,sk0_22,vvar(sk0_21)),sk0_39(vempty,sk0_22,vvar(sk0_21)))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f444]) ).

fof(f447,plain,
    ( pd0_7(sk0_37(vempty,sk0_22,vvar(sk0_21)),vempty,sk0_22,vvar(sk0_21))
    | vvar(sk0_21) = vabs(sk0_38(vempty,sk0_22,vvar(sk0_21)),sk0_40(vempty,sk0_22,vvar(sk0_21)),sk0_39(vempty,sk0_22,vvar(sk0_21)))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f292,f434]) ).

fof(f448,plain,
    ( spl0_2
    | spl0_3
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f447,f441,f444,f433]) ).

fof(f449,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f437,f75]) ).

fof(f450,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f449]) ).

fof(f453,plain,
    ( vlookup(sk0_37(vempty,sk0_22,vvar(sk0_21)),vempty) = vsomeType(sk0_22)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f442,f321]) ).

fof(f454,plain,
    ( vnoType = vsomeType(sk0_22)
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f389,f453]) ).

fof(f455,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f454,f115]) ).

fof(f456,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f455]) ).

fof(f457,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f445,f74]) ).

fof(f458,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f457]) ).

fof(f459,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f440,f448,f450,f456,f458]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM149+1 : TPTP v8.1.2. Released v6.4.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n003.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 : Tue May 30 11:51:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 0.13/0.38  % Refutation found
% 0.13/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.40  % Elapsed time: 0.048655 seconds
% 0.20/0.40  % CPU time: 0.152684 seconds
% 0.20/0.40  % Memory used: 23.167 MB
%------------------------------------------------------------------------------