TSTP Solution File: NUM453+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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 Apr 30 20:34:44 EDT 2024

% Result   : Theorem 0.13s 0.40s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   55 (  14 unt;   0 def)
%            Number of atoms       :  110 (  49 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  100 (  45   ~;  39   |;  10   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   26 (  26   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => aInteger0(smndt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2) )
     => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f46,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f48,conjecture,
    ( sdtpldt0(sz10,xp) != sz10
    & sdtpldt0(sz10,smndt0(xp)) != sz10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f49,negated_conjecture,
    ~ ( sdtpldt0(sz10,xp) != sz10
      & sdtpldt0(sz10,smndt0(xp)) != sz10 ),
    inference(negated_conjecture,[status(cth)],[f48]) ).

fof(f54,plain,
    aInteger0(sz10),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f55,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | aInteger0(smndt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f61,plain,
    ! [W0,W1,W2] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | ~ aInteger0(W2)
      | sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | ~ aInteger0(X2)
      | sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f65,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | X0 = sdtpldt0(sz00,X0) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f68,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,smndt0(X0)) = sz00 ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sz00 = sdtpldt0(smndt0(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f229,plain,
    aInteger0(xp),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f230,plain,
    xp != sz00,
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f234,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | sdtpldt0(sz10,smndt0(xp)) = sz10 ),
    inference(pre_NNF_transformation,[status(esa)],[f49]) ).

fof(f235,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | sdtpldt0(sz10,smndt0(xp)) = sz10 ),
    inference(cnf_transformation,[status(esa)],[f234]) ).

fof(f245,plain,
    ( spl0_0
  <=> sdtpldt0(sz10,xp) = sz10 ),
    introduced(split_symbol_definition) ).

fof(f246,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f245]) ).

fof(f248,plain,
    ( spl0_1
  <=> sdtpldt0(sz10,smndt0(xp)) = sz10 ),
    introduced(split_symbol_definition) ).

fof(f249,plain,
    ( sdtpldt0(sz10,smndt0(xp)) = sz10
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f248]) ).

fof(f251,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f235,f245,f248]) ).

fof(f255,plain,
    aInteger0(smndt0(xp)),
    inference(resolution,[status(thm)],[f56,f229]) ).

fof(f256,plain,
    aInteger0(smndt0(sz10)),
    inference(resolution,[status(thm)],[f56,f54]) ).

fof(f257,plain,
    sdtpldt0(xp,sz00) = xp,
    inference(resolution,[status(thm)],[f66,f229]) ).

fof(f259,plain,
    xp = sdtpldt0(sz00,xp),
    inference(resolution,[status(thm)],[f67,f229]) ).

fof(f265,plain,
    sdtpldt0(xp,smndt0(xp)) = sz00,
    inference(resolution,[status(thm)],[f69,f229]) ).

fof(f268,plain,
    sz00 = sdtpldt0(smndt0(sz10),sz10),
    inference(resolution,[status(thm)],[f70,f54]) ).

fof(f276,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | sdtpldt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtpldt0(X0,sz10),X1) ),
    inference(resolution,[status(thm)],[f62,f54]) ).

fof(f291,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
    inference(resolution,[status(thm)],[f276,f229]) ).

fof(f292,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
      | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f246,f291]) ).

fof(f299,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp)) ),
    inference(resolution,[status(thm)],[f255,f276]) ).

fof(f320,plain,
    smndt0(xp) = sdtpldt0(sz00,smndt0(xp)),
    inference(resolution,[status(thm)],[f255,f67]) ).

fof(f375,plain,
    ( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f256,f292]) ).

fof(f376,plain,
    ( sz00 = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f268,f375]) ).

fof(f377,plain,
    ( sz00 = sdtpldt0(sz00,xp)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f268,f376]) ).

fof(f401,plain,
    ( xp = sz00
    | ~ spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f377,f259]) ).

fof(f402,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f401,f230]) ).

fof(f403,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f402]) ).

fof(f405,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp))
      | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f249,f299]) ).

fof(f409,plain,
    ( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),smndt0(xp))
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f405,f256]) ).

fof(f410,plain,
    ( sz00 = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),smndt0(xp))
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f268,f409]) ).

fof(f411,plain,
    ( sz00 = sdtpldt0(sz00,smndt0(xp))
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f268,f410]) ).

fof(f416,plain,
    ( smndt0(xp) = sz00
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f411,f320]) ).

fof(f423,plain,
    ( sdtpldt0(xp,sz00) = sz00
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f416,f265]) ).

fof(f476,plain,
    ( sz00 = xp
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f423,f257]) ).

fof(f477,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f476,f230]) ).

fof(f478,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f477]) ).

fof(f479,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f251,f403,f478]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n025.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Mon Apr 29 21:08:26 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.13/0.31  % Drodi V3.6.0
% 0.13/0.40  % Refutation found
% 0.13/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41  % Elapsed time: 0.107041 seconds
% 0.13/0.41  % CPU time: 0.746153 seconds
% 0.13/0.41  % Total memory used: 74.451 MB
% 0.13/0.41  % Net memory used: 73.603 MB
%------------------------------------------------------------------------------