TSTP Solution File: NUM430+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM430+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 20:34:40 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   73 (  10 unt;   2 def)
%            Number of atoms       :  237 (  35 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  273 ( 109   ~; 111   |;  33   &)
%                                         (  14 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  13 usr;  11 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   57 (  51   !;   6   ?)

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

fof(f5,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => aInteger0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,definition,
    ! [W0] :
      ( aInteger0(W0)
     => ! [W1] :
          ( aDivisorOf0(W1,W0)
        <=> ( aInteger0(W1)
            & W1 != sz00
            & ? [W2] :
                ( aInteger0(W2)
                & sdtasdt0(W1,W2) = W0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,definition,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2)
        & W2 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
      <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2)
        & W2 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
       => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,hypothesis,
    ( aInteger0(xa)
    & aInteger0(xb)
    & aInteger0(xq)
    & xq != sz00
    & aInteger0(xc) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,hypothesis,
    ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
    & sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,conjecture,
    ? [W0] :
      ( aInteger0(W0)
      & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,negated_conjecture,
    ~ ? [W0] :
        ( aInteger0(W0)
        & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
    inference(negated_conjecture,[status(cth)],[f25]) ).

fof(f32,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | aInteger0(smndt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [W0,W1] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | aInteger0(sdtpldt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f66,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ! [W1] :
          ( aDivisorOf0(W1,W0)
        <=> ( aInteger0(W1)
            & W1 != sz00
            & ? [W2] :
                ( aInteger0(W2)
                & sdtasdt0(W1,W2) = W0 ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f67,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ! [W1] :
          ( ( ~ aDivisorOf0(W1,W0)
            | ( aInteger0(W1)
              & W1 != sz00
              & ? [W2] :
                  ( aInteger0(W2)
                  & sdtasdt0(W1,W2) = W0 ) ) )
          & ( aDivisorOf0(W1,W0)
            | ~ aInteger0(W1)
            | W1 = sz00
            | ! [W2] :
                ( ~ aInteger0(W2)
                | sdtasdt0(W1,W2) != W0 ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( ! [W1] :
            ( ~ aDivisorOf0(W1,W0)
            | ( aInteger0(W1)
              & W1 != sz00
              & ? [W2] :
                  ( aInteger0(W2)
                  & sdtasdt0(W1,W2) = W0 ) ) )
        & ! [W1] :
            ( aDivisorOf0(W1,W0)
            | ~ aInteger0(W1)
            | W1 = sz00
            | ! [W2] :
                ( ~ aInteger0(W2)
                | sdtasdt0(W1,W2) != W0 ) ) ) ),
    inference(miniscoping,[status(esa)],[f67]) ).

fof(f69,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( ! [W1] :
            ( ~ aDivisorOf0(W1,W0)
            | ( aInteger0(W1)
              & W1 != sz00
              & aInteger0(sk0_0(W1,W0))
              & sdtasdt0(W1,sk0_0(W1,W0)) = W0 ) )
        & ! [W1] :
            ( aDivisorOf0(W1,W0)
            | ~ aInteger0(W1)
            | W1 = sz00
            | ! [W2] :
                ( ~ aInteger0(W2)
                | sdtasdt0(W1,W2) != W0 ) ) ) ),
    inference(skolemization,[status(esa)],[f68]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aDivisorOf0(X1,X0)
      | aInteger0(sk0_0(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aDivisorOf0(X1,X0)
      | sdtasdt0(X1,sk0_0(X1,X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f75,plain,
    ! [W0,W1,W2] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | ~ aInteger0(W2)
      | W2 = sz00
      | ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
      <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f76,plain,
    ! [W0,W1,W2] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | ~ aInteger0(W2)
      | W2 = sz00
      | ( ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
          | aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
        & ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
          | ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ),
    inference(NNF_transformation,[status(esa)],[f75]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | ~ aInteger0(X2)
      | X2 = sz00
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
    inference(cnf_transformation,[status(esa)],[f76]) ).

fof(f81,plain,
    ! [W0,W1,W2] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | ~ aInteger0(W2)
      | W2 = sz00
      | ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
      | sdteqdtlpzmzozddtrp0(W1,W0,W2) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | ~ aInteger0(X2)
      | X2 = sz00
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f84,plain,
    aInteger0(xb),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f85,plain,
    aInteger0(xq),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f86,plain,
    xq != sz00,
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f87,plain,
    aInteger0(xc),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f89,plain,
    sdteqdtlpzmzozddtrp0(xb,xc,xq),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f92,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xc)) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xc)) ),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f123,plain,
    ( spl0_5
  <=> aInteger0(sdtpldt0(xb,smndt0(xc))) ),
    introduced(split_symbol_definition) ).

fof(f125,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f123]) ).

fof(f126,plain,
    ( spl0_6
  <=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))) ),
    introduced(split_symbol_definition) ).

fof(f128,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f126]) ).

fof(f129,plain,
    ( spl0_7
  <=> aInteger0(sk0_0(xq,sdtpldt0(xb,smndt0(xc)))) ),
    introduced(split_symbol_definition) ).

fof(f131,plain,
    ( ~ aInteger0(sk0_0(xq,sdtpldt0(xb,smndt0(xc))))
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f129]) ).

fof(f132,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    | ~ aInteger0(sk0_0(xq,sdtpldt0(xb,smndt0(xc)))) ),
    inference(resolution,[status(thm)],[f73,f93]) ).

fof(f133,plain,
    ( ~ spl0_5
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f132,f123,f126,f129]) ).

fof(f139,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    | spl0_7 ),
    inference(resolution,[status(thm)],[f131,f72]) ).

fof(f140,plain,
    ( ~ spl0_5
    | ~ spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f139,f123,f126,f129]) ).

fof(f174,plain,
    ( spl0_15
  <=> aInteger0(xb) ),
    introduced(split_symbol_definition) ).

fof(f176,plain,
    ( ~ aInteger0(xb)
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f174]) ).

fof(f177,plain,
    ( spl0_16
  <=> aInteger0(xq) ),
    introduced(split_symbol_definition) ).

fof(f179,plain,
    ( ~ aInteger0(xq)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f177]) ).

fof(f180,plain,
    ( spl0_17
  <=> xq = sz00 ),
    introduced(split_symbol_definition) ).

fof(f181,plain,
    ( xq = sz00
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f180]) ).

fof(f188,plain,
    ( spl0_19
  <=> aInteger0(xc) ),
    introduced(split_symbol_definition) ).

fof(f190,plain,
    ( ~ aInteger0(xc)
    | spl0_19 ),
    inference(component_clause,[status(thm)],[f188]) ).

fof(f191,plain,
    ( spl0_20
  <=> sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
    introduced(split_symbol_definition) ).

fof(f192,plain,
    ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
    | ~ spl0_20 ),
    inference(component_clause,[status(thm)],[f191]) ).

fof(f194,plain,
    ( ~ aInteger0(xb)
    | ~ aInteger0(xc)
    | ~ aInteger0(xq)
    | xq = sz00
    | sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
    inference(resolution,[status(thm)],[f82,f89]) ).

fof(f195,plain,
    ( ~ spl0_15
    | ~ spl0_19
    | ~ spl0_16
    | spl0_17
    | spl0_20 ),
    inference(split_clause,[status(thm)],[f194,f174,f188,f177,f180,f191]) ).

fof(f198,plain,
    ( $false
    | spl0_19 ),
    inference(forward_subsumption_resolution,[status(thm)],[f190,f87]) ).

fof(f199,plain,
    spl0_19,
    inference(contradiction_clause,[status(thm)],[f198]) ).

fof(f200,plain,
    ( $false
    | spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f179,f85]) ).

fof(f201,plain,
    spl0_16,
    inference(contradiction_clause,[status(thm)],[f200]) ).

fof(f202,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f176,f84]) ).

fof(f203,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f202]) ).

fof(f204,plain,
    ( $false
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f181,f86]) ).

fof(f205,plain,
    ~ spl0_17,
    inference(contradiction_clause,[status(thm)],[f204]) ).

fof(f206,plain,
    ( spl0_21
  <=> sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
    introduced(split_symbol_definition) ).

fof(f209,plain,
    ( ~ aInteger0(xc)
    | ~ aInteger0(xb)
    | ~ aInteger0(xq)
    | xq = sz00
    | sdteqdtlpzmzozddtrp0(xb,xc,xq)
    | ~ spl0_20 ),
    inference(resolution,[status(thm)],[f192,f82]) ).

fof(f210,plain,
    ( ~ spl0_19
    | ~ spl0_15
    | ~ spl0_16
    | spl0_17
    | spl0_21
    | ~ spl0_20 ),
    inference(split_clause,[status(thm)],[f209,f188,f174,f177,f180,f206,f191]) ).

fof(f216,plain,
    ( ~ aInteger0(xb)
    | ~ aInteger0(xc)
    | ~ aInteger0(xq)
    | xq = sz00
    | ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
    | spl0_6 ),
    inference(resolution,[status(thm)],[f77,f128]) ).

fof(f217,plain,
    ( ~ spl0_15
    | ~ spl0_19
    | ~ spl0_16
    | spl0_17
    | ~ spl0_21
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f216,f174,f188,f177,f180,f206,f126]) ).

fof(f228,plain,
    ( spl0_25
  <=> aInteger0(smndt0(xc)) ),
    introduced(split_symbol_definition) ).

fof(f230,plain,
    ( ~ aInteger0(smndt0(xc))
    | spl0_25 ),
    inference(component_clause,[status(thm)],[f228]) ).

fof(f231,plain,
    ( ~ aInteger0(xb)
    | ~ aInteger0(smndt0(xc))
    | spl0_5 ),
    inference(resolution,[status(thm)],[f125,f35]) ).

fof(f232,plain,
    ( ~ spl0_15
    | ~ spl0_25
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f231,f174,f228,f123]) ).

fof(f233,plain,
    ( ~ aInteger0(xc)
    | spl0_25 ),
    inference(resolution,[status(thm)],[f230,f33]) ).

fof(f234,plain,
    ( ~ spl0_19
    | spl0_25 ),
    inference(split_clause,[status(thm)],[f233,f188,f228]) ).

fof(f235,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f133,f140,f195,f199,f201,f203,f205,f210,f217,f232,f234]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM430+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 21:17:02 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.37  % Refutation found
% 0.14/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.38  % Elapsed time: 0.022167 seconds
% 0.21/0.38  % CPU time: 0.042502 seconds
% 0.21/0.38  % Total memory used: 13.250 MB
% 0.21/0.38  % Net memory used: 13.212 MB
%------------------------------------------------------------------------------