TSTP Solution File: NUM516+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 12:29:30 EDT 2023

% Result   : Theorem 0.20s 0.44s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  102 (  21 unt;   2 def)
%            Number of atoms       :  324 (  73 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  376 ( 154   ~; 154   |;  41   &)
%                                         (  19 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  16 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   46 (;  45   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( W0 != W1
          & sdtlseqdt0(W0,W1) )
       => ! [W2] :
            ( aNaturalNumber0(W2)
           => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
              & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
              & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
              & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( W0 != sz00
          & doDivides0(W0,W1) )
       => ! [W2] :
            ( W2 = sdtsldt0(W1,W0)
          <=> ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,definition,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( isPrime0(W0)
      <=> ( W0 != sz00
          & W0 != sz10
          & ! [W1] :
              ( ( aNaturalNumber0(W1)
                & doDivides0(W1,W0) )
             => ( W1 = sz10
                | W1 = W0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f39,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f48,hypothesis,
    ( aNaturalNumber0(xr)
    & doDivides0(xr,xk)
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f52,hypothesis,
    doDivides0(xr,xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f53,hypothesis,
    ( sdtsldt0(xn,xr) != xn
    & sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f55,conjecture,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
    & sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f56,negated_conjecture,
    ~ ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
      & sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(negated_conjecture,[status(cth)],[f55]) ).

fof(f60,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f63,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | aNaturalNumber0(sdtpldt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f119,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = W1
      | ~ sdtlseqdt0(W0,W1)
      | ! [W2] :
          ( ~ aNaturalNumber0(W2)
          | ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
            & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
            & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
            & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | X0 = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | sdtpldt0(X0,X2) != sdtpldt0(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | X0 = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f144,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = sz00
      | ~ doDivides0(W0,W1)
      | ! [W2] :
          ( W2 = sdtsldt0(W1,W0)
        <=> ( aNaturalNumber0(W2)
            & W1 = sdtasdt0(W0,W2) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f145,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = sz00
      | ~ doDivides0(W0,W1)
      | ! [W2] :
          ( ( W2 != sdtsldt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) )
          & ( W2 = sdtsldt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | W1 != sdtasdt0(W0,W2) ) ) ),
    inference(NNF_transformation,[status(esa)],[f144]) ).

fof(f146,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = sz00
      | ~ doDivides0(W0,W1)
      | ( ! [W2] :
            ( W2 != sdtsldt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) )
        & ! [W2] :
            ( W2 = sdtsldt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | W1 != sdtasdt0(W0,W2) ) ) ),
    inference(miniscoping,[status(esa)],[f145]) ).

fof(f147,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | X0 = sz00
      | ~ doDivides0(X0,X1)
      | X2 != sdtsldt0(X1,X0)
      | aNaturalNumber0(X2) ),
    inference(cnf_transformation,[status(esa)],[f146]) ).

fof(f160,plain,
    ! [W0] :
      ( ~ aNaturalNumber0(W0)
      | ( isPrime0(W0)
      <=> ( W0 != sz00
          & W0 != sz10
          & ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | ~ doDivides0(W1,W0)
              | W1 = sz10
              | W1 = W0 ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f161,plain,
    ! [W0] :
      ( ~ aNaturalNumber0(W0)
      | ( ( ~ isPrime0(W0)
          | ( W0 != sz00
            & W0 != sz10
            & ! [W1] :
                ( ~ aNaturalNumber0(W1)
                | ~ doDivides0(W1,W0)
                | W1 = sz10
                | W1 = W0 ) ) )
        & ( isPrime0(W0)
          | W0 = sz00
          | W0 = sz10
          | ? [W1] :
              ( aNaturalNumber0(W1)
              & doDivides0(W1,W0)
              & W1 != sz10
              & W1 != W0 ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f160]) ).

fof(f162,plain,
    ! [W0] :
      ( ~ aNaturalNumber0(W0)
      | ( ( ~ isPrime0(W0)
          | ( W0 != sz00
            & W0 != sz10
            & ! [W1] :
                ( ~ aNaturalNumber0(W1)
                | ~ doDivides0(W1,W0)
                | W1 = sz10
                | W1 = W0 ) ) )
        & ( isPrime0(W0)
          | W0 = sz00
          | W0 = sz10
          | ( aNaturalNumber0(sk0_2(W0))
            & doDivides0(sk0_2(W0),W0)
            & sk0_2(W0) != sz10
            & sk0_2(W0) != W0 ) ) ) ),
    inference(skolemization,[status(esa)],[f161]) ).

fof(f163,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ~ isPrime0(X0)
      | X0 != sz00 ),
    inference(cnf_transformation,[status(esa)],[f162]) ).

fof(f175,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f176,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f177,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f194,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f196,plain,
    isPrime0(xr),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f202,plain,
    doDivides0(xr,xn),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f203,plain,
    sdtsldt0(xn,xr) != xn,
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f204,plain,
    sdtlseqdt0(sdtsldt0(xn,xr),xn),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f206,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(pre_NNF_transformation,[status(esa)],[f56]) ).

fof(f207,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(cnf_transformation,[status(esa)],[f206]) ).

fof(f208,plain,
    ( spl0_0
  <=> doDivides0(xr,xn) ),
    introduced(split_symbol_definition) ).

fof(f210,plain,
    ( ~ doDivides0(xr,xn)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f208]) ).

fof(f215,plain,
    ( spl0_2
  <=> sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
    introduced(split_symbol_definition) ).

fof(f216,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f215]) ).

fof(f218,plain,
    ( spl0_3
  <=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    introduced(split_symbol_definition) ).

fof(f220,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f218]) ).

fof(f221,plain,
    ( spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f207,f215,f218]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | X0 = sz00
      | ~ doDivides0(X0,X1)
      | aNaturalNumber0(sdtsldt0(X1,X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f147]) ).

fof(f232,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ isPrime0(sz00) ),
    inference(destructive_equality_resolution,[status(esa)],[f163]) ).

fof(f234,plain,
    ( spl0_4
  <=> aNaturalNumber0(xm) ),
    introduced(split_symbol_definition) ).

fof(f236,plain,
    ( ~ aNaturalNumber0(xm)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f234]) ).

fof(f237,plain,
    ( spl0_5
  <=> aNaturalNumber0(xp) ),
    introduced(split_symbol_definition) ).

fof(f239,plain,
    ( ~ aNaturalNumber0(xp)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f237]) ).

fof(f245,plain,
    ( spl0_7
  <=> aNaturalNumber0(xn) ),
    introduced(split_symbol_definition) ).

fof(f247,plain,
    ( ~ aNaturalNumber0(xn)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f245]) ).

fof(f264,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f247,f175]) ).

fof(f265,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f264]) ).

fof(f266,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f239,f177]) ).

fof(f267,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f266]) ).

fof(f268,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f236,f176]) ).

fof(f269,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f268]) ).

fof(f270,plain,
    ( spl0_12
  <=> aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
    introduced(split_symbol_definition) ).

fof(f272,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f270]) ).

fof(f276,plain,
    ( spl0_13
  <=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
    introduced(split_symbol_definition) ).

fof(f278,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f276]) ).

fof(f282,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | spl0_13 ),
    inference(resolution,[status(thm)],[f278,f64]) ).

fof(f283,plain,
    ( ~ spl0_7
    | ~ spl0_4
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f282,f245,f234,f276]) ).

fof(f284,plain,
    ( spl0_14
  <=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
    introduced(split_symbol_definition) ).

fof(f286,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f284]) ).

fof(f287,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xm)
    | spl0_12 ),
    inference(resolution,[status(thm)],[f272,f64]) ).

fof(f288,plain,
    ( ~ spl0_14
    | ~ spl0_4
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f287,f284,f234,f270]) ).

fof(f296,plain,
    ( spl0_16
  <=> xn = sdtsldt0(xn,xr) ),
    introduced(split_symbol_definition) ).

fof(f297,plain,
    ( xn = sdtsldt0(xn,xr)
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f296]) ).

fof(f343,plain,
    ( spl0_23
  <=> sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
    introduced(split_symbol_definition) ).

fof(f344,plain,
    ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
    | ~ spl0_23 ),
    inference(component_clause,[status(thm)],[f343]) ).

fof(f346,plain,
    ( spl0_24
  <=> sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm)) ),
    introduced(split_symbol_definition) ).

fof(f348,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
    | spl0_24 ),
    inference(component_clause,[status(thm)],[f346]) ).

fof(f349,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
    | ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | spl0_3 ),
    inference(resolution,[status(thm)],[f123,f220]) ).

fof(f350,plain,
    ( ~ spl0_12
    | ~ spl0_13
    | spl0_23
    | ~ spl0_24
    | ~ spl0_5
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f349,f270,f276,f343,f346,f237,f218]) ).

fof(f711,plain,
    ( spl0_47
  <=> aNaturalNumber0(xr) ),
    introduced(split_symbol_definition) ).

fof(f713,plain,
    ( ~ aNaturalNumber0(xr)
    | spl0_47 ),
    inference(component_clause,[status(thm)],[f711]) ).

fof(f714,plain,
    ( spl0_48
  <=> xr = sz00 ),
    introduced(split_symbol_definition) ).

fof(f715,plain,
    ( xr = sz00
    | ~ spl0_48 ),
    inference(component_clause,[status(thm)],[f714]) ).

fof(f717,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xn)
    | xr = sz00
    | ~ doDivides0(xr,xn)
    | spl0_14 ),
    inference(resolution,[status(thm)],[f229,f286]) ).

fof(f718,plain,
    ( ~ spl0_47
    | ~ spl0_7
    | spl0_48
    | ~ spl0_0
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f717,f711,f245,f714,f208,f284]) ).

fof(f719,plain,
    ( $false
    | spl0_47 ),
    inference(forward_subsumption_resolution,[status(thm)],[f713,f194]) ).

fof(f720,plain,
    spl0_47,
    inference(contradiction_clause,[status(thm)],[f719]) ).

fof(f764,plain,
    ( isPrime0(sz00)
    | ~ spl0_48 ),
    inference(forward_demodulation,[status(thm)],[f715,f196]) ).

fof(f837,plain,
    ~ isPrime0(sz00),
    inference(forward_subsumption_resolution,[status(thm)],[f232,f60]) ).

fof(f838,plain,
    ( $false
    | ~ spl0_48 ),
    inference(backward_subsumption_resolution,[status(thm)],[f764,f837]) ).

fof(f839,plain,
    ~ spl0_48,
    inference(contradiction_clause,[status(thm)],[f838]) ).

fof(f840,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f210,f202]) ).

fof(f841,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f840]) ).

fof(f1012,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
    | ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f216,f122]) ).

fof(f1013,plain,
    ( ~ spl0_12
    | ~ spl0_13
    | spl0_23
    | ~ spl0_24
    | ~ spl0_5
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f1012,f270,f276,f343,f346,f237,f215]) ).

fof(f1129,plain,
    ( spl0_108
  <=> sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    introduced(split_symbol_definition) ).

fof(f1131,plain,
    ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
    | spl0_108 ),
    inference(component_clause,[status(thm)],[f1129]) ).

fof(f1132,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xn)
    | sdtsldt0(xn,xr) = xn
    | ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
    | ~ aNaturalNumber0(xm)
    | ~ spl0_23 ),
    inference(resolution,[status(thm)],[f344,f122]) ).

fof(f1133,plain,
    ( ~ spl0_14
    | ~ spl0_7
    | spl0_16
    | ~ spl0_108
    | ~ spl0_4
    | ~ spl0_23 ),
    inference(split_clause,[status(thm)],[f1132,f284,f245,f296,f1129,f234,f343]) ).

fof(f1233,plain,
    ( $false
    | spl0_108 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1131,f204]) ).

fof(f1234,plain,
    spl0_108,
    inference(contradiction_clause,[status(thm)],[f1233]) ).

fof(f1609,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xn)
    | sdtsldt0(xn,xr) = xn
    | ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
    | ~ aNaturalNumber0(xm)
    | spl0_24 ),
    inference(resolution,[status(thm)],[f348,f123]) ).

fof(f1610,plain,
    ( ~ spl0_14
    | ~ spl0_7
    | spl0_16
    | ~ spl0_108
    | ~ spl0_4
    | spl0_24 ),
    inference(split_clause,[status(thm)],[f1609,f284,f245,f296,f1129,f234,f346]) ).

fof(f2561,plain,
    ( xn != xn
    | ~ spl0_16 ),
    inference(forward_demodulation,[status(thm)],[f297,f203]) ).

fof(f2562,plain,
    ( $false
    | ~ spl0_16 ),
    inference(trivial_equality_resolution,[status(esa)],[f2561]) ).

fof(f2563,plain,
    ~ spl0_16,
    inference(contradiction_clause,[status(thm)],[f2562]) ).

fof(f2564,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f221,f265,f267,f269,f283,f288,f350,f718,f720,f839,f841,f1013,f1133,f1234,f1610,f2563]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n008.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 10:00:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.20/0.44  % Refutation found
% 0.20/0.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.46  % Elapsed time: 0.118931 seconds
% 0.20/0.46  % CPU time: 0.789316 seconds
% 0.20/0.46  % Memory used: 58.599 MB
%------------------------------------------------------------------------------