TSTP Solution File: NUM427+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM427+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 20:34:39 EDT 2024

% Result   : Theorem 0.07s 0.28s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   62 (  17 unt;   2 def)
%            Number of atoms       :  186 (  33 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  201 (  77   ~;  82   |;  27   &)
%                                         (  11 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   47 (  43   !;   4   ?)

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

fof(f6,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => aInteger0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,hypothesis,
    ( aInteger0(xa)
    & aInteger0(xb)
    & aInteger0(xq)
    & xq != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,hypothesis,
    ( aInteger0(xn)
    & sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,hypothesis,
    sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,conjecture,
    sdteqdtlpzmzozddtrp0(xb,xa,xq),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,negated_conjecture,
    ~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
    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(f36,plain,
    ! [W0,W1] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | aInteger0(sdtasdt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | aInteger0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

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(f74,plain,
    ! [X0,X1,X2] :
      ( ~ aInteger0(X0)
      | aDivisorOf0(X1,X0)
      | ~ aInteger0(X1)
      | X1 = sz00
      | ~ aInteger0(X2)
      | sdtasdt0(X1,X2) != 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(f78,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,
    aInteger0(xa),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f82,plain,
    aInteger0(xb),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f83,plain,
    aInteger0(xq),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f84,plain,
    xq != sz00,
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f86,plain,
    aInteger0(xn),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f88,plain,
    sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f89,plain,
    ~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ aInteger0(sdtasdt0(X0,X1))
      | aDivisorOf0(X0,sdtasdt0(X0,X1))
      | ~ aInteger0(X0)
      | X0 = sz00
      | ~ aInteger0(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f74]) ).

fof(f105,plain,
    ( spl0_3
  <=> aInteger0(xa) ),
    introduced(split_symbol_definition) ).

fof(f107,plain,
    ( ~ aInteger0(xa)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f105]) ).

fof(f108,plain,
    ( spl0_4
  <=> aInteger0(xb) ),
    introduced(split_symbol_definition) ).

fof(f110,plain,
    ( ~ aInteger0(xb)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f108]) ).

fof(f129,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f110,f82]) ).

fof(f130,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f129]) ).

fof(f131,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f107,f81]) ).

fof(f132,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f131]) ).

fof(f133,plain,
    ( spl0_9
  <=> aInteger0(xq) ),
    introduced(split_symbol_definition) ).

fof(f135,plain,
    ( ~ aInteger0(xq)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f133]) ).

fof(f136,plain,
    ( spl0_10
  <=> aInteger0(smndt0(xn)) ),
    introduced(split_symbol_definition) ).

fof(f138,plain,
    ( ~ aInteger0(smndt0(xn))
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f136]) ).

fof(f181,plain,
    ( ~ aInteger0(xn)
    | spl0_10 ),
    inference(resolution,[status(thm)],[f138,f33]) ).

fof(f182,plain,
    ( $false
    | spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f181,f86]) ).

fof(f183,plain,
    spl0_10,
    inference(contradiction_clause,[status(thm)],[f182]) ).

fof(f184,plain,
    ( $false
    | spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f135,f83]) ).

fof(f185,plain,
    spl0_9,
    inference(contradiction_clause,[status(thm)],[f184]) ).

fof(f363,plain,
    ( spl0_50
  <=> xq = sz00 ),
    introduced(split_symbol_definition) ).

fof(f364,plain,
    ( xq = sz00
    | ~ spl0_50 ),
    inference(component_clause,[status(thm)],[f363]) ).

fof(f379,plain,
    ! [X0,X1] :
      ( aDivisorOf0(X0,sdtasdt0(X0,X1))
      | ~ aInteger0(X0)
      | X0 = sz00
      | ~ aInteger0(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f91,f37]) ).

fof(f398,plain,
    ( spl0_58
  <=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
    introduced(split_symbol_definition) ).

fof(f399,plain,
    ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
    | ~ spl0_58 ),
    inference(component_clause,[status(thm)],[f398]) ).

fof(f401,plain,
    ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
    | ~ aInteger0(xq)
    | xq = sz00
    | ~ aInteger0(smndt0(xn)) ),
    inference(paramodulation,[status(thm)],[f88,f379]) ).

fof(f402,plain,
    ( spl0_58
    | ~ spl0_9
    | spl0_50
    | ~ spl0_10 ),
    inference(split_clause,[status(thm)],[f401,f398,f133,f363,f136]) ).

fof(f403,plain,
    ( $false
    | ~ spl0_50 ),
    inference(forward_subsumption_resolution,[status(thm)],[f364,f84]) ).

fof(f404,plain,
    ~ spl0_50,
    inference(contradiction_clause,[status(thm)],[f403]) ).

fof(f427,plain,
    ( spl0_63
  <=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
    introduced(split_symbol_definition) ).

fof(f428,plain,
    ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
    | ~ spl0_63 ),
    inference(component_clause,[status(thm)],[f427]) ).

fof(f430,plain,
    ( ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | ~ aInteger0(xq)
    | xq = sz00
    | sdteqdtlpzmzozddtrp0(xb,xa,xq)
    | ~ spl0_58 ),
    inference(resolution,[status(thm)],[f399,f78]) ).

fof(f431,plain,
    ( ~ spl0_4
    | ~ spl0_3
    | ~ spl0_9
    | spl0_50
    | spl0_63
    | ~ spl0_58 ),
    inference(split_clause,[status(thm)],[f430,f108,f105,f133,f363,f427,f398]) ).

fof(f434,plain,
    ( $false
    | ~ spl0_63 ),
    inference(forward_subsumption_resolution,[status(thm)],[f428,f89]) ).

fof(f435,plain,
    ~ spl0_63,
    inference(contradiction_clause,[status(thm)],[f434]) ).

fof(f436,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f130,f132,f183,f185,f402,f404,f431,f435]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : NUM427+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n011.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 20:51:46 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.07/0.27  % Drodi V3.6.0
% 0.07/0.28  % Refutation found
% 0.07/0.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.31  % Elapsed time: 0.032410 seconds
% 0.11/0.31  % CPU time: 0.098342 seconds
% 0.11/0.31  % Total memory used: 21.227 MB
% 0.11/0.31  % Net memory used: 21.102 MB
%------------------------------------------------------------------------------