TSTP Solution File: NUM849+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 20:35:56 EDT 2024

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   7 unt;   0 def)
%            Number of atoms       :   73 (  46 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   59 (  25   ~;  22   |;   4   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (  18   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [Vd454] :
      ( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
     => vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ! [Vd454] :
        ( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
       => vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f4,axiom,
    ! [Vd451] :
      ( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
     => vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [Vd451] :
      ( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
     => vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [Vd396,Vd397] :
      ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
      & vmul(Vd396,v1) = Vd396 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f58,plain,
    ? [Vd454] :
      ( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
      & vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f59,plain,
    ( vmul(vmul(vd448,vd449),sk0_0) = vmul(vd448,vmul(vd449,sk0_0))
    & vmul(vmul(vd448,vd449),vsucc(sk0_0)) != vmul(vd448,vmul(vd449,vsucc(sk0_0))) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f60,plain,
    vmul(vmul(vd448,vd449),sk0_0) = vmul(vd448,vmul(vd449,sk0_0)),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f61,plain,
    vmul(vmul(vd448,vd449),vsucc(sk0_0)) != vmul(vd448,vmul(vd449,vsucc(sk0_0))),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f64,plain,
    ! [Vd451] :
      ( vmul(vmul(vd448,vd449),Vd451) != vmul(vd448,vmul(vd449,Vd451))
      | vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f65,plain,
    ! [X0] :
      ( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
      | vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X0),vd449)) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [Vd451] :
      ( vmul(vmul(vd448,vd449),Vd451) != vmul(vd448,vmul(vd449,Vd451))
      | vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f67,plain,
    ! [X0] :
      ( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
      | vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f76,plain,
    ( ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
    & ! [Vd396] : vmul(Vd396,v1) = Vd396 ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f77,plain,
    ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f76]) ).

fof(f78,plain,
    ! [X0] : vmul(X0,v1) = X0,
    inference(cnf_transformation,[status(esa)],[f76]) ).

fof(f200,plain,
    ( spl0_0
  <=> vmul(vd448,vmul(vd449,sk0_0)) = vmul(vd448,vmul(vd449,sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f202,plain,
    ( vmul(vd448,vmul(vd449,sk0_0)) != vmul(vd448,vmul(vd449,sk0_0))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f200]) ).

fof(f210,plain,
    ( $false
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f202]) ).

fof(f211,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f210]) ).

fof(f260,plain,
    ! [X0] :
      ( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
      | vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(X0))) ),
    inference(forward_demodulation,[status(thm)],[f77,f65]) ).

fof(f262,plain,
    ( spl0_2
  <=> vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(sk0_0))) ),
    introduced(split_symbol_definition) ).

fof(f263,plain,
    ( vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(sk0_0)))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f262]) ).

fof(f265,plain,
    ( vmul(vd448,vmul(vd449,sk0_0)) != vmul(vd448,vmul(vd449,sk0_0))
    | vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(sk0_0))) ),
    inference(paramodulation,[status(thm)],[f60,f260]) ).

fof(f266,plain,
    ( ~ spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f265,f200,f262]) ).

fof(f269,plain,
    ! [X0] :
      ( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
      | vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) ),
    inference(forward_demodulation,[status(thm)],[f77,f67]) ).

fof(f271,plain,
    ( spl0_3
  <=> vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) ),
    introduced(split_symbol_definition) ).

fof(f272,plain,
    ( vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f271]) ).

fof(f274,plain,
    ( vmul(vd448,vmul(vd449,sk0_0)) != vmul(vd448,vmul(vd449,sk0_0))
    | vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) ),
    inference(paramodulation,[status(thm)],[f60,f269]) ).

fof(f275,plain,
    ( ~ spl0_0
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f274,f200,f271]) ).

fof(f300,plain,
    ( spl0_4
  <=> vmul(vd448,vd449) = vmul(vd448,vmul(vd449,v1)) ),
    introduced(split_symbol_definition) ).

fof(f302,plain,
    ( vmul(vd448,vd449) != vmul(vd448,vmul(vd449,v1))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f300]) ).

fof(f318,plain,
    ( vmul(vd448,vd449) != vmul(vd448,vd449)
    | spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f78,f302]) ).

fof(f319,plain,
    ( $false
    | spl0_4 ),
    inference(trivial_equality_resolution,[status(esa)],[f318]) ).

fof(f320,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f319]) ).

fof(f325,plain,
    ( vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vmul(vd448,vmul(vd449,vsucc(sk0_0)))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f263,f272]) ).

fof(f326,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f325,f61]) ).

fof(f327,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(contradiction_clause,[status(thm)],[f326]) ).

fof(f328,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f211,f266,f275,f320,f327]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Apr 29 21:08:39 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.6.0
% 0.12/0.34  % Refutation found
% 0.12/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.35  % Elapsed time: 0.021633 seconds
% 0.17/0.35  % CPU time: 0.038938 seconds
% 0.17/0.35  % Total memory used: 13.556 MB
% 0.17/0.35  % Net memory used: 13.548 MB
%------------------------------------------------------------------------------