TSTP Solution File: NUM845+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 20:35:55 EDT 2024

% Result   : Theorem 0.20s 0.47s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (  21 unt;   0 def)
%            Number of atoms       :   37 (  36 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (   8   ~;   0   |;   6   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (  39   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [Vd416] :
      ( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
     => vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ! [Vd416] :
        ( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
       => vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f12,axiom,
    ! [Vd396,Vd397] :
      ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
      & vmul(Vd396,v1) = Vd396 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [Vd42,Vd43] :
      ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
      & vplus(Vd42,v1) = vsucc(Vd42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,plain,
    ? [Vd416] :
      ( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
      & vmul(vsucc(vd411),vsucc(Vd416)) != vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ( vmul(vsucc(vd411),sk0_0) = vplus(vmul(vd411,sk0_0),sk0_0)
    & vmul(vsucc(vd411),vsucc(sk0_0)) != vplus(vmul(vd411,vsucc(sk0_0)),vsucc(sk0_0)) ),
    inference(skolemization,[status(esa)],[f17]) ).

fof(f19,plain,
    vmul(vsucc(vd411),sk0_0) = vplus(vmul(vd411,sk0_0),sk0_0),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    vmul(vsucc(vd411),vsucc(sk0_0)) != vplus(vmul(vd411,vsucc(sk0_0)),vsucc(sk0_0)),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f38,plain,
    ( ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
    & ! [Vd396] : vmul(Vd396,v1) = Vd396 ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f39,plain,
    ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f41,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f43,plain,
    ! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f44,plain,
    ( ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
    & ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42) ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f45,plain,
    ! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f60,plain,
    vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(vmul(vd411,vsucc(sk0_0)),sk0_0)),
    inference(backward_demodulation,[status(thm)],[f45,f20]) ).

fof(f61,plain,
    vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0)))),
    inference(forward_demodulation,[status(thm)],[f41,f60]) ).

fof(f67,plain,
    vmul(vsucc(vd411),sk0_0) = vplus(sk0_0,vmul(vd411,sk0_0)),
    inference(paramodulation,[status(thm)],[f19,f41]) ).

fof(f78,plain,
    ! [X0,X1] : vmul(vsucc(X0),vsucc(X1)) = vsucc(vplus(vmul(vsucc(X0),X1),X0)),
    inference(paramodulation,[status(thm)],[f45,f39]) ).

fof(f79,plain,
    ! [X0,X1] : vmul(vsucc(X0),vsucc(X1)) = vsucc(vplus(X0,vmul(vsucc(X0),X1))),
    inference(forward_demodulation,[status(thm)],[f41,f78]) ).

fof(f104,plain,
    ! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(X1,vplus(X2,X0)),
    inference(paramodulation,[status(thm)],[f41,f43]) ).

fof(f116,plain,
    ! [X0,X1,X2] : vplus(vmul(X0,vsucc(X1)),X2) = vplus(vmul(X0,X1),vplus(X0,X2)),
    inference(paramodulation,[status(thm)],[f39,f43]) ).

fof(f117,plain,
    ! [X0,X1,X2] : vplus(vmul(X0,vsucc(X1)),X2) = vplus(X0,vplus(X2,vmul(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f104,f116]) ).

fof(f654,plain,
    vplus(vmul(vd411,vsucc(sk0_0)),sk0_0) = vplus(vd411,vmul(vsucc(vd411),sk0_0)),
    inference(paramodulation,[status(thm)],[f67,f117]) ).

fof(f655,plain,
    vplus(sk0_0,vmul(vd411,vsucc(sk0_0))) = vplus(vd411,vmul(vsucc(vd411),sk0_0)),
    inference(forward_demodulation,[status(thm)],[f41,f654]) ).

fof(f696,plain,
    vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(vd411,vmul(vsucc(vd411),sk0_0))),
    inference(backward_demodulation,[status(thm)],[f655,f61]) ).

fof(f697,plain,
    vmul(vsucc(vd411),vsucc(sk0_0)) != vmul(vsucc(vd411),vsucc(sk0_0)),
    inference(forward_demodulation,[status(thm)],[f79,f696]) ).

fof(f698,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f697]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n013.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 : Mon Apr 29 20:46:19 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.20/0.47  % Refutation found
% 0.20/0.47  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.47  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.49  % Elapsed time: 0.135697 seconds
% 0.20/0.49  % CPU time: 0.940193 seconds
% 0.20/0.49  % Total memory used: 47.951 MB
% 0.20/0.49  % Net memory used: 47.713 MB
%------------------------------------------------------------------------------