TSTP Solution File: NUM852+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM852+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 : Wed May 31 12:30:50 EDT 2023

% Result   : Theorem 0.14s 0.48s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (  17 unt;   0 def)
%            Number of atoms       :   43 (  14 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   26 (  13   ~;  10   |;   0   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (;  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,axiom,
    greater(vd481,vd480),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [Vd470,Vd471] :
      ( greater(Vd470,Vd471)
     => greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [Vd470,Vd471] :
      ( greater(Vd470,Vd471)
     => vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [Vd470,Vd471] :
      ( greater(Vd470,Vd471)
     => vmul(Vd470,vd469) = vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,plain,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f23,plain,
    greater(vd481,vd480),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f27,plain,
    ! [Vd470,Vd471] :
      ( ~ greater(Vd470,Vd471)
      | greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | greater(vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)),vmul(X1,vd469)) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f29,plain,
    ! [Vd470,Vd471] :
      ( ~ greater(Vd470,Vd471)
      | vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | vmul(vplus(X1,vskolem9(X0,X1)),vd469) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)) ),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f31,plain,
    ! [Vd470,Vd471] :
      ( ~ greater(Vd470,Vd471)
      | vmul(Vd470,vd469) = vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | vmul(X0,vd469) = vmul(vplus(X1,vskolem9(X0,X1)),vd469) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f37,plain,
    ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f61,plain,
    ~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
    inference(paramodulation,[status(thm)],[f37,f22]) ).

fof(f631,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | greater(vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X0,X1))),vmul(X1,vd469)) ),
    inference(forward_demodulation,[status(thm)],[f37,f28]) ).

fof(f632,plain,
    greater(vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),vmul(vd480,vd469)),
    inference(resolution,[status(thm)],[f631,f23]) ).

fof(f633,plain,
    greater(vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),vmul(vd480,vd469)),
    inference(forward_demodulation,[status(thm)],[f37,f632]) ).

fof(f634,plain,
    greater(vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),vmul(vd469,vd480)),
    inference(forward_demodulation,[status(thm)],[f37,f633]) ).

fof(f635,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)) ),
    inference(forward_demodulation,[status(thm)],[f37,f30]) ).

fof(f636,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X0,X1))) ),
    inference(forward_demodulation,[status(thm)],[f37,f635]) ).

fof(f637,plain,
    vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),
    inference(resolution,[status(thm)],[f636,f23]) ).

fof(f638,plain,
    vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),
    inference(forward_demodulation,[status(thm)],[f37,f637]) ).

fof(f639,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | vmul(X0,vd469) = vmul(vd469,vplus(X1,vskolem9(X0,X1))) ),
    inference(forward_demodulation,[status(thm)],[f37,f32]) ).

fof(f640,plain,
    vmul(vd481,vd469) = vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))),
    inference(resolution,[status(thm)],[f639,f23]) ).

fof(f691,plain,
    greater(vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))),vmul(vd469,vd480)),
    inference(backward_demodulation,[status(thm)],[f638,f634]) ).

fof(f1164,plain,
    greater(vmul(vd481,vd469),vmul(vd469,vd480)),
    inference(forward_demodulation,[status(thm)],[f640,f691]) ).

fof(f1165,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f1164,f61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% 0.05/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32  % Computer : n013.cluster.edu
% 0.09/0.32  % Model    : x86_64 x86_64
% 0.09/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32  % Memory   : 8042.1875MB
% 0.09/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32  % CPULimit : 300
% 0.09/0.32  % WCLimit  : 300
% 0.09/0.32  % DateTime : Tue May 30 09:47:20 EDT 2023
% 0.09/0.32  % CPUTime  : 
% 0.09/0.33  % Drodi V3.5.1
% 0.14/0.48  % Refutation found
% 0.14/0.48  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.48  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50  % Elapsed time: 0.174303 seconds
% 0.14/0.50  % CPU time: 0.916518 seconds
% 0.14/0.50  % Memory used: 65.519 MB
%------------------------------------------------------------------------------