TSTP Solution File: RNG045+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : RNG045+1 : TPTP v8.1.2. Released v4.0.0.
% 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 20:37:48 EDT 2024

% Result   : Theorem 1.54s 0.58s
% Output   : CNFRefutation 1.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (  15 unt;   0 def)
%            Number of atoms       :   38 (  17 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   31 (  14   ~;   9   |;   7   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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;   4 con; 0-2 aty)
%            Number of variables   :   12 (  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [W0,W1,W2] :
      ( ( aScalar0(W0)
        & aScalar0(W1)
        & aScalar0(W2) )
     => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
        & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,hypothesis,
    ( aScalar0(xx)
    & aScalar0(xy)
    & aScalar0(xu)
    & aScalar0(xv) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,hypothesis,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,conjecture,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f61,plain,
    ! [W0,W1,W2] :
      ( ~ aScalar0(W0)
      | ~ aScalar0(W1)
      | ~ aScalar0(W2)
      | ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
        & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ aScalar0(X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X2)
      | sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f64,plain,
    aScalar0(xx),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f65,plain,
    aScalar0(xy),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f66,plain,
    aScalar0(xu),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f67,plain,
    aScalar0(xv),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f68,plain,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f69,plain,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X0)
      | ~ aScalar0(X1)
      | sdtasdt0(X0,sdtpldt0(xu,X1)) = sdtpldt0(sdtasdt0(X0,xu),sdtasdt0(X0,X1)) ),
    inference(resolution,[status(thm)],[f62,f66]) ).

fof(f739,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | sdtasdt0(X0,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(X0,xu),sdtasdt0(X0,xv)) ),
    inference(resolution,[status(thm)],[f145,f67]) ).

fof(f756,plain,
    sdtasdt0(xx,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),
    inference(resolution,[status(thm)],[f739,f64]) ).

fof(f757,plain,
    sdtasdt0(xy,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)),
    inference(resolution,[status(thm)],[f739,f65]) ).

fof(f761,plain,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
    inference(backward_demodulation,[status(thm)],[f756,f69]) ).

fof(f762,plain,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
    inference(forward_demodulation,[status(thm)],[f757,f761]) ).

fof(f763,plain,
    sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
    inference(forward_demodulation,[status(thm)],[f68,f762]) ).

fof(f764,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f763]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14  % Problem  : RNG045+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.36  % Computer : n013.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Mon Apr 29 22:12:34 EDT 2024
% 0.13/0.36  % CPUTime  : 
% 0.13/0.37  % Drodi V3.6.0
% 1.54/0.58  % Refutation found
% 1.54/0.58  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.54/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.64/0.60  % Elapsed time: 0.222767 seconds
% 1.64/0.60  % CPU time: 1.622340 seconds
% 1.64/0.60  % Total memory used: 87.362 MB
% 1.64/0.60  % Net memory used: 85.010 MB
%------------------------------------------------------------------------------