TSTP Solution File: ALG179+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : ALG179+1 : TPTP v8.1.2. Released v2.7.0.
% 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 20:10:38 EDT 2024

% Result   : Theorem 0.20s 0.44s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   39 (  18 unt;   0 def)
%            Number of atoms       :  107 (  36 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  102 (  34   ~;  27   |;  17   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   51 (  49   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [U] :
      ( sorti2(U)
     => ! [V] :
          ( sorti2(V)
         => sorti2(op2(U,V)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [U] :
      ( sorti1(U)
     => ! [V] :
          ( sorti1(V)
         => op1(op1(U,V),V) = U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ~ ! [U] :
        ( sorti2(U)
       => ! [V] :
            ( sorti2(V)
           => op2(op2(U,V),V) = U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,conjecture,
    ( ( ! [U] :
          ( sorti1(U)
         => sorti2(h(U)) )
      & ! [V] :
          ( sorti2(V)
         => sorti1(j(V)) ) )
   => ~ ( ! [W] :
            ( sorti1(W)
           => ! [X] :
                ( sorti1(X)
               => h(op1(W,X)) = op2(h(W),h(X)) ) )
        & ! [Y] :
            ( sorti2(Y)
           => ! [Z] :
                ( sorti2(Z)
               => j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
        & ! [X1] :
            ( sorti2(X1)
           => h(j(X1)) = X1 )
        & ! [X2] :
            ( sorti1(X2)
           => j(h(X2)) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ~ ( ( ! [U] :
            ( sorti1(U)
           => sorti2(h(U)) )
        & ! [V] :
            ( sorti2(V)
           => sorti1(j(V)) ) )
     => ~ ( ! [W] :
              ( sorti1(W)
             => ! [X] :
                  ( sorti1(X)
                 => h(op1(W,X)) = op2(h(W),h(X)) ) )
          & ! [Y] :
              ( sorti2(Y)
             => ! [Z] :
                  ( sorti2(Z)
                 => j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
          & ! [X1] :
              ( sorti2(X1)
             => h(j(X1)) = X1 )
          & ! [X2] :
              ( sorti1(X2)
             => j(h(X2)) = X2 ) ) ),
    inference(negated_conjecture,[status(cth)],[f5]) ).

fof(f9,plain,
    ! [U] :
      ( ~ sorti2(U)
      | ! [V] :
          ( ~ sorti2(V)
          | sorti2(op2(U,V)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ sorti2(X0)
      | ~ sorti2(X1)
      | sorti2(op2(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f11,plain,
    ! [U] :
      ( ~ sorti1(U)
      | ! [V] :
          ( ~ sorti1(V)
          | op1(op1(U,V),V) = U ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ sorti1(X0)
      | ~ sorti1(X1)
      | op1(op1(X0,X1),X1) = X0 ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ? [U] :
      ( sorti2(U)
      & ? [V] :
          ( sorti2(V)
          & op2(op2(U,V),V) != U ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f14,plain,
    ( sorti2(sk0_0)
    & sorti2(sk0_1)
    & op2(op2(sk0_0,sk0_1),sk0_1) != sk0_0 ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f15,plain,
    sorti2(sk0_0),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    sorti2(sk0_1),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    op2(op2(sk0_0,sk0_1),sk0_1) != sk0_0,
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f18,plain,
    ( ! [U] :
        ( ~ sorti1(U)
        | sorti2(h(U)) )
    & ! [V] :
        ( ~ sorti2(V)
        | sorti1(j(V)) )
    & ! [W] :
        ( ~ sorti1(W)
        | ! [X] :
            ( ~ sorti1(X)
            | h(op1(W,X)) = op2(h(W),h(X)) ) )
    & ! [Y] :
        ( ~ sorti2(Y)
        | ! [Z] :
            ( ~ sorti2(Z)
            | j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
    & ! [X1] :
        ( ~ sorti2(X1)
        | h(j(X1)) = X1 )
    & ! [X2] :
        ( ~ sorti1(X2)
        | j(h(X2)) = X2 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f20,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | sorti1(j(X0)) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ sorti1(X0)
      | ~ sorti1(X1)
      | h(op1(X0,X1)) = op2(h(X0),h(X1)) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ sorti2(X0)
      | ~ sorti2(X1)
      | j(op2(X0,X1)) = op1(j(X0),j(X1)) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f23,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | h(j(X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f25,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | sorti2(op2(sk0_0,X0)) ),
    inference(resolution,[status(thm)],[f15,f10]) ).

fof(f26,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | j(op2(sk0_0,X0)) = op1(j(sk0_0),j(X0)) ),
    inference(resolution,[status(thm)],[f15,f22]) ).

fof(f27,plain,
    h(j(sk0_0)) = sk0_0,
    inference(resolution,[status(thm)],[f15,f23]) ).

fof(f28,plain,
    sorti1(j(sk0_0)),
    inference(resolution,[status(thm)],[f15,f20]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | op1(op1(j(sk0_0),X0),X0) = j(sk0_0) ),
    inference(resolution,[status(thm)],[f28,f12]) ).

fof(f50,plain,
    j(op2(sk0_0,sk0_1)) = op1(j(sk0_0),j(sk0_1)),
    inference(resolution,[status(thm)],[f16,f26]) ).

fof(f51,plain,
    sorti2(op2(sk0_0,sk0_1)),
    inference(resolution,[status(thm)],[f16,f25]) ).

fof(f54,plain,
    h(j(sk0_1)) = sk0_1,
    inference(resolution,[status(thm)],[f16,f23]) ).

fof(f55,plain,
    sorti1(j(sk0_1)),
    inference(resolution,[status(thm)],[f16,f20]) ).

fof(f56,plain,
    op1(op1(j(sk0_0),j(sk0_1)),j(sk0_1)) = j(sk0_0),
    inference(resolution,[status(thm)],[f55,f29]) ).

fof(f66,plain,
    h(j(op2(sk0_0,sk0_1))) = op2(sk0_0,sk0_1),
    inference(resolution,[status(thm)],[f51,f23]) ).

fof(f67,plain,
    sorti1(j(op2(sk0_0,sk0_1))),
    inference(resolution,[status(thm)],[f51,f20]) ).

fof(f90,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | h(op1(j(op2(sk0_0,sk0_1)),X0)) = op2(h(j(op2(sk0_0,sk0_1))),h(X0)) ),
    inference(resolution,[status(thm)],[f67,f21]) ).

fof(f563,plain,
    op1(j(op2(sk0_0,sk0_1)),j(sk0_1)) = j(sk0_0),
    inference(forward_demodulation,[status(thm)],[f50,f56]) ).

fof(f2165,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | h(op1(j(op2(sk0_0,sk0_1)),X0)) = op2(op2(sk0_0,sk0_1),h(X0)) ),
    inference(forward_demodulation,[status(thm)],[f66,f90]) ).

fof(f2170,plain,
    h(op1(j(op2(sk0_0,sk0_1)),j(sk0_1))) = op2(op2(sk0_0,sk0_1),h(j(sk0_1))),
    inference(resolution,[status(thm)],[f2165,f55]) ).

fof(f2171,plain,
    h(j(sk0_0)) = op2(op2(sk0_0,sk0_1),h(j(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f563,f2170]) ).

fof(f2172,plain,
    sk0_0 = op2(op2(sk0_0,sk0_1),h(j(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f27,f2171]) ).

fof(f2173,plain,
    sk0_0 = op2(op2(sk0_0,sk0_1),sk0_1),
    inference(forward_demodulation,[status(thm)],[f54,f2172]) ).

fof(f2174,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2173,f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ALG179+1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 23:23:19 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.20/0.44  % Refutation found
% 0.20/0.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.47  % Elapsed time: 0.108739 seconds
% 0.20/0.47  % CPU time: 0.740894 seconds
% 0.20/0.47  % Total memory used: 35.963 MB
% 0.20/0.47  % Net memory used: 34.483 MB
%------------------------------------------------------------------------------