TSTP Solution File: SWV188+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 20:46:11 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (  10 unt;   0 def)
%            Number of atoms       :  140 (  30 equ)
%            Maximal formula atoms :   26 (   6 avg)
%            Number of connectives :  168 (  51   ~;  46   |;  45   &)
%                                         (   1 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  15 con; 0-3 aty)
%            Number of variables   :   56 (  55   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] : ~ gt(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X,Y,Z] :
      ( ( leq(X,Y)
        & leq(Y,Z) )
     => leq(X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y] :
      ( leq(X,Y)
    <=> gt(succ(Y),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    succ(tptp_minus_1) = n0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f53,conjecture,
    ( ( ! [A] :
          ( ( leq(n0,A)
            & leq(A,n135299) )
         => ! [B] :
              ( ( leq(n0,B)
                & leq(B,n4) )
             => a_select3(q_init,A,B) = init ) )
      & ! [C] :
          ( ( leq(n0,C)
            & leq(C,n4) )
         => a_select2(rho_init,C) = init )
      & ! [D] :
          ( ( leq(n0,D)
            & leq(D,n4) )
         => a_select3(center_init,D,n0) = init )
      & ( gt(loopcounter,n1)
       => ! [E] :
            ( ( leq(n0,E)
              & leq(E,n4) )
           => a_select2(muold_init,E) = init ) )
      & ( gt(loopcounter,n1)
       => ! [F] :
            ( ( leq(n0,F)
              & leq(F,n4) )
           => a_select2(rhoold_init,F) = init ) )
      & ( gt(loopcounter,n1)
       => ! [G] :
            ( ( leq(n0,G)
              & leq(G,n4) )
           => a_select2(sigmaold_init,G) = init ) ) )
   => ! [H] :
        ( ( leq(n0,H)
          & leq(H,tptp_minus_1) )
       => a_select2(mu_init,H) = init ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ( ( ! [A] :
            ( ( leq(n0,A)
              & leq(A,n135299) )
           => ! [B] :
                ( ( leq(n0,B)
                  & leq(B,n4) )
               => a_select3(q_init,A,B) = init ) )
        & ! [C] :
            ( ( leq(n0,C)
              & leq(C,n4) )
           => a_select2(rho_init,C) = init )
        & ! [D] :
            ( ( leq(n0,D)
              & leq(D,n4) )
           => a_select3(center_init,D,n0) = init )
        & ( gt(loopcounter,n1)
         => ! [E] :
              ( ( leq(n0,E)
                & leq(E,n4) )
             => a_select2(muold_init,E) = init ) )
        & ( gt(loopcounter,n1)
         => ! [F] :
              ( ( leq(n0,F)
                & leq(F,n4) )
             => a_select2(rhoold_init,F) = init ) )
        & ( gt(loopcounter,n1)
         => ! [G] :
              ( ( leq(n0,G)
                & leq(G,n4) )
             => a_select2(sigmaold_init,G) = init ) ) )
     => ! [H] :
          ( ( leq(n0,H)
            & leq(H,tptp_minus_1) )
         => a_select2(mu_init,H) = init ) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f98,plain,
    ! [X0] : ~ gt(X0,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f100,plain,
    ! [X,Y,Z] :
      ( ~ leq(X,Y)
      | ~ leq(Y,Z)
      | leq(X,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f101,plain,
    ! [X,Z] :
      ( ! [Y] :
          ( ~ leq(X,Y)
          | ~ leq(Y,Z) )
      | leq(X,Z) ),
    inference(miniscoping,[status(esa)],[f100]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ~ leq(X0,X1)
      | ~ leq(X1,X2)
      | leq(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f101]) ).

fof(f122,plain,
    ! [X,Y] :
      ( ( ~ leq(X,Y)
        | gt(succ(Y),X) )
      & ( leq(X,Y)
        | ~ gt(succ(Y),X) ) ),
    inference(NNF_transformation,[status(esa)],[f13]) ).

fof(f123,plain,
    ( ! [X,Y] :
        ( ~ leq(X,Y)
        | gt(succ(Y),X) )
    & ! [X,Y] :
        ( leq(X,Y)
        | ~ gt(succ(Y),X) ) ),
    inference(miniscoping,[status(esa)],[f122]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | gt(succ(X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f206,plain,
    succ(tptp_minus_1) = n0,
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f251,plain,
    ( ! [A] :
        ( ~ leq(n0,A)
        | ~ leq(A,n135299)
        | ! [B] :
            ( ~ leq(n0,B)
            | ~ leq(B,n4)
            | a_select3(q_init,A,B) = init ) )
    & ! [C] :
        ( ~ leq(n0,C)
        | ~ leq(C,n4)
        | a_select2(rho_init,C) = init )
    & ! [D] :
        ( ~ leq(n0,D)
        | ~ leq(D,n4)
        | a_select3(center_init,D,n0) = init )
    & ( ~ gt(loopcounter,n1)
      | ! [E] :
          ( ~ leq(n0,E)
          | ~ leq(E,n4)
          | a_select2(muold_init,E) = init ) )
    & ( ~ gt(loopcounter,n1)
      | ! [F] :
          ( ~ leq(n0,F)
          | ~ leq(F,n4)
          | a_select2(rhoold_init,F) = init ) )
    & ( ~ gt(loopcounter,n1)
      | ! [G] :
          ( ~ leq(n0,G)
          | ~ leq(G,n4)
          | a_select2(sigmaold_init,G) = init ) )
    & ? [H] :
        ( leq(n0,H)
        & leq(H,tptp_minus_1)
        & a_select2(mu_init,H) != init ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f252,plain,
    ( ! [A] :
        ( ~ leq(n0,A)
        | ~ leq(A,n135299)
        | ! [B] :
            ( ~ leq(n0,B)
            | ~ leq(B,n4)
            | a_select3(q_init,A,B) = init ) )
    & ! [C] :
        ( ~ leq(n0,C)
        | ~ leq(C,n4)
        | a_select2(rho_init,C) = init )
    & ! [D] :
        ( ~ leq(n0,D)
        | ~ leq(D,n4)
        | a_select3(center_init,D,n0) = init )
    & ( ~ gt(loopcounter,n1)
      | ! [E] :
          ( ~ leq(n0,E)
          | ~ leq(E,n4)
          | a_select2(muold_init,E) = init ) )
    & ( ~ gt(loopcounter,n1)
      | ! [F] :
          ( ~ leq(n0,F)
          | ~ leq(F,n4)
          | a_select2(rhoold_init,F) = init ) )
    & ( ~ gt(loopcounter,n1)
      | ! [G] :
          ( ~ leq(n0,G)
          | ~ leq(G,n4)
          | a_select2(sigmaold_init,G) = init ) )
    & leq(n0,sk0_23)
    & leq(sk0_23,tptp_minus_1)
    & a_select2(mu_init,sk0_23) != init ),
    inference(skolemization,[status(esa)],[f251]) ).

fof(f259,plain,
    leq(n0,sk0_23),
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f260,plain,
    leq(sk0_23,tptp_minus_1),
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f417,plain,
    ! [X0] :
      ( ~ leq(sk0_23,X0)
      | leq(n0,X0) ),
    inference(resolution,[status(thm)],[f102,f259]) ).

fof(f636,plain,
    leq(n0,tptp_minus_1),
    inference(resolution,[status(thm)],[f417,f260]) ).

fof(f737,plain,
    gt(succ(tptp_minus_1),n0),
    inference(resolution,[status(thm)],[f124,f636]) ).

fof(f738,plain,
    gt(n0,n0),
    inference(forward_demodulation,[status(thm)],[f206,f737]) ).

fof(f739,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f738,f98]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n015.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 : Tue Apr 30 01:00:17 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.029829 seconds
% 0.13/0.38  % CPU time: 0.066964 seconds
% 0.13/0.38  % Total memory used: 16.820 MB
% 0.13/0.38  % Net memory used: 16.671 MB
%------------------------------------------------------------------------------