%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 12:40:48 EDT 2023

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (  12 unt;   0 def)
%            Number of atoms       :   72 (  12 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   70 (  24   ~;  17   |;  21   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-3 aty)
%            Number of variables   :   37 (;  36   !;   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(f10,axiom,
    ! [X,Y] :
      ( leq(X,pred(Y))
    <=> gt(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(f40,axiom,
    ! [X] : pred(succ(X)) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f53,conjecture,
    ( ( leq(n0,pv10)
      & leq(pv10,n135299)
      & ! [A] :
          ( ( leq(n0,A)
            & leq(A,pred(pv10)) )
         => sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
   => ! [B] :
        ( ( leq(n0,B)
          & leq(B,tptp_minus_1) )
       => a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ( ( leq(n0,pv10)
        & leq(pv10,n135299)
        & ! [A] :
            ( ( leq(n0,A)
              & leq(A,pred(pv10)) )
           => sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
     => ! [B] :
          ( ( leq(n0,B)
            & leq(B,tptp_minus_1) )
         => a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
    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(f115,plain,
    ! [X,Y] :
      ( ( ~ leq(X,pred(Y))
        | gt(Y,X) )
      & ( leq(X,pred(Y))
        | ~ gt(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f10]) ).

fof(f116,plain,
    ( ! [X,Y] :
        ( ~ leq(X,pred(Y))
        | gt(Y,X) )
    & ! [X,Y] :
        ( leq(X,pred(Y))
        | ~ gt(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f115]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ~ leq(X0,pred(X1))
      | gt(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f116]) ).

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

fof(f218,plain,
    ! [X0] : pred(succ(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f251,plain,
    ( leq(n0,pv10)
    & leq(pv10,n135299)
    & ! [A] :
        ( ~ leq(n0,A)
        | ~ leq(A,pred(pv10))
        | sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
    & ? [B] :
        ( leq(n0,B)
        & leq(B,tptp_minus_1)
        & a_select3(q,pv10,B) != divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f252,plain,
    ( leq(n0,pv10)
    & leq(pv10,n135299)
    & ! [A] :
        ( ~ leq(n0,A)
        | ~ leq(A,pred(pv10))
        | sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
    & leq(n0,sk0_23)
    & leq(sk0_23,tptp_minus_1)
    & a_select3(q,pv10,sk0_23) != divide(sqrt(times(minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)),minus(a_select3(center,sk0_23,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
    inference(skolemization,[status(esa)],[f251]) ).

fof(f256,plain,
    leq(n0,sk0_23),
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f257,plain,
    leq(sk0_23,tptp_minus_1),
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f334,plain,
    ! [X0] :
      ( ~ leq(X0,sk0_23)
      | leq(X0,tptp_minus_1) ),
    inference(resolution,[status(thm)],[f102,f257]) ).

fof(f339,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | gt(succ(X1),X0) ),
    inference(paramodulation,[status(thm)],[f218,f117]) ).

fof(f361,plain,
    leq(n0,tptp_minus_1),
    inference(resolution,[status(thm)],[f334,f256]) ).

fof(f390,plain,
    ! [X0] : ~ leq(succ(X0),X0),
    inference(resolution,[status(thm)],[f339,f98]) ).

fof(f398,plain,
    ~ leq(n0,tptp_minus_1),
    inference(paramodulation,[status(thm)],[f206,f390]) ).

fof(f399,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f398,f361]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % 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 May 30 11:31:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 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
% 0.21/0.62  % Elapsed time: 0.069021 seconds
% 0.21/0.62  % CPU time: 0.033823 seconds
% 0.21/0.62  % Memory used: 4.082 MB
%------------------------------------------------------------------------------