TSTP Solution File: SWV159+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 20:46:08 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   6 unt;   0 def)
%            Number of atoms       :   85 (  25 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :   90 (  24   ~;  16   |;  38   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  17 con; 0-3 aty)
%            Number of variables   :   12 (  11   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f53,conjecture,
    ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
      & leq(n0,pv10)
      & leq(n0,pv47)
      & leq(pv10,n135299)
      & leq(pv47,n4)
      & ! [A] :
          ( ( leq(n0,A)
            & leq(A,pred(pv47)) )
         => a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
      & ! [B] :
          ( ( leq(n0,B)
            & leq(B,pred(pv10)) )
         => sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
   => ! [C] :
        ( ( leq(n0,C)
          & leq(C,pred(pv10)) )
       => ( pv10 != C
         => sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
        & leq(n0,pv10)
        & leq(n0,pv47)
        & leq(pv10,n135299)
        & leq(pv47,n4)
        & ! [A] :
            ( ( leq(n0,A)
              & leq(A,pred(pv47)) )
           => a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
        & ! [B] :
            ( ( leq(n0,B)
              & leq(B,pred(pv10)) )
           => sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
     => ! [C] :
          ( ( leq(n0,C)
            & leq(C,pred(pv10)) )
         => ( pv10 != C
           => sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f259,plain,
    ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
    & leq(n0,pv10)
    & leq(n0,pv47)
    & leq(pv10,n135299)
    & leq(pv47,n4)
    & ! [A] :
        ( ~ leq(n0,A)
        | ~ leq(A,pred(pv47))
        | a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
    & ! [B] :
        ( ~ leq(n0,B)
        | ~ leq(B,pred(pv10))
        | sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
    & ? [C] :
        ( leq(n0,C)
        & leq(C,pred(pv10))
        & pv10 != C
        & sum(n0,n4,a_select3(q,C,tptp_sum_index)) != n1 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f260,plain,
    ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
    & leq(n0,pv10)
    & leq(n0,pv47)
    & leq(pv10,n135299)
    & leq(pv47,n4)
    & ! [A] :
        ( ~ leq(n0,A)
        | ~ leq(A,pred(pv47))
        | a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
    & ! [B] :
        ( ~ leq(n0,B)
        | ~ leq(B,pred(pv10))
        | sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
    & leq(n0,sk0_23)
    & leq(sk0_23,pred(pv10))
    & pv10 != sk0_23
    & sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) != n1 ),
    inference(skolemization,[status(esa)],[f259]) ).

fof(f267,plain,
    ! [X0] :
      ( ~ leq(n0,X0)
      | ~ leq(X0,pred(pv10))
      | sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ),
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f268,plain,
    leq(n0,sk0_23),
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f269,plain,
    leq(sk0_23,pred(pv10)),
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f271,plain,
    sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) != n1,
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f362,plain,
    ( spl0_0
  <=> leq(n0,sk0_23) ),
    introduced(split_symbol_definition) ).

fof(f364,plain,
    ( ~ leq(n0,sk0_23)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f362]) ).

fof(f365,plain,
    ( spl0_1
  <=> sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) = n1 ),
    introduced(split_symbol_definition) ).

fof(f366,plain,
    ( sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) = n1
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f365]) ).

fof(f368,plain,
    ( ~ leq(n0,sk0_23)
    | sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) = n1 ),
    inference(resolution,[status(thm)],[f267,f269]) ).

fof(f369,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f368,f362,f365]) ).

fof(f379,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f364,f268]) ).

fof(f380,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f379]) ).

fof(f381,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f366,f271]) ).

fof(f382,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f381]) ).

fof(f383,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f369,f380,f382]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue Apr 30 01:16:49 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.11/0.35  % Refutation found
% 0.11/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37  % Elapsed time: 0.027330 seconds
% 0.16/0.37  % CPU time: 0.036419 seconds
% 0.16/0.37  % Total memory used: 14.620 MB
% 0.16/0.37  % Net memory used: 14.598 MB
%------------------------------------------------------------------------------