TSTP Solution File: SWV160+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   15 (   7 unt;   0 def)
%            Number of atoms       :   79 (  21 equ)
%            Maximal formula atoms :   15 (   5 avg)
%            Number of connectives :   82 (  18   ~;  13   |;  40   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  17 con; 0-3 aty)
%            Number of variables   :   23 (  22   !;   1   ?)

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

fof(f10,axiom,
    ! [X,Y] :
      ( leq(X,pred(Y))
    <=> gt(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ),
    file('/export/starexec/sandbox/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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f106,plain,
    ! [X0] : ~ gt(X0,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f123,plain,
    ! [X,Y] :
      ( ( ~ leq(X,pred(Y))
        | gt(Y,X) )
      & ( leq(X,pred(Y))
        | ~ gt(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f10]) ).

fof(f124,plain,
    ( ! [X,Y] :
        ( ~ leq(X,pred(Y))
        | gt(Y,X) )
    & ! [X,Y] :
        ( leq(X,pred(Y))
        | ~ gt(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f123]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ leq(X0,pred(X1))
      | gt(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f124]) ).

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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,sk0_23,tptp_sum_index))) != n1 ),
    inference(skolemization,[status(esa)],[f259]) ).

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

fof(f270,plain,
    pv10 = sk0_23,
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f362,plain,
    leq(pv10,pred(pv10)),
    inference(forward_demodulation,[status(thm)],[f270,f269]) ).

fof(f363,plain,
    gt(pv10,pv10),
    inference(resolution,[status(thm)],[f362,f125]) ).

fof(f364,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f363,f106]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Apr 30 01:00:55 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37  % Elapsed time: 0.024328 seconds
% 0.12/0.37  % CPU time: 0.039387 seconds
% 0.12/0.37  % Total memory used: 14.573 MB
% 0.12/0.37  % Net memory used: 14.552 MB
%------------------------------------------------------------------------------