TSTP Solution File: SWV159+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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 : Thu Aug 31 22:31:23 EDT 2023

% Result   : Theorem 0.46s 1.15s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (  10 unt;   0 def)
%            Number of atoms       :  134 (  47 equ)
%            Maximal formula atoms :   15 (   6 avg)
%            Number of connectives :  154 (  42   ~;  23   |;  73   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  17 con; 0-3 aty)
%            Number of variables   :   26 (   0 sgn;  21   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f39,axiom,
    ! [X0] : minus(X0,n1) = pred(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).

fof(f53,conjecture,
    ( ( ! [X17] :
          ( ( leq(X17,pred(pv10))
            & leq(n0,X17) )
         => n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
      & ! [X13] :
          ( ( leq(X13,pred(pv47))
            & leq(n0,X13) )
         => a_select3(q,pv10,X13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X13)),minus(a_select2(x,pv10),a_select2(mu,X13))),tptp_minus_2),times(a_select2(sigma,X13),a_select2(sigma,X13)))),a_select2(rho,X13)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X13))),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(pv47,n4)
      & leq(pv10,n135299)
      & leq(n0,pv47)
      & leq(n0,pv10)
      & 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)))) )
   => ! [X3] :
        ( ( leq(X3,pred(pv10))
          & leq(n0,X3) )
       => ( pv10 != X3
         => n1 = sum(n0,n4,a_select3(q,X3,tptp_sum_index)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0009) ).

fof(f54,negated_conjecture,
    ~ ( ( ! [X17] :
            ( ( leq(X17,pred(pv10))
              & leq(n0,X17) )
           => n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
        & ! [X13] :
            ( ( leq(X13,pred(pv47))
              & leq(n0,X13) )
           => a_select3(q,pv10,X13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X13)),minus(a_select2(x,pv10),a_select2(mu,X13))),tptp_minus_2),times(a_select2(sigma,X13),a_select2(sigma,X13)))),a_select2(rho,X13)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X13))),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(pv47,n4)
        & leq(pv10,n135299)
        & leq(n0,pv47)
        & leq(n0,pv10)
        & 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)))) )
     => ! [X3] :
          ( ( leq(X3,pred(pv10))
            & leq(n0,X3) )
         => ( pv10 != X3
           => n1 = sum(n0,n4,a_select3(q,X3,tptp_sum_index)) ) ) ),
    inference(negated_conjecture,[],[f53]) ).

fof(f122,plain,
    ~ ( ( ! [X0] :
            ( ( leq(X0,pred(pv10))
              & leq(n0,X0) )
           => n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index)) )
        & ! [X1] :
            ( ( leq(X1,pred(pv47))
              & leq(n0,X1) )
           => a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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(pv47,n4)
        & leq(pv10,n135299)
        & leq(n0,pv47)
        & leq(n0,pv10)
        & 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)))) )
     => ! [X2] :
          ( ( leq(X2,pred(pv10))
            & leq(n0,X2) )
         => ( pv10 != X2
           => n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index)) ) ) ),
    inference(rectify,[],[f54]) ).

fof(f164,plain,
    ( ? [X2] :
        ( n1 != sum(n0,n4,a_select3(q,X2,tptp_sum_index))
        & pv10 != X2
        & leq(X2,pred(pv10))
        & leq(n0,X2) )
    & ! [X0] :
        ( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
        | ~ leq(X0,pred(pv10))
        | ~ leq(n0,X0) )
    & ! [X1] :
        ( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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(X1,pred(pv47))
        | ~ leq(n0,X1) )
    & leq(pv47,n4)
    & leq(pv10,n135299)
    & leq(n0,pv47)
    & leq(n0,pv10)
    & 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)))) ),
    inference(ennf_transformation,[],[f122]) ).

fof(f165,plain,
    ( ? [X2] :
        ( n1 != sum(n0,n4,a_select3(q,X2,tptp_sum_index))
        & pv10 != X2
        & leq(X2,pred(pv10))
        & leq(n0,X2) )
    & ! [X0] :
        ( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
        | ~ leq(X0,pred(pv10))
        | ~ leq(n0,X0) )
    & ! [X1] :
        ( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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(X1,pred(pv47))
        | ~ leq(n0,X1) )
    & leq(pv47,n4)
    & leq(pv10,n135299)
    & leq(n0,pv47)
    & leq(n0,pv10)
    & 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)))) ),
    inference(flattening,[],[f164]) ).

fof(f232,plain,
    ( ? [X0] :
        ( n1 != sum(n0,n4,a_select3(q,X0,tptp_sum_index))
        & pv10 != X0
        & leq(X0,pred(pv10))
        & leq(n0,X0) )
    & ! [X1] :
        ( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
        | ~ leq(X1,pred(pv10))
        | ~ leq(n0,X1) )
    & ! [X2] :
        ( a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(X2,pred(pv47))
        | ~ leq(n0,X2) )
    & leq(pv47,n4)
    & leq(pv10,n135299)
    & leq(n0,pv47)
    & leq(n0,pv10)
    & 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)))) ),
    inference(rectify,[],[f165]) ).

fof(f233,plain,
    ( ? [X0] :
        ( n1 != sum(n0,n4,a_select3(q,X0,tptp_sum_index))
        & pv10 != X0
        & leq(X0,pred(pv10))
        & leq(n0,X0) )
   => ( n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index))
      & pv10 != sK31
      & leq(sK31,pred(pv10))
      & leq(n0,sK31) ) ),
    introduced(choice_axiom,[]) ).

fof(f234,plain,
    ( n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index))
    & pv10 != sK31
    & leq(sK31,pred(pv10))
    & leq(n0,sK31)
    & ! [X1] :
        ( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
        | ~ leq(X1,pred(pv10))
        | ~ leq(n0,X1) )
    & ! [X2] :
        ( a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(X2,pred(pv47))
        | ~ leq(n0,X2) )
    & leq(pv47,n4)
    & leq(pv10,n135299)
    & leq(n0,pv47)
    & leq(n0,pv10)
    & 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)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f232,f233]) ).

fof(f325,plain,
    ! [X0] : minus(X0,n1) = pred(X0),
    inference(cnf_transformation,[],[f39]) ).

fof(f351,plain,
    ! [X1] :
      ( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
      | ~ leq(X1,pred(pv10))
      | ~ leq(n0,X1) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f352,plain,
    leq(n0,sK31),
    inference(cnf_transformation,[],[f234]) ).

fof(f353,plain,
    leq(sK31,pred(pv10)),
    inference(cnf_transformation,[],[f234]) ).

fof(f355,plain,
    n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index)),
    inference(cnf_transformation,[],[f234]) ).

fof(f424,plain,
    leq(sK31,minus(pv10,n1)),
    inference(definition_unfolding,[],[f353,f325]) ).

fof(f425,plain,
    ! [X1] :
      ( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
      | ~ leq(X1,minus(pv10,n1))
      | ~ leq(n0,X1) ),
    inference(definition_unfolding,[],[f351,f325]) ).

cnf(c_157,negated_conjecture,
    sum(n0,n4,a_select3(q,sK31,tptp_sum_index)) != n1,
    inference(cnf_transformation,[],[f355]) ).

cnf(c_159,negated_conjecture,
    leq(sK31,minus(pv10,n1)),
    inference(cnf_transformation,[],[f424]) ).

cnf(c_160,negated_conjecture,
    leq(n0,sK31),
    inference(cnf_transformation,[],[f352]) ).

cnf(c_161,negated_conjecture,
    ( ~ leq(X0,minus(pv10,n1))
    | ~ leq(n0,X0)
    | sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ),
    inference(cnf_transformation,[],[f425]) ).

cnf(c_8977,plain,
    ( ~ leq(n0,sK31)
    | sum(n0,n4,a_select3(q,sK31,tptp_sum_index)) = n1 ),
    inference(superposition,[status(thm)],[c_159,c_161]) ).

cnf(c_8978,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_8977,c_157,c_160]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.33  % Computer : n003.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Tue Aug 29 10:23:40 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.46/1.15  % SZS status Started for theBenchmark.p
% 0.46/1.15  % SZS status Theorem for theBenchmark.p
% 0.46/1.15  
% 0.46/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.46/1.15  
% 0.46/1.15  ------  iProver source info
% 0.46/1.15  
% 0.46/1.15  git: date: 2023-05-31 18:12:56 +0000
% 0.46/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.46/1.15  git: non_committed_changes: false
% 0.46/1.15  git: last_make_outside_of_git: false
% 0.46/1.15  
% 0.46/1.15  ------ Parsing...
% 0.46/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... sup_sim: 17  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.15  ------ Proving...
% 0.46/1.15  ------ Problem Properties 
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  clauses                                 166
% 0.46/1.15  conjectures                             10
% 0.46/1.15  EPR                                     57
% 0.46/1.15  Horn                                    116
% 0.46/1.15  unary                                   70
% 0.46/1.15  binary                                  34
% 0.46/1.15  lits                                    509
% 0.46/1.15  lits eq                                 118
% 0.46/1.15  fd_pure                                 0
% 0.46/1.15  fd_pseudo                               0
% 0.46/1.15  fd_cond                                 6
% 0.46/1.15  fd_pseudo_cond                          4
% 0.46/1.15  AC symbols                              0
% 0.46/1.15  
% 0.46/1.15  ------ Schedule dynamic 5 is on 
% 0.46/1.15  
% 0.46/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  ------ 
% 0.46/1.15  Current options:
% 0.46/1.15  ------ 
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  ------ Proving...
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  % SZS status Theorem for theBenchmark.p
% 0.46/1.15  
% 0.46/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.15  
% 0.46/1.15  
%------------------------------------------------------------------------------