TSTP Solution File: SWV161+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWV161+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   58 (  19 unt;   0 def)
%            Number of atoms       :  134 (  28 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  121 (  45   ~;  37   |;  25   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-3 aty)
%            Number of variables   :   39 (  38   !;   1   ?)

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

fof(f8,axiom,
    ! [X,Y] :
      ( gt(Y,X)
     => leq(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( ( leq(X,Y)
        & X != Y )
     => gt(Y,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(f28,axiom,
    succ(tptp_minus_1) = n0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,axiom,
    ! [X] : pred(succ(X)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f53,conjecture,
    ( ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
      & 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,pv10) )
       => sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ( ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
        & 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,pv10) )
         => sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f68,axiom,
    gt(n1,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f111,plain,
    ! [X,Y] :
      ( ~ gt(Y,X)
      | leq(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ gt(X0,X1)
      | leq(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f111]) ).

fof(f113,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
      | X = Y
      | gt(Y,X) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | X0 = X1
      | gt(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f113]) ).

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(f118,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,
    ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
    & 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,pv10)
        & sum(n0,n4,a_select3(q,B,tptp_sum_index)) != n1 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f252,plain,
    ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
    & 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,pv10)
    & sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) != n1 ),
    inference(skolemization,[status(esa)],[f251]) ).

fof(f253,plain,
    sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1,
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f256,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)],[f252]) ).

fof(f257,plain,
    leq(n0,sk0_23),
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f258,plain,
    leq(sk0_23,pv10),
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f259,plain,
    sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) != n1,
    inference(cnf_transformation,[status(esa)],[f252]) ).

fof(f273,plain,
    gt(n1,n0),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | gt(succ(X1),X0) ),
    inference(paramodulation,[status(thm)],[f218,f117]) ).

fof(f380,plain,
    ( spl0_3
  <=> leq(n0,sk0_23) ),
    introduced(split_symbol_definition) ).

fof(f382,plain,
    ( ~ leq(n0,sk0_23)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f380]) ).

fof(f383,plain,
    ( spl0_4
  <=> leq(sk0_23,pred(pv10)) ),
    introduced(split_symbol_definition) ).

fof(f385,plain,
    ( ~ leq(sk0_23,pred(pv10))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f383]) ).

fof(f386,plain,
    ( ~ leq(n0,sk0_23)
    | ~ leq(sk0_23,pred(pv10)) ),
    inference(resolution,[status(thm)],[f259,f256]) ).

fof(f387,plain,
    ( ~ spl0_3
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f386,f380,f383]) ).

fof(f388,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f382,f257]) ).

fof(f389,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f388]) ).

fof(f409,plain,
    ( spl0_6
  <=> sk0_23 = pv10 ),
    introduced(split_symbol_definition) ).

fof(f410,plain,
    ( sk0_23 = pv10
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f409]) ).

fof(f608,plain,
    ! [X0] : ~ leq(succ(X0),X0),
    inference(resolution,[status(thm)],[f350,f98]) ).

fof(f650,plain,
    ~ leq(n0,tptp_minus_1),
    inference(paramodulation,[status(thm)],[f206,f608]) ).

fof(f822,plain,
    leq(n0,n1),
    inference(resolution,[status(thm)],[f112,f273]) ).

fof(f1066,plain,
    ( spl0_56
  <=> gt(pv10,sk0_23) ),
    introduced(split_symbol_definition) ).

fof(f1067,plain,
    ( gt(pv10,sk0_23)
    | ~ spl0_56 ),
    inference(component_clause,[status(thm)],[f1066]) ).

fof(f1069,plain,
    ( sk0_23 = pv10
    | gt(pv10,sk0_23) ),
    inference(resolution,[status(thm)],[f258,f114]) ).

fof(f1070,plain,
    ( spl0_6
    | spl0_56 ),
    inference(split_clause,[status(thm)],[f1069,f409,f1066]) ).

fof(f1380,plain,
    ( spl0_111
  <=> tptp_minus_1 = n1 ),
    introduced(split_symbol_definition) ).

fof(f1381,plain,
    ( tptp_minus_1 = n1
    | ~ spl0_111 ),
    inference(component_clause,[status(thm)],[f1380]) ).

fof(f1729,plain,
    ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) != n1
    | ~ spl0_6 ),
    inference(forward_demodulation,[status(thm)],[f410,f259]) ).

fof(f1886,plain,
    ( leq(n0,tptp_minus_1)
    | ~ spl0_111 ),
    inference(backward_demodulation,[status(thm)],[f1381,f822]) ).

fof(f2201,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f253,f1729]) ).

fof(f2202,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f2201]) ).

fof(f2299,plain,
    ( $false
    | ~ spl0_111 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1886,f650]) ).

fof(f2300,plain,
    ~ spl0_111,
    inference(contradiction_clause,[status(thm)],[f2299]) ).

fof(f2331,plain,
    ( ~ gt(pv10,sk0_23)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f385,f118]) ).

fof(f2332,plain,
    ( $false
    | ~ spl0_56
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2331,f1067]) ).

fof(f2333,plain,
    ( ~ spl0_56
    | spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f2332]) ).

fof(f2334,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f387,f389,f1070,f2202,f2300,f2333]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWV161+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n014.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 00:50:04 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % Drodi V3.6.0
% 0.20/0.50  % Refutation found
% 0.20/0.50  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.50  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.51  % Elapsed time: 0.162606 seconds
% 0.20/0.51  % CPU time: 1.168557 seconds
% 0.20/0.51  % Total memory used: 74.592 MB
% 0.20/0.51  % Net memory used: 73.744 MB
%------------------------------------------------------------------------------