TSTP Solution File: SWW473+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 12:45:04 EDT 2023

% Result   : Theorem 2.00s 0.79s
% Output   : CNFRefutation 2.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  19 unt;   0 def)
%            Number of atoms       :   70 (   8 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   63 (  31   ~;  22   |;   5   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-2 aty)
%            Number of variables   :   71 (;  71   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f372,axiom,
    ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),A_1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f402,axiom,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f428,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f437,axiom,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f441,axiom,
    ! [F,A_3,B_6] : image_pname_a(F,insert_pname(A_3,B_6)) = insert_a(hAPP_pname_a(F,A_3),image_pname_a(F,B_6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f447,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f912,hypothesis,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f915,hypothesis,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f917,conjecture,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f918,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(negated_conjecture,[status(cth)],[f917]) ).

fof(f2061,plain,
    ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
    inference(cnf_transformation,[status(esa)],[f372]) ).

fof(f2144,plain,
    ! [C_6,A_1,B_6] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6)) ),
    inference(pre_NNF_transformation,[status(esa)],[f402]) ).

fof(f2145,plain,
    ! [A_1,B_6] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ! [C_6] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6)) ) ),
    inference(miniscoping,[status(esa)],[f2144]) ).

fof(f2146,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2)) ),
    inference(cnf_transformation,[status(esa)],[f2145]) ).

fof(f2213,plain,
    ! [X_3,A_1,B_6] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
        | ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) )
      & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ),
    inference(NNF_transformation,[status(esa)],[f428]) ).

fof(f2214,plain,
    ( ! [X_3,A_1,B_6] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
        | ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) )
    & ! [X_3,A_1,B_6] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ),
    inference(miniscoping,[status(esa)],[f2213]) ).

fof(f2216,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(cnf_transformation,[status(esa)],[f2214]) ).

fof(f2248,plain,
    ! [A_3,C_6,D_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))) ),
    inference(pre_NNF_transformation,[status(esa)],[f437]) ).

fof(f2249,plain,
    ! [C_6,D_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1))
      | ! [A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))) ),
    inference(miniscoping,[status(esa)],[f2248]) ).

fof(f2250,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X2,X0)),insert_a(X2,X1))) ),
    inference(cnf_transformation,[status(esa)],[f2249]) ).

fof(f2254,plain,
    ! [X0,X1,X2] : image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f441]) ).

fof(f2270,plain,
    ! [F,X_3,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1) ),
    inference(pre_NNF_transformation,[status(esa)],[f447]) ).

fof(f2271,plain,
    ! [X_3,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | ! [F] : insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1) ),
    inference(miniscoping,[status(esa)],[f2270]) ).

fof(f2272,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | insert_a(hAPP_pname_a(X2,X0),image_pname_a(X2,X1)) = image_pname_a(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f2271]) ).

fof(f3557,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[status(esa)],[f912]) ).

fof(f3560,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(cnf_transformation,[status(esa)],[f915]) ).

fof(f3562,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[status(esa)],[f918]) ).

fof(f3677,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | image_pname_a(X2,insert_pname(X0,X1)) = image_pname_a(X2,X1) ),
    inference(forward_demodulation,[status(thm)],[f2254,f2272]) ).

fof(f4161,plain,
    ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,g)),insert_a(X0,image_pname_a(mgt_call,u)))),
    inference(resolution,[status(thm)],[f2250,f3557]) ).

fof(f4869,plain,
    ! [X0] : image_pname_a(X0,insert_pname(pn,u)) = image_pname_a(X0,u),
    inference(resolution,[status(thm)],[f3677,f3560]) ).

fof(f5872,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(mgt_call,u))) ),
    inference(resolution,[status(thm)],[f2146,f3562]) ).

fof(f5942,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X0)),image_pname_a(mgt_call,u))) ),
    inference(resolution,[status(thm)],[f5872,f2216]) ).

fof(f6324,plain,
    ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,insert_a(hAPP_pname_a(mgt_call,pn),image_pname_a(mgt_call,u)))),image_pname_a(mgt_call,u))),
    inference(resolution,[status(thm)],[f5942,f4161]) ).

fof(f6325,plain,
    ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,image_pname_a(mgt_call,insert_pname(pn,u)))),image_pname_a(mgt_call,u))),
    inference(forward_demodulation,[status(thm)],[f2254,f6324]) ).

fof(f6326,plain,
    ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u))),
    inference(forward_demodulation,[status(thm)],[f4869,f6325]) ).

fof(f6340,plain,
    ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,insert_pname(X0,u))),image_pname_a(mgt_call,u))),
    inference(paramodulation,[status(thm)],[f2254,f6326]) ).

fof(f6343,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,u)),image_pname_a(mgt_call,u))),
    inference(paramodulation,[status(thm)],[f4869,f6340]) ).

fof(f6344,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f6343,f2061]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13  % Problem  : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% 0.05/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34  % Computer : n025.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit : 300
% 0.10/0.34  % WCLimit  : 300
% 0.10/0.34  % DateTime : Tue May 30 11:10:42 EDT 2023
% 0.10/0.34  % CPUTime  : 
% 0.15/0.39  % Drodi V3.5.1
% 2.00/0.79  % Refutation found
% 2.00/0.79  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.00/0.79  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.37/0.83  % Elapsed time: 0.486012 seconds
% 2.37/0.83  % CPU time: 2.476074 seconds
% 2.37/0.83  % Memory used: 146.521 MB
%------------------------------------------------------------------------------