TSTP Solution File: SWW391+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWW391+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 20:50:11 EDT 2024

% Result   : Theorem 23.67s 3.75s
% Output   : CNFRefutation 24.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (  11 unt;   0 def)
%            Number of atoms       :   81 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   82 (  35   ~;  28   |;  10   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;  10 con; 0-2 aty)
%            Number of variables   :   52 (  45   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5228,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5229,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P_H),v_c),v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5230,conjecture,
    ! [B_Z,B_s] :
      ( ( hBOOL(hAPP(hAPP(v_P,B_Z),B_s))
        | hBOOL(hAPP(hAPP(v_P_H,B_Z),B_s)) )
     => ? [B_P_H,B_Q_H] :
          ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
          & ! [B_s_H] :
              ( ! [B_Z_H] :
                  ( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
                 => hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
             => ( hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H))
                | hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s_H)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5231,negated_conjecture,
    ~ ! [B_Z,B_s] :
        ( ( hBOOL(hAPP(hAPP(v_P,B_Z),B_s))
          | hBOOL(hAPP(hAPP(v_P_H,B_Z),B_s)) )
       => ? [B_P_H,B_Q_H] :
            ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
            & ! [B_s_H] :
                ( ! [B_Z_H] :
                    ( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
                   => hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
               => ( hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H))
                  | hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s_H)) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f5230]) ).

fof(f5249,plain,
    ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
      | ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f5250,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),X3))
      | c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)))) ),
    inference(cnf_transformation,[status(esa)],[f5249]) ).

fof(f20072,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(cnf_transformation,[status(esa)],[f5228]) ).

fof(f20073,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P_H),v_c),v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(cnf_transformation,[status(esa)],[f5229]) ).

fof(f20074,plain,
    ? [B_Z,B_s] :
      ( ( hBOOL(hAPP(hAPP(v_P,B_Z),B_s))
        | hBOOL(hAPP(hAPP(v_P_H,B_Z),B_s)) )
      & ! [B_P_H,B_Q_H] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
          | ? [B_s_H] :
              ( ! [B_Z_H] :
                  ( ~ hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
                  | hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
              & ~ hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H))
              & ~ hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s_H)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5231]) ).

fof(f20075,plain,
    ( ( hBOOL(hAPP(hAPP(v_P,sk0_577),sk0_578))
      | hBOOL(hAPP(hAPP(v_P_H,sk0_577),sk0_578)) )
    & ! [B_P_H,B_Q_H] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
        | ( ! [B_Z_H] :
              ( ~ hBOOL(hAPP(hAPP(B_P_H,B_Z_H),sk0_578))
              | hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),sk0_579(B_Q_H,B_P_H))) )
          & ~ hBOOL(hAPP(hAPP(v_Q,sk0_577),sk0_579(B_Q_H,B_P_H)))
          & ~ hBOOL(hAPP(hAPP(v_Q_H,sk0_577),sk0_579(B_Q_H,B_P_H))) ) ) ),
    inference(skolemization,[status(esa)],[f20074]) ).

fof(f20076,plain,
    ( hBOOL(hAPP(hAPP(v_P,sk0_577),sk0_578))
    | hBOOL(hAPP(hAPP(v_P_H,sk0_577),sk0_578)) ),
    inference(cnf_transformation,[status(esa)],[f20075]) ).

fof(f20077,plain,
    ! [X0,X1,X2] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(X0,X2),sk0_578))
      | hBOOL(hAPP(hAPP(X1,X2),sk0_579(X1,X0))) ),
    inference(cnf_transformation,[status(esa)],[f20075]) ).

fof(f20078,plain,
    ! [X0,X1] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(v_Q,sk0_577),sk0_579(X1,X0))) ),
    inference(cnf_transformation,[status(esa)],[f20075]) ).

fof(f20079,plain,
    ! [X0,X1] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(v_Q_H,sk0_577),sk0_579(X1,X0))) ),
    inference(cnf_transformation,[status(esa)],[f20075]) ).

fof(f20358,plain,
    ( spl0_8
  <=> hBOOL(hAPP(hAPP(v_P,sk0_577),sk0_578)) ),
    introduced(split_symbol_definition) ).

fof(f20359,plain,
    ( hBOOL(hAPP(hAPP(v_P,sk0_577),sk0_578))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f20358]) ).

fof(f20361,plain,
    ( spl0_9
  <=> hBOOL(hAPP(hAPP(v_P_H,sk0_577),sk0_578)) ),
    introduced(split_symbol_definition) ).

fof(f20362,plain,
    ( hBOOL(hAPP(hAPP(v_P_H,sk0_577),sk0_578))
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f20361]) ).

fof(f20364,plain,
    ( spl0_8
    | spl0_9 ),
    inference(split_clause,[status(thm)],[f20076,f20358,f20361]) ).

fof(f20861,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),X2))
      | ~ hBOOL(hAPP(hAPP(X0,X3),sk0_578))
      | hBOOL(hAPP(hAPP(X1,X3),sk0_579(X1,X0))) ),
    inference(resolution,[status(thm)],[f5250,f20077]) ).

fof(f20862,plain,
    ! [X0,X1,X2] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),X2))
      | ~ hBOOL(hAPP(hAPP(v_Q_H,sk0_577),sk0_579(X1,X0))) ),
    inference(resolution,[status(thm)],[f5250,f20079]) ).

fof(f20863,plain,
    ! [X0,X1,X2] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),X2))
      | ~ hBOOL(hAPP(hAPP(v_Q,sk0_577),sk0_579(X1,X0))) ),
    inference(resolution,[status(thm)],[f5250,f20078]) ).

fof(f27881,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(hAPP(v_P,X0),sk0_578))
      | hBOOL(hAPP(hAPP(v_Q,X0),sk0_579(v_Q,v_P))) ),
    inference(resolution,[status(thm)],[f20072,f20861]) ).

fof(f27882,plain,
    ~ hBOOL(hAPP(hAPP(v_Q,sk0_577),sk0_579(v_Q,v_P))),
    inference(resolution,[status(thm)],[f20072,f20863]) ).

fof(f27940,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(hAPP(v_P_H,X0),sk0_578))
      | hBOOL(hAPP(hAPP(v_Q_H,X0),sk0_579(v_Q_H,v_P_H))) ),
    inference(resolution,[status(thm)],[f20073,f20861]) ).

fof(f27942,plain,
    ~ hBOOL(hAPP(hAPP(v_Q_H,sk0_577),sk0_579(v_Q_H,v_P_H))),
    inference(resolution,[status(thm)],[f20073,f20862]) ).

fof(f28192,plain,
    ~ hBOOL(hAPP(hAPP(v_P,sk0_577),sk0_578)),
    inference(resolution,[status(thm)],[f27881,f27882]) ).

fof(f28200,plain,
    ~ hBOOL(hAPP(hAPP(v_P_H,sk0_577),sk0_578)),
    inference(resolution,[status(thm)],[f27940,f27942]) ).

fof(f28201,plain,
    ( $false
    | ~ spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f28200,f20362]) ).

fof(f28202,plain,
    ~ spl0_9,
    inference(contradiction_clause,[status(thm)],[f28201]) ).

fof(f28203,plain,
    ( $false
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f20359,f28192]) ).

fof(f28204,plain,
    ~ spl0_8,
    inference(contradiction_clause,[status(thm)],[f28203]) ).

fof(f28205,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f20364,f28202,f28204]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14  % Problem  : SWW391+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.15  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.37  % Computer : n016.cluster.edu
% 0.12/0.37  % Model    : x86_64 x86_64
% 0.12/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37  % Memory   : 8042.1875MB
% 0.12/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37  % CPULimit : 300
% 0.12/0.37  % WCLimit  : 300
% 0.12/0.37  % DateTime : Mon Apr 29 23:44:25 EDT 2024
% 0.12/0.37  % CPUTime  : 
% 0.57/0.79  % Drodi V3.6.0
% 23.67/3.75  % Refutation found
% 23.67/3.75  % SZS status Theorem for theBenchmark: Theorem is valid
% 23.67/3.75  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.86/3.93  % Elapsed time: 3.545715 seconds
% 24.86/3.93  % CPU time: 24.380200 seconds
% 24.86/3.93  % Total memory used: 826.312 MB
% 24.86/3.93  % Net memory used: 823.497 MB
%------------------------------------------------------------------------------