TSTP Solution File: SWW293+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWW293+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 20:49:58 EDT 2024

% Result   : Theorem 28.70s 4.39s
% Output   : CNFRefutation 29.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   18 (   8 unt;   0 def)
%            Number of atoms       :   53 (   7 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   58 (  23   ~;  18   |;  11   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :   17 (  17 usr;   9 con; 0-4 aty)
%            Number of variables   :   81 (  74   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
    <=> ! [B_Z,B_s] :
          ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
         => ! [B_s_H] :
              ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
             => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f191,axiom,
    ! [V_s1,V_n,V_s,V_P] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
     => ~ ! [B_n] :
            ( V_n = hAPP(c_Nat_OSuc,B_n)
           => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f202,axiom,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5205,conjecture,
    c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5206,negated_conjecture,
    ~ c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
    inference(negated_conjecture,[status(cth)],[f5205]) ).

fof(f5229,plain,
    ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
    <=> ! [B_Z,B_s] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
          | ! [B_s_H] :
              ( ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
              | hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f5230,plain,
    ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
      ( ( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
        | ! [B_Z,B_s] :
            ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
            | ! [B_s_H] :
                ( ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
                | hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) )
      & ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
        | ? [B_Z,B_s] :
            ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
            & ? [B_s_H] :
                ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
                & ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5229]) ).

fof(f5231,plain,
    ( ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
        ( ! [T_b] : ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
        | ! [B_Z,B_s] :
            ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
            | ! [B_s_H] :
                ( ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
                | hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) )
    & ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
        ( ! [T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
        | ? [B_Z,B_s] :
            ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
            & ? [B_s_H] :
                ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
                & ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ) ),
    inference(miniscoping,[status(esa)],[f5230]) ).

fof(f5232,plain,
    ( ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
        ( ! [T_b] : ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
        | ! [B_Z,B_s] :
            ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
            | ! [B_s_H] :
                ( ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
                | hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) )
    & ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
        ( ! [T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
        | ( hBOOL(hAPP(hAPP(V_Pa_2,sk0_1(V_n_2,V_Pa_2,V_c_2,V_Qa_2)),sk0_2(V_n_2,V_Pa_2,V_c_2,V_Qa_2)))
          & c_Natural_Oevaln(V_c_2,sk0_2(V_n_2,V_Pa_2,V_c_2,V_Qa_2),V_n_2,sk0_3(V_n_2,V_Pa_2,V_c_2,V_Qa_2))
          & ~ hBOOL(hAPP(hAPP(V_Qa_2,sk0_1(V_n_2,V_Pa_2,V_c_2,V_Qa_2)),sk0_3(V_n_2,V_Pa_2,V_c_2,V_Qa_2))) ) ) ),
    inference(skolemization,[status(esa)],[f5231]) ).

fof(f5235,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_Hoare__Mirabelle_Otriple__valid(X0,X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),X3),X4))
      | c_Natural_Oevaln(X3,sk0_2(X1,X2,X3,X4),X1,sk0_3(X1,X2,X3,X4)) ),
    inference(cnf_transformation,[status(esa)],[f5232]) ).

fof(f5669,plain,
    ! [V_s1,V_n,V_s,V_P] :
      ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
      | ? [B_n] :
          ( V_n = hAPP(c_Nat_OSuc,B_n)
          & c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f191]) ).

fof(f5670,plain,
    ! [V_s1,V_n,V_s,V_P] :
      ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
      | ( V_n = hAPP(c_Nat_OSuc,sk0_26(V_P,V_s,V_n,V_s1))
        & c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,sk0_26(V_P,V_s,V_n,V_s1),V_s1) ) ),
    inference(skolemization,[status(esa)],[f5669]) ).

fof(f5671,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X0),X1,X2,X3)
      | X2 = hAPP(c_Nat_OSuc,sk0_26(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f5670]) ).

fof(f5696,plain,
    ! [X0] : hAPP(c_Nat_OSuc,X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[status(esa)],[f202]) ).

fof(f19790,plain,
    ~ c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
    inference(cnf_transformation,[status(esa)],[f5206]) ).

fof(f20564,plain,
    c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sk0_2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sk0_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q)),
    inference(resolution,[status(thm)],[f5235,f19790]) ).

fof(f29534,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc,sk0_26(v_pn,sk0_2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sk0_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q))),
    inference(resolution,[status(thm)],[f5671,f20564]) ).

fof(f29535,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f29534,f5696]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWW293+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon Apr 29 23:20:59 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.58/0.78  % Drodi V3.6.0
% 28.70/4.39  % Refutation found
% 28.70/4.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 28.70/4.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.24/4.57  % Elapsed time: 4.208848 seconds
% 30.24/4.57  % CPU time: 29.632240 seconds
% 30.24/4.57  % Total memory used: 1.135 GB
% 30.24/4.57  % Net memory used: 1.129 GB
%------------------------------------------------------------------------------