TSTP Solution File: SWV906-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV906-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 Sep 29 15:24:55 EDT 2022

% Result   : Unsatisfiable 0.19s 0.53s
% Output   : Proof 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   70 (  19 unt;  19 typ;   0 def)
%            Number of atoms       :  237 (  47 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  256 ( 111   ~; 108   |;   0   &)
%                                         (  37 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of FOOLs       :   41 (  41 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  11 usr;   4 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   8 con; 0-3 aty)
%            Number of variables   :   54 (  48   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_Option_Ooption_OSome_type,type,
    c_Option_Ooption_OSome: ( $i * $i ) > $i ).

tff(tc_Com_Ocom_type,type,
    tc_Com_Ocom: $i ).

tff(v_y_type,type,
    v_y: $i ).

tff(c_Option_Ooption_ONone_type,type,
    c_Option_Ooption_ONone: $i > $i ).

tff(hAPP_type,type,
    hAPP: ( $i * $i ) > $i ).

tff(v_pn_type,type,
    v_pn: $i ).

tff(c_Com_Obody_type,type,
    c_Com_Obody: $i ).

tff(c_Com_OWT_type,type,
    c_Com_OWT: $i > $o ).

tff(c_Com_Ocom_OBODY_type,type,
    c_Com_Ocom_OBODY: $i ).

tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
    c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).

tff(tc_Com_Ostate_type,type,
    tc_Com_Ostate: $i ).

tff(c_Set_Oinsert_type,type,
    c_Set_Oinsert: ( $i * $i * $i ) > $i ).

tff(tc_Hoare__Mirabelle_Otriple_type,type,
    tc_Hoare__Mirabelle_Otriple: $i > $i ).

tff(c_Orderings_Obot__class_Obot_type,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

tff(tc_fun_type,type,
    tc_fun: ( $i * $i ) > $i ).

tff(tc_bool_type,type,
    tc_bool: $i ).

tff(c_Hoare__Mirabelle_OMGT_type,type,
    c_Hoare__Mirabelle_OMGT: $i ).

tff(c_Com_OWT__bodies_type,type,
    c_Com_OWT__bodies: $o ).

tff(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
    c_Hoare__Mirabelle_Ostate__not__singleton: $o ).

tff(1,plain,
    ( ( c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn) )
  <=> ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(commutativity,[status(thm)],]) ).

tff(2,plain,
    ( ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) )
  <=> ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(4,plain,
    hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    c_Option_Ooption_OSome(v_y,tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn),
    inference(symmetry,[status(thm)],[4]) ).

tff(6,plain,
    ( ( c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) )
  <=> ( c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn) ) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( ( c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) )
  <=> ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(transitivity,[status(thm)],[6,1]) ).

tff(8,plain,
    ( ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) )
  <=> ( c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) ) ),
    inference(symmetry,[status(thm)],[7]) ).

tff(9,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
  <=> ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,axiom,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

tff(11,plain,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
    inference(modus_ponens,[status(thm)],[10,9]) ).

tff(12,plain,
    ^ [V_c: $i] :
      refl(
        ( ( ~ c_Com_OWT(V_c)
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
      <=> ( ~ c_Com_OWT(V_c)
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
    inference(bind,[status(th)],]) ).

tff(13,plain,
    ( ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
  <=> ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    inference(quant_intro,[status(thm)],[12]) ).

tff(14,plain,
    ( ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
  <=> ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ^ [V_c: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              iff_true(asserted(c_Hoare__Mirabelle_Ostate__not__singleton),
                ( c_Hoare__Mirabelle_Ostate__not__singleton
              <=> $true )),
              ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
            <=> ~ $true )),
            rewrite(
              ( ~ $true
            <=> $false )),
            ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
          <=> $false )),
          trans(
            monotonicity(
              iff_true(asserted(c_Com_OWT__bodies),
                ( c_Com_OWT__bodies
              <=> $true )),
              ( ~ c_Com_OWT__bodies
            <=> ~ $true )),
            rewrite(
              ( ~ $true
            <=> $false )),
            ( ~ c_Com_OWT__bodies
          <=> $false )),
          ( ( ~ c_Com_OWT(V_c)
            | ~ c_Hoare__Mirabelle_Ostate__not__singleton
            | ~ c_Com_OWT__bodies
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
        <=> ( ~ c_Com_OWT(V_c)
            | $false
            | $false
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
        rewrite(
          ( ( ~ c_Com_OWT(V_c)
            | $false
            | $false
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
        <=> ( ~ c_Com_OWT(V_c)
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
        ( ( ~ c_Com_OWT(V_c)
          | ~ c_Hoare__Mirabelle_Ostate__not__singleton
          | ~ c_Com_OWT__bodies
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
      <=> ( ~ c_Com_OWT(V_c)
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
    inference(bind,[status(th)],]) ).

tff(16,plain,
    ( ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | ~ c_Hoare__Mirabelle_Ostate__not__singleton
        | ~ c_Com_OWT__bodies
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
  <=> ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ^ [V_c: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
                  | ~ c_Com_OWT(V_c) )
              <=> ( ~ c_Com_OWT(V_c)
                  | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
              ( ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
                | ~ c_Com_OWT(V_c)
                | ~ c_Com_OWT__bodies )
            <=> ( ~ c_Com_OWT(V_c)
                | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
                | ~ c_Com_OWT__bodies ) )),
            rewrite(
              ( ( ~ c_Com_OWT(V_c)
                | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
                | ~ c_Com_OWT__bodies )
            <=> ( ~ c_Com_OWT(V_c)
                | ~ c_Com_OWT__bodies
                | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
            ( ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
              | ~ c_Com_OWT(V_c)
              | ~ c_Com_OWT__bodies )
          <=> ( ~ c_Com_OWT(V_c)
              | ~ c_Com_OWT__bodies
              | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
          ( ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
            | ~ c_Com_OWT(V_c)
            | ~ c_Com_OWT__bodies
            | ~ c_Hoare__Mirabelle_Ostate__not__singleton )
        <=> ( ~ c_Com_OWT(V_c)
            | ~ c_Com_OWT__bodies
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
            | ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )),
        rewrite(
          ( ( ~ c_Com_OWT(V_c)
            | ~ c_Com_OWT__bodies
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
            | ~ c_Hoare__Mirabelle_Ostate__not__singleton )
        <=> ( ~ c_Com_OWT(V_c)
            | ~ c_Hoare__Mirabelle_Ostate__not__singleton
            | ~ c_Com_OWT__bodies
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
        ( ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
          | ~ c_Com_OWT(V_c)
          | ~ c_Com_OWT__bodies
          | ~ c_Hoare__Mirabelle_Ostate__not__singleton )
      <=> ( ~ c_Com_OWT(V_c)
          | ~ c_Hoare__Mirabelle_Ostate__not__singleton
          | ~ c_Com_OWT__bodies
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) )),
    inference(bind,[status(th)],]) ).

tff(18,plain,
    ( ! [V_c: $i] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
        | ~ c_Com_OWT(V_c)
        | ~ c_Com_OWT__bodies
        | ~ c_Hoare__Mirabelle_Ostate__not__singleton )
  <=> ! [V_c: $i] :
        ( ~ c_Com_OWT(V_c)
        | ~ c_Hoare__Mirabelle_Ostate__not__singleton
        | ~ c_Com_OWT__bodies
        | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    inference(quant_intro,[status(thm)],[17]) ).

tff(19,axiom,
    ! [V_c: $i] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
      | ~ c_Com_OWT(V_c)
      | ~ c_Com_OWT__bodies
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF_0) ).

tff(20,plain,
    ! [V_c: $i] :
      ( ~ c_Com_OWT(V_c)
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton
      | ~ c_Com_OWT__bodies
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ! [V_c: $i] :
      ( ~ c_Com_OWT(V_c)
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(modus_ponens,[status(thm)],[20,16]) ).

tff(22,plain,
    ! [V_c: $i] :
      ( ~ c_Com_OWT(V_c)
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(modus_ponens,[status(thm)],[21,14]) ).

tff(23,plain,
    ! [V_c: $i] :
      ( ~ c_Com_OWT(V_c)
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [V_c: $i] :
      ( ~ c_Com_OWT(V_c)
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(modus_ponens,[status(thm)],[23,13]) ).

tff(25,plain,
    ( ( ~ ! [V_c: $i] :
            ( ~ c_Com_OWT(V_c)
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
      | ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
  <=> ( ~ ! [V_c: $i] :
            ( ~ c_Com_OWT(V_c)
            | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
      | ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
      | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [V_c: $i] :
          ( ~ c_Com_OWT(V_c)
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
    | ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [V_c: $i] :
          ( ~ c_Com_OWT(V_c)
          | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) )
    | ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn)),
    inference(unit_resolution,[status(thm)],[27,24,11]) ).

tff(29,plain,
    ^ [V_pn: $i] :
      refl(
        ( ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
          | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
      <=> ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
          | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [V_pn: $i] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
        | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
  <=> ! [V_pn: $i] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
        | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [V_pn: $i] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
        | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
  <=> ! [V_pn: $i] :
        ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
        | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ! [V_pn: $i] :
      ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
      | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).

tff(33,plain,
    ! [V_pn: $i] :
      ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
      | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [V_pn: $i] :
      ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
      | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,plain,
    ! [V_pn: $i] :
      ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
      | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ( ( ~ ! [V_pn: $i] :
            ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
            | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
      | c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
      | ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
  <=> ( ~ ! [V_pn: $i] :
            ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
            | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
      | c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
      | ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,plain,
    ( ~ ! [V_pn: $i] :
          ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
          | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
    | c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [V_pn: $i] :
          ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
          | ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
    | c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    ( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn))
    | ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
    inference(unit_resolution,[status(thm)],[38,35]) ).

tff(40,plain,
    hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom),
    inference(unit_resolution,[status(thm)],[39,28]) ).

tff(41,plain,
    c_Option_Ooption_ONone(tc_Com_Ocom) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
    inference(modus_ponens,[status(thm)],[40,8]) ).

tff(42,plain,
    ^ [V_a_H: $i,T_a: $i] :
      refl(
        ( ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) )
      <=> ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(43,plain,
    ( ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) )
  <=> ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ) ),
    inference(quant_intro,[status(thm)],[42]) ).

tff(44,plain,
    ( ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) )
  <=> ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,axiom,
    ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

tff(46,plain,
    ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ),
    inference(skolemize,[status(sab)],[46]) ).

tff(48,plain,
    ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ),
    inference(modus_ponens,[status(thm)],[47,43]) ).

tff(49,plain,
    ( ~ ! [V_a_H: $i,T_a: $i] : ( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) )
    | ( c_Option_Ooption_ONone(tc_Com_Ocom) != c_Option_Ooption_OSome(v_y,tc_Com_Ocom) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(50,plain,
    c_Option_Ooption_ONone(tc_Com_Ocom) != c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
    inference(unit_resolution,[status(thm)],[49,48]) ).

tff(51,plain,
    $false,
    inference(unit_resolution,[status(thm)],[50,41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWV906-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Sep  4 09:20:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.53  % SZS status Unsatisfiable
% 0.19/0.53  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------