TSTP Solution File: SWV854-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV854-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.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 15:24:44 EDT 2022

% Result   : Unsatisfiable 0.47s 0.58s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   51 (  10 unt;  17 typ;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  126 (  58   ~;  54   |;   0   &)
%                                         (  14 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   8   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   9 con; 0-4 aty)
%            Number of variables   :  102 (  90   !;   0   ?; 102   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_Hoare__Mirabelle_Otriple__valid_type,type,
    c_Hoare__Mirabelle_Otriple__valid: ( $i * $i * $i ) > $o ).

tff(t_a_type,type,
    t_a: $i ).

tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
    c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).

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

tff(v_x_type,type,
    v_x: $i ).

tff(v_Q_type,type,
    v_Q: $i ).

tff(c_Option_Othe_type,type,
    c_Option_Othe: ( $i * $i ) > $i ).

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

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

tff(v_P_type,type,
    v_P: $i ).

tff(v_na_type,type,
    v_na: $i ).

tff(hBOOL_type,type,
    hBOOL: $i > $o ).

tff(c_in_type,type,
    c_in: ( $i * $i * $i ) > $i ).

tff(tc_Com_Opname_type,type,
    tc_Com_Opname: $i ).

tff(v_Procs_type,type,
    v_Procs: $i ).

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

tff(c_Suc_type,type,
    c_Suc: $i ).

tff(1,plain,
    ^ [V_x: $i] :
      refl(
        ( ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
          | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
      <=> ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
          | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_x: $i] :
        ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
        | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
  <=> ! [V_x: $i] :
        ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
        | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_x: $i] :
        ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
        | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
  <=> ! [V_x: $i] :
        ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
        | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [V_x: $i] :
      rewrite(
        ( ( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a)
          | ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname)) )
      <=> ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
          | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_x: $i] :
        ( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a)
        | ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname)) )
  <=> ! [V_x: $i] :
        ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
        | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [V_x: $i] :
      ( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a)
      | ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

tff(7,plain,
    ! [V_x: $i] :
      ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
      | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [V_x: $i] :
      ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
      | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [V_x: $i] :
      ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
      | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_x: $i] :
      ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
      | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
  <=> hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(13,plain,
    hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ( ~ ! [V_x: $i] :
            ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
            | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
      | ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
      | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) )
  <=> ( ~ ! [V_x: $i] :
            ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
            | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
      | ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
      | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [V_x: $i] :
          ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
          | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
    | ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
    | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [V_x: $i] :
          ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
          | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
    | ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
    | c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a),
    inference(unit_resolution,[status(thm)],[16,13,10]) ).

tff(18,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a)
  <=> ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(20,plain,
    ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ^ [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      refl(
        ( ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
          | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
      <=> ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
          | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
        | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
  <=> ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
        | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
        | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
  <=> ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
        | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ^ [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      rewrite(
        ( ( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a)
          | ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a) )
      <=> ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
          | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
        ( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a)
        | ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a) )
  <=> ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
        | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,axiom,
    ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      ( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a)
      | ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).

tff(27,plain,
    ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
      | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
      | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
      | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
      ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
      | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
    inference(modus_ponens,[status(thm)],[29,22]) ).

tff(31,plain,
    ( ( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
            ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
            | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
      | ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
      | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) )
  <=> ( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
            ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
            | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
      | ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
      | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
          | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
    | ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
    | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
          | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
    | ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
    | c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    $false,
    inference(unit_resolution,[status(thm)],[33,30,20,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : SWV854-1 : TPTP v8.1.0. Released v4.1.0.
% 0.01/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun Sep  4 08:43:33 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.47/0.58  % SZS status Unsatisfiable
% 0.47/0.58  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------