TSTP Solution File: SWV898-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV898-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.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 15:24:53 EDT 2022

% Result   : Unsatisfiable 0.20s 0.57s
% Output   : Proof 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   32 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   57 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   66 (  31   ~;  27   |;   0   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   7   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-5 aty)
%            Number of variables   :   68 (  60   !;   0   ?;  68   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_Finite__Set_Ofinite_type,type,
    c_Finite__Set_Ofinite: ( $i * $i ) > $o ).

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

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

tff(c_Set_Oimage_type,type,
    c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).

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

tff(c_Map_Odom_type,type,
    c_Map_Odom: ( $i * $i * $i ) > $i ).

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

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

tff(c_COMBB_type,type,
    c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).

tff(tc_Option_Ooption_type,type,
    tc_Option_Ooption: $i > $i ).

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

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

tff(1,plain,
    ( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
  <=> ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(3,plain,
    ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      refl(
        ( ( ~ c_Finite__Set_Ofinite(V_F,T_a)
          | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
      <=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
          | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
        ( ~ c_Finite__Set_Ofinite(V_F,T_a)
        | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
  <=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
        ( ~ c_Finite__Set_Ofinite(V_F,T_a)
        | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
        ( ~ c_Finite__Set_Ofinite(V_F,T_a)
        | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
  <=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
        ( ~ c_Finite__Set_Ofinite(V_F,T_a)
        | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      rewrite(
        ( ( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
          | ~ c_Finite__Set_Ofinite(V_F,T_a) )
      <=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
          | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
        ( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
        | ~ c_Finite__Set_Ofinite(V_F,T_a) )
  <=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
        ( ~ c_Finite__Set_Ofinite(V_F,T_a)
        | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,axiom,
    ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      ( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
      | ~ c_Finite__Set_Ofinite(V_F,T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

tff(10,plain,
    ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      ( ~ c_Finite__Set_Ofinite(V_F,T_a)
      | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      ( ~ c_Finite__Set_Ofinite(V_F,T_a)
      | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
    inference(modus_ponens,[status(thm)],[10,6]) ).

tff(12,plain,
    ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      ( ~ c_Finite__Set_Ofinite(V_F,T_a)
      | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
      ( ~ c_Finite__Set_Ofinite(V_F,T_a)
      | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
    inference(modus_ponens,[status(thm)],[12,5]) ).

tff(14,plain,
    ( c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
  <=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).

tff(16,plain,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
            ( ~ c_Finite__Set_Ofinite(V_F,T_a)
            | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
      | ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
      | c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) )
  <=> ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
            ( ~ c_Finite__Set_Ofinite(V_F,T_a)
            | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
      | ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
      | c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
          ( ~ c_Finite__Set_Ofinite(V_F,T_a)
          | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
    | ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
    | c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
          ( ~ c_Finite__Set_Ofinite(V_F,T_a)
          | c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
    | ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
    | c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    $false,
    inference(unit_resolution,[status(thm)],[19,16,13,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWV898-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Sep  4 09:35:25 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.20/0.57  % SZS status Unsatisfiable
% 0.20/0.57  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------