TSTP Solution File: SCT027-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SCT027-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n024.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 Sep 20 03:41:22 EDT 2022

% Result   : Unsatisfiable 0.52s 0.70s
% Output   : Proof 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   25 (   9 unt;  10 typ;   0 def)
%            Number of atoms       :   41 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   39 (  23   ~;   7   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    6 (   3 avg)
%            Number of FOOLs       :   10 (  10 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   2 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   14 (  12   !;   0   ?;  14   :)

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

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

tff(c_Arrow__Order__Mirabelle_OLin_type,type,
    c_Arrow__Order__Mirabelle_OLin: $i ).

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

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

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

tff(tc_prod_type,type,
    tc_prod: ( $i * $i ) > $i ).

tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
    tc_Arrow__Order__Mirabelle_Oalt: $i ).

tff(v_thesis_____type,type,
    v_thesis____: $o ).

tff(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_type,type,
    v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).

tff(1,plain,
    ^ [V_R: $i] :
      refl(
        ( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
      <=> ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
  <=> ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
  <=> ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [V_R: $i] :
      trans(
        monotonicity(
          iff_false(asserted(~ v_thesis____),
            ( v_thesis____
          <=> $false )),
          ( ( v_thesis____
            | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )
        <=> ( $false
            | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) ) )),
        rewrite(
          ( ( $false
            | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )
        <=> ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )),
        ( ( v_thesis____
          | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )
      <=> ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_R: $i] :
        ( v_thesis____
        | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) )
  <=> ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [V_R: $i] :
      ( v_thesis____
      | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).

tff(7,plain,
    ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin)),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin))
  <=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__alt_0) ).

tff(13,plain,
    hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ~ ! [V_R: $i] : ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(15,plain,
    $false,
    inference(unit_resolution,[status(thm)],[14,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SCT027-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Sep  2 23:28:33 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36  Usage: tptp [options] [-file:]file
% 0.13/0.36    -h, -?       prints this message.
% 0.13/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.36    -m, -model   generate model.
% 0.13/0.36    -p, -proof   generate proof.
% 0.13/0.36    -c, -core    generate unsat core of named formulas.
% 0.13/0.36    -st, -statistics display statistics.
% 0.13/0.36    -t:timeout   set timeout (in second).
% 0.13/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36    -<param>:<value> configuration parameter and value.
% 0.13/0.36    -o:<output-file> file to place output in.
% 0.52/0.70  % SZS status Unsatisfiable
% 0.52/0.70  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------