TSTP Solution File: NUM548+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM548+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n023.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 : Sun Sep 18 13:10:26 EDT 2022

% Result   : Theorem 0.21s 0.44s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   41 (  10 unt;  10 typ;   0 def)
%            Number of atoms       :  111 (   2 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  109 (  31   ~;  26   |;  10   &)
%                                         (  35 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   21 (  19   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
tff(isFinite0_type,type,
    isFinite0: $i > $o ).

tff(xQ_type,type,
    xQ: $i ).

tff(aElementOf0_type,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(szNzAzT0_type,type,
    szNzAzT0: $i ).

tff(sbrdtbr0_type,type,
    sbrdtbr0: $i > $i ).

tff(xk_type,type,
    xk: $i ).

tff(aSet0_type,type,
    aSet0: $i > $o ).

tff(xS_type,type,
    xS: $i ).

tff(aSubsetOf0_type,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(slbdtsldtrb0_type,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff(1,plain,
    ( ~ isFinite0(xQ)
  <=> ~ isFinite0(xQ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ isFinite0(xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(3,plain,
    ~ isFinite0(xQ),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( aElementOf0(xk,szNzAzT0)
  <=> aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,plain,
    ( aElementOf0(xk,szNzAzT0)
  <=> aElementOf0(xk,szNzAzT0) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).

tff(7,plain,
    aElementOf0(xk,szNzAzT0),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    aElementOf0(sbrdtbr0(xQ),szNzAzT0),
    inference(modus_ponens,[status(thm)],[7,4]) ).

tff(9,plain,
    ( ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
      <=> isFinite0(xQ) )
    | ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0)
    | isFinite0(xQ) ),
    inference(tautology,[status(thm)],]) ).

tff(10,plain,
    ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
    <=> isFinite0(xQ) ),
    inference(unit_resolution,[status(thm)],[9,8,3]) ).

tff(11,plain,
    ( aSet0(xQ)
  <=> aSet0(xQ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xQ,xS)
    & ( sbrdtbr0(xQ) = xk )
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).

tff(13,plain,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xQ,xS)
    & ( sbrdtbr0(xQ) = xk ) ),
    inference(and_elim,[status(thm)],[12]) ).

tff(14,plain,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xQ,xS) ),
    inference(and_elim,[status(thm)],[13]) ).

tff(15,plain,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xS) ) ),
    inference(and_elim,[status(thm)],[14]) ).

tff(16,plain,
    aSet0(xQ),
    inference(and_elim,[status(thm)],[15]) ).

tff(17,plain,
    aSet0(xQ),
    inference(modus_ponens,[status(thm)],[16,11]) ).

tff(18,plain,
    ^ [W0: $i] :
      refl(
        ( ( ~ aSet0(W0)
          | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
          <=> isFinite0(W0) ) )
      <=> ( ~ aSet0(W0)
          | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
          <=> isFinite0(W0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [W0: $i] :
        ( ~ aSet0(W0)
        | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
        <=> isFinite0(W0) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
        <=> isFinite0(W0) ) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [W0: $i] :
        ( ~ aSet0(W0)
        | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
        <=> isFinite0(W0) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
        <=> isFinite0(W0) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( aSet0(W0)
         => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
          <=> isFinite0(W0) ) )
      <=> ( ~ aSet0(W0)
          | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
          <=> isFinite0(W0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [W0: $i] :
        ( aSet0(W0)
       => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
        <=> isFinite0(W0) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
        <=> isFinite0(W0) ) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,axiom,
    ! [W0: $i] :
      ( aSet0(W0)
     => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).

tff(24,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    inference(modus_ponens,[status(thm)],[24,20]) ).

tff(26,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    inference(modus_ponens,[status(thm)],[26,19]) ).

tff(28,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aSet0(W0)
            | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
            <=> isFinite0(W0) ) )
      | ~ aSet0(xQ)
      | ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
      <=> isFinite0(xQ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aSet0(W0)
            | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
            <=> isFinite0(W0) ) )
      | ~ aSet0(xQ)
      | ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
      <=> isFinite0(xQ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ( ~ ! [W0: $i] :
          ( ~ aSet0(W0)
          | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
          <=> isFinite0(W0) ) )
    | ~ aSet0(xQ)
    | ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
    <=> isFinite0(xQ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(30,plain,
    ( ~ ! [W0: $i] :
          ( ~ aSet0(W0)
          | ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
          <=> isFinite0(W0) ) )
    | ~ aSet0(xQ)
    | ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
    <=> isFinite0(xQ) ) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    $false,
    inference(unit_resolution,[status(thm)],[30,27,17,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM548+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Sep  2 12:00:48 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.21/0.44  % SZS status Theorem
% 0.21/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------