TSTP Solution File: HWV027-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : HWV027-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Sat Sep 17 02:10:44 EDT 2022

% Result   : Unsatisfiable 0.19s 0.43s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   56 (  22 unt;   8 typ;   0 def)
%            Number of atoms       :  205 (  69 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  174 (  26   ~; 125   |;   0   &)
%                                         (  23 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    9 (   9 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   6   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   32 (  29   !;   0   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
tff(level_type,type,
    level: $i > $i ).

tff(plus_type,type,
    plus: ( $i * $i ) > $i ).

tff(n1_type,type,
    n1: $i ).

tff(t_139_type,type,
    t_139: $i ).

tff(int_level_type,type,
    int_level: $i > $i ).

tff(p_Reset_type,type,
    p_Reset: $i > $o ).

tff(p_Rd_type,type,
    p_Rd: $i > $o ).

tff(p_Wr_type,type,
    p_Wr: $i > $o ).

tff(1,plain,
    ( ( int_level(plus(t_139,n1)) = level(plus(t_139,n1)) )
  <=> ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
    inference(commutativity,[status(thm)],]) ).

tff(2,plain,
    ( ~ p_Reset(t_139)
  <=> ~ p_Reset(t_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ p_Reset(t_139),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).

tff(4,plain,
    ~ p_Reset(t_139),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ( ~ p_Rd(t_139)
  <=> ~ p_Rd(t_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ~ p_Rd(t_139),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).

tff(7,plain,
    ~ p_Rd(t_139),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ( ~ p_Wr(t_139)
  <=> ~ p_Wr(t_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,axiom,
    ~ p_Wr(t_139),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).

tff(10,plain,
    ~ p_Wr(t_139),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ^ [X_t_42: $i] :
      refl(
        ( ( p_Reset(X_t_42)
          | p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      <=> ( p_Reset(X_t_42)
          | p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
  <=> ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
  <=> ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ^ [X_t_42: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p_Reset(X_t_42)
              | p_Wr(X_t_42)
              | p_Rd(X_t_42) )
          <=> ( p_Reset(X_t_42)
              | p_Rd(X_t_42)
              | p_Wr(X_t_42) ) )),
          ( ( p_Reset(X_t_42)
            | p_Wr(X_t_42)
            | p_Rd(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
        <=> ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
        rewrite(
          ( ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
        <=> ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
        ( ( p_Reset(X_t_42)
          | p_Wr(X_t_42)
          | p_Rd(X_t_42)
          | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      <=> ( p_Reset(X_t_42)
          | p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Wr(X_t_42)
        | p_Rd(X_t_42)
        | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
  <=> ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,axiom,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | p_Wr(X_t_42)
      | p_Rd(X_t_42)
      | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_82) ).

tff(17,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
    inference(skolemize,[status(sab)],[18]) ).

tff(20,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
    inference(modus_ponens,[status(thm)],[19,12]) ).

tff(21,plain,
    ( ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      | p_Wr(t_139)
      | p_Rd(t_139)
      | p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
  <=> ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      | p_Wr(t_139)
      | p_Rd(t_139)
      | p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( ( p_Reset(t_139)
      | p_Rd(t_139)
      | p_Wr(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
  <=> ( p_Wr(t_139)
      | p_Rd(t_139)
      | p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ( ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      | p_Reset(t_139)
      | p_Rd(t_139)
      | p_Wr(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
  <=> ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      | p_Wr(t_139)
      | p_Rd(t_139)
      | p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
    inference(monotonicity,[status(thm)],[22]) ).

tff(24,plain,
    ( ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      | p_Reset(t_139)
      | p_Rd(t_139)
      | p_Wr(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
  <=> ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
      | p_Wr(t_139)
      | p_Rd(t_139)
      | p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
    inference(transitivity,[status(thm)],[23,21]) ).

tff(25,plain,
    ( ~ ! [X_t_42: $i] :
          ( p_Reset(X_t_42)
          | p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
    | p_Reset(t_139)
    | p_Rd(t_139)
    | p_Wr(t_139)
    | ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [X_t_42: $i] :
          ( p_Reset(X_t_42)
          | p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
    | p_Wr(t_139)
    | p_Rd(t_139)
    | p_Reset(t_139)
    | ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    int_level(plus(t_139,n1)) = int_level(t_139),
    inference(unit_resolution,[status(thm)],[26,20,10,7,4]) ).

tff(28,plain,
    int_level(t_139) = int_level(plus(t_139,n1)),
    inference(symmetry,[status(thm)],[27]) ).

tff(29,plain,
    ^ [X_t_32: $i] :
      refl(
        ( ( level(X_t_32) = int_level(X_t_32) )
      <=> ( level(X_t_32) = int_level(X_t_32) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
  <=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
  <=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_21) ).

tff(33,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
    | ( level(t_139) = int_level(t_139) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    level(t_139) = int_level(t_139),
    inference(unit_resolution,[status(thm)],[36,35]) ).

tff(38,plain,
    level(t_139) = int_level(plus(t_139,n1)),
    inference(transitivity,[status(thm)],[37,28]) ).

tff(39,plain,
    ( ( level(t_139) = level(plus(t_139,n1)) )
  <=> ( int_level(plus(t_139,n1)) = level(plus(t_139,n1)) ) ),
    inference(monotonicity,[status(thm)],[38]) ).

tff(40,plain,
    ( ( level(t_139) = level(plus(t_139,n1)) )
  <=> ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
    inference(transitivity,[status(thm)],[39,1]) ).

tff(41,plain,
    ( ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) )
  <=> ( level(t_139) = level(plus(t_139,n1)) ) ),
    inference(symmetry,[status(thm)],[40]) ).

tff(42,plain,
    ( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
    | ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(43,plain,
    level(plus(t_139,n1)) = int_level(plus(t_139,n1)),
    inference(unit_resolution,[status(thm)],[42,35]) ).

tff(44,plain,
    level(t_139) = level(plus(t_139,n1)),
    inference(modus_ponens,[status(thm)],[43,41]) ).

tff(45,plain,
    ( ( level(t_139) != level(plus(t_139,n1)) )
  <=> ( level(t_139) != level(plus(t_139,n1)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,axiom,
    level(t_139) != level(plus(t_139,n1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).

tff(47,plain,
    level(t_139) != level(plus(t_139,n1)),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    $false,
    inference(unit_resolution,[status(thm)],[47,44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HWV027-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n024.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 : Wed Aug 31 22:07:19 EDT 2022
% 0.13/0.34  % 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.
% 0.19/0.43  % SZS status Unsatisfiable
% 0.19/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------