TSTP Solution File: HWV009-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : HWV009-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 02:10:31 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   71 (  17 unt;   9 typ;   0 def)
%            Number of atoms       :  190 (  53 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  249 ( 125   ~; 103   |;   0   &)
%                                         (  21 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   6   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   49 (  45   !;   0   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
tff(n0_type,type,
    n0: $i ).

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_error_type,type,
    p_Rd_error: $i > $o ).

tff(p_Wr_error_type,type,
    p_Wr_error: $i > $o ).

tff(1,plain,
    ( p_Reset(t_139)
  <=> p_Reset(t_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    p_Reset(t_139),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).

tff(3,plain,
    p_Reset(t_139),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [X_t_37: $i] :
      refl(
        ( ( ~ p_Reset(X_t_37)
          | ( int_level(plus(X_t_37,n1)) = n0 ) )
      <=> ( ~ p_Reset(X_t_37)
          | ( int_level(plus(X_t_37,n1)) = n0 ) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ( int_level(plus(X_t_37,n1)) = n0 ) )
  <=> ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ( int_level(plus(X_t_37,n1)) = n0 ) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ( int_level(plus(X_t_37,n1)) = n0 ) )
  <=> ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ( int_level(plus(X_t_37,n1)) = n0 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ( int_level(plus(X_t_37,n1)) = n0 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_26) ).

tff(8,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ( int_level(plus(X_t_37,n1)) = n0 ) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ( int_level(plus(X_t_37,n1)) = n0 ) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ( int_level(plus(X_t_37,n1)) = n0 ) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [X_t_37: $i] :
            ( ~ p_Reset(X_t_37)
            | ( int_level(plus(X_t_37,n1)) = n0 ) )
      | ~ p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = n0 ) )
  <=> ( ~ ! [X_t_37: $i] :
            ( ~ p_Reset(X_t_37)
            | ( int_level(plus(X_t_37,n1)) = n0 ) )
      | ~ p_Reset(t_139)
      | ( int_level(plus(t_139,n1)) = n0 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [X_t_37: $i] :
          ( ~ p_Reset(X_t_37)
          | ( int_level(plus(X_t_37,n1)) = n0 ) )
    | ~ p_Reset(t_139)
    | ( int_level(plus(t_139,n1)) = n0 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [X_t_37: $i] :
          ( ~ p_Reset(X_t_37)
          | ( int_level(plus(X_t_37,n1)) = n0 ) )
    | ~ p_Reset(t_139)
    | ( int_level(plus(t_139,n1)) = n0 ) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    int_level(plus(t_139,n1)) = n0,
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,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(16,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)],[15]) ).

tff(17,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(18,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(19,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(skolemize,[status(sab)],[19]) ).

tff(21,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(modus_ponens,[status(thm)],[20,16]) ).

tff(22,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(23,plain,
    level(plus(t_139,n1)) = int_level(plus(t_139,n1)),
    inference(unit_resolution,[status(thm)],[22,21]) ).

tff(24,plain,
    level(plus(t_139,n1)) = n0,
    inference(transitivity,[status(thm)],[23,14]) ).

tff(25,plain,
    ^ [X_t_37: $i] :
      refl(
        ( ( ~ p_Reset(X_t_37)
          | ~ p_Rd_error(plus(X_t_37,n1)) )
      <=> ( ~ p_Reset(X_t_37)
          | ~ p_Rd_error(plus(X_t_37,n1)) ) )),
    inference(bind,[status(th)],]) ).

tff(26,plain,
    ( ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Rd_error(plus(X_t_37,n1)) )
  <=> ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Rd_error(plus(X_t_37,n1)) ) ),
    inference(quant_intro,[status(thm)],[25]) ).

tff(27,plain,
    ( ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Rd_error(plus(X_t_37,n1)) )
  <=> ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Rd_error(plus(X_t_37,n1)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,axiom,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Rd_error(plus(X_t_37,n1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_30) ).

tff(29,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Rd_error(plus(X_t_37,n1)) ),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Rd_error(plus(X_t_37,n1)) ),
    inference(skolemize,[status(sab)],[29]) ).

tff(31,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Rd_error(plus(X_t_37,n1)) ),
    inference(modus_ponens,[status(thm)],[30,26]) ).

tff(32,plain,
    ( ( ~ ! [X_t_37: $i] :
            ( ~ p_Reset(X_t_37)
            | ~ p_Rd_error(plus(X_t_37,n1)) )
      | ~ p_Reset(t_139)
      | ~ p_Rd_error(plus(t_139,n1)) )
  <=> ( ~ ! [X_t_37: $i] :
            ( ~ p_Reset(X_t_37)
            | ~ p_Rd_error(plus(X_t_37,n1)) )
      | ~ p_Reset(t_139)
      | ~ p_Rd_error(plus(t_139,n1)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [X_t_37: $i] :
          ( ~ p_Reset(X_t_37)
          | ~ p_Rd_error(plus(X_t_37,n1)) )
    | ~ p_Reset(t_139)
    | ~ p_Rd_error(plus(t_139,n1)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [X_t_37: $i] :
          ( ~ p_Reset(X_t_37)
          | ~ p_Rd_error(plus(X_t_37,n1)) )
    | ~ p_Reset(t_139)
    | ~ p_Rd_error(plus(t_139,n1)) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ~ p_Rd_error(plus(t_139,n1)),
    inference(unit_resolution,[status(thm)],[34,31,3]) ).

tff(36,plain,
    ^ [X_t_37: $i] :
      refl(
        ( ( ~ p_Reset(X_t_37)
          | ~ p_Wr_error(plus(X_t_37,n1)) )
      <=> ( ~ p_Reset(X_t_37)
          | ~ p_Wr_error(plus(X_t_37,n1)) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Wr_error(plus(X_t_37,n1)) )
  <=> ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Wr_error(plus(X_t_37,n1)) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Wr_error(plus(X_t_37,n1)) )
  <=> ! [X_t_37: $i] :
        ( ~ p_Reset(X_t_37)
        | ~ p_Wr_error(plus(X_t_37,n1)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,axiom,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Wr_error(plus(X_t_37,n1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_29) ).

tff(40,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Wr_error(plus(X_t_37,n1)) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Wr_error(plus(X_t_37,n1)) ),
    inference(skolemize,[status(sab)],[40]) ).

tff(42,plain,
    ! [X_t_37: $i] :
      ( ~ p_Reset(X_t_37)
      | ~ p_Wr_error(plus(X_t_37,n1)) ),
    inference(modus_ponens,[status(thm)],[41,37]) ).

tff(43,plain,
    ( ( ~ ! [X_t_37: $i] :
            ( ~ p_Reset(X_t_37)
            | ~ p_Wr_error(plus(X_t_37,n1)) )
      | ~ p_Reset(t_139)
      | ~ p_Wr_error(plus(t_139,n1)) )
  <=> ( ~ ! [X_t_37: $i] :
            ( ~ p_Reset(X_t_37)
            | ~ p_Wr_error(plus(X_t_37,n1)) )
      | ~ p_Reset(t_139)
      | ~ p_Wr_error(plus(t_139,n1)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ~ ! [X_t_37: $i] :
          ( ~ p_Reset(X_t_37)
          | ~ p_Wr_error(plus(X_t_37,n1)) )
    | ~ p_Reset(t_139)
    | ~ p_Wr_error(plus(t_139,n1)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [X_t_37: $i] :
          ( ~ p_Reset(X_t_37)
          | ~ p_Wr_error(plus(X_t_37,n1)) )
    | ~ p_Reset(t_139)
    | ~ p_Wr_error(plus(t_139,n1)) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ~ p_Wr_error(plus(t_139,n1)),
    inference(unit_resolution,[status(thm)],[45,42,3]) ).

tff(47,plain,
    ( ( p_Wr_error(plus(t_139,n1))
      | p_Rd_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 ) )
  <=> ( p_Wr_error(plus(t_139,n1))
      | p_Rd_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(48,plain,
    ( ( p_Wr_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 )
      | p_Rd_error(plus(t_139,n1)) )
  <=> ( p_Wr_error(plus(t_139,n1))
      | p_Rd_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( ( ( level(plus(t_139,n1)) != n0 )
      | p_Wr_error(plus(t_139,n1)) )
  <=> ( p_Wr_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ( ( ( level(plus(t_139,n1)) != n0 )
      | p_Wr_error(plus(t_139,n1))
      | p_Rd_error(plus(t_139,n1)) )
  <=> ( p_Wr_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 )
      | p_Rd_error(plus(t_139,n1)) ) ),
    inference(monotonicity,[status(thm)],[49]) ).

tff(51,plain,
    ( ( ( level(plus(t_139,n1)) != n0 )
      | p_Wr_error(plus(t_139,n1))
      | p_Rd_error(plus(t_139,n1)) )
  <=> ( p_Wr_error(plus(t_139,n1))
      | p_Rd_error(plus(t_139,n1))
      | ( level(plus(t_139,n1)) != n0 ) ) ),
    inference(transitivity,[status(thm)],[50,48]) ).

tff(52,axiom,
    ( ( level(plus(t_139,n1)) != n0 )
    | p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).

tff(53,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[53,47]) ).

tff(55,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[54,47]) ).

tff(56,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[55,47]) ).

tff(57,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[56,47]) ).

tff(58,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[57,47]) ).

tff(59,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[58,47]) ).

tff(60,plain,
    ( p_Wr_error(plus(t_139,n1))
    | p_Rd_error(plus(t_139,n1))
    | ( level(plus(t_139,n1)) != n0 ) ),
    inference(modus_ponens,[status(thm)],[59,47]) ).

tff(61,plain,
    level(plus(t_139,n1)) != n0,
    inference(unit_resolution,[status(thm)],[60,46,35]) ).

tff(62,plain,
    $false,
    inference(unit_resolution,[status(thm)],[61,24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : HWV009-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 31 21:56:20 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.42  % SZS status Unsatisfiable
% 0.19/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------