TSTP Solution File: HWV014-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : HWV014-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Sat Sep 17 02:10:35 EDT 2022

% Result   : Unsatisfiable 0.19s 0.43s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   61 (  23 unt;  11 typ;   0 def)
%            Number of atoms       :  272 (  64 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  321 ( 114   ~; 181   |;   0   &)
%                                         (  26 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of FOOLs       :   15 (  15 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   8   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   32 (  29   !;   0   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
tff(gt_type,type,
    gt: ( $i * $i ) > $o ).

tff(n0_type,type,
    n0: $i ).

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

tff(x_139_type,type,
    x_139: $i ).

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

tff(minus_type,type,
    minus: ( $i * $i ) > $i ).

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

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

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

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

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

tff(1,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(2,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)],[1]) ).

tff(3,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(4,axiom,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_21) ).

tff(5,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
    | ( level(x_139) = int_level(x_139) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    level(x_139) = int_level(x_139),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( gt(level(x_139),n0)
  <=> gt(int_level(x_139),n0) ),
    inference(monotonicity,[status(thm)],[9]) ).

tff(11,plain,
    ( gt(level(x_139),n0)
  <=> gt(level(x_139),n0) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    gt(level(x_139),n0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).

tff(13,plain,
    gt(level(x_139),n0),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    gt(int_level(x_139),n0),
    inference(modus_ponens,[status(thm)],[13,10]) ).

tff(15,plain,
    minus(level(x_139),n1) = minus(int_level(x_139),n1),
    inference(monotonicity,[status(thm)],[9]) ).

tff(16,plain,
    ( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
    | ( level(plus(x_139,n1)) = int_level(plus(x_139,n1)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(17,plain,
    level(plus(x_139,n1)) = int_level(plus(x_139,n1)),
    inference(unit_resolution,[status(thm)],[16,7]) ).

tff(18,plain,
    ( ( level(plus(x_139,n1)) = minus(level(x_139),n1) )
  <=> ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ),
    inference(monotonicity,[status(thm)],[17,15]) ).

tff(19,plain,
    ( ( level(plus(x_139,n1)) != minus(level(x_139),n1) )
  <=> ( int_level(plus(x_139,n1)) != minus(int_level(x_139),n1) ) ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ( level(plus(x_139,n1)) != minus(level(x_139),n1) )
  <=> ( level(plus(x_139,n1)) != minus(level(x_139),n1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    level(plus(x_139,n1)) != minus(level(x_139),n1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_5) ).

tff(22,plain,
    level(plus(x_139,n1)) != minus(level(x_139),n1),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    int_level(plus(x_139,n1)) != minus(int_level(x_139),n1),
    inference(modus_ponens,[status(thm)],[22,19]) ).

tff(24,plain,
    ( ~ p_Reset(x_139)
  <=> ~ p_Reset(x_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,axiom,
    ~ p_Reset(x_139),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_4) ).

tff(26,plain,
    ~ p_Reset(x_139),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ( ~ p_Wr(x_139)
  <=> ~ p_Wr(x_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,axiom,
    ~ p_Wr(x_139),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).

tff(29,plain,
    ~ p_Wr(x_139),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ( p_Rd(x_139)
  <=> p_Rd(x_139) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    p_Rd(x_139),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).

tff(32,plain,
    p_Rd(x_139),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,plain,
    ^ [X_t_42: $i] :
      refl(
        ( ( p_Reset(X_t_42)
          | ~ p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ~ gt(int_level(X_t_42),n0)
          | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      <=> ( p_Reset(X_t_42)
          | ~ p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ~ gt(int_level(X_t_42),n0)
          | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
    inference(bind,[status(th)],]) ).

tff(34,plain,
    ( ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | ~ p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ~ gt(int_level(X_t_42),n0)
        | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
  <=> ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | ~ p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ~ gt(int_level(X_t_42),n0)
        | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,plain,
    ( ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | ~ p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ~ gt(int_level(X_t_42),n0)
        | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
  <=> ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | ~ p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ~ gt(int_level(X_t_42),n0)
        | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ^ [X_t_42: $i] :
      trans(
        monotonicity(
          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)
                | ~ gt(int_level(X_t_42),n0) )
            <=> ( p_Reset(X_t_42)
                | ~ p_Rd(X_t_42)
                | p_Wr(X_t_42)
                | ~ gt(int_level(X_t_42),n0) ) )),
            rewrite(
              ( ( p_Reset(X_t_42)
                | ~ p_Rd(X_t_42)
                | p_Wr(X_t_42)
                | ~ gt(int_level(X_t_42),n0) )
            <=> ( p_Reset(X_t_42)
                | ~ p_Rd(X_t_42)
                | p_Wr(X_t_42)
                | ~ gt(int_level(X_t_42),n0) ) )),
            ( ( p_Reset(X_t_42)
              | p_Wr(X_t_42)
              | ~ p_Rd(X_t_42)
              | ~ gt(int_level(X_t_42),n0) )
          <=> ( p_Reset(X_t_42)
              | ~ p_Rd(X_t_42)
              | p_Wr(X_t_42)
              | ~ gt(int_level(X_t_42),n0) ) )),
          ( ( p_Reset(X_t_42)
            | p_Wr(X_t_42)
            | ~ p_Rd(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
        <=> ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
        rewrite(
          ( ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
        <=> ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
        ( ( p_Reset(X_t_42)
          | p_Wr(X_t_42)
          | ~ p_Rd(X_t_42)
          | ~ gt(int_level(X_t_42),n0)
          | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      <=> ( p_Reset(X_t_42)
          | ~ p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ~ gt(int_level(X_t_42),n0)
          | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | p_Wr(X_t_42)
        | ~ p_Rd(X_t_42)
        | ~ gt(int_level(X_t_42),n0)
        | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
  <=> ! [X_t_42: $i] :
        ( p_Reset(X_t_42)
        | ~ p_Rd(X_t_42)
        | p_Wr(X_t_42)
        | ~ gt(int_level(X_t_42),n0)
        | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,axiom,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | p_Wr(X_t_42)
      | ~ p_Rd(X_t_42)
      | ~ gt(int_level(X_t_42),n0)
      | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_71) ).

tff(39,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | ~ p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ~ gt(int_level(X_t_42),n0)
      | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | ~ p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ~ gt(int_level(X_t_42),n0)
      | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
    inference(modus_ponens,[status(thm)],[39,35]) ).

tff(41,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | ~ p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ~ gt(int_level(X_t_42),n0)
      | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
    inference(skolemize,[status(sab)],[40]) ).

tff(42,plain,
    ! [X_t_42: $i] :
      ( p_Reset(X_t_42)
      | ~ p_Rd(X_t_42)
      | p_Wr(X_t_42)
      | ~ gt(int_level(X_t_42),n0)
      | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
    inference(modus_ponens,[status(thm)],[41,34]) ).

tff(43,plain,
    ( ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      | p_Reset(x_139)
      | p_Wr(x_139)
      | ~ p_Rd(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) )
  <=> ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      | p_Reset(x_139)
      | p_Wr(x_139)
      | ~ p_Rd(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ( p_Reset(x_139)
      | ~ p_Rd(x_139)
      | p_Wr(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) )
  <=> ( p_Reset(x_139)
      | p_Wr(x_139)
      | ~ p_Rd(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      | p_Reset(x_139)
      | ~ p_Rd(x_139)
      | p_Wr(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) )
  <=> ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      | p_Reset(x_139)
      | p_Wr(x_139)
      | ~ p_Rd(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ) ),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    ( ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      | p_Reset(x_139)
      | ~ p_Rd(x_139)
      | p_Wr(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) )
  <=> ( ~ ! [X_t_42: $i] :
            ( p_Reset(X_t_42)
            | ~ p_Rd(X_t_42)
            | p_Wr(X_t_42)
            | ~ gt(int_level(X_t_42),n0)
            | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
      | p_Reset(x_139)
      | p_Wr(x_139)
      | ~ p_Rd(x_139)
      | ~ gt(int_level(x_139),n0)
      | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ) ),
    inference(transitivity,[status(thm)],[45,43]) ).

tff(47,plain,
    ( ~ ! [X_t_42: $i] :
          ( p_Reset(X_t_42)
          | ~ p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ~ gt(int_level(X_t_42),n0)
          | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
    | p_Reset(x_139)
    | ~ p_Rd(x_139)
    | p_Wr(x_139)
    | ~ gt(int_level(x_139),n0)
    | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(48,plain,
    ( ~ ! [X_t_42: $i] :
          ( p_Reset(X_t_42)
          | ~ p_Rd(X_t_42)
          | p_Wr(X_t_42)
          | ~ gt(int_level(X_t_42),n0)
          | ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
    | p_Reset(x_139)
    | p_Wr(x_139)
    | ~ p_Rd(x_139)
    | ~ gt(int_level(x_139),n0)
    | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    ( ~ gt(int_level(x_139),n0)
    | ( int_level(plus(x_139,n1)) = minus(int_level(x_139),n1) ) ),
    inference(unit_resolution,[status(thm)],[48,42,32,29,26]) ).

tff(50,plain,
    $false,
    inference(unit_resolution,[status(thm)],[49,23,14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HWV014-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n008.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 22:05:10 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
%------------------------------------------------------------------------------