TSTP Solution File: RNG125+4 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : RNG125+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 03:18:33 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   40 (   3 unt;   7 typ;   0 def)
%            Number of atoms       :  187 (  42 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  173 (  19   ~;  68   |;  65   &)
%                                         (  21 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (   0   !;  42   ?;  42   :)

% Comments : 
%------------------------------------------------------------------------------
tff(xb_type,type,
    xb: $i ).

tff(sdtasdt0_type,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(xu_type,type,
    xu: $i ).

tff(aElement0_type,type,
    aElement0: $i > $o ).

tff(aDivisorOf0_type,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(doDivides0_type,type,
    doDivides0: ( $i * $i ) > $o ).

tff(xa_type,type,
    xa: $i ).

tff(1,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( $true
      & $true )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( $true
      | aDivisorOf0(xu,xb)
      | $true )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ~ ~ ( ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) )
          & doDivides0(xu,xb) )
  <=> ( ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xb ) )
      & doDivides0(xu,xb) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    ~ ~ ( ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) )
        & doDivides0(xu,xb) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).

tff(6,plain,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xu,W0) = xb ) )
    & doDivides0(xu,xb) ),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ? [W0: $i] :
      ( aElement0(W0)
      & ( sdtasdt0(xu,W0) = xb ) ),
    inference(and_elim,[status(thm)],[6]) ).

tff(8,plain,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xu,W0) = xb ) )
  <=> $true ),
    inference(iff_true,[status(thm)],[7]) ).

tff(9,plain,
    doDivides0(xu,xb),
    inference(and_elim,[status(thm)],[6]) ).

tff(10,plain,
    ( doDivides0(xu,xb)
  <=> $true ),
    inference(iff_true,[status(thm)],[9]) ).

tff(11,plain,
    ( ( doDivides0(xu,xb)
      | aDivisorOf0(xu,xb)
      | ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xb ) ) )
  <=> ( $true
      | aDivisorOf0(xu,xb)
      | $true ) ),
    inference(monotonicity,[status(thm)],[10,8]) ).

tff(12,plain,
    ( ( doDivides0(xu,xb)
      | aDivisorOf0(xu,xb)
      | ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xb ) ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[11,3]) ).

tff(13,plain,
    ( ( $true
      | $true
      | aDivisorOf0(xu,xa) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( ~ ~ ( ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          & doDivides0(xu,xa) )
  <=> ( ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xa ) )
      & doDivides0(xu,xa) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    ~ ~ ( ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        & doDivides0(xu,xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2479) ).

tff(16,plain,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xu,W0) = xa ) )
    & doDivides0(xu,xa) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ? [W0: $i] :
      ( aElement0(W0)
      & ( sdtasdt0(xu,W0) = xa ) ),
    inference(and_elim,[status(thm)],[16]) ).

tff(18,plain,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xu,W0) = xa ) )
  <=> $true ),
    inference(iff_true,[status(thm)],[17]) ).

tff(19,plain,
    doDivides0(xu,xa),
    inference(and_elim,[status(thm)],[16]) ).

tff(20,plain,
    ( doDivides0(xu,xa)
  <=> $true ),
    inference(iff_true,[status(thm)],[19]) ).

tff(21,plain,
    ( ( doDivides0(xu,xa)
      | ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xa ) )
      | aDivisorOf0(xu,xa) )
  <=> ( $true
      | $true
      | aDivisorOf0(xu,xa) ) ),
    inference(monotonicity,[status(thm)],[20,18]) ).

tff(22,plain,
    ( ( doDivides0(xu,xa)
      | ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xa ) )
      | aDivisorOf0(xu,xa) )
  <=> $true ),
    inference(transitivity,[status(thm)],[21,13]) ).

tff(23,plain,
    ( ( ( doDivides0(xu,xa)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | aDivisorOf0(xu,xa) )
      & ( doDivides0(xu,xb)
        | aDivisorOf0(xu,xb)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) ) ) )
  <=> ( $true
      & $true ) ),
    inference(monotonicity,[status(thm)],[22,12]) ).

tff(24,plain,
    ( ( ( doDivides0(xu,xa)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | aDivisorOf0(xu,xa) )
      & ( doDivides0(xu,xb)
        | aDivisorOf0(xu,xb)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) ) ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[23,2]) ).

tff(25,plain,
    ( ~ ( ( doDivides0(xu,xa)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          | aDivisorOf0(xu,xa) )
        & ( doDivides0(xu,xb)
          | aDivisorOf0(xu,xb)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) ) ) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[24]) ).

tff(26,plain,
    ( ~ ( ( doDivides0(xu,xa)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          | aDivisorOf0(xu,xa) )
        & ( doDivides0(xu,xb)
          | aDivisorOf0(xu,xb)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) ) ) )
  <=> $false ),
    inference(transitivity,[status(thm)],[25,1]) ).

tff(27,plain,
    ( ( ( doDivides0(xu,xa)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | aDivisorOf0(xu,xa) )
      & ( doDivides0(xu,xb)
        | aDivisorOf0(xu,xb)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) ) ) )
  <=> ( ( doDivides0(xu,xa)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | aDivisorOf0(xu,xa) )
      & ( doDivides0(xu,xb)
        | aDivisorOf0(xu,xb)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    ( ~ ( ( doDivides0(xu,xa)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          | aDivisorOf0(xu,xa) )
        & ( doDivides0(xu,xb)
          | aDivisorOf0(xu,xb)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) ) ) )
  <=> ~ ( ( doDivides0(xu,xa)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          | aDivisorOf0(xu,xa) )
        & ( doDivides0(xu,xb)
          | aDivisorOf0(xu,xb)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) ) ) ) ),
    inference(monotonicity,[status(thm)],[27]) ).

tff(29,plain,
    ( ~ ( ( ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          | doDivides0(xu,xa)
          | aDivisorOf0(xu,xa) )
        & ( ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) )
          | doDivides0(xu,xb)
          | aDivisorOf0(xu,xb) ) )
  <=> ~ ( ( doDivides0(xu,xa)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xa ) )
          | aDivisorOf0(xu,xa) )
        & ( doDivides0(xu,xb)
          | aDivisorOf0(xu,xb)
          | ? [W0: $i] :
              ( aElement0(W0)
              & ( sdtasdt0(xu,W0) = xb ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,axiom,
    ~ ( ( ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | doDivides0(xu,xa)
        | aDivisorOf0(xu,xa) )
      & ( ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) )
        | doDivides0(xu,xb)
        | aDivisorOf0(xu,xb) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2383) ).

tff(31,plain,
    ~ ( ( doDivides0(xu,xa)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | aDivisorOf0(xu,xa) )
      & ( doDivides0(xu,xb)
        | aDivisorOf0(xu,xb)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) ) ) ),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    ~ ( ( doDivides0(xu,xa)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        | aDivisorOf0(xu,xa) )
      & ( doDivides0(xu,xb)
        | aDivisorOf0(xu,xb)
        | ? [W0: $i] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xb ) ) ) ),
    inference(modus_ponens,[status(thm)],[31,28]) ).

tff(33,plain,
    $false,
    inference(modus_ponens,[status(thm)],[32,26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG125+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33  % Computer : n003.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Fri Sep  2 22:48:40 EDT 2022
% 0.14/0.33  % CPUTime  : 
% 0.14/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.33  Usage: tptp [options] [-file:]file
% 0.14/0.33    -h, -?       prints this message.
% 0.14/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.33    -m, -model   generate model.
% 0.14/0.33    -p, -proof   generate proof.
% 0.14/0.33    -c, -core    generate unsat core of named formulas.
% 0.14/0.33    -st, -statistics display statistics.
% 0.14/0.33    -t:timeout   set timeout (in second).
% 0.14/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.33    -<param>:<value> configuration parameter and value.
% 0.14/0.33    -o:<output-file> file to place output in.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------