TSTP Solution File: SWV078+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV078+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 : Thu Sep 29 15:09:53 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   34 (   4 unt;   8 typ;   0 def)
%            Number of atoms       :  104 (  26 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  102 (  24   ~;  24   |;  30   &)
%                                         (  18 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   2 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pv70_type,type,
    pv70: $i ).

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

tff(true_type,type,
    true: $o ).

tff(leq_type,type,
    leq: ( $i * $i ) > $o ).

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

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

tff(n5_type,type,
    n5: $i ).

tff(pv31_type,type,
    pv31: $i ).

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

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

tff(3,plain,
    ( ( $true
      | ( n0 != pv70 ) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    true,
    file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',ttrue) ).

tff(5,plain,
    ( true
  <=> $true ),
    inference(iff_true,[status(thm)],[4]) ).

tff(6,plain,
    ( ( true
      | ( n0 != pv70 ) )
  <=> ( $true
      | ( n0 != pv70 ) ) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( ( true
      | ( n0 != pv70 ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[6,3]) ).

tff(8,plain,
    ( ( ( n0 = pv70 )
      | $true )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    ( ~ ( ( leq(n0,pv31)
          & leq(pv31,minus(n5,n1)) )
       => ( ( ( n0 != pv70 )
           => ( leq(n0,pv31)
              & leq(pv31,minus(n5,n1)) ) )
          & ( ( n0 = pv70 )
           => true ) ) )
  <=> ~ ( ~ ( leq(n0,pv31)
            & leq(pv31,minus(n5,n1)) )
        | ( ( ( n0 = pv70 )
            | ( leq(n0,pv31)
              & leq(pv31,minus(n5,n1)) ) )
          & ( true
            | ( n0 != pv70 ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,axiom,
    ~ ( ( leq(n0,pv31)
        & leq(pv31,minus(n5,n1)) )
     => ( ( ( n0 != pv70 )
         => ( leq(n0,pv31)
            & leq(pv31,minus(n5,n1)) ) )
        & ( ( n0 = pv70 )
         => true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0019) ).

tff(11,plain,
    ~ ( ~ ( leq(n0,pv31)
          & leq(pv31,minus(n5,n1)) )
      | ( ( ( n0 = pv70 )
          | ( leq(n0,pv31)
            & leq(pv31,minus(n5,n1)) ) )
        & ( true
          | ( n0 != pv70 ) ) ) ),
    inference(modus_ponens,[status(thm)],[10,9]) ).

tff(12,plain,
    ( leq(n0,pv31)
    & leq(pv31,minus(n5,n1)) ),
    inference(or_elim,[status(thm)],[11]) ).

tff(13,plain,
    leq(pv31,minus(n5,n1)),
    inference(and_elim,[status(thm)],[12]) ).

tff(14,plain,
    ( leq(pv31,minus(n5,n1))
  <=> $true ),
    inference(iff_true,[status(thm)],[13]) ).

tff(15,plain,
    leq(n0,pv31),
    inference(and_elim,[status(thm)],[12]) ).

tff(16,plain,
    ( leq(n0,pv31)
  <=> $true ),
    inference(iff_true,[status(thm)],[15]) ).

tff(17,plain,
    ( ( leq(n0,pv31)
      & leq(pv31,minus(n5,n1)) )
  <=> ( $true
      & $true ) ),
    inference(monotonicity,[status(thm)],[16,14]) ).

tff(18,plain,
    ( ( leq(n0,pv31)
      & leq(pv31,minus(n5,n1)) )
  <=> $true ),
    inference(transitivity,[status(thm)],[17,2]) ).

tff(19,plain,
    ( ( ( n0 = pv70 )
      | ( leq(n0,pv31)
        & leq(pv31,minus(n5,n1)) ) )
  <=> ( ( n0 = pv70 )
      | $true ) ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ( ( n0 = pv70 )
      | ( leq(n0,pv31)
        & leq(pv31,minus(n5,n1)) ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[19,8]) ).

tff(21,plain,
    ( ( ( ( n0 = pv70 )
        | ( leq(n0,pv31)
          & leq(pv31,minus(n5,n1)) ) )
      & ( true
        | ( n0 != pv70 ) ) )
  <=> ( $true
      & $true ) ),
    inference(monotonicity,[status(thm)],[20,7]) ).

tff(22,plain,
    ( ( ( ( n0 = pv70 )
        | ( leq(n0,pv31)
          & leq(pv31,minus(n5,n1)) ) )
      & ( true
        | ( n0 != pv70 ) ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[21,2]) ).

tff(23,plain,
    ( ~ ( ( ( n0 = pv70 )
          | ( leq(n0,pv31)
            & leq(pv31,minus(n5,n1)) ) )
        & ( true
          | ( n0 != pv70 ) ) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[22]) ).

tff(24,plain,
    ( ~ ( ( ( n0 = pv70 )
          | ( leq(n0,pv31)
            & leq(pv31,minus(n5,n1)) ) )
        & ( true
          | ( n0 != pv70 ) ) )
  <=> $false ),
    inference(transitivity,[status(thm)],[23,1]) ).

tff(25,plain,
    ~ ( ( ( n0 = pv70 )
        | ( leq(n0,pv31)
          & leq(pv31,minus(n5,n1)) ) )
      & ( true
        | ( n0 != pv70 ) ) ),
    inference(or_elim,[status(thm)],[11]) ).

tff(26,plain,
    $false,
    inference(modus_ponens,[status(thm)],[25,24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV078+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n025.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 : Sun Sep  4 01:26:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------