TSTP Solution File: PUZ009-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : PUZ009-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Sun Sep 18 14:10:49 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   64 (   6 unt;   5 typ;   0 def)
%            Number of atoms       :  191 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  195 (  63   ~;  92   |;   0   &)
%                                         (  40 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   7 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(e_is_a_knight_type,type,
    e_is_a_knight: $o ).

tff(c_is_a_knight_type,type,
    c_is_a_knight: $o ).

tff(d_is_a_knight_type,type,
    d_is_a_knight: $o ).

tff(a_is_a_knight_type,type,
    a_is_a_knight: $o ).

tff(b_is_a_knight_type,type,
    b_is_a_knight: $o ).

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

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

tff(3,plain,
    ( ( $false
      | e_is_a_knight )
  <=> e_is_a_knight ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ( ~ a_is_a_knight
      | $false )
  <=> ~ a_is_a_knight ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    b_is_a_knight,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c18) ).

tff(6,plain,
    ( b_is_a_knight
  <=> $true ),
    inference(iff_true,[status(thm)],[5]) ).

tff(7,plain,
    ( ~ b_is_a_knight
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[6]) ).

tff(8,plain,
    ( ~ b_is_a_knight
  <=> $false ),
    inference(transitivity,[status(thm)],[7,2]) ).

tff(9,plain,
    ( ( ~ a_is_a_knight
      | ~ b_is_a_knight )
  <=> ( ~ a_is_a_knight
      | $false ) ),
    inference(monotonicity,[status(thm)],[8]) ).

tff(10,plain,
    ( ( ~ a_is_a_knight
      | ~ b_is_a_knight )
  <=> ~ a_is_a_knight ),
    inference(transitivity,[status(thm)],[9,4]) ).

tff(11,axiom,
    ( ~ a_is_a_knight
    | ~ b_is_a_knight ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).

tff(12,plain,
    ~ a_is_a_knight,
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ( a_is_a_knight
  <=> $false ),
    inference(iff_false,[status(thm)],[12]) ).

tff(14,plain,
    ( ( a_is_a_knight
      | e_is_a_knight )
  <=> ( $false
      | e_is_a_knight ) ),
    inference(monotonicity,[status(thm)],[13]) ).

tff(15,plain,
    ( ( a_is_a_knight
      | e_is_a_knight )
  <=> e_is_a_knight ),
    inference(transitivity,[status(thm)],[14,3]) ).

tff(16,axiom,
    ( a_is_a_knight
    | e_is_a_knight ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c16) ).

tff(17,plain,
    e_is_a_knight,
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ( e_is_a_knight
  <=> $true ),
    inference(iff_true,[status(thm)],[17]) ).

tff(19,plain,
    ( ~ e_is_a_knight
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ~ e_is_a_knight
  <=> $false ),
    inference(transitivity,[status(thm)],[19,2]) ).

tff(21,plain,
    ( ( $false
      | ~ c_is_a_knight )
  <=> ~ c_is_a_knight ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( ( a_is_a_knight
      | ~ c_is_a_knight )
  <=> ( $false
      | ~ c_is_a_knight ) ),
    inference(monotonicity,[status(thm)],[13]) ).

tff(23,plain,
    ( ( a_is_a_knight
      | ~ c_is_a_knight )
  <=> ~ c_is_a_knight ),
    inference(transitivity,[status(thm)],[22,21]) ).

tff(24,axiom,
    ( a_is_a_knight
    | ~ c_is_a_knight ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c17) ).

tff(25,plain,
    ~ c_is_a_knight,
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ( c_is_a_knight
  <=> $false ),
    inference(iff_false,[status(thm)],[25]) ).

tff(27,plain,
    ( ( d_is_a_knight
      | $false )
  <=> d_is_a_knight ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    ( ( d_is_a_knight
      | c_is_a_knight )
  <=> ( d_is_a_knight
      | $false ) ),
    inference(monotonicity,[status(thm)],[26]) ).

tff(29,plain,
    ( ( d_is_a_knight
      | c_is_a_knight )
  <=> d_is_a_knight ),
    inference(transitivity,[status(thm)],[28,27]) ).

tff(30,plain,
    ( ( $false
      | d_is_a_knight
      | c_is_a_knight )
  <=> ( d_is_a_knight
      | c_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight )
  <=> ( $false
      | d_is_a_knight
      | c_is_a_knight ) ),
    inference(monotonicity,[status(thm)],[13]) ).

tff(32,plain,
    ( ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight )
  <=> ( d_is_a_knight
      | c_is_a_knight ) ),
    inference(transitivity,[status(thm)],[31,30]) ).

tff(33,plain,
    ( ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight )
  <=> ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ( ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight )
  <=> ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( d_is_a_knight
      | a_is_a_knight )
  <=> ( a_is_a_knight
      | d_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ( d_is_a_knight
      | a_is_a_knight
      | c_is_a_knight )
  <=> ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight ) ),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    ( ( d_is_a_knight
      | a_is_a_knight
      | c_is_a_knight )
  <=> ( a_is_a_knight
      | d_is_a_knight
      | c_is_a_knight ) ),
    inference(transitivity,[status(thm)],[36,34]) ).

tff(38,axiom,
    ( d_is_a_knight
    | a_is_a_knight
    | c_is_a_knight ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c13) ).

tff(39,plain,
    ( a_is_a_knight
    | d_is_a_knight
    | c_is_a_knight ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ( a_is_a_knight
    | d_is_a_knight
    | c_is_a_knight ),
    inference(modus_ponens,[status(thm)],[39,33]) ).

tff(41,plain,
    ( a_is_a_knight
    | d_is_a_knight
    | c_is_a_knight ),
    inference(modus_ponens,[status(thm)],[40,33]) ).

tff(42,plain,
    ( d_is_a_knight
    | c_is_a_knight ),
    inference(modus_ponens,[status(thm)],[41,32]) ).

tff(43,plain,
    d_is_a_knight,
    inference(modus_ponens,[status(thm)],[42,29]) ).

tff(44,plain,
    ( d_is_a_knight
  <=> $true ),
    inference(iff_true,[status(thm)],[43]) ).

tff(45,plain,
    ( ~ d_is_a_knight
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    ( ~ d_is_a_knight
  <=> $false ),
    inference(transitivity,[status(thm)],[45,2]) ).

tff(47,plain,
    ( ( ~ d_is_a_knight
      | c_is_a_knight
      | ~ e_is_a_knight )
  <=> ( $false
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[46,26,20]) ).

tff(48,plain,
    ( ( ~ d_is_a_knight
      | c_is_a_knight
      | ~ e_is_a_knight )
  <=> $false ),
    inference(transitivity,[status(thm)],[47,1]) ).

tff(49,plain,
    ( ( ~ d_is_a_knight
      | c_is_a_knight
      | ~ e_is_a_knight )
  <=> ( ~ d_is_a_knight
      | c_is_a_knight
      | ~ e_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ( ( ~ d_is_a_knight
      | ~ e_is_a_knight
      | c_is_a_knight )
  <=> ( ~ d_is_a_knight
      | c_is_a_knight
      | ~ e_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ( ( ~ e_is_a_knight
      | ~ d_is_a_knight )
  <=> ( ~ d_is_a_knight
      | ~ e_is_a_knight ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,plain,
    ( ( ~ e_is_a_knight
      | ~ d_is_a_knight
      | c_is_a_knight )
  <=> ( ~ d_is_a_knight
      | ~ e_is_a_knight
      | c_is_a_knight ) ),
    inference(monotonicity,[status(thm)],[51]) ).

tff(53,plain,
    ( ( ~ e_is_a_knight
      | ~ d_is_a_knight
      | c_is_a_knight )
  <=> ( ~ d_is_a_knight
      | c_is_a_knight
      | ~ e_is_a_knight ) ),
    inference(transitivity,[status(thm)],[52,50]) ).

tff(54,axiom,
    ( ~ e_is_a_knight
    | ~ d_is_a_knight
    | c_is_a_knight ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).

tff(55,plain,
    ( ~ d_is_a_knight
    | c_is_a_knight
    | ~ e_is_a_knight ),
    inference(modus_ponens,[status(thm)],[54,53]) ).

tff(56,plain,
    ( ~ d_is_a_knight
    | c_is_a_knight
    | ~ e_is_a_knight ),
    inference(modus_ponens,[status(thm)],[55,49]) ).

tff(57,plain,
    ( ~ d_is_a_knight
    | c_is_a_knight
    | ~ e_is_a_knight ),
    inference(modus_ponens,[status(thm)],[56,49]) ).

tff(58,plain,
    ( ~ d_is_a_knight
    | c_is_a_knight
    | ~ e_is_a_knight ),
    inference(modus_ponens,[status(thm)],[57,49]) ).

tff(59,plain,
    $false,
    inference(modus_ponens,[status(thm)],[58,48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n009.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 : Fri Sep  2 18:13:50 EDT 2022
% 0.13/0.35  % 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.
% 0.13/0.39  % SZS status Unsatisfiable
% 0.13/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------