TSTP Solution File: PUZ013-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : PUZ013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n027.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 14:10:50 EDT 2022

% Result   : Unsatisfiable 0.08s 0.31s
% Output   : Proof 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   83 (   9 unt;   7 typ;   0 def)
%            Number of atoms       :  278 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  352 ( 150   ~; 150   |;   0   &)
%                                         (  52 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 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  :    9 (   7 usr;   9 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(some_germans_play_type,type,
    some_germans_play: $o ).

tff(some_english_sing_not_type,type,
    some_english_sing_not: $o ).

tff(some_monitors_are_awake_type,type,
    some_monitors_are_awake: $o ).

tff(some_english_sing_type,type,
    some_english_sing: $o ).

tff(some_scotch_dance_not_type,type,
    some_scotch_dance_not: $o ).

tff(some_irish_fight_not_type,type,
    some_irish_fight_not: $o ).

tff(some_monitors_are_not_awake_type,type,
    some_monitors_are_not_awake: $o ).

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

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

tff(3,axiom,
    ~ some_monitors_are_awake,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_some_monitors_are_awake) ).

tff(4,plain,
    ( some_monitors_are_awake
  <=> $false ),
    inference(iff_false,[status(thm)],[3]) ).

tff(5,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    some_english_sing,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c18) ).

tff(7,plain,
    ( some_english_sing
  <=> $true ),
    inference(iff_true,[status(thm)],[6]) ).

tff(8,plain,
    ( ~ some_english_sing
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(9,plain,
    ( ~ some_english_sing
  <=> $false ),
    inference(transitivity,[status(thm)],[8,5]) ).

tff(10,plain,
    ( ( ~ some_english_sing
      | ~ some_english_sing_not
      | some_monitors_are_awake )
  <=> ( $false
      | ~ some_english_sing_not
      | $false ) ),
    inference(monotonicity,[status(thm)],[9,4]) ).

tff(11,plain,
    ( ( ~ some_english_sing
      | ~ some_english_sing_not
      | some_monitors_are_awake )
  <=> ~ some_english_sing_not ),
    inference(transitivity,[status(thm)],[10,2]) ).

tff(12,plain,
    ( ( ~ some_english_sing
      | ~ some_english_sing_not
      | some_monitors_are_awake )
  <=> ( ~ some_english_sing
      | ~ some_english_sing_not
      | some_monitors_are_awake ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ( ( ~ some_english_sing
      | ~ some_english_sing_not
      | some_monitors_are_awake )
  <=> ( ~ some_english_sing
      | ~ some_english_sing_not
      | some_monitors_are_awake ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    ( ~ some_english_sing
    | ~ some_english_sing_not
    | some_monitors_are_awake ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).

tff(15,plain,
    ( ~ some_english_sing
    | ~ some_english_sing_not
    | some_monitors_are_awake ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ( ~ some_english_sing
    | ~ some_english_sing_not
    | some_monitors_are_awake ),
    inference(modus_ponens,[status(thm)],[15,12]) ).

tff(17,plain,
    ~ some_english_sing_not,
    inference(modus_ponens,[status(thm)],[16,11]) ).

tff(18,plain,
    ( some_english_sing_not
  <=> $false ),
    inference(iff_false,[status(thm)],[17]) ).

tff(19,plain,
    ( ( some_english_sing_not
      | ~ some_germans_play )
  <=> ( $false
      | ~ some_germans_play ) ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ( some_english_sing_not
      | ~ some_germans_play )
  <=> ~ some_germans_play ),
    inference(transitivity,[status(thm)],[19,1]) ).

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

tff(22,axiom,
    some_scotch_dance_not,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c19) ).

tff(23,plain,
    ( some_scotch_dance_not
  <=> $true ),
    inference(iff_true,[status(thm)],[22]) ).

tff(24,plain,
    ( ~ some_scotch_dance_not
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[23]) ).

tff(25,plain,
    ( ~ some_scotch_dance_not
  <=> $false ),
    inference(transitivity,[status(thm)],[24,5]) ).

tff(26,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_germans_play
      | ~ some_scotch_dance_not )
  <=> ( $false
      | some_english_sing_not
      | ~ some_germans_play
      | $false ) ),
    inference(monotonicity,[status(thm)],[9,25]) ).

tff(27,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_germans_play
      | ~ some_scotch_dance_not )
  <=> ( some_english_sing_not
      | ~ some_germans_play ) ),
    inference(transitivity,[status(thm)],[26,21]) ).

tff(28,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_germans_play
      | ~ some_scotch_dance_not )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_germans_play
      | ~ some_scotch_dance_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not
      | ~ some_germans_play )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_germans_play
      | ~ some_scotch_dance_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not )
  <=> ( ~ some_english_sing
      | some_english_sing_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not ) ),
    inference(monotonicity,[status(thm)],[31]) ).

tff(33,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not ) ),
    inference(transitivity,[status(thm)],[32,30]) ).

tff(34,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not
      | ~ some_germans_play )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not
      | ~ some_germans_play ) ),
    inference(monotonicity,[status(thm)],[33]) ).

tff(35,plain,
    ( ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_scotch_dance_not
      | ~ some_germans_play )
  <=> ( ~ some_english_sing
      | some_english_sing_not
      | ~ some_germans_play
      | ~ some_scotch_dance_not ) ),
    inference(transitivity,[status(thm)],[34,29]) ).

tff(36,axiom,
    ( ~ some_english_sing
    | some_english_sing_not
    | ~ some_scotch_dance_not
    | ~ some_germans_play ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).

tff(37,plain,
    ( ~ some_english_sing
    | some_english_sing_not
    | ~ some_germans_play
    | ~ some_scotch_dance_not ),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    ( ~ some_english_sing
    | some_english_sing_not
    | ~ some_germans_play
    | ~ some_scotch_dance_not ),
    inference(modus_ponens,[status(thm)],[37,28]) ).

tff(39,plain,
    ( some_english_sing_not
    | ~ some_germans_play ),
    inference(modus_ponens,[status(thm)],[38,27]) ).

tff(40,plain,
    ~ some_germans_play,
    inference(modus_ponens,[status(thm)],[39,20]) ).

tff(41,plain,
    ( some_germans_play
  <=> $false ),
    inference(iff_false,[status(thm)],[40]) ).

tff(42,plain,
    ( ( some_germans_play
      | $false
      | $false )
  <=> some_germans_play ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ( ( $false
      | $false
      | some_irish_fight_not )
  <=> some_irish_fight_not ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ( $false
      | some_monitors_are_not_awake )
  <=> some_monitors_are_not_awake ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( some_monitors_are_awake
      | some_monitors_are_not_awake )
  <=> ( $false
      | some_monitors_are_not_awake ) ),
    inference(monotonicity,[status(thm)],[4]) ).

tff(46,plain,
    ( ( some_monitors_are_awake
      | some_monitors_are_not_awake )
  <=> some_monitors_are_not_awake ),
    inference(transitivity,[status(thm)],[45,44]) ).

tff(47,plain,
    ( ( some_monitors_are_not_awake
      | some_monitors_are_awake )
  <=> ( some_monitors_are_awake
      | some_monitors_are_not_awake ) ),
    inference(rewrite,[status(thm)],]) ).

tff(48,axiom,
    ( some_monitors_are_not_awake
    | some_monitors_are_awake ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c13) ).

tff(49,plain,
    ( some_monitors_are_awake
    | some_monitors_are_not_awake ),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    some_monitors_are_not_awake,
    inference(modus_ponens,[status(thm)],[49,46]) ).

tff(51,plain,
    ( some_monitors_are_not_awake
  <=> $true ),
    inference(iff_true,[status(thm)],[50]) ).

tff(52,plain,
    ( ~ some_monitors_are_not_awake
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[51]) ).

tff(53,plain,
    ( ~ some_monitors_are_not_awake
  <=> $false ),
    inference(transitivity,[status(thm)],[52,5]) ).

tff(54,plain,
    ( ( ~ some_english_sing
      | ~ some_monitors_are_not_awake
      | some_irish_fight_not )
  <=> ( $false
      | $false
      | some_irish_fight_not ) ),
    inference(monotonicity,[status(thm)],[9,53]) ).

tff(55,plain,
    ( ( ~ some_english_sing
      | ~ some_monitors_are_not_awake
      | some_irish_fight_not )
  <=> some_irish_fight_not ),
    inference(transitivity,[status(thm)],[54,43]) ).

tff(56,plain,
    ( ( ~ some_english_sing
      | ~ some_monitors_are_not_awake
      | some_irish_fight_not )
  <=> ( ~ some_english_sing
      | ~ some_monitors_are_not_awake
      | some_irish_fight_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(57,plain,
    ( ( ~ some_english_sing
      | ~ some_monitors_are_not_awake
      | some_irish_fight_not )
  <=> ( ~ some_english_sing
      | ~ some_monitors_are_not_awake
      | some_irish_fight_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,axiom,
    ( ~ some_english_sing
    | ~ some_monitors_are_not_awake
    | some_irish_fight_not ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).

tff(59,plain,
    ( ~ some_english_sing
    | ~ some_monitors_are_not_awake
    | some_irish_fight_not ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ( ~ some_english_sing
    | ~ some_monitors_are_not_awake
    | some_irish_fight_not ),
    inference(modus_ponens,[status(thm)],[59,56]) ).

tff(61,plain,
    some_irish_fight_not,
    inference(modus_ponens,[status(thm)],[60,55]) ).

tff(62,plain,
    ( some_irish_fight_not
  <=> $true ),
    inference(iff_true,[status(thm)],[61]) ).

tff(63,plain,
    ( ~ some_irish_fight_not
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[62]) ).

tff(64,plain,
    ( ~ some_irish_fight_not
  <=> $false ),
    inference(transitivity,[status(thm)],[63,5]) ).

tff(65,plain,
    ( ( some_germans_play
      | ~ some_scotch_dance_not
      | ~ some_irish_fight_not )
  <=> ( some_germans_play
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[25,64]) ).

tff(66,plain,
    ( ( some_germans_play
      | ~ some_scotch_dance_not
      | ~ some_irish_fight_not )
  <=> some_germans_play ),
    inference(transitivity,[status(thm)],[65,42]) ).

tff(67,plain,
    ( ( some_germans_play
      | ~ some_scotch_dance_not
      | ~ some_irish_fight_not )
  <=> ( some_germans_play
      | ~ some_scotch_dance_not
      | ~ some_irish_fight_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(68,plain,
    ( ( ~ some_scotch_dance_not
      | ~ some_irish_fight_not
      | some_germans_play )
  <=> ( some_germans_play
      | ~ some_scotch_dance_not
      | ~ some_irish_fight_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,plain,
    ( ( ~ some_scotch_dance_not
      | ~ some_irish_fight_not )
  <=> ( ~ some_scotch_dance_not
      | ~ some_irish_fight_not ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ( ( ~ some_scotch_dance_not
      | ~ some_irish_fight_not
      | some_germans_play )
  <=> ( ~ some_scotch_dance_not
      | ~ some_irish_fight_not
      | some_germans_play ) ),
    inference(monotonicity,[status(thm)],[69]) ).

tff(71,plain,
    ( ( ~ some_scotch_dance_not
      | ~ some_irish_fight_not
      | some_germans_play )
  <=> ( some_germans_play
      | ~ some_scotch_dance_not
      | ~ some_irish_fight_not ) ),
    inference(transitivity,[status(thm)],[70,68]) ).

tff(72,axiom,
    ( ~ some_scotch_dance_not
    | ~ some_irish_fight_not
    | some_germans_play ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).

tff(73,plain,
    ( some_germans_play
    | ~ some_scotch_dance_not
    | ~ some_irish_fight_not ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ( some_germans_play
    | ~ some_scotch_dance_not
    | ~ some_irish_fight_not ),
    inference(modus_ponens,[status(thm)],[73,67]) ).

tff(75,plain,
    some_germans_play,
    inference(modus_ponens,[status(thm)],[74,66]) ).

tff(76,plain,
    $false,
    inference(modus_ponens,[status(thm)],[75,41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem  : PUZ013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.09  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29  % Computer : n027.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit : 300
% 0.08/0.29  % WCLimit  : 300
% 0.08/0.29  % DateTime : Fri Sep  2 18:33:19 EDT 2022
% 0.08/0.29  % CPUTime  : 
% 0.08/0.29  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29  Usage: tptp [options] [-file:]file
% 0.08/0.29    -h, -?       prints this message.
% 0.08/0.29    -smt2        print SMT-LIB2 benchmark.
% 0.08/0.29    -m, -model   generate model.
% 0.08/0.29    -p, -proof   generate proof.
% 0.08/0.29    -c, -core    generate unsat core of named formulas.
% 0.08/0.29    -st, -statistics display statistics.
% 0.08/0.29    -t:timeout   set timeout (in second).
% 0.08/0.29    -smt2status  display status in smt2 format instead of SZS.
% 0.08/0.29    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29    -<param>:<value> configuration parameter and value.
% 0.08/0.29    -o:<output-file> file to place output in.
% 0.08/0.31  % SZS status Unsatisfiable
% 0.08/0.31  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------