TSTP Solution File: SYN028-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN028-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Thu Sep 29 23:53:12 EDT 2022

% Result   : Unsatisfiable 0.14s 0.38s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   67 (   6 unt;   5 typ;   0 def)
%            Number of atoms       :  177 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  197 (  82   ~;  76   |;   0   &)
%                                         (  39 <=>;   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(s_type,type,
    s: $o ).

tff(r_type,type,
    r: $o ).

tff(q_type,type,
    q: $o ).

tff(p_type,type,
    p: $o ).

tff(t_type,type,
    t: $o ).

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

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

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

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

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

tff(6,axiom,
    ~ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_something) ).

tff(7,plain,
    ( p
  <=> $false ),
    inference(iff_false,[status(thm)],[6]) ).

tff(8,plain,
    ( ( q
      | p )
  <=> ( q
      | $false ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(9,plain,
    ( ( q
      | p )
  <=> q ),
    inference(transitivity,[status(thm)],[8,5]) ).

tff(10,plain,
    ( ( q
      | p )
  <=> ( q
      | p ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ( q
    | p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).

tff(12,plain,
    ( q
    | p ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ( q
    | p ),
    inference(modus_ponens,[status(thm)],[12,10]) ).

tff(14,plain,
    q,
    inference(modus_ponens,[status(thm)],[13,9]) ).

tff(15,plain,
    ( q
  <=> $true ),
    inference(iff_true,[status(thm)],[14]) ).

tff(16,plain,
    ( ~ q
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( ~ q
  <=> $false ),
    inference(transitivity,[status(thm)],[16,2]) ).

tff(18,plain,
    ( ( ~ q
      | r )
  <=> ( $false
      | r ) ),
    inference(monotonicity,[status(thm)],[17]) ).

tff(19,plain,
    ( ( ~ q
      | r )
  <=> r ),
    inference(transitivity,[status(thm)],[18,4]) ).

tff(20,plain,
    ( ( ~ q
      | r )
  <=> ( ~ q
      | r ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ( ~ q
    | r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).

tff(22,plain,
    ( ~ q
    | r ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( ~ q
    | r ),
    inference(modus_ponens,[status(thm)],[22,20]) ).

tff(24,plain,
    ( ~ q
    | r ),
    inference(modus_ponens,[status(thm)],[23,20]) ).

tff(25,plain,
    r,
    inference(modus_ponens,[status(thm)],[24,19]) ).

tff(26,plain,
    ( r
  <=> $true ),
    inference(iff_true,[status(thm)],[25]) ).

tff(27,plain,
    ( ~ r
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[26]) ).

tff(28,plain,
    ( ~ r
  <=> $false ),
    inference(transitivity,[status(thm)],[27,2]) ).

tff(29,plain,
    ( ( ~ r
      | s )
  <=> ( $false
      | s ) ),
    inference(monotonicity,[status(thm)],[28]) ).

tff(30,plain,
    ( ( ~ r
      | s )
  <=> s ),
    inference(transitivity,[status(thm)],[29,3]) ).

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

tff(32,axiom,
    ( ~ r
    | s ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).

tff(33,plain,
    ( ~ r
    | s ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ( ~ r
    | s ),
    inference(modus_ponens,[status(thm)],[33,31]) ).

tff(35,plain,
    ( ~ r
    | s ),
    inference(modus_ponens,[status(thm)],[34,31]) ).

tff(36,plain,
    s,
    inference(modus_ponens,[status(thm)],[35,30]) ).

tff(37,plain,
    ( s
  <=> $true ),
    inference(iff_true,[status(thm)],[36]) ).

tff(38,plain,
    ( ~ s
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[37]) ).

tff(39,plain,
    ( ~ s
  <=> $false ),
    inference(transitivity,[status(thm)],[38,2]) ).

tff(40,plain,
    ( ( ~ r
      | ~ s )
  <=> ( $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[28,39]) ).

tff(41,plain,
    ( ( ~ r
      | ~ s )
  <=> $false ),
    inference(transitivity,[status(thm)],[40,1]) ).

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

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

tff(44,plain,
    ( ( p
      | ~ t )
  <=> ( $false
      | ~ t ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(45,plain,
    ( ( p
      | ~ t )
  <=> ~ t ),
    inference(transitivity,[status(thm)],[44,43]) ).

tff(46,plain,
    ( ( ~ t
      | p )
  <=> ( p
      | ~ t ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,axiom,
    ( ~ t
    | p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).

tff(48,plain,
    ( p
    | ~ t ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    ~ t,
    inference(modus_ponens,[status(thm)],[48,45]) ).

tff(50,plain,
    ( t
  <=> $false ),
    inference(iff_false,[status(thm)],[49]) ).

tff(51,plain,
    ( ( ~ r
      | ~ s
      | t )
  <=> ( ~ r
      | ~ s
      | $false ) ),
    inference(monotonicity,[status(thm)],[50]) ).

tff(52,plain,
    ( ( ~ r
      | ~ s
      | t )
  <=> ( ~ r
      | ~ s ) ),
    inference(transitivity,[status(thm)],[51,42]) ).

tff(53,plain,
    ( ( ~ r
      | ~ s
      | t )
  <=> ( ~ r
      | ~ s
      | t ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( ~ r
      | ~ s
      | t )
  <=> ( ~ r
      | ~ s
      | t ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( ~ s
      | ~ r )
  <=> ( ~ r
      | ~ s ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ( ( ~ s
      | ~ r
      | t )
  <=> ( ~ r
      | ~ s
      | t ) ),
    inference(monotonicity,[status(thm)],[55]) ).

tff(57,plain,
    ( ( ~ s
      | ~ r
      | t )
  <=> ( ~ r
      | ~ s
      | t ) ),
    inference(transitivity,[status(thm)],[56,54]) ).

tff(58,axiom,
    ( ~ s
    | ~ r
    | t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).

tff(59,plain,
    ( ~ r
    | ~ s
    | t ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ( ~ r
    | ~ s
    | t ),
    inference(modus_ponens,[status(thm)],[59,53]) ).

tff(61,plain,
    ( ~ r
    | ~ s ),
    inference(modus_ponens,[status(thm)],[60,52]) ).

tff(62,plain,
    $false,
    inference(modus_ponens,[status(thm)],[61,41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN028-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33  % Computer : n008.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 : Mon Sep  5 01:08:40 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.14/0.38  % SZS status Unsatisfiable
% 0.14/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------