TSTP Solution File: MGT059-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : MGT059-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 05:22:17 EDT 2022

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   46 (  14 unt;   7 typ;   0 def)
%            Number of atoms       :  153 (  56 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  210 (  98   ~;  94   |;   0   &)
%                                         (  18 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   50 (  46   !;   0   ?;  50   :)

% Comments : 
%------------------------------------------------------------------------------
tff(hazard_of_mortality_type,type,
    hazard_of_mortality: ( $i * $i ) > $i ).

tff(sk3_type,type,
    sk3: $i ).

tff(sk1_type,type,
    sk1: $i ).

tff(sk2_type,type,
    sk2: $i ).

tff(very_low_type,type,
    very_low: $i ).

tff(has_immunity_type,type,
    has_immunity: ( $i * $i ) > $o ).

tff(organization_type,type,
    organization: $i > $o ).

tff(1,plain,
    ( ( very_low = hazard_of_mortality(sk1,sk3) )
  <=> ( hazard_of_mortality(sk1,sk3) = very_low ) ),
    inference(commutativity,[status(thm)],]) ).

tff(2,plain,
    ( has_immunity(sk1,sk2)
  <=> has_immunity(sk1,sk2) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    has_immunity(sk1,sk2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_38) ).

tff(4,plain,
    has_immunity(sk1,sk2),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ( organization(sk1)
  <=> organization(sk1) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    organization(sk1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_37) ).

tff(7,plain,
    organization(sk1),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) )
      <=> ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [B: $i,A: $i] :
        ( ( hazard_of_mortality(A,B) = very_low )
        | ~ has_immunity(A,B)
        | ~ organization(A) )
  <=> ! [B: $i,A: $i] :
        ( ( hazard_of_mortality(A,B) = very_low )
        | ~ has_immunity(A,B)
        | ~ organization(A) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [B: $i,A: $i] :
        ( ( hazard_of_mortality(A,B) = very_low )
        | ~ has_immunity(A,B)
        | ~ organization(A) )
  <=> ! [B: $i,A: $i] :
        ( ( hazard_of_mortality(A,B) = very_low )
        | ~ has_immunity(A,B)
        | ~ organization(A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    ^ [B: $i,A: $i] :
      rewrite(
        ( ( ~ organization(A)
          | ~ has_immunity(A,B)
          | ( hazard_of_mortality(A,B) = very_low ) )
      <=> ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [B: $i,A: $i] :
        ( ~ organization(A)
        | ~ has_immunity(A,B)
        | ( hazard_of_mortality(A,B) = very_low ) )
  <=> ! [B: $i,A: $i] :
        ( ( hazard_of_mortality(A,B) = very_low )
        | ~ has_immunity(A,B)
        | ~ organization(A) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,axiom,
    ! [B: $i,A: $i] :
      ( ~ organization(A)
      | ~ has_immunity(A,B)
      | ( hazard_of_mortality(A,B) = very_low ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_17_32) ).

tff(14,plain,
    ! [B: $i,A: $i] :
      ( ( hazard_of_mortality(A,B) = very_low )
      | ~ has_immunity(A,B)
      | ~ organization(A) ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [B: $i,A: $i] :
      ( ( hazard_of_mortality(A,B) = very_low )
      | ~ has_immunity(A,B)
      | ~ organization(A) ),
    inference(modus_ponens,[status(thm)],[14,10]) ).

tff(16,plain,
    ! [B: $i,A: $i] :
      ( ( hazard_of_mortality(A,B) = very_low )
      | ~ has_immunity(A,B)
      | ~ organization(A) ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [B: $i,A: $i] :
      ( ( hazard_of_mortality(A,B) = very_low )
      | ~ has_immunity(A,B)
      | ~ organization(A) ),
    inference(modus_ponens,[status(thm)],[16,9]) ).

tff(18,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ( hazard_of_mortality(sk1,sk2) = very_low )
      | ~ has_immunity(sk1,sk2)
      | ~ organization(sk1) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ( hazard_of_mortality(sk1,sk2) = very_low )
      | ~ has_immunity(sk1,sk2)
      | ~ organization(sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) )
    | ( hazard_of_mortality(sk1,sk2) = very_low )
    | ~ has_immunity(sk1,sk2)
    | ~ organization(sk1) ),
    inference(quant_inst,[status(thm)],]) ).

tff(20,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) )
    | ( hazard_of_mortality(sk1,sk2) = very_low )
    | ~ has_immunity(sk1,sk2)
    | ~ organization(sk1) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    hazard_of_mortality(sk1,sk2) = very_low,
    inference(unit_resolution,[status(thm)],[20,17,7,4]) ).

tff(22,plain,
    ( ( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3) )
  <=> ( very_low = hazard_of_mortality(sk1,sk3) ) ),
    inference(monotonicity,[status(thm)],[21]) ).

tff(23,plain,
    ( ( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3) )
  <=> ( hazard_of_mortality(sk1,sk3) = very_low ) ),
    inference(transitivity,[status(thm)],[22,1]) ).

tff(24,plain,
    ( ( hazard_of_mortality(sk1,sk3) = very_low )
  <=> ( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3) ) ),
    inference(symmetry,[status(thm)],[23]) ).

tff(25,plain,
    ( has_immunity(sk1,sk3)
  <=> has_immunity(sk1,sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,axiom,
    has_immunity(sk1,sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_39) ).

tff(27,plain,
    has_immunity(sk1,sk3),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ~ organization(sk1)
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ~ organization(sk1)
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ( ( ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3)
      | ~ organization(sk1) )
  <=> ( ~ organization(sk1)
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3)
      | ~ organization(sk1) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ~ organization(sk1)
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3) ) ),
    inference(monotonicity,[status(thm)],[29]) ).

tff(31,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3)
      | ~ organization(sk1) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ( hazard_of_mortality(A,B) = very_low )
            | ~ has_immunity(A,B)
            | ~ organization(A) )
      | ~ organization(sk1)
      | ( hazard_of_mortality(sk1,sk3) = very_low )
      | ~ has_immunity(sk1,sk3) ) ),
    inference(transitivity,[status(thm)],[30,28]) ).

tff(32,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) )
    | ( hazard_of_mortality(sk1,sk3) = very_low )
    | ~ has_immunity(sk1,sk3)
    | ~ organization(sk1) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( hazard_of_mortality(A,B) = very_low )
          | ~ has_immunity(A,B)
          | ~ organization(A) )
    | ~ organization(sk1)
    | ( hazard_of_mortality(sk1,sk3) = very_low )
    | ~ has_immunity(sk1,sk3) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    hazard_of_mortality(sk1,sk3) = very_low,
    inference(unit_resolution,[status(thm)],[33,17,7,27]) ).

tff(35,plain,
    hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3),
    inference(modus_ponens,[status(thm)],[34,24]) ).

tff(36,plain,
    ( ( hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3) )
  <=> ( hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,axiom,
    hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_40) ).

tff(38,plain,
    hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    $false,
    inference(unit_resolution,[status(thm)],[38,35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : MGT059-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Sep  2 02:41:33 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34  Usage: tptp [options] [-file:]file
% 0.19/0.34    -h, -?       prints this message.
% 0.19/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.19/0.34    -m, -model   generate model.
% 0.19/0.34    -p, -proof   generate proof.
% 0.19/0.34    -c, -core    generate unsat core of named formulas.
% 0.19/0.34    -st, -statistics display statistics.
% 0.19/0.34    -t:timeout   set timeout (in second).
% 0.19/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.19/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34    -<param>:<value> configuration parameter and value.
% 0.19/0.34    -o:<output-file> file to place output in.
% 0.19/0.39  % SZS status Unsatisfiable
% 0.19/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------