TSTP Solution File: SET589^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET589^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 : Tue May 21 03:06:20 EDT 2024

% Result   : Theorem 2.57s 1.60s
% Output   : Refutation 2.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (   6 unt;   6 typ;   0 def)
%            Number of atoms       :   27 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   97 (  21   ~;   9   |;   9   &;  46   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (   0   ^  26   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(sk1_type,type,
    sk1: a > $o ).

thf(sk2_type,type,
    sk2: a > $o ).

thf(sk3_type,type,
    sk3: a > $o ).

thf(sk4_type,type,
    sk4: a > $o ).

thf(sk5_type,type,
    sk5: a ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
      ( ( ! [E: a] :
            ( ( A @ E )
           => ( B @ E ) )
        & ! [E: a] :
            ( ( C @ E )
           => ( D @ E ) ) )
     => ! [E: a] :
          ( ( ( A @ E )
            & ~ ( D @ E ) )
         => ( ( B @ E )
            & ~ ( C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_48_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
        ( ( ! [E: a] :
              ( ( A @ E )
             => ( B @ E ) )
          & ! [E: a] :
              ( ( C @ E )
             => ( D @ E ) ) )
       => ! [E: a] :
            ( ( ( A @ E )
              & ~ ( D @ E ) )
           => ( ( B @ E )
              & ~ ( C @ E ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
        ( ( ! [E: a] :
              ( ( A @ E )
             => ( B @ E ) )
          & ! [E: a] :
              ( ( C @ E )
             => ( D @ E ) ) )
       => ! [E: a] :
            ( ( ( A @ E )
              & ~ ( D @ E ) )
           => ( ( B @ E )
              & ~ ( C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(8,plain,
    ~ ( sk4 @ sk5 ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( ( sk4 @ A )
       != ( sk4 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[9,8]) ).

thf(17,plain,
    ~ ( sk3 @ sk5 ),
    inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk5 ))]]) ).

thf(5,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ( ~ ( sk2 @ sk5 )
    | ( sk3 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk3 @ sk5 )
      | ( ( sk2 @ A )
       != ( sk2 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[5,6]) ).

thf(13,plain,
    ( ~ ( sk1 @ sk5 )
    | ( sk3 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk5 ))]]) ).

thf(4,plain,
    sk1 @ sk5,
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ( ~ $true
    | ( sk3 @ sk5 ) ),
    inference(rewrite,[status(thm)],[13,4]) ).

thf(15,plain,
    sk3 @ sk5,
    inference(simp,[status(thm)],[14]) ).

thf(20,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[17,15]) ).

thf(21,plain,
    $false,
    inference(simp,[status(thm)],[20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET589^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 12:42:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.16/0.95  % [INFO] 	 Parsing done (103ms). 
% 1.16/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.41/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.41/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.82/1.26  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.82/1.26  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.82/1.26  % [INFO] 	 Type checking passed. 
% 1.82/1.26  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 2.57/1.56  % [INFO] 	 Killing All external provers ... 
% 2.57/1.56  % Time passed: 1038ms (effective reasoning time: 592ms)
% 2.57/1.56  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.57/1.56  % Axioms used in derivation (0): 
% 2.57/1.56  % No. of inferences in proof: 17
% 2.57/1.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1038 ms resp. 592 ms w/o parsing
% 2.57/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.57/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------