TSTP Solution File: SET619^5 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SET619^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May  7 08:07:39 EDT 2024

% Result   : Theorem 3.50s 1.95s
% Output   : Refutation 3.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   19 (   9 unt;   4 typ;   0 def)
%            Number of atoms       :   63 (   8 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  165 (  35   ~;  32   |;  24   &;  74   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (  10   ^   6   !;   0   ?;  16   :)

% 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 ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o] :
      ( ( ^ [C: a] :
            ( ( A @ C )
            | ( B @ C ) ) )
      = ( ^ [C: a] :
            ( ( ( A @ C )
              & ~ ( B @ C ) )
            | ( ( B @ C )
              & ~ ( A @ C ) )
            | ( ( A @ C )
              & ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_95_pme) ).

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

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

thf(4,plain,
    ( ( ^ [A: a] :
          ( ( sk1 @ A )
          | ( sk2 @ A ) ) )
   != ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ~ ( sk2 @ A ) )
          | ( ( sk2 @ A )
            & ~ ( sk1 @ A ) )
          | ( ( sk1 @ A )
            & ( sk2 @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ~ ( sk2 @ A ) )
          | ( ( sk2 @ A )
            & ~ ( sk1 @ A ) )
          | ( ( sk1 @ A )
            & ( sk2 @ A ) ) ) )
   != ( ^ [A: a] :
          ( ( sk1 @ A )
          | ( sk2 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( ( sk1 @ sk3 )
        & ~ ( sk2 @ sk3 ) )
      | ( ( sk2 @ sk3 )
        & ~ ( sk1 @ sk3 ) )
      | ( ( sk1 @ sk3 )
        & ( sk2 @ sk3 ) ) )
   != ( ( sk1 @ sk3 )
      | ( sk2 @ sk3 ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(9,plain,
    ( ~ ( ( ( sk1 @ sk3 )
          & ~ ( sk2 @ sk3 ) )
        | ( ( sk2 @ sk3 )
          & ~ ( sk1 @ sk3 ) )
        | ( ( sk1 @ sk3 )
          & ( sk2 @ sk3 ) ) )
    | ~ ( ( sk1 @ sk3 )
        | ( sk2 @ sk3 ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(13,plain,
    ( ~ ( sk1 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ( sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(18,plain,
    ( ~ ( sk1 @ sk3 )
    | ( sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[13]) ).

thf(12,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ~ ( sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(19,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 ) ),
    inference(simp,[status(thm)],[12]) ).

thf(40,plain,
    ( ~ ( sk1 @ sk3 )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[18,19]) ).

thf(41,plain,
    ~ ( sk1 @ sk3 ),
    inference(pattern_uni,[status(thm)],[40:[]]) ).

thf(44,plain,
    ( ( ( $false
        & ~ ( sk2 @ sk3 ) )
      | ( ( sk2 @ sk3 )
        & ~ $false )
      | ( $false
        & ( sk2 @ sk3 ) ) )
   != ( $false
      | ( sk2 @ sk3 ) ) ),
    inference(rewrite,[status(thm)],[7,41]) ).

thf(45,plain,
    $false,
    inference(simp,[status(thm)],[44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET619^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n027.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon May  6 13:13:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/0.97  % [INFO] 	 Parsing done (111ms). 
% 1.17/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.23  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.83/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.83/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.26  % [INFO] 	 Type checking passed. 
% 1.83/1.26  % [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 ... 
% 3.50/1.95  % [INFO] 	 Killing All external provers ... 
% 3.50/1.95  % Time passed: 1415ms (effective reasoning time: 964ms)
% 3.50/1.95  % 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)>
% 3.50/1.95  % Axioms used in derivation (0): 
% 3.50/1.95  % No. of inferences in proof: 15
% 3.50/1.95  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1415 ms resp. 964 ms w/o parsing
% 3.50/1.98  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.50/1.98  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------