TSTP Solution File: SET010^5 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET010^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 10:48:41 EDT 2024

% Result   : Theorem 2.84s 1.93s
% Output   : Refutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   21 (  12 unt;   5 typ;   0 def)
%            Number of atoms       :   64 (   9 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  164 (  43   ~;  16   |;  35   &;  70   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   19 (  10   ^   9   !;   0   ?;  19   :)

% 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 ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o] :
      ( ( ^ [D: a] :
            ( ( A @ D )
            & ~ ( ( B @ D )
                & ( C @ D ) ) ) )
      = ( ^ [D: a] :
            ( ( ( A @ D )
              & ~ ( B @ D ) )
            | ( ( A @ D )
              & ~ ( C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_86_pme) ).

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

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

thf(4,plain,
    ( ( ^ [A: a] :
          ( ( sk1 @ A )
          & ~ ( ( sk2 @ A )
              & ( sk3 @ A ) ) ) )
   != ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ~ ( sk2 @ A ) )
          | ( ( sk1 @ A )
            & ~ ( sk3 @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: a] :
          ( ( sk1 @ A )
          & ~ ( ( sk2 @ A )
              & ( sk3 @ A ) ) ) )
   != ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ~ ( sk2 @ A ) )
          | ( ( sk1 @ A )
            & ~ ( sk3 @ A ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( sk1 @ sk4 )
      & ~ ( ( sk2 @ sk4 )
          & ( sk3 @ sk4 ) ) )
   != ( ( ( sk1 @ sk4 )
        & ~ ( sk2 @ sk4 ) )
      | ( ( sk1 @ sk4 )
        & ~ ( sk3 @ sk4 ) ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(8,plain,
    ( ( ( sk1 @ sk4 )
      & ~ ( ( sk2 @ sk4 )
          & ( sk3 @ sk4 ) ) )
    | ( ( sk1 @ sk4 )
      & ~ ( sk2 @ sk4 ) )
    | ( ( sk1 @ sk4 )
      & ~ ( sk3 @ sk4 ) ) ),
    inference(bool_ext,[status(thm)],[6]) ).

thf(20,plain,
    ( ( sk1 @ sk4 )
    | ( sk1 @ sk4 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(23,plain,
    sk1 @ sk4,
    inference(simp,[status(thm)],[20]) ).

thf(30,plain,
    ( ( $true
      & ~ ( ( sk2 @ sk4 )
          & ( sk3 @ sk4 ) ) )
   != ( ( $true
        & ~ ( sk2 @ sk4 ) )
      | ( $true
        & ~ ( sk3 @ sk4 ) ) ) ),
    inference(rewrite,[status(thm)],[6,23]) ).

thf(31,plain,
    ( ( ~ ( ( sk2 @ sk4 )
          & ( sk3 @ sk4 ) ) )
   != ( ~ ( sk2 @ sk4 )
      | ~ ( sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[30]) ).

thf(32,plain,
    ( ~ ~ ( ( sk2 @ sk4 )
          & ( sk3 @ sk4 ) )
    | ~ ( ~ ( sk2 @ sk4 )
        | ~ ( sk3 @ sk4 ) ) ),
    inference(bool_ext,[status(thm)],[31]) ).

thf(35,plain,
    ( ( sk3 @ sk4 )
    | ( sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[32]) ).

thf(37,plain,
    sk3 @ sk4,
    inference(simp,[status(thm)],[35]) ).

thf(43,plain,
    ( ( ~ ( ( sk2 @ sk4 )
          & $true ) )
   != ( ~ ( sk2 @ sk4 )
      | ~ $true ) ),
    inference(rewrite,[status(thm)],[31,37]) ).

thf(44,plain,
    $false,
    inference(simp,[status(thm)],[43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : SET010^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n006.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 20:47:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.92/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.02/1.02  % [INFO] 	 Parsing done (125ms). 
% 1.24/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.34  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.34  % [INFO] 	 Scanning for conjecture ... 
% 1.83/1.42  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.83/1.46  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.83/1.46  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.46  % [INFO] 	 Type checking passed. 
% 2.00/1.47  % [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 ... 
% 2.84/1.92  % [INFO] 	 Killing All external provers ... 
% 2.84/1.93  % Time passed: 1408ms (effective reasoning time: 890ms)
% 2.84/1.93  % 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)>
% 2.84/1.93  % Axioms used in derivation (0): 
% 2.84/1.93  % No. of inferences in proof: 16
% 2.84/1.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1408 ms resp. 890 ms w/o parsing
% 2.84/1.96  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.84/1.96  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------