TSTP Solution File: SET044+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET044+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 03:05:03 EDT 2024

% Result   : Theorem 3.70s 1.86s
% Output   : Refutation 3.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   27 (   5 unt;   3 typ;   0 def)
%            Number of atoms       :   73 (   5 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  224 (  36   ~;  19   |;   4   &; 149   @)
%                                         (   4 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   45 (   0   ^  37   !;   8   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(element_type,type,
    element: $i > $i > $o ).

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

thf(sk2_type,type,
    sk2: $i > $i ).

thf(1,conjecture,
    ( ? [A: $i] :
      ! [B: $i] :
        ( ( element @ B @ A )
      <=> ( element @ B @ B ) )
   => ~ ! [A: $i] :
        ? [B: $i] :
        ! [C: $i] :
          ( ( element @ C @ B )
        <=> ~ ( element @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel40) ).

thf(2,negated_conjecture,
    ~ ( ? [A: $i] :
        ! [B: $i] :
          ( ( element @ B @ A )
        <=> ( element @ B @ B ) )
     => ~ ! [A: $i] :
          ? [B: $i] :
          ! [C: $i] :
            ( ( element @ C @ B )
          <=> ~ ( element @ C @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ? [A: $i] :
        ! [B: $i] :
          ( ( ( element @ B @ A )
           => ( element @ B @ B ) )
          & ( ( element @ B @ B )
           => ( element @ B @ A ) ) )
     => ~ ! [A: $i] :
          ? [B: $i] :
          ! [C: $i] :
            ( ( ( element @ C @ B )
             => ~ ( element @ C @ A ) )
            & ( ~ ( element @ C @ A )
             => ( element @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ? [A: $i] :
          ( ! [B: $i] :
              ( ( element @ B @ A )
             => ( element @ B @ B ) )
          & ! [B: $i] :
              ( ( element @ B @ B )
             => ( element @ B @ A ) ) )
     => ~ ! [A: $i] :
          ? [B: $i] :
            ( ! [C: $i] :
                ( ( element @ C @ B )
               => ~ ( element @ C @ A ) )
            & ! [C: $i] :
                ( ~ ( element @ C @ A )
               => ( element @ C @ B ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ sk1 )
      | ( element @ A @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ A )
      | ( element @ A @ sk1 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ A )
      | ( element @ A @ sk1 ) ),
    inference(simp,[status(thm)],[7]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element @ B @ ( sk2 @ A ) )
      | ~ ( element @ B @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element @ B @ ( sk2 @ A ) )
      | ~ ( element @ B @ A ) ),
    inference(simp,[status(thm)],[6]) ).

thf(53,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element @ A @ A )
      | ~ ( element @ C @ ( sk2 @ B ) )
      | ( ( element @ A @ sk1 )
       != ( element @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[11,10]) ).

thf(54,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ A )
      | ~ ( element @ A @ ( sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).

thf(87,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ A )
      | ( ( element @ A @ ( sk2 @ sk1 ) )
       != ( element @ A @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[54]) ).

thf(90,plain,
    ~ ( element @ ( sk2 @ sk1 ) @ ( sk2 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk2 @ sk1 ))]]) ).

thf(118,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ sk1 )
      | ( ( element @ A @ A )
       != ( element @ ( sk2 @ sk1 ) @ ( sk2 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,90]) ).

thf(119,plain,
    ~ ( element @ ( sk2 @ sk1 ) @ sk1 ),
    inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk2 @ sk1 ))]]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ( element @ B @ A )
      | ( element @ B @ ( sk2 @ A ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( element @ B @ A )
      | ( element @ B @ ( sk2 @ A ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( element @ B @ A )
      | ( element @ C @ sk1 )
      | ( ( element @ B @ ( sk2 @ A ) )
       != ( element @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9,11]) ).

thf(20,plain,
    ! [A: $i] :
      ( ( element @ ( sk2 @ A ) @ A )
      | ( element @ ( sk2 @ A ) @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( D )),bind(B,$thf( sk2 @ D )),bind(C,$thf( sk2 @ D ))]]) ).

thf(25,plain,
    ! [A: $i] :
      ( ( element @ ( sk2 @ A ) @ A )
      | ( element @ ( sk2 @ A ) @ sk1 ) ),
    inference(simp,[status(thm)],[20]) ).

thf(34,plain,
    ! [A: $i] :
      ( ( element @ ( sk2 @ A ) @ A )
      | ( ( element @ ( sk2 @ A ) @ sk1 )
       != ( element @ ( sk2 @ A ) @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[25]) ).

thf(37,plain,
    element @ ( sk2 @ sk1 ) @ sk1,
    inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk1 ))]]) ).

thf(144,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[119,37]) ).

thf(145,plain,
    $false,
    inference(simp,[status(thm)],[144]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET044+1 : TPTP v8.2.0. Released v2.0.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.36  % Computer : n008.cluster.edu
% 0.17/0.36  % Model    : x86_64 x86_64
% 0.17/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36  % Memory   : 8042.1875MB
% 0.17/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36  % CPULimit : 300
% 0.17/0.36  % WCLimit  : 300
% 0.17/0.36  % DateTime : Mon May 20 13:18:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.13/0.97  % [INFO] 	 Parsing done (100ms). 
% 1.13/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.60/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.77/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.77/1.27  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.77/1.28  % [INFO] 	 Type checking passed. 
% 1.77/1.28  % [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 ... 
% 3.70/1.86  % [INFO] 	 Killing All external provers ... 
% 3.70/1.86  % Time passed: 1331ms (effective reasoning time: 878ms)
% 3.70/1.86  % 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)>
% 3.70/1.86  % Axioms used in derivation (0): 
% 3.70/1.86  % No. of inferences in proof: 24
% 3.70/1.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1331 ms resp. 878 ms w/o parsing
% 3.70/1.91  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.70/1.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------