TSTP Solution File: SET632^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET632^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 03:03:20 EDT 2024

% Result   : Theorem 3.07s 2.10s
% Output   : Refutation 3.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   25 (  12 unt;   5 typ;   0 def)
%            Number of atoms       :   42 (   9 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  100 (  21   ~;   8   |;  12   &;  47   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   38 (   6   ^  26   !;   6   ?;  38   :)

% 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 ) )
        & ! [D: a] :
            ( ( A @ D )
           => ( C @ D ) )
        & ~ ? [D: a] :
              ( ( B @ D )
              & ( C @ D ) ) )
     => ( A
        = ( ^ [D: a] : $false ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_114_pme) ).

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

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

thf(4,plain,
    ~ ! [A: a > $o] :
        ( ? [B: a > $o] :
            ( ! [C: a] :
                ( ( A @ C )
               => ( B @ C ) )
            & ? [C: a > $o] :
                ( ! [D: a] :
                    ( ( A @ D )
                   => ( C @ D ) )
                & ~ ? [D: a] :
                      ( ( B @ D )
                      & ( C @ D ) ) ) )
       => ( A
          = ( ^ [B: a] : $false ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(5,plain,
    ( sk1
   != ( ^ [A: a] : $false ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ( sk1
   != ( ^ [A: a] : $false ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(12,plain,
    sk1 @ sk4,
    inference(func_ext,[status(esa)],[9]) ).

thf(7,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk3 @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(21,plain,
    ! [A: a] :
      ( ( sk3 @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,11]) ).

thf(22,plain,
    sk3 @ sk4,
    inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk4 ))]]) ).

thf(8,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(13,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,8]) ).

thf(14,plain,
    sk2 @ sk4,
    inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( sk4 ))]]) ).

thf(6,plain,
    ! [A: a] :
      ( ~ ( sk2 @ A )
      | ~ ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [A: a] :
      ( ~ ( sk2 @ A )
      | ~ ( sk3 @ A ) ),
    inference(simp,[status(thm)],[6]) ).

thf(15,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( ( sk2 @ sk4 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[14,10]) ).

thf(16,plain,
    ~ ( sk3 @ sk4 ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk4 ))]]) ).

thf(25,plain,
    $false,
    inference(rewrite,[status(thm)],[22,16]) ).

thf(26,plain,
    $false,
    inference(simp,[status(thm)],[25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SET632^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n009.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 12:07:39 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.93/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/1.03  % [INFO] 	 Parsing done (145ms). 
% 1.18/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.38  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.38  % [INFO] 	 cvc4 registered as external prover. 
% 1.63/1.39  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.47  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.91/1.50  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.91/1.50  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.91/1.50  % [INFO] 	 Type checking passed. 
% 1.91/1.51  % [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 ... 
% 3.07/2.09  % [INFO] 	 Killing All external provers ... 
% 3.07/2.10  % Time passed: 1648ms (effective reasoning time: 1043ms)
% 3.07/2.10  % 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)>
% 3.07/2.10  % Axioms used in derivation (0): 
% 3.07/2.10  % No. of inferences in proof: 20
% 3.07/2.10  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1648 ms resp. 1043 ms w/o parsing
% 3.46/2.14  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.46/2.14  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------