TSTP Solution File: SET600^5 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SET600^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 08:07:34 EDT 2024

% Result   : Theorem 3.76s 1.88s
% Output   : Refutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   18 (   8 unt;   3 typ;   0 def)
%            Number of atoms       :  100 (  35 equ;   0 cnn)
%            Maximal formula atoms :    3 (   6 avg)
%            Number of connectives :   68 (  13   ~;  19   |;   8   &;  28   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   52 (  39   ^  13   !;   0   ?;  52   :)

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

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

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

thf(1,conjecture,
    ! [A: a > $o,B: a > $o] :
      ( ( ( ^ [C: a] :
              ( ( A @ C )
              | ( B @ C ) ) )
        = ( ^ [C: a] : $false ) )
      = ( ( A
          = ( ^ [C: a] : $false ) )
        & ( B
          = ( ^ [C: a] : $false ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_59_pme) ).

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

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

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

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

thf(7,plain,
    ( ( ( sk1
        = ( ^ [A: a] : $false ) )
      & ( sk2
        = ( ^ [A: a] : $false ) ) )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            | ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            | ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) )
    | ( ( sk1
        = ( ^ [A: a] : $false ) )
      & ( sk2
        = ( ^ [A: a] : $false ) ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(12,plain,
    ( ( sk2
      = ( ^ [A: a] : $false ) )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            | ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(14,plain,
    ( ( sk2
      = ( ^ [A: a] : $false ) )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            | ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(16,plain,
    ! [B: a,A: a] :
      ( ~ ( sk2 @ A )
      | ~ ( ( sk1 @ B )
          | ( sk2 @ B ) ) ),
    inference(func_ext,[status(esa)],[14]) ).

thf(17,plain,
    ! [B: a,A: a] :
      ( ~ ( sk2 @ B )
      | ~ ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(26,plain,
    ! [B: a,A: a] :
      ( ~ ( sk2 @ B )
      | ( ( sk2 @ A )
       != ( sk2 @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[17]) ).

thf(27,plain,
    ! [A: a] :
      ~ ( sk2 @ A ),
    inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(28,plain,
    ( ( ( sk1
        = ( ^ [A: a] : $false ) )
      & ( ( ^ [A: a] : $false )
        = ( ^ [A: a] : $false ) ) )
   != ( ( ^ [A: a] :
            ( ( sk1 @ A )
            | $false ) )
      = ( ^ [A: a] : $false ) ) ),
    inference(rewrite,[status(thm)],[5,27]) ).

thf(29,plain,
    $false,
    inference(simp,[status(thm)],[28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET600^5 : TPTP v8.1.2. Released v4.0.0.
% 0.16/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n021.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Mon May  6 13:13:24 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.92/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/0.99  % [INFO] 	 Parsing done (112ms). 
% 1.25/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.27  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.87/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.87/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.87/1.30  % [INFO] 	 Type checking passed. 
% 1.87/1.30  % [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 ... 
% 3.76/1.88  % [INFO] 	 Killing All external provers ... 
% 3.76/1.88  % Time passed: 1334ms (effective reasoning time: 877ms)
% 3.76/1.88  % 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)>
% 3.76/1.88  % Axioms used in derivation (0): 
% 3.76/1.88  % No. of inferences in proof: 15
% 3.76/1.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1334 ms resp. 877 ms w/o parsing
% 3.76/1.91  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/1.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------