TSTP Solution File: SET630^3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET630^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 03:06:35 EDT 2024

% Result   : Theorem 2.82s 1.91s
% Output   : Refutation 2.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   18 (   6 unt;   6 typ;   3 def)
%            Number of atoms       :   19 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   69 (  16   ~;   5   |;  12   &;  36   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   19 (   8   ^   6   !;   5   ?;  19   :)

% Comments : 
%------------------------------------------------------------------------------
thf(excl_union_type,type,
    excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(excl_union_def,definition,
    ( excl_union
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( ( A @ C )
            & ~ ( B @ C ) )
          | ( ~ ( A @ C )
            & ( B @ C ) ) ) ) ) ).

thf(intersection_type,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(intersection_def,definition,
    ( intersection
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(misses_type,type,
    misses: ( $i > $o ) > ( $i > $o ) > $o ).

thf(misses_def,definition,
    ( misses
    = ( ^ [A: $i > $o,B: $i > $o] :
          ~ ? [C: $i] :
              ( ( A @ C )
              & ( B @ C ) ) ) ) ).

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

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

thf(sk3_type,type,
    sk3: $i ).

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o] : ( misses @ ( intersection @ A @ B ) @ ( excl_union @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $o,B: $i > $o] : ( misses @ ( intersection @ A @ B ) @ ( excl_union @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

thf(5,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    sk1 @ sk3,
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    sk2 @ sk3,
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[5,8,10]) ).

thf(12,plain,
    $false,
    inference(simp,[status(thm)],[11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SET630^3 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n028.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 11:06:54 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.94/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/1.11  % [INFO] 	 Parsing done (194ms). 
% 1.34/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.97/1.47  % [INFO] 	 nitpick registered as external prover. 
% 1.99/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.11/1.61  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.11/1.61  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.11/1.62  % [INFO] 	 Type checking passed. 
% 2.32/1.62  % [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 ... 
% 2.82/1.91  % [INFO] 	 Killing All external provers ... 
% 2.82/1.91  % Time passed: 1452ms (effective reasoning time: 783ms)
% 2.82/1.91  % 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)>
% 2.82/1.91  % Axioms used in derivation (0): 
% 2.82/1.91  % No. of inferences in proof: 9
% 2.82/1.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1452 ms resp. 783 ms w/o parsing
% 2.82/1.95  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.82/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------