TSTP Solution File: SEU720^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU720^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 03:43:30 EDT 2024

% Result   : Theorem 2.77s 1.70s
% Output   : Refutation 2.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   19 (   5 unt;   7 typ;   1 def)
%            Number of atoms       :   38 (   2 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  117 (  14   ~;   6   |;   0   &;  81   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  21   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf(setminus_type,type,
    setminus: $i > $i > $i ).

thf(setminusI_type,type,
    setminusI: $o ).

thf(setminusI_def,definition,
    ( setminusI
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( ~ ( in @ C @ B )
           => ( in @ C @ ( setminus @ A @ B ) ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( setminusI
   => ! [A: $i,B: $i] :
        ( ( in @ B @ ( powerset @ A ) )
       => ! [C: $i] :
            ( ( in @ C @ A )
           => ( ~ ( in @ C @ ( setminus @ A @ B ) )
             => ( in @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTE1) ).

thf(2,negated_conjecture,
    ~ ( setminusI
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ A )
             => ( ~ ( in @ C @ ( setminus @ A @ B ) )
               => ( in @ C @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( in @ C @ ( setminus @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ~ ( in @ sk3 @ ( setminus @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( ( in @ C @ ( setminus @ A @ B ) )
       != ( in @ sk3 @ ( setminus @ sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4,8]) ).

thf(25,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(5,plain,
    ~ ( in @ sk3 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    in @ sk3 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(37,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[25,5,7]) ).

thf(38,plain,
    $false,
    inference(simp,[status(thm)],[37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU720^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n017.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 : Sun May 19 17:53:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.97  % [INFO] 	 Parsing done (103ms). 
% 1.18/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.58/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.58/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.79/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.79/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.79/1.27  % [INFO] 	 Type checking passed. 
% 1.79/1.28  % [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 ... 
% 2.77/1.69  % [INFO] 	 Killing All external provers ... 
% 2.77/1.70  % Time passed: 1164ms (effective reasoning time: 708ms)
% 2.77/1.70  % 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)>
% 2.77/1.70  % Axioms used in derivation (0): 
% 2.77/1.70  % No. of inferences in proof: 11
% 2.77/1.70  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1164 ms resp. 708 ms w/o parsing
% 2.95/1.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.95/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------