TSTP Solution File: SEU623^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 03:38:39 EDT 2024

% Result   : Theorem 2.91s 1.67s
% Output   : Refutation 3.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   18 (   5 unt;  10 typ;   4 def)
%            Number of atoms       :   39 (   4 equ;   0 cnn)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :   98 (   2   ~;   0   |;   0   &;  73   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   27 (   0   ^  27   !;   0   ?;  27   :)

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

thf(emptyset_type,type,
    emptyset: $i ).

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

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

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(subsetE_type,type,
    subsetE: $o ).

thf(subsetE_def,definition,
    ( subsetE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ C @ A )
           => ( in @ C @ B ) ) ) ) ) ).

thf(powersetsubset_type,type,
    powersetsubset: $o ).

thf(powersetsubset_def,definition,
    ( powersetsubset
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(binunionLsub_type,type,
    binunionLsub: $o ).

thf(binunionLsub_def,definition,
    ( binunionLsub
    = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).

thf(singletoninpowerset_type,type,
    singletoninpowerset: $o ).

thf(singletoninpowerset_def,definition,
    ( singletoninpowerset
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ A )
         => ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).

thf(1,conjecture,
    ( subsetE
   => ( powersetsubset
     => ( binunionLsub
       => ( singletoninpowerset
         => ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ A )
             => ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(2,negated_conjecture,
    ~ ( subsetE
     => ( powersetsubset
       => ( binunionLsub
         => ( singletoninpowerset
           => ! [A: $i,B: $i,C: $i] :
                ( ( in @ C @ A )
               => ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(16,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% 0.16/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n002.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 16:12:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.99/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/0.98  % [INFO] 	 Parsing done (115ms). 
% 1.28/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.31  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.31  % [INFO] 	 Type checking passed. 
% 1.88/1.31  % [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 ... 
% 2.91/1.67  % External prover 'e' found a proof!
% 2.91/1.67  % [INFO] 	 Killing All external provers ... 
% 2.91/1.67  % Time passed: 1141ms (effective reasoning time: 676ms)
% 2.91/1.67  % 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)>
% 2.91/1.67  % Axioms used in derivation (0): 
% 2.91/1.67  % No. of inferences in proof: 4
% 2.91/1.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1141 ms resp. 676 ms w/o parsing
% 3.03/1.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/1.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------