TSTP Solution File: SET947+1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 : Fri May 19 11:54:54 EDT 2023

% Result   : Theorem 2.70s 1.58s
% Output   : Refutation 2.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   23 (  10 unt;   5 typ;   0 def)
%            Number of atoms       :   40 (   3 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  107 (   6   ~;   0   |;   4   &;  79   @)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   32 (   0   ^;  28   !;   4   ?;  32   :)

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

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

thf(union_type,type,
    union: $i > $i ).

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

thf(empty_type,type,
    empty: $i > $o ).

thf(1,conjecture,
    ! [A: $i] : ( subset @ A @ ( powerset @ ( union @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] : ( subset @ A @ ( powerset @ ( union @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: $i] : ( subset @ A @ ( powerset @ ( union @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( powerset @ A ) )
    <=> ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( subset @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(14,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( powerset @ A ) )
       => ! [C: $i] :
            ( ( ( in @ C @ B )
             => ( subset @ C @ A ) )
            & ( ( subset @ C @ A )
             => ( in @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( in @ C @ B )
             => ( subset @ C @ A ) )
            & ( ( subset @ C @ A )
             => ( in @ C @ B ) ) )
       => ( B
          = ( powerset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( subset @ A @ ( union @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).

thf(41,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( subset @ A @ ( union @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(12,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(48,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(43,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

thf(34,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( in @ C @ A )
           => ( in @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( in @ C @ A )
           => ( in @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(45,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(52,plain,
    $false,
    inference(e,[status(thm)],[10,14,41,12,48,43,34,45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May 18 19:10:18 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.95/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.95  % [INFO] 	 Parsing done (101ms). 
% 1.20/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.13  % [INFO] 	 eprover registered as external prover. 
% 1.48/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.48/1.14  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.19  % [INFO] 	 Found a conjecture and 7 axioms. Running axiom selection ... 
% 1.75/1.20  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.75/1.22  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.75/1.22  % [INFO] 	 Type checking passed. 
% 1.75/1.22  % [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 ... 
% 2.70/1.54  % External prover 'e' found a proof!
% 2.70/1.54  % [INFO] 	 Killing All external provers ... 
% 2.70/1.58  % Time passed: 1056ms (effective reasoning time: 622ms)
% 2.70/1.58  % 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)>
% 2.70/1.58  % Axioms used in derivation (7): l50_zfmisc_1, d1_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, d3_tarski, reflexivity_r1_tarski
% 2.70/1.58  % No. of inferences in proof: 18
% 2.70/1.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1056 ms resp. 622 ms w/o parsing
% 2.70/1.61  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.70/1.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------