TSTP Solution File: SEU158+3 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU158+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 11:57:17 EDT 2023

% Result   : Theorem 2.80s 1.63s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   18 (   7 unt;   4 typ;   0 def)
%            Number of atoms       :   25 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   68 (   6   ~;   0   |;   2   &;  51   @)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^;  17   !;   4   ?;  21   :)

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

thf(singleton_type,type,
    singleton: $i > $i ).

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

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

thf(3,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(14,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(20,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(18,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(16,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ ( singleton @ A ) @ B )
    <=> ( in @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).

thf(23,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ ( singleton @ A ) @ B )
       => ( in @ A @ B ) )
      & ( ( in @ A @ B )
       => ( subset @ ( singleton @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( subset @ ( singleton @ A ) @ B )
    <=> ( in @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ ( singleton @ A ) @ B )
      <=> ( in @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( subset @ ( singleton @ A ) @ B )
         => ( in @ A @ B ) )
        & ( ( in @ A @ B )
         => ( subset @ ( singleton @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(30,plain,
    $false,
    inference(e,[status(thm)],[14,20,18,16,23,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem  : SEU158+3 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n011.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit : 300
% 0.15/0.38  % WCLimit  : 300
% 0.15/0.38  % DateTime : Thu May 18 12:50:18 EDT 2023
% 0.15/0.38  % CPUTime  : 
% 0.89/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/0.94  % [INFO] 	 Parsing done (113ms). 
% 1.22/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.50/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.50/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.50/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.22  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.84/1.25  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.84/1.25  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.84/1.26  % [INFO] 	 Type checking passed. 
% 1.84/1.26  % [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 ... 
% 2.80/1.63  % External prover 'e' found a proof!
% 2.80/1.63  % [INFO] 	 Killing All external provers ... 
% 2.80/1.63  % Time passed: 1106ms (effective reasoning time: 679ms)
% 2.80/1.63  % 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)>
% 2.80/1.63  % Axioms used in derivation (5): l2_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 2.80/1.63  % No. of inferences in proof: 14
% 2.80/1.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1106 ms resp. 679 ms w/o parsing
% 3.01/1.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.01/1.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------