%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET904+1 : TPTP v8.2.0. Released v3.2.0.
% 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 03:07:19 EDT 2024

% Result   : Theorem 4.74s 2.55s
% Output   : Refutation 4.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   18 (   5 unt;   6 typ;   0 def)
%            Number of atoms       :   21 (   1 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   75 (   5   ~;   2   |;   0   &;  63   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^  14   !;   0   ?;  14   :)

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

thf(set_union2_type,type,
    set_union2: $i > $i > $i ).

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

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

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
     => ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
       => ( in @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(12,plain,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
       => ( in @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14,plain,
    subset @ ( set_union2 @ ( singleton @ sk1 ) @ sk2 ) @ sk2,
    inference(cnf,[status(esa)],[12]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
     => ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).

thf(36,plain,
    ! [A: $i,B: $i] :
      ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
     => ( in @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
      | ( in @ A @ B ) ),
    inference(cnf,[status(esa)],[36]) ).

thf(97,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( ( subset @ ( set_union2 @ ( singleton @ sk1 ) @ sk2 ) @ sk2 )
       != ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,37]) ).

thf(98,plain,
    in @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(13,plain,
    ~ ( in @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[12]) ).

thf(126,plain,
    $false,
    inference(rewrite,[status(thm)],[98,13]) ).

thf(127,plain,
    $false,
    inference(simp,[status(thm)],[126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET904+1 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n017.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Mon May 20 12:00:09 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.12  % [INFO] 	 Parsing done (169ms). 
% 1.26/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.50  % [INFO] 	 nitpick registered as external prover. 
% 1.86/1.51  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ... 
% 2.11/1.64  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 2.11/1.65  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.11/1.66  % [INFO] 	 Type checking passed. 
% 2.11/1.66  % [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 ... 
% 4.74/2.54  % [INFO] 	 Killing All external provers ... 
% 4.74/2.55  % Time passed: 2067ms (effective reasoning time: 1400ms)
% 4.74/2.55  % 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)>
% 4.74/2.55  % Axioms used in derivation (1): l21_zfmisc_1
% 4.74/2.55  % No. of inferences in proof: 12
% 4.74/2.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2067 ms resp. 1400 ms w/o parsing
% 4.74/2.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.74/2.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------