TSTP Solution File: SEU633^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU633^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 03:43:04 EDT 2024

% Result   : Theorem 4.24s 2.00s
% Output   : Refutation 4.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   27 (   7 unt;   6 typ;   1 def)
%            Number of atoms       :   56 (   4 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  175 (  17   ~;  15   |;   3   &; 126   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-3 aty)
%            Number of variables   :   34 (   0   ^  31   !;   3   ?;  34   :)

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

thf(setunion_type,type,
    setunion: $i > $i ).

thf(setunionE_type,type,
    setunionE: $o ).

thf(setunionE_def,definition,
    ( setunionE
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
         => ! [C: $o] :
              ( ! [D: $i] :
                  ( ( in @ B @ D )
                 => ( ( in @ D @ A )
                   => C ) )
             => C ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( setunionE
   => ! [A: $i,B: $i] :
        ( ( in @ B @ ( setunion @ A ) )
       => ? [C: $i] :
            ( ( in @ C @ A )
            & ( in @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).

thf(2,negated_conjecture,
    ~ ( setunionE
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
         => ? [C: $i] :
              ( ( in @ C @ A )
              & ( in @ B @ C ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
         => ! [C: $o] :
              ( ! [D: $i] :
                  ( ( in @ B @ D )
                 => ( ( in @ D @ A )
                   => C ) )
             => C ) )
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
         => ? [C: $i] :
              ( ( in @ C @ A )
              & ( in @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | ( in @ B @ ( sk1 @ C @ B @ A ) )
      | C ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    in @ sk3 @ ( setunion @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | ( in @ ( sk1 @ C @ B @ A ) @ A )
      | C ),
    inference(cnf,[status(esa)],[3]) ).

thf(27,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ ( sk1 @ C @ B @ A ) @ A )
      | C
      | ( ( in @ sk3 @ ( setunion @ sk2 ) )
       != ( in @ B @ ( setunion @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,4]) ).

thf(28,plain,
    ! [A: $o] :
      ( ( in @ ( sk1 @ A @ sk3 @ sk2 ) @ sk2 )
      | A ),
    inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(59,plain,
    ! [A: $o] :
      ( ( in @ ( sk1 @ A @ sk3 @ sk2 ) @ sk2 )
      | A ),
    inference(simp,[status(thm)],[28]) ).

thf(110,plain,
    ( ( in @ ( sk1 @ $false @ sk3 @ sk2 ) @ sk2 )
    | $false ),
    inference(prim_subst,[status(thm)],[59:[bind(A,$thf( $false ))]]) ).

thf(123,plain,
    in @ ( sk1 @ $false @ sk3 @ sk2 ) @ sk2,
    inference(simp,[status(thm)],[110]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk2 )
      | ~ ( in @ sk3 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk2 )
      | ~ ( in @ sk3 @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(135,plain,
    ! [A: $i] :
      ( ~ ( in @ sk3 @ A )
      | ( ( in @ ( sk1 @ $false @ sk3 @ sk2 ) @ sk2 )
       != ( in @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[123,9]) ).

thf(136,plain,
    ~ ( in @ sk3 @ ( sk1 @ $false @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk1 @ $false @ sk3 @ sk2 ))]]) ).

thf(153,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | C
      | ( ( in @ B @ ( sk1 @ C @ B @ A ) )
       != ( in @ sk3 @ ( sk1 @ $false @ sk3 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5,136]) ).

thf(154,plain,
    ( ~ ( in @ sk3 @ ( setunion @ sk2 ) )
    | $false ),
    inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( $false ))]]) ).

thf(165,plain,
    ~ ( in @ sk3 @ ( setunion @ sk2 ) ),
    inference(simp,[status(thm)],[154]) ).

thf(166,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[165,6]) ).

thf(167,plain,
    $false,
    inference(simp,[status(thm)],[166]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU633^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n025.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 16:50:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.02  % [INFO] 	 Parsing done (112ms). 
% 1.27/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.66/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.93/1.33  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.93/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.93/1.33  % [INFO] 	 Type checking passed. 
% 1.93/1.33  % [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 ... 
% 4.24/2.00  % [INFO] 	 Killing All external provers ... 
% 4.24/2.00  % Time passed: 1489ms (effective reasoning time: 966ms)
% 4.24/2.00  % 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)>
% 4.24/2.00  % Axioms used in derivation (0): 
% 4.24/2.00  % No. of inferences in proof: 20
% 4.24/2.00  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1489 ms resp. 966 ms w/o parsing
% 4.24/2.03  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.24/2.03  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------