TSTP Solution File: SEU523^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU523^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 03:42:28 EDT 2024

% Result   : Theorem 3.10s 1.87s
% Output   : Refutation 3.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   27 (  10 unt;   7 typ;   1 def)
%            Number of atoms       :   58 (   7 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  139 (  15   ~;   9   |;   6   &;  94   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  27   !;   6   ?;  33   :)

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

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

thf(setunionAx_type,type,
    setunionAx: $o ).

thf(setunionAx_def,definition,
    ( setunionAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
          = ( ? [C: $i] :
                ( ( in @ B @ C )
                & ( in @ C @ A ) ) ) ) ) ) ).

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

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

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

thf(sk5_type,type,
    sk5: $i ).

thf(1,conjecture,
    ( setunionAx
   => ! [A: $i,B: $i] :
        ( ( in @ B @ ( setunion @ A ) )
       => ! [C: $o] :
            ( ! [D: $i] :
                ( ( in @ B @ D )
               => ( ( in @ D @ A )
                 => C ) )
           => C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).

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

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

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( setunion @ A ) )
      = ( ? [C: $i] :
            ( ( in @ B @ C )
            & ( in @ C @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( setunion @ A ) )
      = ( ? [C: $i] :
            ( ( in @ B @ C )
            & ( in @ C @ A ) ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(6,plain,
    in @ sk2 @ ( setunion @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ? [C: $i] :
          ( ( in @ B @ C )
          & ( in @ C @ A ) )
      | ( ( in @ B @ ( setunion @ A ) )
       != ( in @ sk2 @ ( setunion @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,6]) ).

thf(13,plain,
    ? [A: $i] :
      ( ( in @ sk2 @ A )
      & ( in @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(20,plain,
    in @ sk2 @ sk5,
    inference(cnf,[status(esa)],[13]) ).

thf(19,plain,
    in @ sk5 @ sk1,
    inference(cnf,[status(esa)],[13]) ).

thf(5,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ~ ( in @ A @ sk1 )
      | sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ~ ( in @ A @ sk1 )
      | sk3 ),
    inference(simp,[status(thm)],[5]) ).

thf(4,plain,
    ~ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(35,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ~ ( in @ A @ sk1 )
      | $false ),
    inference(rewrite,[status(thm)],[8,4]) ).

thf(36,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ~ ( in @ A @ sk1 ) ),
    inference(simp,[status(thm)],[35]) ).

thf(44,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ( ( in @ sk5 @ sk1 )
       != ( in @ A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[19,36]) ).

thf(45,plain,
    ~ ( in @ sk2 @ sk5 ),
    inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( sk5 ))]]) ).

thf(68,plain,
    $false,
    inference(rewrite,[status(thm)],[20,45]) ).

thf(69,plain,
    $false,
    inference(simp,[status(thm)],[68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU523^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n016.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sun May 19 17:25:38 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 1.05/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.07  % [INFO] 	 Parsing done (119ms). 
% 1.26/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.31  % [INFO] 	 nitpick registered as external prover. 
% 1.80/1.31  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.97/1.40  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.97/1.40  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.97/1.41  % [INFO] 	 Type checking passed. 
% 1.97/1.41  % [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 ... 
% 3.10/1.86  % [INFO] 	 Killing All external provers ... 
% 3.10/1.87  % Time passed: 1314ms (effective reasoning time: 783ms)
% 3.10/1.87  % 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)>
% 3.10/1.87  % Axioms used in derivation (0): 
% 3.10/1.87  % No. of inferences in proof: 19
% 3.10/1.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1314 ms resp. 783 ms w/o parsing
% 3.10/1.91  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.10/1.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------