TSTP Solution File: SEU736^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU736^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 03:43:34 EDT 2024

% Result   : Theorem 5.50s 2.30s
% Output   : Refutation 5.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   37 (  10 unt;  10 typ;   2 def)
%            Number of atoms       :  111 (   5 equ;   0 cnn)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  377 (  55   ~;  39   |;   0   &; 248   @)
%                                         (   0 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   49 (   0   ^  49   !;   0   ?;  49   :)

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

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

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

thf(setminus_type,type,
    setminus: $i > $i > $i ).

thf(setminusI_type,type,
    setminusI: $o ).

thf(setminusI_def,definition,
    ( setminusI
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( ~ ( in @ C @ B )
           => ( in @ C @ ( setminus @ A @ B ) ) ) ) ) ) ).

thf(contrasubsetT_type,type,
    contrasubsetT: $o ).

thf(contrasubsetT_def,definition,
    ( contrasubsetT
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ( subset @ B @ ( setminus @ A @ C ) )
                   => ( ( in @ D @ C )
                     => ~ ( in @ D @ B ) ) ) ) ) ) ) ) ).

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

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

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

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ( setminusI
   => ( contrasubsetT
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ( ( subset @ B @ ( setminus @ A @ C ) )
               => ! [D: $i] :
                    ( ( in @ D @ A )
                   => ( ( in @ D @ C )
                     => ( in @ D @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).

thf(2,negated_conjecture,
    ~ ( setminusI
     => ( contrasubsetT
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ( ( subset @ B @ ( setminus @ A @ C ) )
                 => ! [D: $i] :
                      ( ( in @ D @ A )
                     => ( ( in @ D @ C )
                       => ( in @ D @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( ~ ( in @ C @ B )
           => ( in @ C @ ( setminus @ A @ B ) ) ) )
     => ( ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ! [D: $i] :
                    ( ( in @ D @ A )
                   => ( ( subset @ B @ ( setminus @ A @ C ) )
                     => ( ( in @ D @ C )
                       => ~ ( in @ D @ B ) ) ) ) ) )
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ( ( subset @ B @ ( setminus @ A @ C ) )
                 => ! [D: $i] :
                      ( ( in @ D @ A )
                     => ( ( in @ D @ C )
                       => ( in @ D @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    in @ sk4 @ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    subset @ sk2 @ ( setminus @ sk1 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( subset @ B @ ( setminus @ A @ C ) )
      | ~ ( in @ D @ C )
      | ~ ( in @ D @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( subset @ B @ ( setminus @ A @ C ) )
      | ~ ( in @ D @ C )
      | ~ ( in @ D @ B ) ),
    inference(simp,[status(thm)],[5]) ).

thf(113,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ D @ C )
      | ~ ( in @ D @ B )
      | ( ( subset @ sk2 @ ( setminus @ sk1 @ sk3 ) )
       != ( subset @ B @ ( setminus @ A @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,12]) ).

thf(114,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
      | ~ ( in @ sk3 @ ( powerset @ sk1 ) )
      | ~ ( in @ A @ sk1 )
      | ~ ( in @ A @ sk3 )
      | ~ ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(189,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
      | ~ ( in @ sk3 @ ( powerset @ sk1 ) )
      | ~ ( in @ A @ sk1 )
      | ~ ( in @ A @ sk3 )
      | ~ ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[114]) ).

thf(8,plain,
    in @ sk2 @ ( powerset @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    in @ sk3 @ ( powerset @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(193,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ $true
      | ~ ( in @ A @ sk1 )
      | ~ ( in @ A @ sk3 )
      | ~ ( in @ A @ sk2 ) ),
    inference(rewrite,[status(thm)],[189,8,9]) ).

thf(194,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk1 )
      | ~ ( in @ A @ sk3 )
      | ~ ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[193]) ).

thf(196,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk1 )
      | ~ ( in @ A @ sk2 )
      | ( ( in @ sk4 @ sk3 )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[10,194]) ).

thf(197,plain,
    ( ~ ( in @ sk4 @ sk1 )
    | ~ ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( sk4 ))]]) ).

thf(4,plain,
    in @ sk4 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( in @ C @ ( setminus @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ~ ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( ( in @ C @ ( setminus @ A @ B ) )
       != ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,11]) ).

thf(30,plain,
    ( ~ ( in @ sk4 @ sk1 )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(44,plain,
    ( ~ $true
    | ( in @ sk4 @ sk2 ) ),
    inference(rewrite,[status(thm)],[30,4]) ).

thf(45,plain,
    in @ sk4 @ sk2,
    inference(simp,[status(thm)],[44]) ).

thf(297,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[197,4,45]) ).

thf(298,plain,
    $false,
    inference(simp,[status(thm)],[297]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEU736^2 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n002.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 17:32:24 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 1.07/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.41/1.07  % [INFO] 	 Parsing done (126ms). 
% 1.41/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.31  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.31  % [INFO] 	 Scanning for conjecture ... 
% 2.13/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.13/1.41  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.13/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.13/1.41  % [INFO] 	 Type checking passed. 
% 2.13/1.41  % [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 ... 
% 5.50/2.29  % [INFO] 	 Killing All external provers ... 
% 5.50/2.30  % Time passed: 1741ms (effective reasoning time: 1207ms)
% 5.50/2.30  % 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)>
% 5.50/2.30  % Axioms used in derivation (0): 
% 5.50/2.30  % No. of inferences in proof: 25
% 5.50/2.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1741 ms resp. 1207 ms w/o parsing
% 5.50/2.34  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.50/2.34  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------