TSTP Solution File: SEU738^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU738^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 03:43:35 EDT 2024

% Result   : Theorem 2.88s 1.68s
% Output   : Refutation 2.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   18 (   6 unt;   7 typ;   1 def)
%            Number of atoms       :   34 (   2 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  111 (  14   ~;   2   |;   0   &;  78   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  24   !;   0   ?;  24   :)

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

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

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(binunionIL_type,type,
    binunionIL: $o ).

thf(binunionIL_def,definition,
    ( binunionIL
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ ( binunion @ A @ B ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( binunionIL
   => ! [A: $i,B: $i] :
        ( ( in @ B @ ( powerset @ A ) )
       => ! [C: $i] :
            ( ( in @ C @ ( powerset @ A ) )
           => ! [D: $i] :
                ( ( in @ D @ A )
               => ( ~ ( in @ D @ ( binunion @ B @ C ) )
                 => ~ ( in @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).

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

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

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

thf(5,plain,
    ~ ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(20,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( ( in @ C @ ( binunion @ A @ B ) )
       != ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4,5]) ).

thf(21,plain,
    ~ ( in @ sk4 @ sk2 ),
    inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(9,plain,
    in @ sk4 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(37,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[21,9]) ).

thf(38,plain,
    $false,
    inference(simp,[status(thm)],[37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU738^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.35  % Computer : n026.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Sun May 19 17:18:39 EDT 2024
% 0.16/0.35  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.98  % [INFO] 	 Parsing done (105ms). 
% 1.23/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.60/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.81/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.81/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.81/1.29  % [INFO] 	 Type checking passed. 
% 1.81/1.29  % [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 ... 
% 2.88/1.67  % [INFO] 	 Killing All external provers ... 
% 2.88/1.68  % Time passed: 1154ms (effective reasoning time: 684ms)
% 2.88/1.68  % 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)>
% 2.88/1.68  % Axioms used in derivation (0): 
% 2.88/1.68  % No. of inferences in proof: 10
% 2.88/1.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1154 ms resp. 684 ms w/o parsing
% 2.89/1.70  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.89/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------