TSTP Solution File: SEU611^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 03:42:58 EDT 2024

% Result   : Theorem 5.76s 2.69s
% Output   : Refutation 5.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   42 (  12 unt;  11 typ;   4 def)
%            Number of atoms       :  104 (   8 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  325 (  40   ~;  32   |;   0   &; 217   @)
%                                         (   0 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   61 (   7   ^  54   !;   0   ?;  61   :)

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

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(dsetconstrEL_type,type,
    dsetconstrEL: $o ).

thf(dsetconstrEL_def,definition,
    ( dsetconstrEL
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( in @ C @ A ) ) ) ) ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(dsetconstrER_def,definition,
    ( dsetconstrER
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) ) ) ) ).

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

thf(binunionE_type,type,
    binunionE: $o ).

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

thf(symdiff_type,type,
    symdiff: $i > $i > $i ).

thf(symdiff_def,definition,
    ( symdiff
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( binunion @ A @ B )
          @ ^ [C: $i] :
              ( ~ ( in @ C @ A )
              | ~ ( in @ C @ B ) ) ) ) ) ).

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

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

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

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

thf(1,conjecture,
    ( dsetconstrEL
   => ( dsetconstrER
     => ( binunionE
       => ! [A: $i,B: $i,C: $i] :
            ( ( in @ C @ ( symdiff @ A @ B ) )
           => ! [D: $o] :
                ( ( ( in @ C @ A )
                 => ( ~ ( in @ C @ B )
                   => D ) )
               => ( ( ~ ( in @ C @ A )
                   => ( ( in @ C @ B )
                     => D ) )
                 => D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).

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

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

thf(10,plain,
    ( in @ sk3
    @ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
      @ ^ [A: $i] :
          ( ~ ( in @ A @ sk1 )
          | ~ ( in @ A @ sk2 ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( in @ C @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(123,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( in @ C @ A )
      | ( ( in @ sk3
          @ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
            @ ^ [D: $i] :
                ( ~ ( in @ D @ sk1 )
                | ~ ( in @ D @ sk2 ) ) ) )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,8]) ).

thf(124,plain,
    in @ sk3 @ ( binunion @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ( ~ ( in @ D @ sk1 ) | ~ ( in @ D @ sk2 ) ) )),bind(C,$thf( sk3 ))]]) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B ) ),
    inference(simp,[status(thm)],[7]) ).

thf(166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | ( ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[124,12]) ).

thf(167,plain,
    ( ( in @ sk3 @ sk1 )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(6,plain,
    ( ( in @ sk3 @ sk1 )
    | ~ ( in @ sk3 @ sk2 )
    | sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ( in @ sk3 @ sk2 )
    | sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ sk4,
    inference(cnf,[status(esa)],[3]) ).

thf(78,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ( in @ sk3 @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[5,4]) ).

thf(79,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ( in @ sk3 @ sk2 ) ),
    inference(simp,[status(thm)],[78]) ).

thf(9,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( B @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( B @ C ) ),
    inference(simp,[status(thm)],[9]) ).

thf(14,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk3
          @ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
            @ ^ [D: $i] :
                ( ~ ( in @ D @ sk1 )
                | ~ ( in @ D @ sk2 ) ) ) )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,11]) ).

thf(15,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ~ ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ( ~ ( in @ D @ sk1 ) | ~ ( in @ D @ sk2 ) ) )),bind(C,$thf( sk3 ))]]) ).

thf(38,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ~ ( in @ sk3 @ sk2 ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(82,plain,
    ( ~ ( in @ sk3 @ sk1 )
    | ( ( in @ sk3 @ sk2 )
     != ( in @ sk3 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[79,38]) ).

thf(83,plain,
    ~ ( in @ sk3 @ sk1 ),
    inference(pattern_uni,[status(thm)],[82:[]]) ).

thf(113,plain,
    ( $false
    | ~ ( in @ sk3 @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[6,83,4]) ).

thf(114,plain,
    ~ ( in @ sk3 @ sk2 ),
    inference(simp,[status(thm)],[113]) ).

thf(174,plain,
    ( $false
    | $false ),
    inference(rewrite,[status(thm)],[167,114,83]) ).

thf(175,plain,
    $false,
    inference(simp,[status(thm)],[174]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n007.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 : Sun May 19 16:16:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.11  % [INFO] 	 Parsing done (168ms). 
% 1.27/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.47  % [INFO] 	 nitpick registered as external prover. 
% 1.86/1.48  % [INFO] 	 Scanning for conjecture ... 
% 1.99/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.99/1.63  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.99/1.63  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.15/1.64  % [INFO] 	 Type checking passed. 
% 2.15/1.64  % [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 ... 
% 5.76/2.68  % [INFO] 	 Killing All external provers ... 
% 5.76/2.69  % Time passed: 2209ms (effective reasoning time: 1556ms)
% 5.76/2.69  % 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)>
% 5.76/2.69  % Axioms used in derivation (0): 
% 5.76/2.69  % No. of inferences in proof: 27
% 5.76/2.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2209 ms resp. 1556 ms w/o parsing
% 5.76/2.75  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.76/2.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------