TSTP Solution File: SEU613^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU613^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 13.29s 3.88s
% Output   : Refutation 13.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   28 (   7 unt;   9 typ;   3 def)
%            Number of atoms       :   60 (   5 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  202 (  29   ~;  15   |;   0   &; 140   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   43 (   6   ^  37   !;   0   ?;  43   :)

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

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

thf(dsetconstrI_type,type,
    dsetconstrI: $o ).

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

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

thf(binunionIR_type,type,
    binunionIR: $o ).

thf(binunionIR_def,definition,
    ( binunionIR
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ B )
         => ( in @ C @ ( binunion @ A @ 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(1,conjecture,
    ( dsetconstrI
   => ( binunionIR
     => ! [A: $i,B: $i,C: $i] :
          ( ~ ( in @ C @ A )
         => ( ( in @ C @ B )
           => ( in @ C @ ( symdiff @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrI
     => ( binunionIR
       => ! [A: $i,B: $i,C: $i] :
            ( ~ ( in @ C @ A )
           => ( ( in @ C @ B )
             => ( in @ C @ ( symdiff @ A @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

thf(8,plain,
    ~ ( in @ sk3
      @ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
        @ ^ [A: $i] :
            ( ~ ( in @ A @ sk1 )
            | ~ ( in @ A @ sk2 ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(22,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( B @ C )
      | ( ( in @ C @ ( dsetconstr @ A @ B ) )
       != ( in @ sk3
          @ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
            @ ^ [D: $i] :
                ( ~ ( in @ D @ sk1 )
                | ~ ( in @ D @ sk2 ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,8]) ).

thf(23,plain,
    ( ~ ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) )
    | ~ ( ~ ( in @ sk3 @ sk1 )
        | ~ ( in @ sk3 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ( ~ ( in @ D @ sk1 ) | ~ ( in @ D @ sk2 ) ) )),bind(C,$thf( sk3 ))]]) ).

thf(46,plain,
    ( ( in @ sk3 @ sk1 )
    | ~ ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(4,plain,
    ~ ( in @ sk3 @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

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

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

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ ( binunion @ A @ B ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ ( binunion @ A @ B ) )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6,9]) ).

thf(186,plain,
    ! [A: $i] : ( in @ sk3 @ ( binunion @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(568,plain,
    ( $false
    | ~ $true ),
    inference(rewrite,[status(thm)],[46,4,186]) ).

thf(569,plain,
    $false,
    inference(simp,[status(thm)],[568]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SEU613^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun May 19 16:20:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.03/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.38/1.19  % [INFO] 	 Parsing done (191ms). 
% 1.48/1.20  % [INFO] 	 Running in sequential loop mode. 
% 1.92/1.59  % [INFO] 	 nitpick registered as external prover. 
% 1.92/1.59  % [INFO] 	 Scanning for conjecture ... 
% 2.29/1.71  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.29/1.75  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.29/1.75  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.29/1.75  % [INFO] 	 Type checking passed. 
% 2.29/1.76  % [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 ... 
% 13.29/3.86  % [INFO] 	 Killing All external provers ... 
% 13.29/3.88  % Time passed: 3385ms (effective reasoning time: 2657ms)
% 13.29/3.88  % 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)>
% 13.29/3.88  % Axioms used in derivation (0): 
% 13.29/3.88  % No. of inferences in proof: 16
% 13.29/3.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3385 ms resp. 2657 ms w/o parsing
% 13.29/3.94  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.29/3.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------