%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET067^1 : TPTP v8.1.2. Released v3.6.0.
% 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  7 10:49:02 EDT 2024

% Result   : Theorem 2.37s 1.62s
% Output   : Refutation 2.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   17 (   7 unt;   5 typ;   2 def)
%            Number of atoms       :   25 (  16 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   27 (   6   ~;   5   |;   0   &;  14   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   13 (   5   ^   8   !;   0   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
thf(unord_pair_type,type,
    unord_pair: $i > $i > $i > $o ).

thf(unord_pair_def,definition,
    ( unord_pair
    = ( ^ [A: $i,B: $i,C: $i] :
          ( ( C = A )
          | ( C = B ) ) ) ) ).

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

thf(subset_def,definition,
    ( subset
    = ( ^ [A: $i > $o,B: $i > $o] :
        ! [C: $i] :
          ( ( A @ C )
         => ( B @ C ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] : ( subset @ ( unord_pair @ A @ B ) @ ( unord_pair @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] : ( subset @ ( unord_pair @ A @ B ) @ ( unord_pair @ B @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(6,plain,
    ( ( sk3 = sk1 )
    | ( sk3 = sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ( ( sk3 = sk1 )
    | ( sk3 = sk2 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(4,plain,
    sk3 != sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    sk3 != sk1,
    inference(lifteq,[status(thm)],[4]) ).

thf(5,plain,
    sk3 != sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    sk3 != sk2,
    inference(lifteq,[status(thm)],[5]) ).

thf(10,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[9,7,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET067^1 : TPTP v8.1.2. Released v3.6.0.
% 0.08/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n016.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 20:35:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.91/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.02  % [INFO] 	 Parsing done (147ms). 
% 1.25/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.29  % [INFO] 	 nitpick registered as external prover. 
% 1.67/1.29  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.37  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.00/1.39  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.00/1.39  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.39  % [INFO] 	 Type checking passed. 
% 2.00/1.40  % [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 ... 
% 2.37/1.62  % [INFO] 	 Killing All external provers ... 
% 2.37/1.62  % Time passed: 1119ms (effective reasoning time: 585ms)
% 2.37/1.62  % 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)>
% 2.37/1.62  % Axioms used in derivation (0): 
% 2.37/1.62  % No. of inferences in proof: 10
% 2.37/1.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1119 ms resp. 585 ms w/o parsing
% 2.56/1.65  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.56/1.65  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------