TSTP Solution File: SET580^3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET580^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 03:06:17 EDT 2024

% Result   : Theorem 3.51s 1.81s
% Output   : Refutation 3.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (   9 unt;   4 typ;   1 def)
%            Number of atoms       :   98 (  20 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  204 (  63   ~;  32   |;  18   &;  91   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-3 aty)
%            Number of variables   :   12 (   3   ^   9   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(excl_union_type,type,
    excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(excl_union_def,definition,
    ( excl_union
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( ( A @ C )
            & ~ ( B @ C ) )
          | ( ~ ( A @ C )
            & ( B @ C ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o,C: $i] :
      ( ( excl_union @ A @ B @ C )
      = ( ( A @ C )
        = ( ~ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

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

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

thf(4,plain,
    ( ( ( ( sk1 @ sk3 )
        & ~ ( sk2 @ sk3 ) )
      | ( ~ ( sk1 @ sk3 )
        & ( sk2 @ sk3 ) ) )
   != ( ( sk1 @ sk3 )
      = ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ( sk1 @ sk3 )
        & ~ ( sk2 @ sk3 ) )
      | ( ~ ( sk1 @ sk3 )
        & ( sk2 @ sk3 ) ) )
   != ( ( sk1 @ sk3 )
      = ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ~ ( ( ( sk1 @ sk3 )
          & ~ ( sk2 @ sk3 ) )
        | ( ~ ( sk1 @ sk3 )
          & ( sk2 @ sk3 ) ) )
    | ( ( sk1 @ sk3 )
     != ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( sk1 @ sk3 )
     != ( ~ ( sk2 @ sk3 ) ) )
    | ~ ( ( ( sk1 @ sk3 )
          & ~ ( sk2 @ sk3 ) )
        | ( ~ ( sk1 @ sk3 )
          & ( sk2 @ sk3 ) ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(11,plain,
    ( ~ ( sk1 @ sk3 )
    | ( sk2 @ sk3 )
    | ( ( sk1 @ sk3 )
     != ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(20,plain,
    ( ~ ( sk1 @ sk3 )
    | ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ~ ~ ( sk2 @ sk3 ) ),
    inference(bool_ext,[status(thm)],[11]) ).

thf(22,plain,
    ( ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(23,plain,
    ( ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 ) ),
    inference(simp,[status(thm)],[22]) ).

thf(7,plain,
    ( ( ( sk1 @ sk3 )
      & ~ ( sk2 @ sk3 ) )
    | ( ~ ( sk1 @ sk3 )
      & ( sk2 @ sk3 ) )
    | ( ( sk1 @ sk3 )
      = ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( sk1 @ sk3 )
      = ( ~ ( sk2 @ sk3 ) ) )
    | ( ( sk1 @ sk3 )
      & ~ ( sk2 @ sk3 ) )
    | ( ~ ( sk1 @ sk3 )
      & ( sk2 @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(14,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ( ( sk1 @ sk3 )
      = ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(24,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ~ ( sk2 @ sk3 ) ),
    inference(bool_ext,[status(thm)],[14]) ).

thf(42,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ~ ( sk1 @ sk3 )
    | ~ ( sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(43,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk1 @ sk3 ) ),
    inference(simp,[status(thm)],[42]) ).

thf(72,plain,
    ( ~ ( sk1 @ sk3 )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[23,43]) ).

thf(73,plain,
    ~ ( sk1 @ sk3 ),
    inference(pattern_uni,[status(thm)],[72:[]]) ).

thf(78,plain,
    ( ( ( $false
        & ~ ( sk2 @ sk3 ) )
      | ( ~ $false
        & ( sk2 @ sk3 ) ) )
   != ( $false
      = ( ~ ( sk2 @ sk3 ) ) ) ),
    inference(rewrite,[status(thm)],[5,73]) ).

thf(79,plain,
    $false,
    inference(simp,[status(thm)],[78]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET580^3 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n004.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 20 11:46:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.90/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.97  % [INFO] 	 Parsing done (127ms). 
% 1.18/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.68/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.98/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.98/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.98/1.30  % [INFO] 	 Type checking passed. 
% 1.98/1.31  % [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 ... 
% 3.51/1.80  % [INFO] 	 Killing All external provers ... 
% 3.51/1.81  % Time passed: 1290ms (effective reasoning time: 819ms)
% 3.51/1.81  % 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)>
% 3.51/1.81  % Axioms used in derivation (0): 
% 3.51/1.81  % No. of inferences in proof: 21
% 3.51/1.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1290 ms resp. 819 ms w/o parsing
% 3.51/1.84  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.51/1.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------