TSTP Solution File: SEU458^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU458^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 03:37:42 EDT 2024

% Result   : Theorem 3.76s 1.78s
% Output   : Refutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   18 (   9 unt;   5 typ;   2 def)
%            Number of atoms       :   48 (   8 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  119 (  11   ~;  27   |;   0   &;  81   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   18 (  16   ^   2   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(idem_type,type,
    idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).

thf(idem_def,definition,
    ( idem
    = ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
        ! [B: $i > $i > $o] :
          ( ( A @ ( A @ B ) )
          = ( A @ B ) ) ) ) ).

thf(sc_type,type,
    sc: ( $i > $i > $o ) > $i > $i > $o ).

thf(sc_def,definition,
    ( sc
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] :
          ( ( A @ C @ B )
          | ( A @ B @ C ) ) ) ) ).

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

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

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

thf(1,conjecture,
    idem @ sc,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure_op_is_idempotent) ).

thf(2,negated_conjecture,
    ~ ( idem @ sc ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ( ( ^ [A: $i,B: $i] :
          ( ( sk1 @ A @ B )
          | ( sk1 @ B @ A )
          | ( sk1 @ B @ A )
          | ( sk1 @ A @ B ) ) )
   != ( ^ [A: $i,B: $i] :
          ( ( sk1 @ B @ A )
          | ( sk1 @ A @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: $i,B: $i] :
          ( ( sk1 @ A @ B )
          | ( sk1 @ B @ A )
          | ( sk1 @ B @ A )
          | ( sk1 @ A @ B ) ) )
   != ( ^ [A: $i,B: $i] :
          ( ( sk1 @ B @ A )
          | ( sk1 @ A @ B ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( sk1 @ sk2 @ sk3 )
      | ( sk1 @ sk3 @ sk2 )
      | ( sk1 @ sk3 @ sk2 )
      | ( sk1 @ sk2 @ sk3 ) )
   != ( ( sk1 @ sk3 @ sk2 )
      | ( sk1 @ sk2 @ sk3 ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

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

thf(11,plain,
    ( ~ ( sk1 @ sk2 @ sk3 )
    | ~ ( sk1 @ sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(14,plain,
    ~ ( sk1 @ sk2 @ sk3 ),
    inference(simp,[status(thm)],[11]) ).

thf(18,plain,
    ( ( $false
      | ( sk1 @ sk3 @ sk2 )
      | ( sk1 @ sk3 @ sk2 )
      | $false )
   != ( ( sk1 @ sk3 @ sk2 )
      | $false ) ),
    inference(rewrite,[status(thm)],[7,14]) ).

thf(19,plain,
    $false,
    inference(simp,[status(thm)],[18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU458^1 : TPTP v8.2.0. Released v3.6.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n025.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sun May 19 17:02:24 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.96/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.01  % [INFO] 	 Parsing done (133ms). 
% 1.29/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.23  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.23/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.23/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.23/1.35  % [INFO] 	 Type checking passed. 
% 2.23/1.35  % [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 ... 
% 3.76/1.77  % [INFO] 	 Killing All external provers ... 
% 3.76/1.77  % Time passed: 1229ms (effective reasoning time: 748ms)
% 3.76/1.77  % 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)>
% 3.76/1.77  % Axioms used in derivation (0): 
% 3.76/1.77  % No. of inferences in proof: 11
% 3.76/1.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1229 ms resp. 748 ms w/o parsing
% 3.76/1.80  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/1.80  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------