TSTP Solution File: SET066^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET066^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 03:01:19 EDT 2024

% Result   : Theorem 3.61s 1.72s
% Output   : Refutation 3.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   23 (  10 unt;   4 typ;   1 def)
%            Number of atoms       :   59 (  53 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   51 (  17   ~;  26   |;   0   &;   8   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   4 con; 0-3 aty)
%            Number of variables   :   15 (   9   ^   6   !;   0   ?;  15   :)

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

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

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

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

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

thf(4,plain,
    ( ( ^ [A: $i] :
          ( ( A = sk1 )
          | ( A = sk2 ) ) )
   != ( ^ [A: $i] :
          ( ( A = sk2 )
          | ( A = sk1 ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: $i] :
          ( ( A = sk1 )
          | ( A = sk2 ) ) )
   != ( ^ [A: $i] :
          ( ( A = sk2 )
          | ( A = sk1 ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

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

thf(28,plain,
    ( ( sk3 = sk1 )
    | ( sk3 = sk2 )
    | ( sk3 = sk2 )
    | ( sk3 = sk1 ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(38,plain,
    ( ( sk3 = sk2 )
    | ( sk3 = sk1 )
    | ( sk3 = sk1 )
    | ( sk3 = sk2 ) ),
    inference(cnf,[status(esa)],[28]) ).

thf(39,plain,
    ( ( sk3 = sk2 )
    | ( sk3 = sk1 )
    | ( sk3 = sk1 )
    | ( sk3 = sk2 ) ),
    inference(lifteq,[status(thm)],[38]) ).

thf(40,plain,
    ( ( sk3 = sk2 )
    | ( sk3 = sk1 ) ),
    inference(simp,[status(thm)],[39]) ).

thf(27,plain,
    ( ~ ( ( sk3 = sk1 )
        | ( sk3 = sk2 ) )
    | ~ ( ( sk3 = sk2 )
        | ( sk3 = sk1 ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(30,plain,
    ( ( sk3 != sk1 )
    | ( sk3 != sk1 ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(33,plain,
    ( ( sk3 != sk1 )
    | ( sk3 != sk1 ) ),
    inference(lifteq,[status(thm)],[30]) ).

thf(34,plain,
    sk3 != sk1,
    inference(simp,[status(thm)],[33]) ).

thf(32,plain,
    ( ( sk3 != sk2 )
    | ( sk3 != sk2 ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(36,plain,
    ( ( sk3 != sk2 )
    | ( sk3 != sk2 ) ),
    inference(lifteq,[status(thm)],[32]) ).

thf(37,plain,
    sk3 != sk2,
    inference(simp,[status(thm)],[36]) ).

thf(47,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[40,34,37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET066^1 : TPTP v8.2.0. Released v3.6.0.
% 0.13/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n013.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 11:28:39 EDT 2024
% 0.16/0.38  % CPUTime  : 
% 0.94/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/0.96  % [INFO] 	 Parsing done (108ms). 
% 1.28/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.93/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.93/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.93/1.26  % [INFO] 	 Type checking passed. 
% 1.93/1.26  % [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 ... 
% 3.61/1.71  % [INFO] 	 Killing All external provers ... 
% 3.61/1.72  % Time passed: 1186ms (effective reasoning time: 737ms)
% 3.61/1.72  % 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)>
% 3.61/1.72  % Axioms used in derivation (0): 
% 3.61/1.72  % No. of inferences in proof: 18
% 3.61/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1186 ms resp. 737 ms w/o parsing
% 3.61/1.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/1.73  % [INFO] 	 Killing All external provers ... 
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