TSTP Solution File: SET672^3 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET672^3 : 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 10:50:19 EDT 2024

% Result   : Theorem 3.31s 2.18s
% Output   : Refutation 3.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   23 (   8 unt;   7 typ;   2 def)
%            Number of atoms       :   26 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   88 (  10   ~;   4   |;   8   &;  57   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  45   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-4 aty)
%            Number of variables   :   37 (   7   ^  29   !;   1   ?;  37   :)

% Comments : 
%------------------------------------------------------------------------------
thf(is_rel_on_type,type,
    is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).

thf(is_rel_on_def,definition,
    ( is_rel_on
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
        ! [D: $i,E: $i] :
          ( ( A @ D @ E )
         => ( ( B @ D )
            & ( C @ E ) ) ) ) ) ).

thf(restrict_rel_codomain_type,type,
    restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).

thf(restrict_rel_codomain_def,definition,
    ( restrict_rel_codomain
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i,D: $i] :
          ( ( B @ D )
          & ( A @ C @ D ) ) ) ) ).

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

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

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

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i ).

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

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

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

thf(4,plain,
    ~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o] :
        ( ? [D: $i > $o] :
          ! [E: $i,F: $i] :
            ( ( B @ E @ F )
           => ( ( C @ E )
              & ( D @ F ) ) )
       => ! [D: $i,E: $i] :
            ( ( ( A @ E )
              & ( B @ D @ E ) )
           => ( ( C @ D )
              & ( A @ E ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(6,plain,
    sk2 @ sk5 @ sk6,
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk2 @ A @ B )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ( sk3 @ A )
      | ( ( sk2 @ sk5 @ sk6 )
       != ( sk2 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6,8]) ).

thf(13,plain,
    sk3 @ sk5,
    inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(5,plain,
    ( ~ ( sk3 @ sk5 )
    | ~ ( sk1 @ sk6 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    sk1 @ sk6,
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ( ~ ( sk3 @ sk5 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[5,7]) ).

thf(11,plain,
    ~ ( sk3 @ sk5 ),
    inference(simp,[status(thm)],[10]) ).

thf(16,plain,
    $false,
    inference(rewrite,[status(thm)],[13,11]) ).

thf(17,plain,
    $false,
    inference(simp,[status(thm)],[16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SET672^3 : TPTP v8.1.2. Released v3.6.0.
% 0.09/0.10  % Command  : run_Leo-III %s %d
% 0.09/0.30  % Computer : n016.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Mon May  6 20:41:39 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.93/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.33/1.16  % [INFO] 	 Parsing done (256ms). 
% 1.33/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.09/1.51  % [INFO] 	 nitpick registered as external prover. 
% 2.09/1.52  % [INFO] 	 Scanning for conjecture ... 
% 2.38/1.68  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.55/1.71  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.55/1.72  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.55/1.72  % [INFO] 	 Type checking passed. 
% 2.55/1.72  % [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 ... 
% 3.31/2.17  % [INFO] 	 Killing All external provers ... 
% 3.31/2.17  % Time passed: 1717ms (effective reasoning time: 996ms)
% 3.31/2.17  % 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)>
% 3.31/2.18  % Axioms used in derivation (0): 
% 3.31/2.18  % No. of inferences in proof: 14
% 3.31/2.18  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1717 ms resp. 996 ms w/o parsing
% 3.47/2.30  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.47/2.30  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------