TSTP Solution File: SET651^3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET651^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 03:06:41 EDT 2024

% Result   : Theorem 3.06s 1.68s
% Output   : Refutation 3.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   23 (   9 unt;   8 typ;   4 def)
%            Number of atoms       :   37 (   5 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   67 (   6   ~;   2   |;   1   &;  48   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   41 (  41   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   4 con; 0-4 aty)
%            Number of variables   :   32 (  12   ^  16   !;   4   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
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(cartesian_product_type,type,
    cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).

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

thf(sub_rel_type,type,
    sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

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

thf(rel_domain_type,type,
    rel_domain: ( $i > $i > $o ) > $i > $o ).

thf(rel_domain_def,definition,
    ( rel_domain
    = ( ^ [A: $i > $i > $o,B: $i] :
        ? [C: $i] : ( A @ B @ C ) ) ) ).

thf(a_type,type,
    a: $i > $o ).

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

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

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

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( subset @ ( rel_domain @ A ) @ a )
     => ( sub_rel @ A
        @ ( cartesian_product @ a
          @ ^ [B: $i] : $true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( ( subset @ ( rel_domain @ A ) @ a )
       => ( sub_rel @ A
          @ ( cartesian_product @ a
            @ ^ [B: $i] : $true ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

thf(6,plain,
    sk1 @ sk2 @ sk3,
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ( a @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ( a @ A )
      | ( ( sk1 @ sk2 @ sk3 )
       != ( sk1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6,7]) ).

thf(9,plain,
    a @ sk2,
    inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(5,plain,
    ~ ( a @ sk2 ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    $false,
    inference(rewrite,[status(thm)],[9,5]) ).

thf(11,plain,
    $false,
    inference(simp,[status(thm)],[10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET651^3 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n022.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 12:42:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.94/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.42/1.01  % [INFO] 	 Parsing done (158ms). 
% 1.42/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.91/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.26/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.32/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.32/1.38  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.32/1.38  % [INFO] 	 Type checking passed. 
% 2.32/1.38  % [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 ... 
% 3.06/1.68  % [INFO] 	 Killing All external provers ... 
% 3.06/1.68  % Time passed: 1160ms (effective reasoning time: 659ms)
% 3.06/1.68  % 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)>
% 3.06/1.68  % Axioms used in derivation (0): 
% 3.06/1.68  % No. of inferences in proof: 11
% 3.06/1.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1160 ms resp. 659 ms w/o parsing
% 3.08/1.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.08/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------