%------------------------------------------------------------------------------
% File     : Leo-III---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 : n029.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 03:03:25 EDT 2024

% Result   : Theorem 3.33s 1.74s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   13 (   5 unt;   5 typ;   4 def)
%            Number of atoms       :   25 (   4 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   40 (   2   ~;   0   |;   1   &;  30   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   2 con; 0-4 aty)
%            Number of variables   :   23 (  12   ^   9   !;   2   ?;  23   :)

% 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(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( subset @ ( rel_domain @ A ) @ a )
     => ( sub_rel @ A
        @ ( cartesian_product @ a
          @ ^ [B: $i] : $true ) ) ),
    file('/export/starexec/sandbox2/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(10,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET651^3 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n029.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 12:42:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.01/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/1.08  % [INFO] 	 Parsing done (155ms). 
% 1.60/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.90/1.30  % [INFO] 	 cvc4 registered as external prover. 
% 1.90/1.30  % [INFO] 	 Scanning for conjecture ... 
% 2.37/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.37/1.42  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.37/1.42  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.37/1.42  % [INFO] 	 Type checking passed. 
% 2.37/1.43  % [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 ... 
% 3.33/1.74  % External prover 'e' found a proof!
% 3.33/1.74  % [INFO] 	 Killing All external provers ... 
% 3.33/1.74  % Time passed: 1217ms (effective reasoning time: 651ms)
% 3.33/1.74  % 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)>
% 3.33/1.74  % Axioms used in derivation (0): 
% 3.33/1.74  % No. of inferences in proof: 4
% 3.33/1.74  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1217 ms resp. 651 ms w/o parsing
% 3.33/1.76  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------