%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU775^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 03:39:47 EDT 2024

% Result   : Theorem 3.06s 1.68s
% Output   : Refutation 3.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   4 unt;   8 typ;   3 def)
%            Number of atoms       :   19 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   56 (   2   ~;   0   |;   0   &;  48   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   17 (   7   ^  10   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(cartprod_type,type,
    cartprod: $i > $i > $i ).

thf(dpsetconstr_type,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(breln1_type,type,
    breln1: $i > $i > $o ).

thf(breln1_def,definition,
    ( breln1
    = ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).

thf(setOfPairsIsBReln1_type,type,
    setOfPairsIsBReln1: $o ).

thf(setOfPairsIsBReln1_def,definition,
    ( setOfPairsIsBReln1
    = ( ! [A: $i,B: $i > $i > $o] : ( breln1 @ A @ ( dpsetconstr @ A @ A @ B ) ) ) ) ).

thf(breln1invset_type,type,
    breln1invset: $i > $i > $i ).

thf(breln1invset_def,definition,
    ( breln1invset
    = ( ^ [A: $i,B: $i] :
          ( dpsetconstr @ A @ A
          @ ^ [C: $i,D: $i] : ( in @ ( kpair @ D @ C ) @ B ) ) ) ) ).

thf(1,conjecture,
    ( setOfPairsIsBReln1
   => ! [A: $i,B: $i] :
        ( ( breln1 @ A @ B )
       => ( breln1 @ A @ ( breln1invset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invprop) ).

thf(2,negated_conjecture,
    ~ ( setOfPairsIsBReln1
     => ! [A: $i,B: $i] :
          ( ( breln1 @ A @ B )
         => ( breln1 @ A @ ( breln1invset @ A @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i > $i > $o] : ( subset @ ( dpsetconstr @ A @ A @ B ) @ ( cartprod @ A @ A ) )
     => ! [A: $i,B: $i] :
          ( ( subset @ B @ ( cartprod @ A @ A ) )
         => ( subset
            @ ( dpsetconstr @ A @ A
              @ ^ [C: $i,D: $i] : ( in @ ( kpair @ D @ C ) @ B ) )
            @ ( cartprod @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU775^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n005.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 : Sun May 19 17:37:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.27/1.00  % [INFO] 	 Parsing done (112ms). 
% 1.27/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.68/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.83/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.95/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.95/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.32  % [INFO] 	 Type checking passed. 
% 1.95/1.32  % [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  % External prover 'e' found a proof!
% 3.06/1.68  % [INFO] 	 Killing All external provers ... 
% 3.06/1.68  % Time passed: 1134ms (effective reasoning time: 666ms)
% 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: 4
% 3.06/1.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1134 ms resp. 666 ms w/o parsing
% 3.06/1.74  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/1.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------