TSTP Solution File: SEU775^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : 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 03:43:43 EDT 2024

% Result   : Theorem 3.73s 2.52s
% Output   : Refutation 3.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   20 (   6 unt;  10 typ;   3 def)
%            Number of atoms       :   23 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   76 (   4   ~;   0   |;   0   &;  66   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   21 (   9   ^  12   !;   0   ?;  21   :)

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

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

thf(1,conjecture,
    ( setOfPairsIsBReln1
   => ! [A: $i,B: $i] :
        ( ( breln1 @ A @ B )
       => ( breln1 @ A @ ( breln1invset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/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(4,plain,
    ~ ( subset
      @ ( dpsetconstr @ sk1 @ sk1
        @ ^ [A: $i,B: $i] : ( in @ ( kpair @ B @ A ) @ sk2 ) )
      @ ( cartprod @ sk1 @ sk1 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [B: $i > $i > $o,A: $i] : ( subset @ ( dpsetconstr @ A @ A @ B ) @ ( cartprod @ A @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[4,6]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU775^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 17:37:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.23/1.13  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.56/1.32  % [INFO] 	 Parsing done (192ms). 
% 1.56/1.34  % [INFO] 	 Running in sequential loop mode. 
% 2.25/1.79  % [INFO] 	 nitpick registered as external prover. 
% 2.25/1.80  % [INFO] 	 Scanning for conjecture ... 
% 2.50/1.93  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.66/1.96  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.66/1.96  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.66/1.97  % [INFO] 	 Type checking passed. 
% 2.66/1.97  % [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 ... 
% 3.55/2.46  % [INFO] 	 Killing All external provers ... 
% 3.55/2.47  % Time passed: 1942ms (effective reasoning time: 1115ms)
% 3.55/2.47  % 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)>
% 3.73/2.52  % Axioms used in derivation (0): 
% 3.73/2.52  % No. of inferences in proof: 7
% 3.73/2.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1942 ms resp. 1115 ms w/o parsing
% 3.92/2.57  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.92/2.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------