TSTP Solution File: SEU781^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 03:39:50 EDT 2024

% Result   : Theorem 3.22s 1.98s
% Output   : Refutation 3.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   13 (   3 unt;   7 typ;   2 def)
%            Number of atoms       :   48 (   2 equ;   0 cnn)
%            Maximal formula atoms :   16 (   8 avg)
%            Number of connectives :  181 (   2   ~;   0   |;   4   &; 135   @)
%                                         (   0 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   34 (   1   ^  31   !;   2   ?;  34   :)

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

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

thf(breln1compset_type,type,
    breln1compset: $i > $i > $i > $i ).

thf(breln1compE_type,type,
    breln1compE: $o ).

thf(breln1compE_def,definition,
    ( breln1compE
    = ( ! [A: $i,B: $i] :
          ( ( breln1 @ A @ B )
         => ! [C: $i] :
              ( ( breln1 @ A @ C )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ? [F: $i] :
                            ( ( in @ F @ A )
                            & ( in @ ( kpair @ D @ F ) @ B )
                            & ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( breln1compE
   => ! [A: $i,B: $i] :
        ( ( breln1 @ A @ B )
       => ! [C: $i] :
            ( ( breln1 @ A @ C )
           => ! [D: $i] :
                ( ( in @ D @ A )
               => ! [E: $i] :
                    ( ( in @ E @ A )
                   => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                     => ! [F: $o] :
                          ( ! [G: $i] :
                              ( ( in @ G @ A )
                             => ( ( in @ ( kpair @ D @ G ) @ B )
                               => ( ( in @ ( kpair @ G @ E ) @ C )
                                 => F ) ) )
                         => F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).

thf(2,negated_conjecture,
    ~ ( breln1compE
     => ! [A: $i,B: $i] :
          ( ( breln1 @ A @ B )
         => ! [C: $i] :
              ( ( breln1 @ A @ C )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ! [F: $o] :
                            ( ! [G: $i] :
                                ( ( in @ G @ A )
                               => ( ( in @ ( kpair @ D @ G ) @ B )
                                 => ( ( in @ ( kpair @ G @ E ) @ C )
                                   => F ) ) )
                           => F ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( subset @ B @ ( cartprod @ A @ A ) )
         => ! [C: $i] :
              ( ( subset @ C @ ( cartprod @ A @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ? [F: $i] :
                            ( ( in @ F @ A )
                            & ( in @ ( kpair @ D @ F ) @ B )
                            & ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) )
     => ! [A: $i,B: $i] :
          ( ( subset @ B @ ( cartprod @ A @ A ) )
         => ! [C: $i] :
              ( ( subset @ C @ ( cartprod @ A @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ! [F: $o] :
                            ( ! [G: $i] :
                                ( ( in @ G @ A )
                               => ( ( in @ ( kpair @ D @ G ) @ B )
                                 => ( ( in @ ( kpair @ G @ E ) @ C )
                                   => F ) ) )
                           => F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15  % Problem  : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% 0.17/0.19  % Command  : run_Leo-III %s %d
% 0.18/0.41  % Computer : n002.cluster.edu
% 0.18/0.41  % Model    : x86_64 x86_64
% 0.18/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41  % Memory   : 8042.1875MB
% 0.18/0.41  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.41  % CPULimit : 300
% 0.25/0.41  % WCLimit  : 300
% 0.25/0.41  % DateTime : Sun May 19 18:18:24 EDT 2024
% 0.25/0.41  % CPUTime  : 
% 1.02/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.08  % [INFO] 	 Parsing done (132ms). 
% 1.28/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.37  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.47  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.00/1.49  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.00/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.50  % [INFO] 	 Type checking passed. 
% 2.00/1.50  % [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 ... 
% 3.22/1.98  % External prover 'e' found a proof!
% 3.22/1.98  % [INFO] 	 Killing All external provers ... 
% 3.22/1.98  % Time passed: 1398ms (effective reasoning time: 879ms)
% 3.22/1.98  % 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)>
% 3.22/1.98  % Axioms used in derivation (0): 
% 3.22/1.98  % No. of inferences in proof: 4
% 3.22/1.98  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1398 ms resp. 879 ms w/o parsing
% 3.22/2.03  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.22/2.03  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------