TSTP Solution File: SEU787^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU787^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 03:39:53 EDT 2024

% Result   : Theorem 2.92s 1.65s
% Output   : Refutation 3.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   10 (   2 unt;   5 typ;   1 def)
%            Number of atoms       :   40 (   1 equ;   0 cnn)
%            Maximal formula atoms :   14 (   8 avg)
%            Number of connectives :  154 (   2   ~;   2   |;   0   &; 110   @)
%                                         (   0 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   28 (   0   ^  28   !;   0   ?;  28   :)

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

thf(binunion_type,type,
    binunion: $i > $i > $i ).

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

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

thf(breln1unionE_type,type,
    breln1unionE: $o ).

thf(breln1unionE_def,definition,
    ( breln1unionE
    = ( ! [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 ) @ ( binunion @ B @ C ) )
                       => ( ( in @ ( kpair @ D @ E ) @ B )
                          | ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( breln1unionE
   => ! [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 ) @ ( binunion @ B @ C ) )
                     => ! [F: $o] :
                          ( ( ( in @ ( kpair @ D @ E ) @ B )
                           => F )
                         => ( ( ( in @ ( kpair @ D @ E ) @ C )
                             => F )
                           => F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionEcases) ).

thf(2,negated_conjecture,
    ~ ( breln1unionE
     => ! [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 ) @ ( binunion @ B @ C ) )
                       => ! [F: $o] :
                            ( ( ( in @ ( kpair @ D @ E ) @ B )
                             => F )
                           => ( ( ( in @ ( kpair @ D @ E ) @ C )
                               => F )
                             => F ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [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 ) @ ( binunion @ B @ C ) )
                       => ( ( in @ ( kpair @ D @ E ) @ B )
                          | ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) )
     => ! [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 ) @ ( binunion @ B @ C ) )
                       => ! [F: $o] :
                            ( ( ( in @ ( kpair @ D @ E ) @ B )
                             => F )
                           => ( ( ( in @ ( kpair @ D @ E ) @ C )
                               => F )
                             => F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU787^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n003.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 16:25:39 EDT 2024
% 0.16/0.38  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/0.98  % [INFO] 	 Parsing done (106ms). 
% 1.28/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.06/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.06/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.32  % [INFO] 	 Type checking passed. 
% 2.06/1.32  % [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 ... 
% 2.92/1.64  % External prover 'cvc4' found a proof!
% 2.92/1.64  % [INFO] 	 Killing All external provers ... 
% 2.92/1.65  % Time passed: 1108ms (effective reasoning time: 652ms)
% 2.92/1.65  % 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)>
% 2.92/1.65  % Axioms used in derivation (0): 
% 2.92/1.65  % No. of inferences in proof: 4
% 2.92/1.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1108 ms resp. 652 ms w/o parsing
% 3.10/1.68  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.10/1.68  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------