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

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 03:43:48 EDT 2024

% Result   : Theorem 4.24s 2.07s
% Output   : Refutation 4.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   36 (  10 unt;  11 typ;   1 def)
%            Number of atoms       :  100 (   3 equ;   0 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  365 (  41   ~;  38   |;   0   &; 246   @)
%                                         (   0 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   42 (   0   ^  42   !;   0   ?;  42   :)

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

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

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $o ).

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/sandbox2/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(9,plain,
    in @ sk5 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    in @ ( kpair @ sk4 @ sk5 ) @ ( binunion @ sk2 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( breln1 @ A @ B )
      | ~ ( breln1 @ A @ C )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ~ ( in @ ( kpair @ D @ E ) @ ( binunion @ B @ C ) )
      | ( in @ ( kpair @ D @ E ) @ B )
      | ( in @ ( kpair @ D @ E ) @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(110,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( breln1 @ A @ B )
      | ~ ( breln1 @ A @ C )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ( in @ ( kpair @ D @ E ) @ B )
      | ( in @ ( kpair @ D @ E ) @ C )
      | ( ( in @ ( kpair @ sk4 @ sk5 ) @ ( binunion @ sk2 @ sk3 ) )
       != ( in @ ( kpair @ D @ E ) @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,7]) ).

thf(111,plain,
    ! [A: $i] :
      ( ~ ( breln1 @ A @ sk2 )
      | ~ ( breln1 @ A @ sk3 )
      | ~ ( in @ sk4 @ A )
      | ~ ( in @ sk5 @ A )
      | ( in @ ( kpair @ sk4 @ sk5 ) @ sk2 )
      | ( in @ ( kpair @ sk4 @ sk5 ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind(D,$thf( sk4 )),bind(E,$thf( sk5 ))]]) ).

thf(6,plain,
    ( ~ ( in @ ( kpair @ sk4 @ sk5 ) @ sk2 )
    | sk6 ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ~ sk6,
    inference(cnf,[status(esa)],[3]) ).

thf(88,plain,
    ( ~ ( in @ ( kpair @ sk4 @ sk5 ) @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[6,5]) ).

thf(89,plain,
    ~ ( in @ ( kpair @ sk4 @ sk5 ) @ sk2 ),
    inference(simp,[status(thm)],[88]) ).

thf(12,plain,
    ( ~ ( in @ ( kpair @ sk4 @ sk5 ) @ sk3 )
    | sk6 ),
    inference(cnf,[status(esa)],[3]) ).

thf(94,plain,
    ( ~ ( in @ ( kpair @ sk4 @ sk5 ) @ sk3 )
    | $false ),
    inference(rewrite,[status(thm)],[12,5]) ).

thf(95,plain,
    ~ ( in @ ( kpair @ sk4 @ sk5 ) @ sk3 ),
    inference(simp,[status(thm)],[94]) ).

thf(122,plain,
    ! [A: $i] :
      ( ~ ( breln1 @ A @ sk2 )
      | ~ ( breln1 @ A @ sk3 )
      | ~ ( in @ sk4 @ A )
      | ~ ( in @ sk5 @ A )
      | $false
      | $false ),
    inference(rewrite,[status(thm)],[111,89,95]) ).

thf(123,plain,
    ! [A: $i] :
      ( ~ ( breln1 @ A @ sk2 )
      | ~ ( breln1 @ A @ sk3 )
      | ~ ( in @ sk4 @ A )
      | ~ ( in @ sk5 @ A ) ),
    inference(simp,[status(thm)],[122]) ).

thf(127,plain,
    ! [A: $i] :
      ( ~ ( breln1 @ A @ sk2 )
      | ~ ( breln1 @ A @ sk3 )
      | ~ ( in @ sk4 @ A )
      | ( ( in @ sk5 @ sk1 )
       != ( in @ sk5 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,123]) ).

thf(128,plain,
    ( ~ ( breln1 @ sk1 @ sk2 )
    | ~ ( breln1 @ sk1 @ sk3 )
    | ~ ( in @ sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( sk1 ))]]) ).

thf(4,plain,
    breln1 @ sk1 @ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    in @ sk4 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    breln1 @ sk1 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(154,plain,
    ( ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[128,4,8,11]) ).

thf(155,plain,
    $false,
    inference(simp,[status(thm)],[154]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU787^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n003.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sun May 19 16:25:39 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.13/0.98  % [INFO] 	 Parsing done (115ms). 
% 1.13/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.64/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.02/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.02/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.02/1.32  % [INFO] 	 Type checking passed. 
% 2.02/1.33  % [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 ... 
% 4.24/2.07  % [INFO] 	 Killing All external provers ... 
% 4.24/2.07  % Time passed: 1541ms (effective reasoning time: 1075ms)
% 4.24/2.07  % 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)>
% 4.24/2.07  % Axioms used in derivation (0): 
% 4.24/2.07  % No. of inferences in proof: 24
% 4.24/2.07  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1541 ms resp. 1075 ms w/o parsing
% 4.34/2.11  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.34/2.11  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------