TSTP Solution File: SEU794^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU794^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 03:39:56 EDT 2024

% Result   : Theorem 28.22s 5.81s
% Output   : Refutation 28.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   14 (   5 unt;   6 typ;   4 def)
%            Number of atoms       :   55 (  20 equ;   0 cnn)
%            Maximal formula atoms :   10 (   6 avg)
%            Number of connectives :   83 (   2   ~;   0   |;   8   &;  54   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   41 (   3   ^  28   !;  10   ?;  41   :)

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

thf(exu_type,type,
    exu: ( $i > $o ) > $o ).

thf(exu_def,definition,
    ( exu
    = ( ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ! [C: $i] :
              ( ( A @ C )
             => ( B = C ) ) ) ) ) ).

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

thf(subsetI1_type,type,
    subsetI1: $o ).

thf(subsetI1_def,definition,
    ( subsetI1
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

thf(setextsub_type,type,
    setextsub: $o ).

thf(setextsub_def,definition,
    ( setextsub
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ A )
           => ( A = B ) ) ) ) ) ).

thf(image1Ex_type,type,
    image1Ex: $o ).

thf(image1Ex_def,definition,
    ( image1Ex
    = ( ! [A: $i,B: $i > $i] :
        ? [C: $i] :
        ! [D: $i] :
          ( ( in @ D @ C )
          = ( ? [E: $i] :
                ( ( in @ E @ A )
                & ( D
                  = ( B @ E ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( subsetI1
   => ( setextsub
     => ( image1Ex
       => ! [A: $i,B: $i > $i] :
            ( exu
            @ ^ [C: $i] :
              ! [D: $i] :
                ( ( in @ D @ C )
                = ( ? [E: $i] :
                      ( ( in @ E @ A )
                      & ( D
                        = ( B @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex1) ).

thf(2,negated_conjecture,
    ~ ( subsetI1
     => ( setextsub
       => ( image1Ex
         => ! [A: $i,B: $i > $i] :
              ( exu
              @ ^ [C: $i] :
                ! [D: $i] :
                  ( ( in @ D @ C )
                  = ( ? [E: $i] :
                        ( ( in @ E @ A )
                        & ( D
                          = ( B @ E ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4466,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : SEU794^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 15:50:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.94/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.00/1.00  % [INFO] 	 Parsing done (118ms). 
% 1.24/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.60/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.60/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.60/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.85/1.34  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.85/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.85/1.34  % [INFO] 	 Type checking passed. 
% 1.85/1.34  % [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 ... 
% 28.11/5.78  % External prover 'e' found a proof!
% 28.11/5.78  % [INFO] 	 Killing All external provers ... 
% 28.22/5.80  % Time passed: 5262ms (effective reasoning time: 4787ms)
% 28.22/5.80  % 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)>
% 28.22/5.81  % Axioms used in derivation (0): 
% 28.22/5.81  % No. of inferences in proof: 4
% 28.22/5.81  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5262 ms resp. 4787 ms w/o parsing
% 28.22/5.83  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.22/5.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------