TSTP Solution File: SEU706^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 03:39:12 EDT 2024

% Result   : Theorem 2.80s 1.67s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   20 (   7 unt;  10 typ;   6 def)
%            Number of atoms       :   61 (  31 equ;   0 cnn)
%            Maximal formula atoms :   15 (   6 avg)
%            Number of connectives :   90 (   2   ~;   0   |;   2   &;  53   @)
%                                         (   0 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   35 (   1   ^  32   !;   2   ?;  35   :)

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

thf(emptyset_type,type,
    emptyset: $i ).

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(setunion_type,type,
    setunion: $i > $i ).

thf(uniqinunit_type,type,
    uniqinunit: $o ).

thf(uniqinunit_def,definition,
    ( uniqinunit
    = ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) ) ) ) ).

thf(in__Cong_type,type,
    in__Cong: $o ).

thf(in__Cong_def,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( in @ C @ A )
                = ( in @ D @ B ) ) ) ) ) ) ).

thf(setadjoin__Cong_type,type,
    setadjoin__Cong: $o ).

thf(setadjoin__Cong_def,definition,
    ( setadjoin__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( setadjoin @ A @ C )
                = ( setadjoin @ B @ D ) ) ) ) ) ) ).

thf(setunion__Cong_type,type,
    setunion__Cong: $o ).

thf(setunion__Cong_def,definition,
    ( setunion__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( setunion @ A )
            = ( setunion @ B ) ) ) ) ) ).

thf(setunionsingleton_type,type,
    setunionsingleton: $o ).

thf(setunionsingleton_def,definition,
    ( setunionsingleton
    = ( ! [A: $i] :
          ( ( setunion @ ( setadjoin @ A @ emptyset ) )
          = A ) ) ) ).

thf(singleton_type,type,
    singleton: $i > $o ).

thf(singleton_def,definition,
    ( singleton
    = ( ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ A )
          & ( A
            = ( setadjoin @ B @ emptyset ) ) ) ) ) ).

thf(1,conjecture,
    ( uniqinunit
   => ( in__Cong
     => ( setadjoin__Cong
       => ( setunion__Cong
         => ( setunionsingleton
           => ! [A: $i] :
                ( ( singleton @ A )
               => ! [B: $i] :
                    ( ( in @ B @ A )
                   => ( ( setunion @ A )
                      = B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).

thf(2,negated_conjecture,
    ~ ( uniqinunit
     => ( in__Cong
       => ( setadjoin__Cong
         => ( setunion__Cong
           => ( setunionsingleton
             => ! [A: $i] :
                  ( ( singleton @ A )
                 => ! [B: $i] :
                      ( ( in @ B @ A )
                     => ( ( setunion @ A )
                        = B ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(24,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n012.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 17:37:09 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.02/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/1.03  % [INFO] 	 Parsing done (121ms). 
% 1.33/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.04/1.34  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.04/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.04/1.34  % [INFO] 	 Type checking passed. 
% 2.04/1.34  % [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 ... 
% 2.80/1.67  % External prover 'e' found a proof!
% 2.80/1.67  % [INFO] 	 Killing All external provers ... 
% 2.80/1.67  % Time passed: 1140ms (effective reasoning time: 627ms)
% 2.80/1.67  % 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)>
% 2.80/1.67  % Axioms used in derivation (0): 
% 2.80/1.67  % No. of inferences in proof: 4
% 2.80/1.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1140 ms resp. 627 ms w/o parsing
% 2.80/1.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.80/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------