TSTP Solution File: SEU619^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 03:43:00 EDT 2024

% Result   : Theorem 4.29s 2.80s
% Output   : Refutation 4.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   24 (   7 unt;   9 typ;   3 def)
%            Number of atoms       :   39 (   8 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  372 (  15   ~;   8   |;   4   &; 339   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   31 (   1   ^  26   !;   4   ?;  31   :)

% 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(iskpair_type,type,
    iskpair: $i > $o ).

thf(iskpair_def,definition,
    ( iskpair
    = ( ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
          & ? [C: $i] :
              ( ( in @ C @ ( setunion @ A ) )
              & ( A
                = ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).

thf(setukpairIL_type,type,
    setukpairIL: $o ).

thf(setukpairIL_def,definition,
    ( setukpairIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).

thf(setukpairIR_type,type,
    setukpairIR: $o ).

thf(setukpairIR_def,definition,
    ( setukpairIR
    = ( ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).

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

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

thf(1,conjecture,
    ( setukpairIL
   => ( setukpairIR
     => ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).

thf(2,negated_conjecture,
    ~ ( setukpairIL
     => ( setukpairIR
       => ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
      | ( ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ( ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ( ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(simp,[status(thm)],[7]) ).

thf(11,plain,
    ( ~ ( in @ sk2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
    | ~ ( in @ sk1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(6,plain,
    ! [B: $i,A: $i] : ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [B: $i,A: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [B: $i,A: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(27,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[11,6,9]) ).

thf(28,plain,
    $false,
    inference(simp,[status(thm)],[27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n018.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 16:23:24 EDT 2024
% 0.15/0.38  % CPUTime  : 
% 1.22/1.13  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.51/1.33  % [INFO] 	 Parsing done (198ms). 
% 1.66/1.35  % [INFO] 	 Running in sequential loop mode. 
% 2.24/1.79  % [INFO] 	 nitpick registered as external prover. 
% 2.24/1.80  % [INFO] 	 Scanning for conjecture ... 
% 2.63/1.94  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.63/1.98  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.63/1.98  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.72/1.98  % [INFO] 	 Type checking passed. 
% 2.72/1.99  % [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 ... 
% 4.29/2.78  % [INFO] 	 Killing All external provers ... 
% 4.29/2.79  % Time passed: 2233ms (effective reasoning time: 1429ms)
% 4.29/2.79  % 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)>
% 4.29/2.80  % Axioms used in derivation (0): 
% 4.29/2.80  % No. of inferences in proof: 12
% 4.29/2.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2233 ms resp. 1429 ms w/o parsing
% 4.67/2.89  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.67/2.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------