TSTP Solution File: SEU618^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU618^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 3.31s 1.86s
% Output   : Refutation 3.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   24 (   8 unt;   8 typ;   2 def)
%            Number of atoms       :   41 (   4 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  204 (  16   ~;   7   |;   0   &; 171   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^  31   !;   0   ?;  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(setunionI_type,type,
    setunionI: $o ).

thf(setunionI_def,definition,
    ( setunionI
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ B @ C )
         => ( ( in @ C @ A )
           => ( in @ B @ ( setunion @ A ) ) ) ) ) ) ).

thf(secondinupair_type,type,
    secondinupair: $o ).

thf(secondinupair_def,definition,
    ( secondinupair
    = ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).

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

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

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

thf(2,negated_conjecture,
    ~ ( setunionI
     => ( secondinupair
       => ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

thf(7,plain,
    ! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(simp,[status(thm)],[5]) ).

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

thf(4,plain,
    ~ ( in @ sk2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ C )
      | ~ ( in @ C @ A )
      | ( ( in @ B @ ( setunion @ A ) )
       != ( in @ sk2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,4]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ~ ( in @ A @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ~ ( in @ A @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ sk2 @ C )
      | ( ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
       != ( in @ C @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,26]) ).

thf(34,plain,
    ~ ( in @ sk2 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( setadjoin @ sk1 @ emptyset )),bind(B,$thf( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )),bind(C,$thf( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ))]]) ).

thf(43,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[34,7]) ).

thf(44,plain,
    $false,
    inference(simp,[status(thm)],[43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU618^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n016.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 17:08:08 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.11/0.97  % [INFO] 	 Parsing done (117ms). 
% 1.11/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.66/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.84/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.84/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.84/1.33  % [INFO] 	 Type checking passed. 
% 1.84/1.33  % [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 ... 
% 3.31/1.86  % [INFO] 	 Killing All external provers ... 
% 3.31/1.86  % Time passed: 1354ms (effective reasoning time: 875ms)
% 3.31/1.86  % 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)>
% 3.31/1.86  % Axioms used in derivation (0): 
% 3.31/1.86  % No. of inferences in proof: 14
% 3.31/1.86  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1354 ms resp. 875 ms w/o parsing
% 3.31/1.92  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.31/1.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------