TSTP Solution File: SEU603^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU603^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 03:42:55 EDT 2024

% Result   : Theorem 3.06s 1.75s
% Output   : Refutation 3.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   20 (   9 unt;   7 typ;   2 def)
%            Number of atoms       :   27 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   86 (  14   ~;   2   |;   0   &;  62   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   27 (   6   ^  21   !;   0   ?;  27   :)

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

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(dsetconstrER_def,definition,
    ( dsetconstrER
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) ) ) ) ).

thf(setminus_type,type,
    setminus: $i > $i > $i ).

thf(setminus_def,definition,
    ( setminus
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( in @ C @ B ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( dsetconstrER
   => ! [A: $i,B: $i,C: $i] :
        ( ( in @ C @ ( setminus @ A @ B ) )
       => ~ ( in @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrER
     => ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setminus @ A @ B ) )
         => ~ ( in @ C @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) )
     => ! [A: $i,B: $i,C: $i] :
          ( ( in @ C
            @ ( dsetconstr @ A
              @ ^ [D: $i] :
                  ~ ( in @ D @ B ) ) )
         => ~ ( in @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ( in @ sk3
    @ ( dsetconstr @ sk1
      @ ^ [A: $i] :
          ~ ( in @ A @ sk2 ) ) ),
    inference(cnf,[status(esa)],[3]) ).

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

thf(8,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk3
          @ ( dsetconstr @ sk1
            @ ^ [D: $i] :
                ~ ( in @ D @ sk2 ) ) )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5,6]) ).

thf(9,plain,
    ~ ( in @ sk3 @ sk2 ),
    inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( sk1 )),bind(B,$thf( ^ [D: $i] : ~ ( in @ D @ sk2 ) )),bind(C,$thf( sk3 ))]]) ).

thf(24,plain,
    ~ ( in @ sk3 @ sk2 ),
    inference(cnf,[status(esa)],[9]) ).

thf(4,plain,
    in @ sk3 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(31,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[24,4]) ).

thf(32,plain,
    $false,
    inference(simp,[status(thm)],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU603^2 : TPTP v8.2.0. Released v3.7.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n020.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 15:36:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.96/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.24/0.97  % [INFO] 	 Parsing done (109ms). 
% 1.24/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.61/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.78/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.78/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.78/1.29  % [INFO] 	 Type checking passed. 
% 1.78/1.30  % [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 ... 
% 3.06/1.74  % [INFO] 	 Killing All external provers ... 
% 3.06/1.75  % Time passed: 1214ms (effective reasoning time: 765ms)
% 3.06/1.75  % 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)>
% 3.06/1.75  % Axioms used in derivation (0): 
% 3.06/1.75  % No. of inferences in proof: 11
% 3.06/1.75  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1214 ms resp. 765 ms w/o parsing
% 3.07/1.77  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.07/1.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------